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Title: Sensors for Mechatronics
Description: Provides a clear and practical overview of sensor use in mechatronics for all levels of engineers and students
Description: Provides a clear and practical overview of sensor use in mechatronics for all levels of engineers and students
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1 Introduction
Worldwide, sensor development is a fast growing discipline
...
Many research groups are
active in the sensor field, exploring new technologies, investigating new principles
and structures, aiming at reduced size and price, at the same or even better
performance
...
A well motivated choice requires thorough knowledge of what is available on the market, and
a good insight in current sensor research to be able to anticipate forthcoming sensor
solutions
...
1
...
1
...
These domains are characterized by the type of
quantity that provides the carrier of the relevant information
...
A transducer is that
part of a measurement system that converts information about a measurand from
one domain to another, ideally without information loss
...
In measuring instruments,
where information processing is performed by electrical signals, either the output
or the input is of electrical nature (voltage, current, resistance, capacitance and so
on), whereas the other is a non-electrical signal (displacement, temperature, elasticity and so on)
...
A transducer with a non-electrical output is called an output
Sensors for Mechatronics
...
1016/B978-0-12-391497-2
...
All rights reserved
...
1 Sensors and
actuators
...
So, a more explicit definition of a transducer is an
electrical device that converts one form of energy into another, with the intention
of preserving information
...
1)
...
It should be noted, however, that this terminology is not
standardized
...
Some authors make an explicit
difference between a sensor and a (input) transducer, stressing a distinction between
the element that performs the physical conversion and the complete device À for
instance, a strain gauge (the transducer) and a load cell (the sensor) with one or
more strain gauges and an elastic element
...
According to this docuthe Vocabulaire International de Me
ment a transducer is a device, used in measurement, that provides an output quantity having a specified relation to the input quantity
...
Modern sensors not only contain the converting element but also part of the signal processing (analogue processing such as amplification and filtering, AD conversion and even some digital electronics)
...
Present-day sensors may
have a bus-compatible output, implying full signal conditioning on board
...
Signal conditioning may be included:
G
G
G
G
G
to protect the sensor from being loaded or to reduce loading errors;
to match the sensor output range to the input range of the ADC;
to enhance the S/N (signal-to-noise ratio) prior to further signal processing;
to generate a digital, bus-compatible electrical output; or
to transmit measurement data for wireless applications
...
g
...
Introduction
1
...
2
3
Sensor Development
Sensors provide the essential information about the state of a (mechatronic) system
and its environment
...
Sensors play an important role not only in mechatronics but also in many other
areas
...
A few examples are as follows:
G
G
G
G
G
G
G
Consumer electronics
Household products
Public transport, automotive
Process industry
Manufacturing, production
Agriculture and breeding industry
Medical instruments
and many other areas where the introduction of sensors has increased dramatically
the performance of instruments, machines and products
...
The worldwide sensor
market offers over 100,000 different types of sensors
...
Reasons for the increasing interest
in sensors are as follows:
G
G
G
Reduced prices: the price of sensors not only depends on the technology but also on production volume
...
Miniaturization: the IC-compatible technology and progress in micromachining technology are responsible for this trend [2À4]
...
Micro-ElectroMechanical Systems (MEMS) are
gradually taking over many traditionally designed mechanical sensors [5À7]
...
Smart sensing: the same technology allows the integration of signal processing and sensing
functions on a single chip
...
Popular MEMS sensors are accelerometers and gyroscopes
...
The seismic mass is connected to the substrate by thin, flexible beams, acting as a
spring
...
In mechatronics, mainly sensors for the measurement of mechanical quantities
are encountered
...
Many sensors are commercially available and can be added to or integrated into
a mechatronic system
...
However, for more versatile tasks and specific applications,
dedicated sensor systems are required, which are often not available
...
1
...
3
Sensor Nomenclature
In this book, we follow a strict categorization of sensors according to their main
physical principle
...
For example, a
position sensor can be realized using resistive, capacitive, inductive, acoustic and
optical methods
...
However, a magnetic sensor of a particular type
could be applied as, for instance, a displacement sensor, a velocity sensor or a tactile sensor
...
Apparently, position and movement lead the list of measurement quantities
...
Often, transducers are named after these words
...
Distance sensor
Position sensor
Displacement
sensor
Range sensor
Proximity
sensor
Level sensor
Angular sensor
Encoder
Measures the length of the straight line between two defined points
Measures the co-ordinates of a specified point of an object in a specified
reference system
Measures the change of position relative to a reference point
Measures in a 3D space the shortest distance from a reference point (the
observer) to various points of object boundaries in order to determine
their position and orientation relative to the observer or to get an
image of these objects
(a) Determines the sign (positive or negative) of the linear distance
between an object point and a fixed reference point; also called a
switch
(b) A contact-free displacement or distance sensor for short distances
(down to zero)
Measures the distance of the top level of a liquid or granular substance in
a container with respect to a specified horizontal reference plane
Measures the angle of rotation relative to a reference position
Displacement sensor (linear or angular) containing a binary coded ruler
or disk
Introduction
Tilt sensor
Tachometer
Vibration
sensor
Accelerometer
5
Measures the angle relative to the earth’s normal
Measures rotational speed
Measures the motion of a vibrating object in terms of displacement,
velocity or acceleration
Measures acceleration
Transducers for the measurement of force and related quantities are as follows:
Pressure sensor
Force sensor
Torque sensor
ForceÀtorque
sensor
Load cell
Strain gauge
Touch sensor
Tactile sensor
Measures pressure difference, relative to either vacuum (absolute
pressure), a reference pressure or ambient pressure
Measures the (normal and/or shear) force exerted on the active point of
the transducer
Measures torque (moment)
Measures both forces and torques (up to six components)
Force or pressure sensor, for measuring weight
Measures linear relative elongation (positive or negative) of an object,
caused by compressive or tensile stress
Detects the presence or (combined with a displacement sensor) the
position of an object by making mechanical contact
Measures 3D shape of an object by the act of touch, either sequentially
using an exploring touch sensor or instantaneously by a matrix of
force sensors
Many transducers have been given names according to their operating principle,
construction or a particular property
...
A displacement sensor,
combined with a spring, can act as a force sensor
...
The performance of
such transducers not only depends on the primary sensor but also on the added
6
Sensors for Mechatronics
components: in the examples above the spring compliance and the seismic mass,
respectively
...
The accuracy of the result depends not only on the
errors in the quantities that are measured directly but also on the accuracy of the
parameters in the model that describes the relation between the quantities involved
...
An accurate measurement result requires knowledge of the acoustic velocity of the
medium at the prevailing temperature
...
Speed and acceleration can be measured using a displacement sensor, by differentiating its output signal once or twice, respectively
...
Obviously, the performance of the final result
depends on the quality of the signal processing
...
1
...
4
Sensors and Information
According to the amount of information a sensor or sensing system offers, three
groups of sensors can be distinguished: binary sensors, analogue sensors and image
sensors
...
They are utilized as end stops, as event detectors and as safety
devices
...
The binary nature of the output makes them highly insensitive to electrical interference
...
g
...
g
...
g
...
A wide variety of industrial sensors for these purposes are available
...
Depending on the application, the sensor data refer to one-, two- or three-dimensional images
...
As a consequence, the data
acquisition and processing for such sensors are more complex and more time
consuming
...
Actually, the
section serves as a general overview of the sensors and sensing systems which are
discussed in more detail in subsequent chapters
...
Here, the
Introduction
7
y
y
Uncertainly
margin
1
1
Tolerance
margin
Tolerance
margin
0
0
x
xt
xmin
(A)
Active range
Input range
xt1
xmax
xt2
xmin
(B)
x
xmax
Hysteresis range
Input range
Figure 1
...
differences in approach are highlighted and their consequences for the applicability
in mechatronic systems are emphasized
...
It converts
the (analogue) input quantity to an one-bit output signal
...
They have a fixed or an adjustable threshold
level xt (Figure 1
...
In fact, there are essentially two levels, marking the hysteresis interval (Figure 1
...
Any analogue sensor can be converted to a binary sensor
by adding a Schmitt trigger (comparator with hysteresis, Appendix C
...
Although
hysteresis lowers the accuracy of the threshold detection (down to the hysteresis
interval), it may help reduce unwanted bouncing due to noise in the input signal
...
Binary displacement sensors are also
referred to as proximity sensors
...
Two major types are the mechanically and the
magnetically controlled switches
...
They are available
in a large variety of sizes and constructions; for special conditions there are waterproof and explosion-proof types; for precision measurements there are switches
with an inaccuracy less than 61 µm and a hysteresis interval in the same order,
guaranteed over a temperature range from 220 C to 75 C
...
Mechanical switches have a reliability of about 106
...
The switch is
normally off; it can be switched on mechanically by a permanent magnet approaching the sensor
...
A disadvantage is the bouncing effect, the chattering
of the contacts during a transition of state
...
1 Typical Specifications of Commercial Binary Sensors
Type
Working Range
Response Time
Mechanical
Reed switch
Optical
Inductive
Capacitive
Magnetic
0 (contact)
0À2 cm
0À2/10/35 mÃ
0À50 cm
0À40 mm
0À100 mm
0
...
commercial systems, from cars (monitoring broken lights, level indicators) to electronic organs (playing contacts), to telecommunication devices and testing and
measurement equipments
...
The technical aspects are described in
Chapter 6 on inductive and magnetic sensors
...
2 ms) and wear
...
There is a wide range of binary displacement sensors on the market, for a variety
of distances and performance
...
1 presents a concise overview of
specifications
...
Obviously, the
optical types have the widest distance range
...
The specifications include interface and read-out electronics
...
Accuracy
data include hysteresis and apply for the whole temperature range (maximum operating temperature range 70 C typical)
...
In mechatronics, the major measurement quantities of interest are linear and angular displacement, their time derivatives (velocity and acceleration) and force
(including torque and pressure)
...
Image Sensors
Imaging is a powerful method to obtain information about geometrical parameters
of objects with a complex shape
...
3 Imaging techniques: (A) 2D
point scanning, (B) 1D line scanning and
(C) projection on 2D matrix sensor
...
An essential condition in imaging is
the preservation of the required information
...
Three basic concepts for image acquisition are depicted schematically in
Figure 1
...
In the first method the scene to be imaged is scanned point by point by
some mechanical means (e
...
a mirror on a stepping motor) or electronically
(for instance with phased arrays)
...
The output is a sequential data stream containing 3D information about the scene: depth data from the scanning sensor and
angular data from the scanning mechanism
...
Therefore, range data are sometimes called 2
...
In Figure 1
...
Most scanning
systems consist of several parts, for instance a fixed transmitter and receiver and
10
Sensors for Mechatronics
one or more rotating mirrors or reflectors
...
Although the scanning method is
slow, it requires only a single sensor which can therefore be of high quality
...
3B) the scene is scanned line by line, again
using some mechanical scanning device
...
The sensor array may
include electronic scanning to process the data in a proper way
...
The third method (Figure 1
...
This matrix is electronically scanned for serial
processing of the data
...
The best known imaging device is the CCD matrix
camera (Charge Coupled Device)
...
Considering the nature of the various possible information carriers, there are at
least three candidates for image acquisition: light, (ultra)sound and contact force
...
Most popular is the
CCD camera as imager for exploring and analyzing the work space of a mechatronic system or a robot’s environment
...
The acquisition of an image is just the first step in getting the required information; data processing is another important item
...
The main problem
of the CCD camera is the provision of superfluous data
...
For instance, a
mere contour might be sufficient for proper object identification; the point is how
to find the right contour
...
Here the main problem is the extraction of information from the lowresolution image and À in the case of scanning systems À from other sensors
...
Optical Imaging
Most optical imaging systems applied in mechatronics and robotics use a camera
(CCD-type or CMOS) and a proper illumination of the scene
...
Particular object features are extracted from particular patterns in light intensity in the image
...
Specified conditions for getting a proper image must be fulfilled: an illumination
that yields adequate contrast and no disturbing shadows and a camera set-up with a
Introduction
11
full view on the object or the scene and with a camera that has a sufficiently high
resolution, so as not to lose relevant details
...
In case of
more than one object, some of them could be (partially) hidden behind others
(occlusion), a situation that makes the identification much more difficult
...
Besides a proper model of the object, we need a
model of the imaging process: position and orientation of the camera(s) and camera
parameters like focal length and position of the light source(s) with respect to the
object and camera
...
The pose of the object in the scene can be
derived from the available information and knowledge of the imaging system
...
The image is
searched for particular combinations of adjacent pixels such as edges, from which
region boundaries are derived
...
The result is an
image that reveals at least some characteristics of the object
...
Acoustic Imaging
The interest in acoustic waves for imaging is steadily growing, mainly because of
the low cost and simple construction of acoustic transducers
...
Applications in mechatronics have, however, some severe limitations going
back to ultrasonic wave propagation in air (where most mechatronic systems operate)
...
The most striking drawback of acoustic imaging is the low spatial resolution,
due to the diverging beam of acoustic transducers
...
Even at medium frequencies (i
...
40 kHz), this results in rather
large devices
...
Due to interference, the main beam (in the direction of the
acoustic axis) is narrowed
...
This technique, known as phased arrays, applies to transmitters as well as
receivers
...
3
...
12
Sensors for Mechatronics
Generator
Interface
Transmitter
Stimulus
Echo
pattern
Receiver
Response
Object
Base plate
Figure 1
...
Instead of geometric models for use in object recognition, other models may be
used
...
4
...
The
shape of the echo pattern (the response) is determined by the object’s shape and
orientation
...
They can be considered acoustic signatures of the objects
...
Using a minimum distance criterion reveals the best candidate [12]
...
The comparison process may be performed either in the frequency domain or in
the time domain
...
With an adaptive stimulus and a suitable algorithm, even small
defects in an object can be detected by ultrasonic techniques
...
Tactile Imaging
In contrast to optical and acoustic imaging, tactile imaging is performed by
mechanical contact between sensor and object
...
Disadvantages are the mechanical load of the object (it may
move or be pressed) and the necessity of moving the sensor actively towards the
object
...
g
...
Another advantage
over optical imaging is the insensitivity to environmental conditions
...
Moreover, tactile and vision data can be fused, to benefit from both modalities
...
For inline control the tactile sensor should be incorporated into the gripper of the robot,
allowing simultaneous force distribution and position measurements during the
motion of the gripper
...
In inspection systems (like coordinate measuring machines), the object under
test is scanned mechanically by a motion mechanism, with a touch sensor as the
end effector
...
Position data follow from back transformation of the tip (sensor) co-ordinates to world co-ordinates
...
1
...
First of all, the task that is
to be supported by one or more sensors needs to be thoroughly analyzed and all
possible strategies to be reviewed
...
If
commercial sensors can be found that satisfy the requirements, purchase is recommended
...
If the market does not offer the right sensor system, such a system may
be assembled from commercial sensor components and electronics
...
Sensor selection is based on satisfying requirements; however, these requirements are often not known precisely or in detail, in particular when the designer of
the system and its user are different persons
...
The list of demands should be exhaustive
...
This will leave more room to the designer and
minimizes the risk of having to start all over again
...
Once the designer has a complete idea about the future use of
the system, the phase of the conceptual design can start
...
For the instrumentation of each measurement principle, the designer has a
14
Sensors for Mechatronics
Figure 1
...
F
C
E
B
D
F
A
multitude of sensing methods at his disposal
...
This design process is illustrated by an example of a measurement for just a single, static quantity: the amount of fluid in a container (for instance, a drink dispenser)
...
Figure 1
...
Obviously, many more principles can be found to measure a quantity that is
related to the amount of fluid in the reservoir
...
Based on the list of demands it should
be possible to find a proper candidate principle from this list, or at least to delete
many of the principles, on an argued base
...
Further, for very large tanks, method A can possibly be eliminated because of
high costs
...
After having specified a list of candidate principles, the next step is to find a
suitable sensing method for each of them
...
5 we will further investigate principle E, a level detector placed at the top of the tank
...
Again, a list of the various
possible sensor methods is made, as follows:
E1: a float, connected to an electronic read-out system;
E2: optical ToF measurement;
E3: optical range measurement;
E4: electromagnetic distance measurement (radar);
E5: acoustic ToF measurement and so on
...
g
...
For the tank system, the acoustic ToF
method could be an excellent candidate because of its being contact free
...
Ultimately, this phase concludes with a list of candidate sensing
methods and their merits and demerits with respect to the requirements
...
Here a decision must be made between the purchase of a commercially available system and the development of a dedicated system
...
In this phase of the selection process, sensor specifications become important
...
However,
the accessibility of such data is still poor, making this part of the selection process
critical and time consuming, in particular for non-specialists in the sensor field
...
Since the sensor is often just
one element in the design of a complex mechatronic system, close and frequent
interaction with other design disciplines as well as the customer is recommended
...
[2] K
...
Petersen: Silicon as a mechanical material, Proc
...
[3] S
...
A
...
[4] J
...
Gardner: Microsensors À principles and applications; Wiley, New York, Chichester,
Weinheim, Brisbane, Singapore, Toronto, 1994; ISBN 0-471-94135-2/94136-0
...
F
...
): Silicon sensors and circuits; on-chip compatibility; Chapman &
Hall, London, Glasgow, Weinheim, New York, Tokyo, Melbourne, Madras, 1996;
ISBN 0-412-70970-8
...
-H
...
[7] M
...
Wiegerink: Mechanical microsensors; Springer-Verlag, Berlin,
Heidelberg, New York, (Barcelona, Hong Kong, London, Milan, Paris, Singapore,
Tokyo), 2001; ISBN 3-540-67582-5
...
Conf
...
[9] Various international journals, for instance ‘Sens
...
J
...
[10] P
...
Siirtola, R
...
Actuators A, 55 (1996),
107À113
...
D
...
R
...
J
...
A
...
X
...
V
...
Actuators A, 46À47
(1995), 542À546
...
Cai, P
...
L
...
Sci
...
, 4 (1993), 95À100
...
M
...
Freire Bastos, L
...
Actuators A, 31 (1992), 182À187
...
Ripka, A
...
): Modern sensors handbook; Wiley-ISTE, London; Newport Beach,
CA, 2007; ISBN 978-1-905209-66-8
...
G
...
D
...
H
...
[3] R
...
Figliola, D
...
Beasley: Theory and design for mechanical measurements; Wiley,
New York, Chichester, Weinheim, Brisbane, Singapore, Toronto, 2006; ISBN 0-47144593-2
...
Preumont: Mechatronics À dynamics of electromechanical and piezoelectric systems; Springer, Berlin, Heidelberg, New York, (etc
...
[5] R
...
Figliola, D
...
Beasley: Theory and design for mechanical measurements; Wiley,
New York, Chichester, Weinheim, Brisbane, Singapore, Toronto, 2006; ISBN 0-47144593-2
...
K
...
Inasaki (eds
...
[7] R
...
G
...
[8] G
...
Jenkin: Computational principles of mobile robotics; Cambridge
University Press, Cambridge, 2000; ISBN 0-521-56876-5
...
J
...
) 1999; ISBN 0-387-98495-X
...
Hauptmann: Sensors À principles and applications; Hanser, Munich; Prentice Hall,
Hemel Hempstead, Engelwood Cliffs NJ, 1993; ISBN 0-13-805-789-3P
...
C
...
Meijer (ed
...
[2] S
...
Yurish, M
...
S
...
Gomes (eds
...
) 2005; ISBN 1-402-02927-6
...
J
...
R
...
[4] M
...
Wiegerink: Mechanical microsensors; Springer-Verlag, Berlin,
Heidelberg, New York, (etc
...
[5] M
...
Bao: Micro mechanical transducers; Elsevier, Amsterdam, Lausanne,
New York, Oxford, Shannon, Singapore, Tokyo, 2000; ISBN 0-444-50558-X
...
F
...
): Silicon sensors and circuits; on-chip compatibility; Chapman &
Hall, London, Glasgow, Weinheim, New York, Tokyo, Melbourne, Madras, 1996;
ISBN 0-412-70970-8
...
M
...
): Semiconductor sensors; Wiley, New York, Chichester, Weinheim,
Brisbane, Singapore, Toronto, 1994; ISBN 0-471-54609-7
...
W
...
[9] L
...
[10] S
...
A
...
2 Sensor Fundamentals
A sensor performs the exchange of information (hence energy) from one domain to
another and as such it operates at the interface between different physical domains
...
To avoid confusion with notations, we define unambiguous symbols for each
quantity
...
In this book
we use ε for dielectric constant only; strain is denoted by S
...
Various approaches
are presented in this chapter
...
2
...
1
...
Physical quantities can be divided into subgroups according to various criteria
...
G
G
With respect to direction:
a quantity having a direction is called a vector (e
...
velocity);
a quantity that does not have a direction is a scalar (e
...
temperature)
...
Within one domain state and rate variables are related as follows:
d
_
Xrate 5
Xstate 5 X state
dt
ð
or Xstate 5
Sensors for Mechatronics
...
1016/B978-0-12-391497-2
...
All rights reserved
...
g
...
g
...
Sometimes a property is also called a constant, but
the value of most properties is not constant at all, so we will not use this term
...
g
...
g
...
Resistivity ρ (Ωm) is a pure material property, whereas the resistance R (Ω)
depends on the material as well as the dimensions of the resistor body
...
In most
cases the value of a material property is orientation dependent
...
Extensive variables are state variables; their time derivatives are rate variables
or flows
...
Flow and effort variables are
discussed when conjugated pairs of variables are introduced
...
A lumped element symbolizes a particular property of a physical component
...
Exchange of
energy or information occurs only through these terminals
...
g
...
g
...
Through-variables are also called generalized I-variables; across-variables are called generalized V-variables
...
It is perfectly justified
to call them generalized forces and displacements
...
1
...
Sensor Fundamentals
21
Table 2
...
Input variables can bring a system into a particular state which is represented by its output variables
...
Obviously, a variable can be dependent or independent, according to its function in the
system
...
In the former case the voltage is the independent variable, and it is the
dependent variable in the latter
...
It either acts within one physical domain or crosses domain boundaries
...
This is further discussed in
Section 2
...
2
...
They are called power conjugated variables
...
Table 2
...
Note that the dimension of each product is power (W)
...
Its power conjugate variable ‘voltage’ is actually the rate of
change in magnetic flux, with unit Wb/s, but this is equal to the induction voltage
...
The domain is therefore sometimes called pseudothermal (see last row
of Table 2
...
Table 2
...
G
With respect to energy conjugation:
Another way to define pairs of variables is based on the property that their product equals
energy per unit volume (J/m3)
...
3 lists these pairs for the major domains
...
2 Summary of Relations Between Types of Variables
Domain
State/Extensive
Rate/
Flow
Effort/Intensive
Energy
(J)
Power
(W)
Mechanical
(translation)
Mechanical
(rotation)
Electrical
Magnetic
Thermal
Position x (m)
_
v5x
Force F (N)
F Á dx
FÁv
Angle ϕ (rad)
_
ω5ϕ
Torque T (Nm)
T Á dϕ
TÁω
Charge Q (C)
Flux Φ (Wb)
Entropy σ (J/K/m3)
_
I 5Q
_
V 5Φ
σ
_
Voltage V (V)
Current I (A)
Temperature Θ (K)
V Á dQ
I Á dΦ
Θ Á dσ
VÁI
IÁV
ΘUσ
_
Table 2
...
The description is in particular useful in the field of material research and
optimization of sensor materials
...
1
...
This method is not only useful for the description of sensors but
also has great significance in the design of all kind of technical systems, irrespective of the domain type
...
3, together with
their symbols:
G
G
G
G
G
mechanical (translation): tension T (N/m2) and deformation S (À);
mechanical (rotation): shear tension τ (N/m2) and shear angle γ (À);
electrical: field strength E (V/m) and dielectric displacement D (C/m2);
magnetic: magnetic induction B (Wb/m2) and magnetic field strength H (A/m);
thermal: temperature Θ (K) and entropy σ (J/Km3)
...
The quantities E, D, B, H, T and S are
vector variables, whereas σ and Θ are scalars (therefore often denoted as Δσ and
ΔΘ indicating the difference between two values)
...
On the other hand, S, D and σ are
through-variables
...
1 have the dimension power (W)
...
1
...
If only through-variables affect the energy content, the change can be written as follows:
dU 5 TdS 1 EdD 1 Θdσ
ð2:4Þ
where we disregard the magnetic domain (in Appendix B this domain is included)
...
The through-variables can be
written as follows:
0
1
@GA
SðT; E; ΘÞ 5 2@
@T
Θ;E
0 1
@G
DðT; E; ΘÞ 5 2@ A
@E
T;Θ
0 1
@G
σðT; E; ΘÞ 5 2@ A
@Θ
T;E
ð2:7Þ
24
Sensors for Mechatronics
From these equations we can derive the various material properties
...
(2
...
5) and (2
...
The variables S, D and Δσ are approximated by linear functions, so:
0
1
0 1
0 1
@S A
@S A
@S
dT 1 @
dE 1 @ A dΘ
dSðT; E; ΘÞ 5 @
@T
@E
@Θ
E;Θ
0
T;Θ
T;E
1
0 1
0 1
@DA
@DA
@D
dDðT; E; ΘÞ 5 @
dT 1 @
dE 1 @ A dΘ
@T
@E
@Θ
E;Θ
0
dσðT; E; ΘÞ 5 @
1
T;Θ
0
1
ð2:8Þ
T;E
0
1
@σ A
@σ
@σ
dT 1 @ A dE 1 @ A dΘ
@T
@E
@Θ
E;Θ
T;Θ
T;E
Combining Eqs (2
...
7) results in:
0
dS 5 2@
1
0
1
0
1
@ GA
@ GA
@GA
dT 2 @
dE 2 @
dΘ
@T 2
@T@E
@T@Θ
2
2
Θ;E
Θ
E
1
0
1
@2 G A
@2 GA
@2 G A
dD 5 2@
dT 2 @ 2
dE 2 @
dΘ
@E@T
@E
@E@Θ
0
0
1
Θ
1
0
2
0
Θ;T
1
0
1
ð2:9Þ
T
@2 G A
@2 G A
@2 G
dσ 5 2@
dT 2 @
dE 2 @ 2 A dΘ
@Θ@T
@Θ@E
@Θ
E
T
E;T
Now we have a set of equations connecting the (dependent) through-variables
S, D and σ with the (independent) across-variables T, E and Θ
...
The second
order derivatives in the diagonal represent properties in the respective domains:
mechanical, electrical and thermal
...
(2
...
All other derivatives represent cross effects
...
(2
...
The variables denoting constancy are put as superscripts, to
make place for the subscripts denoting orientation
...
The nine associated effects are displayed in Table 2
...
Table 2
...
The parameters for just a single domain (ε, cp and s) correspond to those in Tables A
...
5 and A
...
The other parameters denote ‘cross effects’ and describe the conversion from one domain to another
...
Note that direct piezoelectricity and converse piezoelectricity have the same
symbol (d) because the dimensions are equal (m/V and C/N)
...
Equations (2
...
10) can be extended just by adding other couples of conjugate quantities, for instance from the chemical or the magnetic domain
...
With three couples we
have nine parameters, as listed in Table 2
...
With four couples of intensive and
extensive quantities we have 16 parameters, so seven more (for instance the magnetocaloric effect, expressed as the partial derivative of entropy to magnetic field
strength, see Appendix B)
...
Table 2
...
(2
...
5 Symbols, Parameter Names and Units of the Effects
in Table 2
...
2
Sensor Classifications
A sensor (or input transducer) performs the conversion of information from the
physical domain of the measurand to the electrical domain
...
Such a classification of the millions of available sensors would facilitate understanding of their operation and making proper choices, but a useful basis
for a categorization is difficult to define
...
These schemes will be briefly discussed in the next sections
...
2
...
The more experienced designer may
also consult books that deal with just one quantity (for instance temperature or liquid flow)
...
However, an application field provides no restricted set of sensors
since in each field many types of sensors could be applied
...
1 presents a list of physical quantities (measurands) [6]
...
For each of these
quantities one or more measurement principles are available
...
2
...
2)
...
Sensors that use an
additional energy source for their operation are called modulating sensors or interrogating sensors
...
Since information transport cannot exist without energy transport, a direct sensor withdraws the
output energy directly from the measurement object
...
There even might be
energy loss too À for instance heat
...
1 List of physical quantities
...
[6]
...
2 Energy flow in direct and modulating sensors
...
Examples of direct
sensors are the piezoelectric acceleration sensor and the thermocouple
...
The terms modulating and interrogating refer to the fact that the measurand
affects a specific material property which in turn is interrogated by an auxiliary
quantity
...
3 Port models of a sensor: (A) twoport model; (B) three-port model
...
g
...
Likewise, most displacement sensors are of the
modulating type: displacement of an object modulates optical or acoustic properties
(e
...
transmission, reflection and interference), where light or sound is the interrogating quantity
...
We distinguish input ports and output ports
...
3A)
...
Likewise, a modulating sensor can be conceived as a system with three ports: an input port, an output port and a port through
which the auxiliary energy is supplied (Figure 2
...
In these models the variables
are indicated with across or effort variables and through or flow variables F,
respectively
...
2
...
Direct sensors provide the information about the measurand as an output signal,
an energetic quantity
...
The information
enters the system through the input port, where the measurand affects specific
material or geometric parameters
...
The information stored in the sensor is available latently, in the latent information parameters or LIP [7]
...
At zero input the LIPs of a modulating sensor have initial values, set by the
material and the construction
...
Note that
direct sensors too have LIPs, set by materials and construction
...
So the input port of all sensors
can be denoted as the LIP input port
...
3B
...
Sensor Fundamentals
29
Interrogating input
Design
controlled
LIP
input
Environment
controlled
Design
controlled
Source
Direct sensor
Environment
controlled
Modulating
sensor
Multiplying
devices
Figure 2
...
According to the ‘unified transducer model’ as introduced in [7], an input
port can be controlled either by design (it has a fixed value) or by the environment
(the measurand or some unwanted input variable)
...
4)
...
All inputs are fixed
...
The output is totally
determined by the construction and the materials that have been chosen
...
Design-controlled LIP input and environment-controlled interrogating input
...
When this is the measurand, the transducer
behaves as a direct sensor
...
Piezoelectric accelerometer: the sensitivity is fixed by the seismic mass and the piezoelectric properties of the crystal
...
The measurand affects particular material properties or geometric parameters
...
The
transducer behaves as a modulating sensor
...
An AC signal on the primary coil acts as interrogating quantity
...
Environment-controlled LIP input and environment-controlled interrogating input
...
For instance a Hall sensor could act as such, when the
interrogating input is not a fixed current (by design) but a current that is related to just
another measurand
...
A strain gauge (a modulating transducer) produces, when interrogated,
30
Sensors for Mechatronics
an output voltage related to the strain-induced change in resistance
...
A thermocouple (a direct transducer) produces an output voltage proportional to the measurand at the interrogating input
...
Since just one response is desired, other responses should be minimized by a
proper design
...
2
...
3
Classification Based on Conversion Principles
The classification according to conversion principles is often used for the reason
that the sensor performance is mainly determined by the physics of the underlying
principle of operation
...
For instance a
magnetic sensor of a particular type could be applied as displacement sensor, a
velocity sensor, a tactile sensor and so on
...
A closer look at the various conversion effects
may lead to the observation that the electrical output of a sensor depends either on
a material property or the geometry or a movement
...
5 tabulates these three
phenomena for various types of sensors
...
5 Classification based on electrical conversion principles (and sensor examples)
...
2
...
First, the energy domains have to be defined
...
Finally,
since many sensors are of the modulating type, the domain of the auxiliary quantity
should also be considered
...
G
G
G
G
G
G
G
G
G
This classification is rather impractical for the description of sensors
...
These six
domains are: radiant, thermal, magnetic, mechanical, chemical and electrical
...
Information contained in each of the six domains can be converted to any other
domain
...
Figure 2
...
An input transducer or sensor
performs the conversion from a non-electrical to the electrical domain (the shaded
column), and an output transducer or actuator performs the conversion from the
OUTPUT DOMAIN
Mechanical
Radiant
Magnetic
Radiant
Luminescense
Radiation
heating
Radiation
Photomagnetism
pressure
Thermal
Incandescense
Thermal
conductivity
Curie–Weiss law
Thermal
expansion
Magnetic
Faraday effect
Ettinghausen
effect
Magnetic
induction
Converse
magnetostriction
Mechanical
Photo-elastic
effect
Friction heat
Magnetostriction Gear
Chemical
Chemoluminescense
Exothermal
reaction
Electrical
I
N
P
U
T
D
O
M
A
I
N
Thermal
Injection
luminescense
Peltier effect
Chemical
Electrical
Photochemical
process
Photoconductivity
Endothermal
reaction
Seebeck effect;
pyroelectricity
Hall effect
Piezoelectricity
Explosive
reaction
Ampere’s law
Pressureinduced reaction
Chemical
reaction
Volta effect
Converse
piezoelectricity
Electrolysis
Ohm’s law
Figure 2
...
Source: After Ref
...
32
Sensors for Mechatronics
Figure 2
...
electrical to another domain (the shaded row)
...
This two-dimensional representation can be extended to three dimensions, when
the interrogating energy domain is included
...
To get
a clear overview of all these possible combinations, they can be represented in a
3D Cartesian space, the ‘sensor cube’ (Figure 2
...
The three axes refer to the input
energy domain, the output energy domain and the interrogating input energy
...
When restricting to electrical transducers, there are 5 direct input transducers, 5 direct output transducers, 25 modulating input transducers and 25 modulating output transducers
...
The x-index is the input domain,
the y-index the output domain and the z-index the domain of the interrogating
quantity
...
Some examples are as follows:
Direct input transducer: thermocouple [th, el, 0]
Modulating input transducer: Hall sensor [ma, el, el]
Direct output transducer: LED [el, ra, 0]
Modulating output transducer: LCD [ra, ra, el]
...
7
...
It may serve as the basis of a categorization for
overviews or as a guide in the process of sensor selection
...
R
...
K
...
, 1995; ISBN 1-56881-048-2
...
Loughlin: Sensors for industrial inspection; Kluwer Academic Publishers, Dordrecht
...
[3] O
...
Meixner: Sensors in intelligent buildings; Wiley-VCH Verlag GmbH,
Weinheim, FRG, 2001; ISBN 3-527-29557-7
...
K
...
Inasaki: Sensors in manufacturing; Wiley-VCH Verlag GmbH,
Weinheim, FRG, 2001; ISBN 3-527-29558-5
...
M
...
[6] S
...
A
...
[7] P
...
Stein: Classification system for transducers and measuring systems, Symposium on
Environmental measurements: valid data and logical interpretation, 4À6 September
1963; US Department of Health Education and Welfare, Washington D
...
1964, pp
...
[8] K
...
Ind
...
Control
Instrum
...
Literature for Further Reading
Some books and articles on quantities and systems
[1] Q
...
Butler: An object-oriented model of measurement systems, IEEE Trans
...
Measurement, 47(1) (February 1998), 104À107
...
Kwaaitaal: The fundamentals of sensors, Sens
...
[3] B
...
Petley: The fundamental physical constants and the frontier of measurement,
Adam Hilger, Bristol (1985); ISBN 0-85274-427-7
...
S
...
, London, 1971; ISBN 0-442-05178-6
...
3 Uncertainty Aspects
No sensor is perfect
...
Specifying sensor quality in terms
of accuracy only is not sufficient: a larger number of precisely defined parameters
is necessary to fully characterize the sensor’s behaviour
...
Similar measures can also be considered
when environmental influences should be eliminated
...
3
...
These sensor specifications inform the user about deviations from the
ideal behaviour
...
Any measuring instrument, and hence any sensor, has to be fully specified with
respect to its performance
...
Gradually, international agreements about formal error descriptions are being established
...
Various international committees are
working towards a uniform framework to specify sensors [3]
...
The characteristics that describe sensor performance can be classified into four
groups:
G
G
G
G
Static characteristics, describing the performance with respect to very slow changes
...
Environmental characteristics, relating the sensor performance after or during exposure
to specified external conditions (e
...
pressure, temperature, vibration and radiation)
...
Sensors for Mechatronics
...
1016/B978-0-12-391497-2
...
All rights reserved
...
In this section we first define some general specifications:
G
G
G
G
G
G
G
G
Sensitivity
Non-linearity and hysteresis
Resolution
Accuracy
Offset and zero drift
Noise
Response time
Frequency response
...
1
...
Mathematically, the sensitivity is expressed as S 5 dy/dx, where x is the input signal (measurand) and y is the output (an electrical signal)
...
These unwelcome sensitivities should
be specified as well, for a proper interpretation of the measurement result
...
Example 1
The sensitivity of a particular displacement sensor with voltage output is specified as
10 mV/mm
...
1 mV/K
...
1 mV corresponds with a displacement of 10 μm, the temperature sensitivity can also be
expressed as 10 μm/K
...
Example 2
The sensitivity of a particular type of temperature sensor is 100 mV/K, including the
signal conditioning unit
...
5 mV for each
degree celcius rise in ambient temperature (not necessarily the sensor temperature)
...
5 mV/K or 0
...
A change
in ambient temperature of 610 C gives an apparent change in sensor temperature
equal to 650 mK
...
1
...
In the case of a non-linear transfer function y 5 f(x), S does depend on the
input or output value
...
In that case the sensitivity
can be expressed with a single parameter
...
The transfer of a sensor with a slight non-linearity may be approximated by
a straight line, to specify its sensitivity by just one number
...
The linearity error of a system is the maximum deviation of the actual transfer
characteristic from a prescribed straight line
...
Non-linearity should always
be given together with a specification of the straight line
...
End-point non-linearity: based on the end-point line, the straight line between the calibrated end points of the range; coincides with the terminal (theoretical) line after calibration of zero and scale
...
Hysteresis is the maximum difference in output signal when the measurand first
increases over a specified range and then returns to the starting value
...
3
...
3
Resolution
The resolution indicates the smallest detectable increment of the input quantity
...
The value of the corresponding smallest detectable change in the input
variable is the resolution: Δxmin
...
This mixed use of definitions seems confusing, although it is easy to see from the units or the value itself which definition
is used
...
Example 2
A particular type of optical encoder has a resolution of 14 bit
...
8 3 1024 rad or 0
...
38
Sensors for Mechatronics
3
...
4
Accuracy
Formally, the accuracy reflects the closeness of the agreement between the actual
measurement result and a true value of the measurand
...
Many sensor manufacturers
specify the sensor performance in terms of accuracy
...
g
...
Precision is not the same as accuracy
...
3
...
5
Offset and Zero Drift
Most sensors are designed such that the output is zero at zero input
...
The offset is expressed in terms of the input or the output quantity
...
Example
The sensitivity of a particular type of force sensing system is 0
...
At zero force
the output appears to be 3 mV
...
03 N
...
Offset compensation can be performed in the interface electronics or the signal processing unit
...
This relatively slow change
in the offset is called zero drift
...
c
...
Sometimes a system is deliberately designed with offset
...
This facilitates the detection
of cable fractures or a short circuit, producing a zero output clearly distinguishable
from a zero input
...
1
...
They are present in any electronic system and arise from thermal motion of the
electrons and from the quantized nature of electric charge
...
White noise (noise with constant power over a wide frequency
range) is usually expressed in terms of spectral noise power (W/Hz), spectral noise
voltage (V/OHz) or spectral noise current (A/OHz)
...
Uncertainty Aspects
39
Another important type of noise is 1/f noise (one-over-f noise), a collection of
noise phenomena with a spectral noise power that is proportional to f 2n, with
n 5 1À2
...
The rounding
off results in a (continuous) deviation from the original signal
...
3
...
7
Response Time
The response time is associated with the speed of change in the output on a stepwise change of the measurand
...
Creep and oscillations may make the specification of the response time meaningless or at least misleading
...
1
...
A measure for the useful frequency range is the frequency band
...
For voltage
or current quantities the criterion is 1/2O2 of the nominal value
...
The extent of
the frequency band is called the bandwidth of the system, expressed in Hz
...
1
...
It is given by the measurement range, the required
supply voltage, the environmental conditions and possibly other parameters
...
Table 3
...
Example 2
Many humidity sensors have non-linear behaviour
...
2 is an example of the specifications of a humidity sensor EMD 2000 from Phys-Chem SCIENTIFIC Corp
...
Despite the specified limitations of sensors, a sensing system can be configured
in a way that the effect of some of these limitations are eliminated or at least
reduced
...
40
Sensors for Mechatronics
Table 3
...
01 dB
0
...
800 Hz
10 nA rms
100 nA rms
2 μA rms
Table 3
...
3% RH at 25 C
Note: Step response and hysteresis curves are included in the specification sheets
...
2
Sensor Error Reduction Techniques
Any sensor system has imperfections, introducing measurement errors
...
Sensor manufacturers try to minimize such intrinsic errors
through proper design of the sensor layout and encapsulation; the remaining imperfections should be given in the data sheets of the sensor
...
In this section we present
some general concepts to minimize or to reduce the effect of the intrinsic errors
when applying sensors
...
The result is a sensor that is sensitive not only to the
quantity to be measured but also in a greater or lesser degree to other quantities;
this is called the cross-sensitivity of the device
...
Besides cross-sensitivities, sensors may suffer from many other imperfections
...
Figure 3
...
1 Simplified sensor model
including error signals
...
2 General layout of compensation: (A) compensation signal; (B) balanced
configuration
...
In this figure, xm is the measurement signal and
yo the output signal
...
They
model all kind of interference from the environment and the equivalent error signals due to system offset and noise
...
For this simplified
model, the output signal of a sensor can be written according to Eq
...
1):
yo 5 Sð1 1 εd 1 εs Þðxm 1 xd 1 xs Þ
ð3:1Þ
where S is the nominal sensitivity
...
Some of these methods will reduce mainly additive sensors; others minimize multiplicative errors
...
We will discuss five basic error reduction methods:
1
...
3
...
5
...
3
...
1
Compensation
Compensation is a simple and effective method to minimize additive errors due to
interference signals
...
2
...
2A
42
Sensors for Mechatronics
the output of the sensor is y1, which contains unwanted signal components, for
instance due to interference xi or offset
...
The condition for full compensation is yc 5 Sxi, making yo 5 Sxm,
independent of xi
...
One way to accomplish compensation is by an
adjustable compensation signal: at zero input yc is (manually) adjusted to a value
for which the output is zero
...
2B
...
g
...
A minus
sign represents the opposite sensitivity of the sensors
...
Because of the anti-symmetric structure
with respect to the measurement signal only, many interference signals appear as
common output signals and thus are eliminated by taking the difference of the two
outputs
...
From Figure 3
...
So, the output signal of the sensor system equals
yo 5 ðSm1 1 Sm2 Þxm 1 ðSi1 2 Si2 Þxi
ð3:3Þ
The sensitivities Sm1 and Sm2 are about equal, so the output signal becomes
ΔSi
xi
yo 5 2Sm xm 1 ΔSi xi 5 2Sm xm 1
2Sm
ð3:4Þ
Analogous to the definition of the rejection ratio for differential amplifiers we
can define a quality measure for the imbalance of the differential sensor:
H5
2Sm
ΔSi
ð3:5Þ
a parameter characterizing the system’s ability to distinguish between measurand
and interfering signals
...
3)
...
3 Measurement bridge with two active elements R1
and R2
...
Their resistance values change with a particular physical quantity as
well as an interfering signal, according to:
R1 5 Rð1 1 Sm1 xm1 1 Si1 xi1 Þ
R2 5 Rð1 1 Sm2 xm2 1 Si2 xi2 Þ
ð3:6Þ
Here, Smk is the sensitivity of sensor k (k 5 1,2) to the measurand (for instance
deformation), and Sik is the sensitivity to the interference signal (for instance temperature)
...
Assuming both sensor parts
experience the same measurement signal and have equal but opposite sensitivities
to the measurand, the bridge output voltage satisfies, approximately, the equation:
Vo 1
1
5 Sm xm 1 ΔðSi xi Þ
Vi 2
4
ð3:7Þ
If both sensor parts have equal sensitivity to interference (by a symmetric sensor
design) and both sensor parts experience the interference equally, the error term in
Eq
...
7) is zero, and the interference is completely eliminated
...
7) is
useful to make a quick assessment of the error due to asymmetry, relative to the
measurement signal
...
3 are strain gauges with strain sensitivity Sm 5 K
(gauge factor) and t
...
α (K21)
...
So, the transfer of
this bridge is:
Vo
1 Δl 1
1 ðαΔΘ 1 ΘΔαÞ
52 K
Vi
2
l
4
ð3:8Þ
where ΔΘ is the temperature difference between the two sensor parts and Δα the difference in temperature sensitivity
...
44
Sensors for Mechatronics
3
...
2
Feedback Methods
Feedback is an error reduction method originating from the early amplifiers with
vacuum tubes
...
Figure 3
...
The sensor has a nominal transfer S, but due to multiplicative
interference it has changed to S(1 1 εi)
...
From classical control theory the error reduction factor can easily be found
...
The penalty for this improvement is a reduction of the
overall sensitivity with the same factor
...
Two cases are discussed in Figure 3
...
The
output due to two interfering signals xi1 and xi2 equals:
yo 5
S
1
Uxi1 1
Uxi2
1 1 kS
1 1 kS
ð3:11Þ
Obviously, signals entering at the input of the system are reduced by feedback
as much as the measurement signal (so the SNR is not better)
...
Feedback reduces errors in the forward signal path: the transfer is mainly determined by the feedback path
...
4 Feedback system: (A) basic configuration; (B) with additive interference signals
...
Prerequisites for an effective error reduction are as follows:
G
G
High forward path transfer
Stable feedback path transfer
...
Imperfections of the sensor are
reduced; however, the demands on the actuator are high
...
5)
...
The amplified voltage difference is supplied to an electromagnetic
actuator that drives the mass back towards its initial position
...
The current
required to keep equilibrium is a measure for the applied force or acceleration
...
6
...
Obviously, the feedback is performed in the mechanical domain by counteracting
the inertial force Fi with the electromagnetic force Fa of the actuator
...
5 Illustration of a feedback system to reduce sensor errors: capacitive
accelerometer
...
6 Model of the differential capacitive accelerometer with feedback
...
(3
...
Hs is the transfer of the mechanical spring: from force to displacement Δx
...
Finally, Ha is the transfer of the actuator
...
1,
the transfer function of the total sensor system becomes:
Vo 5
Hi
a
Ha
ð3:13Þ
Indeed this is independent of the spring stiffness, the sensor transfer, the interface and the gain of the amplifier, according to the feedback principle
...
Hence, no particular demands have to be
made on the spring, the sensor and the interface circuit; the only requirement is a
small zero error
...
The system transfer depends only on
the seismic mass m and the actuator transfer Ha
...
Assume the
sensor in Figure 3
...
Substitution in Eq
...
9) results in the transfer of the system
with feedback:
Sf 5
S0
1
À
Á
1 1 kS0 1 1 2zf ðjω=ωf Þ 2 ω2 =ω2
f
ð3:15Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
with a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
new damping factor zf 5 z= 1 1 kS0 and a new natural frequency
ωfffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 kS0
...
The principle is also applicable for other measurands, for instance pressure
...
Usually, this deformation is measured by some displacement sensor, providing the output signal
...
There are various sensors on the market that are based on
the feedback principle
...
3
...
3
Filtering
Error signals can be reduced or avoided by filtering, to be performed either in the
domain of the interfering signal (prior to transduction) or in the electrical domain
(after transduction)
...
Sometimes the technique is referred to
as shielding
...
The capacitively induced current flows directly to
ground and does not reach the input of the sensor
...
Changes in environmental temperature; thermal shielding (an encapsulation with high
thermal resistance or a temperature-controlled housing) reduces thermal effects
...
Measurand and interferences should have a substantial difference in wavelength
...
g
...
Filtering after Transduction
In case the interfering signals are of the same type (in the same signal domain)
as the measurand itself, error reduction is accomplished with filters based on differences in particular properties of the signals
...
Electrical interfering signals with a frequency
spectrum different from that of the measurand can easily be filtered by electronic
filters (Appendix C)
...
A solution to this problem is to modulate (if possible)
the measurement signal prior to transduction, to create a sufficiently large frequency difference enabling effective filtering in the electrical domain (see
Section 3
...
4)
...
2
...
We shortly review the basics of amplitude modulation and demodulation and show that this combination behaves as a narrow band-pass filter process
...
One of the parameters of this carrier signal is varied analogously to the input (or measurement) signal
...
Due to this property, modulation is also referred to as frequency conversion
...
In measurement systems modulation offers the possibility of
bypassing offset and drift from amplifiers
...
^
A general expression for an AM signal with a sinusoidal carrier vc 5 vc cos ωc t
modulated by an input signal vi(t) is as follows:
^
vm 5 vc f1 1 kUvi ðtÞgcos ωc t
ð3:16Þ
where ωc is the frequency of the carrier, and k is a scale factor determined by the
modulator
...
Figure 3
...
The input signal is still recognized in the ‘envelope’ of the modulated signal,
although its frequency component is not present
...
7B) produces two new components, with the
sum and the difference frequency
...
7C)
...
Each side band carries the
full information content of the input signal
...
Therefore, it can be amplified without being disturbed by offset and drift
...
Uncertainty Aspects
49
Figure 3
...
v(t)
0
t
(A)
vi(ω)
(B)
ωc
ωi
ω
ωc
ω
ωc + ωi
vm(ω)
(C)
ωi
ωc – ωi
v(t)
v(t)
t
(A)
t
(B)
Figure 3
...
There are many ways to modulate the amplitude of a carrier signal
...
Multiplier as Modulator
Multiplication of two sinusoidal signals vc and vi (carrier and input) results in an
output signal:
È
É
^ ^
vm 5 KUvc vi cosðωc 1 ωi Þt 1 cosðωc 2 ωi Þt
ð3:19Þ
with K the scale factor of the multiplier
...
For arbitrary input signals the spectrum of the AM signal consists of two (identical)
side bands without carrier
...
8A shows an example of such an AM signal
...
Further, the AM signal shows a phase shift in the zero crossings of the original
input signal (Figure 3
...
50
Sensors for Mechatronics
Switch Modulator
In the switch modulator the measurement signal is periodically switched on and
off, a process that can be described by multiplying the input signal with a switch
signal s(t), being 1 when the switch is on and 0 when it is off (Figure 3
...
To show that this product is indeed a modulated signal with side bands, we
expand s(t) into its Fourier series:
sðtÞ 5
&
'
1
2
1
1
1
sin ωt 1 sin 3ωt 1 sin 5ωt 1
...
For a sinusoidal input signal with frequency ωi, the output signal contains sums and differences of ωi and
each of the components of s(t)
...
), as shown in
Figure 3
...
The low-frequency component originates from the multiplication by
the mean of s(t) (here 1/2)
...
The resulting signal is just
an AM signal with suppressed carrier
...
A similar modulator can be achieved by periodically changing the polarity of the input signal
...
10
...
9 (A) Series-shunt switch as modulator; (B) time representation of the switch
signal
...
10 Spectrum of an AM signal from a switching modulator
...
When very low voltages must be
measured, it is recommended to modulate these prior to any other analogue signal
processing that might introduce DC errors
...
11
...
This AC signal (usually a
sine or square wave) acts as the carrier
...
Assuming equal values
of the three other resistances, the signal Va is just half the carrier, whereas Vb is an
AM signal: half the carrier modulated by R3
...
This output can be amplified by a differential amplifier with high gain; its lowfrequency properties are irrelevant; the only requirements are a sufficiently high
bandwidth and a high CMRR for the carrier frequency to accurately amplify the
difference Va 2 Vb
...
An optical signal
can be modulated using a LED or laser diode
...
Also, some magnetic sensors
employ the modulation principle
...
3
...
5
Demodulation
The reverse process of modulation is demodulation (sometimes called detection)
...
7), we observe the
similarity between the envelope of the amplitude and the original signal shape
...
Clearly, envelope detectors operate only for AM signals with carrier
...
Apparently, additional information is required with respect to the phase of the
input, for a full recovery of the original waveform
...
11 Wheatstone bridge as modulator
...
This method consists of multiplying
the AM signal by a signal having the same frequency as the carrier
...
Assume a modulated sinusoidal input signal with suppressed carrier:
È
É
^
vm 5 vm cosðωc 1 ωi Þt 1 cosðωc 2 ωi Þt
ð3:21Þ
This signal is multiplied by a synchronous signal with a frequency equal to that
of the original carrier, and a phase angle ϕ
...
This component has a maximum value for ϕ 5 0,
i
...
when the synchronous signal has the same phase as the carrier
...
This phase sensitivity is an essential property of synchronous detection
...
12 reviews the whole measurement process in terms of frequency spectra
...
This signal is modulated and subsequently amplified
...
Figure 3
...
By multiplication
with the synchronous signal, all frequency components are converted to a new position
...
A
low-pass filter removes all components with frequencies higher than that of the
original band
...
If the measurement signal has a narrow band (slowly fluctuating measurement
quantities), a low cut-off frequency of the filter can be chosen
...
The low-pass filter with bandwidth B, acting on the demodulated signal, is
equivalent to a band-pass filter acting on the modulated signal (around the carrier)
...
The selectivity of a band-pass filter
is expressed with the quality factor Q, defined as the ratio between its central
Uncertainty Aspects
53
vi(ω)
(A)
ωc
vm(ω)
ω
Drift
White noise
1/f noise
(B)
ωe
ω
vd(ω)
LP filter
(C)
ωc
2ωc
ω
Figure 3
...
frequency fc and the (23 dB) bandwidth B
...
If, for example, the
measurement signal has a bandwidth of 0
...
5 Hz
...
Active band-pass filters
can achieve Q-factors of about 100 at most, so synchronous detection offers a
much higher selectivity compared to active filtering
...
2
...
Two different strategies can be
distinguished:
G
G
Static correction
Dynamic correction
...
Figure 3
...
In the
model-based approach, the sensor signal is corrected based on prior knowledge
about the origin of the error, for instance non-linearity or a calibration curve, stored
in a look-up table
...
The output of these sensors is used
54
Sensors for Mechatronics
xm
xi
y1
S
Si
y2
xoff
xm
+
xref
y o Figure 3
...
Model
data
xs
+
S
yo
Figure 3
...
to correct the original sensor signal
...
Dynamic correction involves a particular sensor design
...
This can be done in various ways, according to
the type of quantity and error:
G
G
G
multiple input signal measurements, eliminating scale and offset errors;
cyclic interchanging of components (dynamic matching);
cyclic changing the sensitivity direction of the sensor (flipping)
...
14
...
Multiplicative errors due to the interfering signal xs are represented
by the relative error εs
...
The three system outputs are as follows:
yo1 5 Sð1 1 εs Þðxm 1 xoff Þ
yo2 5 Sð1 1 εs Þðxoff Þ
ð3:23Þ
yo3 5 Sð1 1 εs Þðxref 1 xoff Þ
From these equations the measurand can be calculated as follows:
xm 5
yo1 2 yo2
xref
yo3 2 yo2
ð3:24Þ
Offset and scale errors are completely eliminated if the errors do not change
during the sequence of the three measurements
...
For most electrical quantities,
like voltage, capacitance, and resistance, this is quite an easy task
...
15 Overview of error reduction methods
...
All sensor systems suffer from offset and drift, which hampers the measurement
of small, slowly varying signals
...
However, modulation of the input signal is not always
possible
...
Clearly, the method can only
be applied for sensors that are sensitive to the direction of the input quantity (which
should be a vector)
...
An example of a modulating sensor (Chapter 2)
is the Hall sensor for the measurement of magnetic field strength (Chapter 6)
...
Assuming the offset
being independent of the bias, the offset reduction follows from Eq
...
25), where
xc is the carrier signal that is flipped between two successive measurements
...
When the sensor is not of the modulating type, the
same effect is obtained by just rotating the sensor [7]
...
All error reduction methods discussed in this section are illustrated schematically in Figure 3
...
In this scheme, the basic signal flow is shown in dark
colour
...
When designing a sensor system, other techniques are worth consideration, for
instance the inclusion of a compensating sensor in a balanced configuration, or the
incorporation of a modulator whenever possible (white parts in Figure 3
...
During
the design process of a particular sensing system, it is recommended to consider all
these possibilities, in connection to the possible occurrence of errors
...
[2] ISA S37
...
[3] Various documents of the ISA working groups, for instance:
ISA-S37
...
ISA-S37
...
ISA-S37
...
ISA-S37
...
ISA-S37
...
ISA-S37
...
ISA-S37
...
[4] International Vocabulary of Metrology À Basic and general concepts and associated
terms (VIM); Document produced by Working Group 2 of the Joint Committee for
Guides in Metrology (JCGM/WG 2), JCGM 200: 2008
...
S
...
Tech
...
13 (January 1934)
...
M
...
-A
...
P
...
S
...
Actuators, 81 (2000), 328À331
...
J
...
M
...
H
...
M
...
F
...
van Putten: Full additive drift elimination in vector sensors using the alternating direction method (ADM), Sens
...
Literature for Further Reading
Many Books on Instrumentation and Measurement Comprise Chapters
on Accuracy and Noise Reduction, for Instance
[1] A
...
P
...
[2] P
...
L
...
van der Heijden, M
...
Korsten, W
...
, London, 2004; ISBN 1-9039-9658-9
...
These sensors behave
as an electric resistor whose resistance is affected by a particular physical quantity
...
Quantities that can easily be measured using resistive effects are temperature (thermistors and metal thermometers),
light (LDR or light dependent resistor), deformation (piezoresistors) and magnetic
field strength (magnetoresistors)
...
After having defined resistance and resistivity, we discuss successively potentiometric sensors, strain gauges, piezoresistive and magnetoresistive sensors
...
Where
appropriate, a discussion on interfacing is included
...
1
Resistivity and Resistance
The electrical conductivity σ (the inverse of electrical resistivity ρ) is defined as
the ratio between current density J (A m22) and electric field strength E (V m21):
σ5
1
J
5
ρ E
ð4:1Þ
Conductivity is a pure material property: it does not depend on shape or size of
the device (skin effect and thin-layer effects are disregarded here)
...
The resistance between the endpoints
of a bar with length l and constant cross section A equals:
R5ρ
l
A
ð4:2Þ
The parameter l is used to create distance sensors and angular displacement sensors: these sensors are called potentiometric sensors and are discussed in
Section 4
...
Strain gauges are based on changes in l/A (applied in force and pressure
sensors, Section 4
...
4À4
...
Sensors for Mechatronics
...
1016/B978-0-12-391497-2
...
All rights reserved
...
1 Overview of Resistive Sensor Types
Domain
Measurand
Geometry
Mechanical
Linear displacement
Angle
Strain
Force, torque, pressure
Acceleration
Magnetic field
Temperature
Light flux
Potentiometer
Potentiometer
Magnetic
Thermal
Optical
Resistivity
Metal strain gauge
Piezoresistor
Potentiometric
Magnetoresistor
Thermistor, Pt100
LDR
Figure 4
...
Table 4
...
4
...
2
...
A potentiometric sensor
consists of a (linear or toroidal) body which is either wire wound or covered with a
conductive film
...
The connection between the slider and the object
of which the displacement should be measured is performed by a rotating shaft
(angular potentiometers), a moving rod, an externally accessible slider (sledge
type) or a flexible cable that is kept stretched during operation
...
1 shows a
schematic view of some of these constructions
...
This is an important issue when applied
in mechatronic systems that operate in harsh environments
...
The moving parts of the potentiometer are provided with bearings, to
Resistive Sensors
59
minimize the mechanical force needed to initiate movement of the slider and minimizing wear
...
Linear types
vary in length from several mm up to a few m, angular types have ranges from
about π/2 rad up to multiples (2À10) of 2π (multi-turn potentiometers), achieved
by built-in gears or a spindle construction
...
We list here the major items, in a short formulation
...
A manufacturer should mention all these specifications in the data sheets of the
device
...
2 lists the main specifications for various types of potentiometers
...
Some of them are listed below:
G
G
G
G
G
maximum allowable force or torque on the wiper;
minimum force or torque to move the wiper; typical starting torque is 0
...
002 Ncm and for a robust type as high
as 10 Ncm;
maximum (rotational) wiper speed (usually about 1000 rev/min);
maximum voltage across the resistance (typically 10 V);
maximum current through the wiper contact (typically 10 mA)
...
2
...
2)
...
2 Typical Specifications of Potentiometric Sensors
Parameter
Linear
Rotational
Range
Resistance
Resolution
Normal
Lowest, wire
Lowest, film
Non-linearity
Temperature coefficient
Temperature range
vmax wiper
Reliability, wire
Reliability, film
Maximum power
2 mm to 8 m
1 kΩ to 1 MΩ 6 5%
10À60 rev
As linear
60
...
1 μm
0
...
1À50 W
0
...
d
...
d
...
2 (A) Potentiometric wiring and
(B) rheostat wiring
...
3 Transfer characteristic of an
ideal potentiometer
...
5)
...
3)
...
A linear relationship between position and wiper voltage requires a wire or
film with homogeneous resistivity over the whole range
...
4 (A) Slider on top a
winding, (B) slider between two
windings and (C) illustration of
the resolution of a wire-wound
potentiometer
...
5 Interface circuit for a potentiometer
...
01% (see Table 4
...
Improper interfacing may introduce additional
non-linearity, as will be explained in Section 4
...
3
...
With R the total resistance, the resistance of a single turn amounts ΔR 5 R/n
...
4A); hence the resolution equals ΔR/R 5 1/n
...
Actually the wiper may short circuit one turn
when positioned just between two windings (Figure 4
...
In those particular positions the total resistance drops down to (n 2 1)ΔR, hence VR 5 i/(n 2 1), which is
slightly more than i/n as shown in Figure 4
...
The resolution can be increased (without change of outer dimension) by reducing the wire thickness
...
The resolution of a film potentiometer is limited by the
size of the carbon or silver grains that are impregnated in the plastic layer to turn it
into a conductor
...
01 μm; the resolution is about 0
...
4
...
3
Interfacing
The interfacing of a potentiometric sensor is essentially simple (Figure 4
...
To measure the position of the wiper, the sensor is connected to a voltage source
Vi with source resistance Rs; the output voltage on the wiper, Vo, is measured by an
instrument with input resistance Ri
...
Due to the presence of a source resistance and load resistance, the transfer
might differ from the VR
...
62
Sensors for Mechatronics
First assume Rs 5 0 and Ri-N; under this condition, the output voltage of the
sensor satisfies Eq
...
3) for a linear potentiometer or Eq
...
4) for an angular
potentiometer:
Vo 5
x
Vi
L
ð4:3Þ
Vo 5
α
Vi
αmax
ð4:4Þ
where L is the total electrical length and αmax the maximum electrical angle
...
The sensitivity can be increased by increasing the source voltage
...
When ambient temperature increases, the maximum allowable dissipation
drops; it is wise to carefully check the data sheets on this aspect
...
The effect is maximal for x 5 L, so a stability criterion for Vi is:
ΔVi
Δxm
,
Vi
L
ð4:6Þ
where Δxm is the smallest detectable displacement
...
A non-zero value of the source resistance introduces a scale error
...
A load resistance Ri results in an additional non-linearity error
...
6 Non-linearity error for
R/Ri 5 0
...
The approximation is valid when R/Ri{1
...
1), in this case the deviation from the ideal transfer x/L, amounts:
NL ðabsÞ 5
Vo x
x2
x R
2 52 2 12
Vi L
L
L Ri
ð4:9Þ
The maximal error is (24/27)(R/Ri), occurring at x/L 5 2/3
...
The relative non-linearity is:
NL ðrelÞ 5
NL ðabsÞ
x
x R
52 12
Vo =Vi
L
L Ri
ð4:10Þ
from which follows a maximum relative deviation of (21/4)(R/Ri), occurring at the
position x/L 5 0
...
Both errors are proportional to
the resistance ratio R/Ri
...
6 shows the absolute and relative non-linearity
error for the case R/Ri 5 1%
...
15%
...
05% over the full range of the potentiometer, then the minimum value for
the load resistance should be 300 times that of the potentiometer
...
7 Buffering the wiper
voltage
...
8 Elimination of source
voltage variations
...
7
...
The influence of source voltage changes can be reduced by applying a ratio
method, as is illustrated in Figure 4
...
The transfer of the ADC is Va 5 Gn 3 Vr,
where Gn is the binary coded fraction between 0 and 1
...
(4
...
The ADC output can be
directly processed by a computer
...
2
...
However one important drawback still remains: wear due to the sliding contact of the wiper
...
In this type the slider has been
replaced by a floating electrode; the resistance track acts as counter electrode of
the capacitor
...
The basic construction of potentiometers with capacitive readout is shown in
Figure 4
...
The floating wiper is capacitively coupled to the resistance track and
a conductive return track
...
Figure 4
...
9 Contact-free
potentiometer: (A) basic layout
and (B) electric circuit model
and interface
...
The inverting input of the operational amplifier is virtually at ground potential (Appendix C), so the voltage across the cable impedance
Zc is zero
...
When the stray capacitance C3 is small compared to C1 and C2, the voltage
transfer of this circuit is given by
Vo
x Cw
1
52 U
U
Vi
L C4 1 1 jωRp Cw
ð4:11Þ
where Cw 5 C1 1 C2 and Rp is the parallel resistance of the two parts of the potentiometer
...
The transfer
function shows a first-order low-pass behaviour, characterized by the time constant
RpCw
...
For low frequencies of the source voltage, the output voltage
is directly proportional to the VR of the potentiometer, hence proportional to the
displacement of the wiper
...
Note that the feedback capacitor C4 should be shunted by a resistance to prevent
the operational amplifier from running into saturation due to integration of its offset
voltage and bias current (see also Appendix C
...
Together with C4 this resistance
introduces another time constant, so the associated cut-off frequency should be chosen well above the frequency of the voltage source
...
However the transfer characteristic is
somewhat smoothed due to the extension of the floating wiper: small local irregularities are averaged out
...
2
...
Evidently linear and angular potentiometers can be used as
sensors for linear displacement and angle of rotation, respectively
...
If the range of movement does not
match that of the potentiometer, a mechanical transmission can be inserted
...
Proper alignment of object and sensor is extremely
important here
...
When small dimensions
should be combined with a high resolution, potentiometers may be preferred over
the popular optical encoders (Chapter 7)
...
Potentiometers have been considered as one of the possibilities to achieve
this goal (see for instance Ref
...
Figure 4
...
A particular application of a potentiometric sensing device is an angular sensor
for knee rotation, described in Ref
...
Two non-elastic wires are positioned along
the leg, in parallel to the plane of rotation
...
Springs keep the wires stretched
...
The potentiometers form a Wheatstone
bridge, so only the position difference of the wire ends is measured
...
1 over a range of 100
...
They can also be used for the measurement of acceleration,
force, pressure and level
...
Combined with a spring, a potentiometer can act as a force sensor; with a seismic mass fixed to the slider the
construction is sensitive to acceleration
...
e
...
Potentiometers find also application in gyroscopes with spinning rotor
...
10 Potentiometers in a robot finger for grip control (A) untouched
(B) when touched
...
Gyroscopes are
available in which two angles, roll and pitch, are measured by built-in
potentiometers
...
For this purpose potentiometers
of the type shown in Figure 4
...
In case of a liquid the one end of the
flexible cable is connected to a float and at the other end wound on a drum
...
In case of a granular material the
measurement is usually performed intermittently: a weight on a flexible cable drops
down until it reaches the top level of the material
...
A potentiometer-like sensor for measuring tilt is presented in Ref
...
Although
not a potentiometer in the usual sense, it functions in a similar way
...
In horizontal position the resistances between the middle electrode and
both end electrodes are equal, but when tilted the resistance ratio varies according
to the angle of rotation
...
A resolution of better than 1
over an inclination range of 6 60 is achieved
...
3
4
...
1
Strain Gauges
Construction and Properties
Strain gauges are wire or film resistors deposited on a thin, flexible carrier material
...
In 1843, in his first publication on the now well-known bridge circuit, C, Wheatstone
mentioned that the resistance of a wire changes due to mechanical stress
...
E
...
C
...
The latter fixed the measuring wire
onto a carrier material, resulting in an independent measuring device for stress and strain
[6]
...
Eisler, appeared in 1952
...
The transversal sensitivity is smaller but not unimportant
...
11): a thin film of conducting material is deposited on an insulating backing material and etched to create a meanderlike structure (the grid)
...
68
Sensors for Mechatronics
Figure 4
...
The sensitivity of a strain gauge is expressed in relative resistance change per
unit of strain:
K5
dR=R
dl=l
ð4:12Þ
K is called the gauge factor of the strain gauge
...
(4
...
In general all three parameters change simultaneously upon applying strain
...
When an object is
stressed in one direction, it experiences strain not only in this direction but also in
perpendicular directions due to the Poisson effect
...
The ratio of change in length and change in diameter
is the Poisson ratio:
ν 52
dr=r
dl=l
ð4:14Þ
where l is the length of the wire and r the radius of the circular cross section
...
The area of a wire with cylindrical cross section is A 5 πr2, so
dA
dr
52
A
r
ð4:15Þ
hence
dR dρ dl
dr
5
1 22
R
ρ
l
r
ð4:16Þ
Resistive Sensors
69
or, using Eq
...
14):
dR dρ
dl
5
1 ð1 1 2νÞ
R
ρ
l
ð4:17Þ
from which finally the gauge factor results:
K 5 1 1 2ν 1
dρ=ρ
dl=l
ð4:18Þ
To find a value for the Poisson ratio, we assume the volume V 5 A Á l of the wire
is unaffected by stress:
dV
dA dl
5
1 50
V
A
l
ð4:19Þ
resulting in
dl
dA
dr
52
5 22
l
A
r
ð4:20Þ
The Poisson ratio in this ideal case, therefore, equals ν 5 0
...
For metals of
which the strain dependency of the resistivity can be neglected, the gauge factor
equals K 5 1 1 2ν
...
In other
words: the relative resistance change equals twice the strain
...
First of all the value of 2 for the Poisson ratio is a theoretical maximum: in practice the volume will increase somewhat when the wire is
stressed, hence the Poisson ratio will be less than 0
...
25 to 0
...
Further, common strain gauges, built from alloys,
have a gauge factor larger than 2; typical values range from 2
...
This means
that for such materials the stress dependency of the resistivity cannot be neglected,
and the most right term in Eq
...
18) can be as large as 1
...
The resistivity of a
semiconductor material shows a much higher strain dependence; therefore, semiconductor strain gauges have a gauge factor much larger than 2; this will be discussed in Section 4
...
The maximum strain of a strain gauge is not large: about 1023
...
Consequently the resistance change is small
too: a strain of 1 microstrain results in a resistance change of only 2 3 1026
...
Table 4
...
For comparison, a column
for user mountable semiconductor strain gauges has been added
...
70
Sensors for Mechatronics
Table 4
...
c
...
c
...
6 3 1 mm up to 150 mm
2À2
...
1% (up to 4000 μ strain)
20
...
8 3 0
...
02% (min)
0À175 C (max 400)
Typical (standardized) resistance values of strain gauges are 120, 350, 700 and
1000 Ω
...
So the system
bandwidth depends mainly on the (mechanical) interface and read-out electronics
...
Two parameters are important: the temperature coefficient of the resistivity and the thermal expansion coefficient
...
The effect on resistivity is minimized by a
proper material choice for the strain gauge film or wire, for instance constantan, an
alloy of copper and nickel with a low temperature coefficient
...
3
...
To compensate for thermal expansion, manufacturers supply gauges that can be
matched to the material on which the gauges are mounted (so-called matched
gauges)
...
In this case the
relative resistance change due to temperature effects is expressed by
ΔR
5 αT ΔT 1ðαs 2 αg ÞKΔT
R
ð4:21Þ
where αT is the temperature coefficient of the metal, αs and αg the thermal expansion coefficients of the specimen and the gauge, respectively
...
Strain gauges are sensitive not only in the main or axial direction but also in the
transverse direction
...
The factor Ft is determined by the
Resistive Sensors
71
manufacturer, using a specified calibration procedure
...
The transverse sensitivity of the strain gauge is responsible for an additional
resistance change as a result of this transverse strain
...
This, however, requires knowledge of both the factor Ft and the Poisson
ratio ν a of the object material
...
285
...
If, on the other hand, the Poisson
ratio differs substantially from the value during calibration, a correction factor
Ct 5
1 2 ν o Ft
1 2 ν a Ft
ð4:22Þ
should be applied, for the most accurate measurement result
...
Manufacturers provide multi-element strain gauges deposited on a single carrier (see Figure 4
...
Other configurations are also available, for instance a strain gauge rosette (three
gauges making angles of 120 )
...
From the multiple output of this set of gauges, all strain
components of a biaxial strain field (including the shear component) can be calculated [7]
...
3
...
The
bridge may contain just one, but more often two or four active strain gauges, resulting in a ‘half-’ and ‘full-bridge’ configuration, respectively
...
Figure 4
...
72
Sensors for Mechatronics
The general expression for the bridge circuit from Figure 3
...
(4
...
We consider first the case of three fixed resistors and one strain gauge, for
instance R2
...
The transfer is non-linear; only for small relative resistance changes the bridge output can be approximated by
Vo %
ΔR
UVi
4R
ð4:25Þ
Better bridge behaviour is achieved when both R1 and R2 are replaced by strain
gauges, in such a way that, upon loading, one gauge experiences tensile stress and
the other compressive stress (compare the balancing technique as discussed in
Chapter 3)
...
The resulting bridge output becomes:
Vo 5
ΔR
UVi
2R
ð4:26Þ
The transfer is linear, and twice as high compared to the bridge with only one gauge
...
In a bridge configuration, this temperature-induced interference can be partly reduced
...
Assume in a half-bridge the two
active resistances vary according to R1 5 R 2 ΔRS 1 ΔRT and R2 5 R 1 ΔRS 1
ΔRT, where ΔRS is the change due to strain and ΔRT the change due to
Resistive Sensors
73
temperature
...
Substitution of these
values in Eq
...
23) results in
Vo 5
1 ΔRS
UVi
2 R 1 ΔRT
ð4:28Þ
In equilibrium (ΔRS 5 0), the output voltage (the offset) is independent of ΔRT
...
(4
...
The combined gauges in Figure 4
...
Strain gauges in a differential bridge configuration allow the measurement of very
small strain values, down to 0
...
The problem of measuring such small strain
is actually shifted to the bridge amplifier
...
The way out is modulation: the bridge circuit
supply voltage is not a DC but an AC voltage with fixed amplitude and frequency
...
Demodulation (by
synchronous detection) yields the original, amplified signal
...
01 μ strain can be measured easily
...
Manufacturers
of strain gauge measurement transducers provide signal processing systems with these
facilities
...
For example, in Ref
...
4
...
3
Applications of Strain Gauges
Strain gauges are suitable for the measurement of all kind of force-related quantities, for example normal and shear force, pressure, torsion, bending and stress
...
Using Hooke’s law the applied
force is found from the value of the compliance or elasticity of the material on
which the strain gauge is fixed
...
mounted directly on the object whose strain and stress behaviour has to be measured;
when cemented properly, the strain of the object is transferred ideally to the strain gauge
(for instance to measure the bending of a robot arm);
2
...
Strain gauges are excellent devices for the measurement of force and torque in a
mechatronic construction
...
Another approach is to include load cells in the construction
...
The load is
applied to this spring element
...
If the construction does not allow such a configuration, the two pairs of strain gauges are
mounted in a way that one pair experiences the strain that has to be measured,
while the other pair is (ideally) not affected by the strain
...
Obviously, the construction of the spring element and the strain gauge arrangement determine the major
properties of the device
...
13 shows several designs of spring elements for
the measurement of force, for various ranges
...
13A presents a typical construction for large loads
...
There are four strain gauges in a full-bridge configuration
...
The gauges
Tensile
Back
axial
Right
transverse
Left
transverse
F
Tensile
Compressive
Compressive
Tensile
Front
axial
(A)
F
(B)
(C)
F
Figure 4
...
Resistive Sensors
75
are arranged in the bridge of Figure 3
...
The axially positioned gauges respond to a strain as
ΔR1
ΔR3
Δl
5
5K
R1
R3
l
ð4:31Þ
and the resistance of the transverse gauges change as
ΔR2
ΔR4
Δl
5
5 2νK
R2
R4
l
ð4:32Þ
Substitution in Eq
...
23) and assuming ΔRi/Ri{1 for all four gauges, the
bridge transfer is:
Vo
Δl
% 2Kð1 1 νÞ
Vi
l
ð4:33Þ
The applied force F is found using Hooke’s law or, rewritten in terms of force
and deformation, F 5 (Δl/l) Á A Á E, with A the cross-section area of the bar and E
Young’s modulus of the material (or the elasticity c)
...
With strain gauges mounted
directly on a construction part, the same relations between the bridge output and
the force apply
...
13B shows a ring- or yoke-type spring element
...
For this arrangement Eq
...
27)
applies and full benefit from the advantages of a full bridge is achieved
...
13C allows a differential mode measurement of the
strain as well
...
Torque measurements are performed in a similar way as axial force measurements
...
14
...
The
transfer of a measurement bridge composed of these four gauges satisfies
Eq
...
27)
...
Figure 4
...
76
Sensors for Mechatronics
To determine the applied torque (or torsion moment) TM (N m) from the
response of the strain gauges, we use the relation between the torque and the shear
stress Tshear (N m22) at the outer surface of the shaft
...
Further, with Hooke’s law and assuming all normal
stress components zero (pure torsion) the bridge output is found to be:
Vo 5 KUTshear U
11ν
1 1 ν 16
UVi 5 KUTM U
U 3 UVi
c
c
πD
ð4:35Þ
where K is the gauge factor of the strain gauges and ν the Poisson ratio of the shaft
material
...
Possible solutions are slip rings (wear sensitive) and
transformer coupling (with coils around the rotating shaft)
...
Many motion control tasks require both torque and force information, up to all
six degrees of freedom (d
...
f
...
They are incorporated,
for instance, between a link and the end effector of the machine
...
A simple design of a forceÀtorque sensor consists of a spring element with six
or more strain gauges, mounted on a spring element of particular shape
...
15A for a simplified sketch
...
Both
Figure 4
...
o
...
torqueÀforce sensor: (A) mounting between
mechanical interface, (B) positioning of strain gauges
...
On each of the four ‘spokes’ two pairs of strain gauges are
mounted (Figure 4
...
When a force or torque is applied to part 2 of the specimen, the eight differential
pairs of strain gauges respond in proportion to these quantities, with a sensitivity
that depends on the construction of the spring element
...
Each gauge pair responds to more
than just one of the components Fx, Fy, Fz, Tx, Ty and Tz
...
The force and torque components are calculated using the
inverse expression:
½F 5 ½C 21 U½S
ð4:37Þ
with [C]21 the decoupling matrix
...
Various other mechanical structures have been studied with the objective of
combining minimal coupling between the force components with constructive simplicity
...
[9] gives an extensive analysis of a six-d
...
f
...
The construction consists of a set of parallel-plate
beams provided with strain gauges and allows the simultaneous measurement of
three force and three torque components
...
Using finite element methods (FEM) techniques the sensitivity matrix can be calculated and the geometry can be optimized to a minimum coupling of the forceÀ torque
components (see for instance Refs [10,11])
...
4
...
4
...
Many materials show piezoresistivity, but only those with a
high sensitivity are suitable to be applied in sensors
...
The most popular piezoresistive semiconductor is
78
Sensors for Mechatronics
silicon: this material can be used as the carrier of the sensor and, moreover, part of
the interface electronics can be integrated with the sensor on the same carrier
...
Piezoresistive Silicon Sensors
The underlying physical principle of piezoresistivity in silicon goes back to the
energy band structure of the silicon atom
...
Depending on the direction of the applied force with respect to the
crystal orientation, the average mobility of electrons in n-type silicon is reduced,
resulting in an increase of the resistivity
...
The absolute gauge factor increases
with increasing doping concentration
...
The gauge factor of p-silicon appears to be larger
than n-silicon (at the same temperature and doping concentration), and has a positive value
...
Table 4
...
Figure 4
...
Table 4
...
16 Three orientation surfaces in silicon
...
(4
...
This is a
simplified expression: the piezoresistive coefficient depends strongly on the direction of the applied force relative to the crystal orientation
...
the conductivity (orientation dependent)
2
...
the orientation of the resistors with respect to the crystal orientation
...
; 6
ð4:39Þ
The combined orientation-dependent conductivity and compliance yields an
expression for the relative resistance change r as a function of the vector T:
ri 5 πij UTj ;
i; j 5 1;
...
This results in the piezoresistivity matrix equation for
silicon:
0
r1
1
0
π11
Br C Bπ
B 2 C B 12
B C B
B r3 C B π12
B C5B
Br C B 0
B 4C B
B C B
@ r5 A @ 0
r6
0
π12
π12
0
0
π11
π12
0
0
π12
0
π11
0
0
π44
0
0
0
0
0
0
0
0
π44
0
0
1 0
T1
1
0 C B T2 C
C B C
C B C
0 C B T3 C
CU B C
0 C B T4 C
C B C
C B C
0 A @ T5 A
π44
ð4:41Þ
T6
So there are only three independent components describing the piezoresistivity
of silicon
...
5
...
However a shear force (with respect to an arbitrary
direction) results in a large resistance change
...
5 The Piezoresistivity Components of Silicon for p- and
n-Type, in 10212 Pa21 [12]
Material
p-Type
n-Type
π11
π12
π44
66
211
1381
21022
534
2136
Figure 4
...
600
Resistance (Ω)
500
400
300
200
100
0
0
10
20
Pressure (N m–2)
30
Piezoresistive Elastomers
Piezoresistive elastomers are elastomers that are made conductive by impregnation
with conductive particles (e
...
carbon and silver)
...
When the material is pressed, more particles make contact, tending to decrease the resistivity of the material
...
Figure 4
...
Unfortunately most piezoresistive materials show also hysteresis, poor reproducibility and creep, mainly because of permanent position changes of the conductive
particles within the elastomer after being compressed, or lack of elasticity
...
[14])
...
Membranes and piezoresistors based on materials other than silicon have been
studied as well
...
[15] presents research on a MEMS pressure sensor (intended as touch sensor) using a CrÀAl membrane and indium tin oxide
piezoresistors
...
Resistive Sensors
4
...
2
81
Micromachined Piezoresistive Sensors
The unremitting progress in micromachining technology and the creation of microelectromechanical devices (MEMS) have great impact on sensor development
...
Sensors based on this technology are now widely spread, but much research is
still going on to further improve the (overall) performance
...
There is also a tendency to combine technologies to benefit from the advantages provided by each of them
...
18 shows the basic configurations of a silicon pressure sensor and a silicon force sensor, both based on piezoresistive silicon
...
6 mm
...
On top of the wafer, a thin layer of
n-type silicon is grown, called the epitaxial layer or epilayer
...
The result is a thin silicon membrane consisting of only the epitaxial layer, the thickness of which is some μm
...
Using standard silicon processing technology, piezoresistive sensors are deposited at positions on the membrane where the deformation is greatest
...
18 Cross section of (A) a piezoresistive pressure sensor in silicon technology
(simplified), (B) shear force sensor (not on scale)
...
Therefore, silicon strain sensors are
invariably configured in a full-bridge arrangement
...
16)
...
Piezoresistors usually have a meanderlike
elongated shape, to obtain directional sensitivity in a restricted area (as with metal
strain gauges)
...
The membrane deforms under a pressure difference (as in Figure 4
...
18B)
...
Independent measurement of the force components
is accomplished by proper positioning of a set of piezoresistors on the membrane
(see for instance Ref
...
A common problem with all these types of sensors is the packaging
...
g
...
On the other hand, the silicon
chip must be protected against mechanical damage
...
Force sensors require mechanical contact between the membrane
and the (solid) object, which is accomplished by a force-transmitting structure, for
instance a small steel ball, a small piece of material fixed in the centre of the membrane (a mesa) or a thin overlayer from an elastic material
...
In commercial force sensors the
piezoresistors on the micromachined silicon are configured in a half- or full-bridge,
to reduce temperature sensitivity
...
Figure 4
...
All mechanical elements are created in silicon, by selective etching
...
The springs are silicon beams made from the
epitaxial layer, by etching holes in the membrane
...
When the structure experiences an acceleration in a direction perpendicular to the
Piezoresistors
Suspension
Mass
Figure 4
...
Resistive Sensors
83
chip surface, the mass will move up or down due to its inertia
...
Since the device is sensitive to inertial forces, it can be packed in a hermetically
closed housing, making it resistant against mechanical and chemical influences
from the environment
...
They basically consist of a
vibrating mass connected by a thin beam to the sensor base
...
Upon rotation
of the structure, the suspension undergoes torsion that is measured by piezoresistors
integrated in the suspending beam
...
Examples of such micromachined angular rate sensors with piezoresistive sensors are presented in Refs [17]
and [18]
...
4
...
4 g) and low cost
...
Mounted at suitable spots on a mechatronic construction they furnish
useful information on position, orientation and rotation of movable parts
...
One of the first silicon accelerometers with a
complete interface circuit is described in Ref
...
The rectangular seismic mass is
made using bulk micromachining and the circuit is realized in CMOS technology
...
The sensor has a construction similar to the one shown in Figure 4
...
Piezoresistors located at proper places on the square
silicon frame (2
...
3 mm) measure three components of the force (0À2 N)
applied to a short (one-half mm) protruding mesa
...
Another application of a piezoresistive sensor is the displacement sensor
described in Ref
...
The high elasticity of the rubber and the paste allows large strain values,
up to 40%
...
As with all
sensors based on piezoresistive elastomers, this sensor also exhibits a significant
hysteresis
...
For the measurement of body parameters (e
...
posture, gesture and gait), wearable sensors are being developed
...
84
Sensors for Mechatronics
Suitable sensor materials are piezoresistive polymers, rubbers and carbon as coating
material
...
Stretching
and bending of the textile result in elongation of the fibres, and hence a change in
resistance
...
[22],
reporting about such sensors for the measurement of aspiration
...
Piezoresistive sensors are also found in inclinometers
...
Mounted on a robot,
for instance, the sensor provides important data about its vertical orientation, which
is of particular interest for walking (or legged) robots
...
[23] a micromachined inclinometer was proposed, based on silicon piezoresistive sensors
...
Gravity forces the mass to
move towards the earth’s centre of gravity
...
The
authors report an average sensitivity of about 0
...
Tactile Sensors
Piezoresistive elastomers can be used for a variety of sensing tasks in robotics
...
The
material is shaped in sheets, which is very convenient for the construction of flat
sensors, and in particular for tactile sensors
...
They still receive much attention
from designers of robots intended for human-like capabilities, in particular soft
gripping (in horticultural applications, for example)
...
At least one company offers such pressure-sensitive
devices, which can also be used for the construction of tactile sensors [26]
...
Not only is the bulk resistivity a proper sensing parameter, but it is also possible to
utilize the surface resistivity of such materials
...
20)
...
17
...
20 Piezoresistive tactile sensors: (A) bulk mode and (B) contact mode
...
21 Basic idea of rowÀcolumn readout of a tactile matrix: (A) row and column
electrodes on a piezoresistive elastomer and (B) model with four taxels, showing shunt
resistances
...
Most popular is the rowÀ
column readout, accomplished by a line grid of highly conductive electrodes on
either side of the elastomer, making right angles and thus defining the pressure
points of the sensor matrix (Figure 4
...
Individual taxels are addressed by selecting the corresponding row and column,
for instance by applying a reference voltage on the column electrode and measuring
the current through the selected row electrode
...
However
due to the continuous nature of the resistivity of the sheet, the selected taxel resistance is shunted by resistances of all other taxels, as can be seen in the model of
the tactile sensor given in Figure 4
...
For instance when selecting taxel a-1, the
taxel resistance Ra1 is shunted by resistances Rab 1 Rb1 and Ra2 1 R12, resulting in
unwanted crosstalk between the taxels
...
As a consequence when one or more of the taxels a-2,
b-2 and b-1 are loaded, the unloaded taxel a-1 is virtually loaded
...
In an n 3 m matrix many of such phantom images
are seen by the selected taxel, an effect that is more pronounced when loading multiple taxels of the tactile device
...
The principle is illustrated with the simple 2 3 2 matrix of Figure 4
...
In Figure 4
...
Obviously since an additional
current component I2 flows through the other three taxel resistances, the apparent
taxel resistance amounts Va/I1 5 Ra1//(Ra2 1 R2b 1 Rb1)
...
22B the nonselected row electrodes are all connected to ground; the additional current, which is
now I20 , flows directly to ground, so the measured resistance is Va/I1 5 Ra1, which
is just the resistance of the selected taxel
...
22 Reduction of crosstalk: (A) original selection mode and (B) improved selection
mode
...
23 Taxel layout (A) top view, (B) cross section through AÀA0
...
Although not
strictly necessary, grounding of the non-selected column electrodes is preferred
too, to prevent possible interference due to the large resistance of non-loaded taxels
...
Glued onto the elastic layer, the conductive electrodes affect significantly the elastic
properties of the pressure sensitive material
...
[33])
...
[32], where the functions of pressure sensitivity and read-out electrodes
are combined: the sensor consists of two orthogonally positioned arrays of conductive
fibres
...
The contact
resistance changes with pressure, mainly due to a reduction in contact area
...
One of the solutions, applied in, for instance, the tactile sensor described in
Ref
...
The 16 3 16 taxel sensor
responds to the contact resistance between a highly conductive elastomeric sheet
and an electrode pattern deposited on the printed circuit board
...
23, showing how the crossings between
Resistive Sensors
87
column electrodes and row electrodes can be realized
...
An often overlooked aspect is mechanical crosstalk between adjacent taxels, due
to the stiffness of the elastic layer or an additional protective layer
...
Hence the spatial resolution is not equal to the pitch of the electrodes but might be substantially lower
...
One of the first results of this approach is described in
Ref
...
An all-silicon tactile sensor lacks the piezoresistive elastomer: it
consists of an array or matrix of pressure sensors, similar to the devices shown in
Section 4
...
A few examples of such completely integrated resistive tactile sensors
are given here
...
The chip contains signal processing
circuitry as well
...
A further example [38] concerns a 4 3 8
tactile sensor specifically designed for a large force range (up to 50 N)
...
[39] a 4 3 4 tactile sensor with a different architecture is presented
...
Each element contains one piezoresistor
...
A last aspect to be discussed here is the measurement of shear forces using a
tactile sensor
...
A shear sensor
should also be sensitive to tangential forces
...
4
...
5
...
This property
arises from the interaction between the charge carriers and the magnetic moments
in the material
...
This effect, called anisotropic magnetoresistivity (AMR), was discovered by W
...
The effect is rather small and requires very thin
layers to be useful for sensing applications
...
To describe anisotropic resistivity, Eq
...
1) is rewritten into
Ex
Ey
5
ρx
0
0
ρy
Jx
Jy
ð4:42Þ
Here ρx and ρy are the components of the resistivity in x- and y-directions
...
Assume the magnetization is in the x-direction
...
The
angle φ runs from 0 (where the resistivity is maximal) to 90 (minimum resistivity)
...
The sensitivity of an AMR material is usually expressed
as
Δρ ρx 2 ρy
5
ρx 1 ρy
ρ
ð4:45Þ
so the maximum relative change in resistivity (at room temperature) amounts to
only a few percent
...
So when the current remains flowing along the
z-axis, the angle φ changes, and hence the resistivity of the layer (Figure 4
...
The magnetization vector M has a preferred direction, set by the shape of the
ferromagnetic body
...
The relative change in
Figure 4
...
Resistive Sensors
89
resistance can now be expressed in terms of H0 and the external field Hy, according
to the equations:
2
ΔR
Hy
512
H0
ðΔRÞmax
ðHy , H0 Þ
ΔR
5 0 ðHy
...
For sensor purposes, this symmetric sensitivity is very
unlucky: it is strongly non-linear and multi-valued
...
One way to
achieve this is the introduction of an extra magnetic field
...
This is accomplished by a special arrangement of the electrodes, called the ‘Barber pole’ construction [44], after
the similarity to the red-white spinning poles at barber shops (Figure 4
...
Due to
the low resistance of the electrodes (deposited as thin layers on the ferromagnetic
sheet) the current is forced to flow through the device under an angle of approximately 45
...
When a
magnetic field is applied in positive y-direction, the angle decreases, so the resistivity increases and vice versa
...
25, arranged in a full bridge to compensate for common mode errors
...
Resolution and offset are mainly determined by the interface
electronics; the resolution is good enough to measure the earth’s magnetic field,
allowing compass heading (mobile robots) and attitude sensing (walking robots)
...
Around 1980 magnetoresistive devices were realized that exhibit a much larger
sensitivity, according to the so-called giant magnetic resistance effect (GMR) and
Figure 4
...
H
current
M
Conducting
film
90
Sensors for Mechatronics
the giant magnetic impedance effect (GMI)
...
The physical principle differs fundamentally from the AMR sensors
...
In this
state the resistance is maximum
...
The GMI
sensor employs the skin effect, the phenomena in which conduction at high frequencies is restricted to a thin layer at the surface of the material
...
Present research is aiming at higher sensitivity, better thermal
stability and wider frequency range (see for instance Refs [46,47])
...
Current research
focuses on even higher sensitivity: in layered structures of amorphous ribbons
made up of particular alloys, GMR ratios of up to 2400% have been reported [48]
...
In 1993 another group of materials, manganese-based perovskites, was discovered; these exhibit an even stronger magnetoresistive effect, at least at low temperatures and high magnetic fields
...
Unfortunately at room temperature the effect is
much smaller, but nevertheless can be employed for sensor purposes [50]
...
6 presents some specifications of these three types of magnetoresistive
sensors
...
The selected GMR sensor uses a Wheatstone bridge as well
...
The GMI sensor in Table 4
...
This wire is driven by an AC current of 200 kHz
...
The sensor package contains three GMI
sensing elements; the output signals are buffered in a sample-hold circuit, amplified
and multiplexed
...
6 Comparison of Magnetoresistive Sensors
Typea
AMR
GMR
GMI
Units
Sensitivity
Linear range
Frequency range
Number of axes
5
6
5000
2
75
2
1000
1
240
...
); GMI: AGMI302 (Aichi Corp
...
5
...
Therefore
many applications are feasible, for instance as a compass (for mobile robots)
...
g
...
Various possibilities for linear and angular position detection using AMR sensors are presented in Ref
...
In Ref
...
The system is used to monitor the traffic on highways
...
They appear also useful for
non-destructive testing [57] and, because of their small size, for biomedical applications; see for instance Refs [58] and [59]
...
4
...
6
...
The mobility is a parameter that accounts for the ability
of charge carriers to move more or less freely throughout the atom lattice; their
movement is constantly hampered by collisions
...
In intrinsic (or pure) semiconductors, the electrons are bound quite strongly to
their atoms; only a very few have enough energy (at room temperature) to move
freely
...
As the temperature has much less effect on the mobility of
the charge carriers, the resistivity of a semiconductor decreases with increasing
temperature: its resistance has a negative temperature coefficient
...
Increasing the temperature will not affect the concentration
...
Hence the resistivity of a metal increases at higher temperature: their resistivity has a positive temperature coefficient (PTC)
...
Both metals and semiconductors are applied
...
92
Sensors for Mechatronics
4
...
2
Resistance Thermometer
The construction of a high-quality resistance thermometer requires a material
(metal) with a resistivity temperature coefficient that is stable and reproducible
over a wide temperature range
...
Platinum has a high melting point (1769 C), is chemically very stable, resistant against oxidation, and available with high purity
...
8033 K)
and the freezing point of silver (1961
...
A platinum thermometer has a high linearity
...
The values of the coefficients R(0), a, b,
...
As an example
the resistance of a Pt100 is characterized, according to the DIN-IEC 751
standard, as
Rð0Þ 5 100:00 Ω
a 5 3:90802 3 1023 K 21
b 5 5:8020 3 1027 K 22
c 5 4:2735 3 10210 K 23
for a temperature range 2200 C , T , 0 C; for temperatures from 0 C to 850 C
the parameters a and b are the same, and c 5 0
...
For instance the resistance value of a ‘class A’ Pt100 temperature sensor at 0 C is 0
...
15 K
...
14% or 1
...
Class B sensors have wider specified tolerances, for instance 0
...
There also exist resistance temperature sensors with other values than 100 Ω at
0 C, for instance the Pt1000 with a resistance value of 1000 Ω at 0 C
...
The sensitivity of a Pt100 is approximately 0
...
39 Ω/K
...
Within a limited temperature range the non-linearity might be neglected, when a
high accuracy is not required
...
Additional errors may arise due to:
G
G
G
self-heating
errors of the interface circuit
connecting cable resistance
...
A measurement current I
Resistive Sensors
93
Figure 4
...
introduces heat dissipation of I2R(T) in the sensor
...
1 mW
...
1 C, the sensor should be mounted in such a way that the thermal resistance is
less than 103 K/W
...
They are based on either
single-, two-, or three-point calibration techniques (see Section 3
...
6)
...
For instance the interface circuit for a Pt1000 resistive temperature sensor presented in Ref
...
1 Ω, a relative systematic
error less than 0
...
5 3 1027 K21 over
the range 10À50
...
26
...
The resistor R1 sets the sensitivity of the circuit
...
Resistive sensors can also be connected in a bridge configuration, in order to
reduce non-linearity and unwanted common mode interferences
...
Its influence can be compensated for (see Chapter 3)
...
6
...
Commonly used materials are sintered
94
Sensors for Mechatronics
oxides from the iron group (e
...
chromium, manganese, nickel, cobalt and iron);
the most popular material is Mn3O4
...
Several other oxides are added to improve the reproducibility
...
A typical value of the drift in resistance after aging treatment is 10
...
Thermistors cover a temperature range from 2100 C to 1350 C, but particular
types go down to 2 K (ruthenium oxide)
...
Furthermore the size of thermistors can be very
small, so that they are applicable for temperature measurements in or on small
objects
...
The resistance of most semiconductors has a negative temperature coefficient
...
That is why a thermistor is also called an NTCthermistor or just an NTC, although also thermistors with a PTC do exist
...
From this equation it follows for the temperature coefficient (or sensitivity) of
an NTC:
S5
1 dR
B
52 2
R R
T
ðK21 Þ
ð4:51Þ
Further it should be realized that due to the non-linearity of the temperature
characteristic, the sensitivity varies with temperature (as also appears from the
expression given above)
...
For
instance at B 5 3600 K and room temperature (T 5 300 K) the sensitivity amounts
to 24% per K
...
The resistance value of a thermistor at the reference temperature depends on the
material, the doping type and concentration, the device dimension and geometry
...
The
accuracy of thermistors is in the order of 61 C for standard types and 60
...
Like metal resistive sensors, NTCs too suffer from self-heating
...
Generally a current less than 0
...
The effect of self-heating also depends on the encapsulation material and on the dimensions and shape of the sensor
...
A measure
for this effect is the thermal dissipation constant, a figure that is provided by the manufacturer for various sensor types and various environmental conditions
...
5 mW/K to some 10 mW/K
...
The device is encapsulated in a coating of
thermally conductive epoxy to ensure mechanical protection and a low thermal
resistance to the measurement object
...
The smallest devices have a size down to
1 mm
...
This type of interfacing is
used when small temperature changes or temperature differences have to be
measured
...
They can be found
in all kind of systems, for the purpose of temperature monitoring and control, for
temperature compensation in electrical circuits (e
...
amplifiers and oscillators) and
many other uses
...
The base material is
barium or strontium titanate, made semiconductive by adding particular impurities
...
PTCs have a
PTC over a rather restricted temperature range
...
Within the range of a PTC, the characteristic is approximated by
RðTÞ 5 RðT0 ÞeBT ;
T1 , T , T2
ð4:52Þ
The sensitivity in that range is B (K21) and can be as high as 60% per K
...
They are mainly
applied as safety components to prevent overheating at short circuits or overload
...
7
Optoresistive Sensors
The resistivity of some materials, for instance cadmium sulphide (CdS) and cadmium selenide (CdSe), depends on the intensity of incident light
...
A resistor made up of such a material is the LDR (photoresistor)
...
When light falls on the material, freecharge carriers are generated; the concentration increases and thus the resistance
decreases with increasing intensity
...
96
Sensors for Mechatronics
Figure 4
...
The sensitivity of an LDR depends on the wavelength of the light, so it is
expressed in terms of spectral sensitivity (ΔR/Ed per unit of wavelength)
...
27B shows the relative spectral sensitivity for two types of CdS resistors,
one typical and one with high sensitivity for red light
...
Apparently below 400 nm and
above 850 nm the LDR is not sensitive
...
Therefore the sensitivity is also
expressed in terms of lux
...
Figure 4
...
Note the strongly non-linear
response of the device
...
The light resistance is usually defined as the resistance at an intensity of 1000 lux; it may vary from 30 to
300 Ω for different types
...
5 s
...
References and Literature
References to Cited Literature
[1] ISA-S37
...
Resistive Sensors
97
[2] X
...
C
...
Meijer: A novel smart resistive-capacitive position sensor, IEEE Trans
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[3] I
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Takemura, T
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2648À2653
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Roduit, P
...
Besse, J
...
Micallef: Flexible angular sensor, IEEE Trans
...
Meas
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[5] H
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J
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H
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Actuators A, 139 (2007), 23À30
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Vaughan: Application of B&K equipment to strain measurements; Bruel & Kjaer;
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W
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F
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G
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[8] H
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Poussier, S
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[9] J
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Park, G
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Kim: Development of the 6-axis force/moment sensor for an intelligent
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...
[10] Lu-Ping Chao, Kuen-Tzong Chen: Shape optimal design and force sensitivity evaluation of six-axis force sensors, Sens
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[11] Gab-Soon Kim, Dea-Im Kang, Se-Hun Ree: Design and fabrication of a six-component
force/moment sensor, Sens
...
[12] S
...
A
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[13] Measurement data from student projects, unpublished, University of Twente, The
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...
Hussain, Y
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Choa, K
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[15] A
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Patthanasetakul, T
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J Beebe: A silicon-based shear force sensor: development and characterization, Sens
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Voss, J
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Stenzel, T
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Ficker, W
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Bauer, M
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Yang, M
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Yin, S
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Actuators A, 96 (2002), 145À151
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Seidel, U
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Gottinger, J
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Beccai, S
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Arena, F
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Valdastri, A
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Chiara
Carrozza, P
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Kure, T
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Suzumori, S
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Actuators A, 143 (2008), 272À278
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T
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L
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F
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H
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Actuators A, 141 (2008), 396À403
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Mescheder, S
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1133À1136
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E
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St
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Instrum
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, IM-27(1) (1978), 94À99
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H
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Larcombe: Tactile perception for robot devices, First Conference on Industrial
Robot Technology, Nottingham, UK, 27-29 March 1973, pp
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[26] M
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Gu: Force and position sensing resistors: an emerging technology,
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M
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S
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S
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Yeung, N
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Instrum
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, 41(1) (1992), 87À92
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H
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J
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[29] H
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Meusel, G
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91À96
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van Brussel, H
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49À59
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D
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Res
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[32] B
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Robertson, A
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Walkden: Tactile sensor system for robotics, Proceedings 3rd
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[33] L
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Chen, S
...
H
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Phys
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, 62(19) (1993), 2440À2442
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G
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Holweg: Autonomous control in dexterous gripping, PhD thesis, Delft
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, 13(1) (1997), 128À132
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H
...
E
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Kawahata, M
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Igarashi: Tactile image detection using a
1k-element silicon pressure sensor array, Sens
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[38] T
...
J
...
Ge, Y
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Ni, M
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Chan: An integrated MEMS threedimensional tactile sensor with large force range, Sens
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[39] L
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Zheng, Z
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Actuators A, 32 (1993), 193À196
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Zee, E
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M
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Wen, W
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Fluitman, H
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J
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van Mierlo: Contactless angle
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E
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J
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W Gorter: The barber pole, a linear magnetoresistive
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Atkinson, P
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Squire, M
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Maylin, J
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M
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Nesteruk, H
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Lachowicz: Magnetic field meter based on giant
z n
magnetoimpedance effect, Sens
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[47] P
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Sirisathitkul: Giant magnetoimpedance in silicon steels, J
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Magn
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, 281 (2004), 399À404
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Amalou, M
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World, (2000), 24À26
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Castano, J
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Castellano, F
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Gracia: Magnetic position sensor based
on nanocrystalline colossal magnetoresistances, Sens
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Adelerhof, W
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Actuators A, 118 (2005), 278À284
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Rieger, K
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Hauch, W
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Actuators A, 91 (2001), 7À11
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Giebeler, D
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van Zon, D
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Mitamura: New magnetostrictive type torque sensor for steering
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Reverter, J
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Gasulla, R
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Actuators A, 121 (2005), 78À87
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Ripka: Magnetic sensors and magnetometers, Artech House Publ
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[2] K
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H
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Kuiper, G
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S
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[4] J
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Lenz: A review of magnetic sensors, Proc
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Books and Review Articles on Tactile Sensors
[5] H
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Nicholls (ed
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[6] R
...
Russell: Robot tactile sensing, 1990; ISBN 0À13-781592-1
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Pugh (ed
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2: Tactile and non-vision, 1986; ISBN 0À94850702-0
...
D Harmon: Automated tactile sensing, Int
...
Rob
...
, 1(2) (1982), 3À32
...
A capacitor consists of a pair of conductors; since no other materials
are involved, capacitive sensors are very robust and stable and applicable at high
temperatures and in harsh environments
...
The theoretical relation between displacement and capacitance is governed by a simple
expression, which in practice can be approximated with high accuracy, resulting in
a very high linearity
...
Moreover, because of the analogue nature of the capacitive principle, the
sensors have excellent resolution
...
Next,
we discuss basic configurations for capacitive sensors
...
We will focus in particular on linear and
angular displacement sensors and on force sensors
...
5
...
To put it differently, when a
charge Q from infinite distance is transferred to the conductor, its potential
becomes V 5 Q/C
...
When a
charge Q is transferred from one conductor to another, the result is a voltage difference V equal to Q/C; the conductors are oppositely charged with Q and 2Q,
respectively (Figure 5
...
Again, for this pair of conductors, Q 5 C Á V, where V is
the voltage difference between these conductors
...
The set of conductors is called a capacitor
...
DOI: 10
...
00005-4
© 2012 Elsevier Inc
...
102
Sensors for Mechatronics
Figure 5
...
Table 5
...
000576
87
...
10
4
...
2
εr
Material
Al2O3
SiO2
Mica
Teflon
PVC
Silicon (20 C)
Glass, Pyrex 7740
10
3
...
1
3À5
11
...
00
A well-known configuration is a set of two parallel plates, the flat-plate capacitor,
with capacitance
C 5 εU
A
d
ð5:1Þ
where A is the surface area of the plates and d the distance between the plates
...
The parameter ε is called the permittivity and describes the dielectric properties
of the matter in between the conductors
...
8 Á 10212 F/m) and εr, the relative permittivity
...
For vacuum εr 5 1, for air and other gases the dielectric constant is
fractionally higher, liquids and solids have larger values (Table 5
...
For all kind of configurations the capacitance can be calculated [3]
...
2A) with radius a and centres at spacing d have a
capacitance per unit length of:
C0 5
πε0 εr
πε0 εr
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
or; for dca; C 0 5
2 24a2 Þ=2ag
ln ðd=aÞ
ln fðd 1 d
ðF=mÞ
ð5:2Þ
Capacitive Sensors
103
Figure 5
...
Figure 5
...
A coaxial cable (two concentric cylinders, Figure 5
...
For instance consider a flatplate capacitor (Figure 5
...
The capacitance of this
structure (as often encountered in capacitive displacement sensors) is expressed as
follows [4]:
ε0 εr l cosh ðπðw1 1 w2 Þ=4dÞcosh ð2 πðw1 1 w2 Þ=4dÞ
ln
C5
π
cosh ð2 πðw1 2 w2 Þ=4dÞcosh ðπðw1 2 w2 Þ=4dÞ
ð5:4Þ
Anyhow, for a homogeneous dielectric, the capacitance can always be written in
the form
C 5 εUG
ð5:5Þ
where G is a geometric factor
...
When the plates have finite dimensions, as
104
Sensors for Mechatronics
for instance for the structure described by Eq
...
4), G can still be approximated by
A/d; we will discuss the conditions for this approximation later
...
As a fair approximation, the value for the dielectric constant εr of air can be set to 1
...
(5
...
Ad, Ac, Aw and Bw are empirical parameters, and T the
absolute temperature
...
The
dielectric constant is expressed in complex notation: ε 5 ε02jεv, where both the real
and imaginary part are frequency dependent
...
For liquid water at 0 C τ r amounts 17
...
In mechatronics we will consider only the static dielectric
constant, that is, the value at frequencies far below the relaxation frequency
...
The influence of atmospheric changes on the dielectric constant can be summarized as follows [5]: starting with standard air (T 5 293
...
5 Pa and pc 5 30 Pa),
the dielectric constant changes by:
22
...
3 3 1026 per kPa absolute pressure,
90 3 1026 per kPa water vapour pressure,
9 3 1026 per kPa CO2 pressure
...
2)
and proper electrode materials
...
Capacitive Sensors
105
Figure 5
...
Many capacitive displacement sensors are based on flat-plate capacitors
(Figure 5
...
Either the plate distance d or the effective plate area A is used as a position-dependent parameter
...
3C
...
1), an error is made due to stray fields (fringes) at the edges of the plates
...
The effect of stray fields can be reduced by the application of guarding
...
4)
...
The result is that the electric field is homogeneous over the total area of the active
electrode, assuming infinite guard electrodes and a zero gap width between the two
electrodes
...
This error depends on the dimensions of the guard
electrode and the gap width [3]:
ΔC
# e2πx=d
C
ΔC
# e2πd=s
C
ð5:9Þ
with d the plate distance, x the width of the guard electrode and s the gap width
between guard and active electrodes
...
Finally, when the plates are not exactly in parallel, Eq
...
1) does not hold
anymore
...
For 1
(or 0
...
5
...
2
...
(5
...
If one of the plates is part of a
106
Sensors for Mechatronics
Figure 5
...
deformable membrane, pressure can also be measured using the capacitive principle
...
This is the major reason that displacement sensors based on capacitive
principles have excellent linearity
...
5 shows, schematically, two basic configurations for linear displacement
...
In these examples the parameter A (effective surface
area) varies with displacement
...
5A a linear displacement of the upper plate in the indicated direction
introduces a capacitance change which is, ideally, ΔC 5 εΔxa/d, or a relative
change ΔC/C 5 Δx/x
...
Capacitive sensors for rotation can be configured in a similar way,
with segmented plates rotating relatively to each other, where the distance d
remains constant
...
Figure 5
...
The initial position is defined as the position for
which C1 5 C2
...
An additional advantage of the differential configuration is the extended dynamic
range: in the reference or initial position the capacitances of the two capacitors
are equal
...
A small displacement results in a small output signal that can be electronically
amplified without overload problems
...
However,
compensation by an equally shaped sensor is more stable than compensation in the
electrical domain
...
5 is the electrical
connection to the moving plate, required for the supply and transmission of the
measurement signals
...
6 shows a configuration without the need for such a
connection
...
6 Differential capacitive displacement sensor with current read-out: (A) top view
of a flat-plate capacitor and (B) electronic model
...
All fixed electrodes are in the same
plane
...
In this position, both
(balanced) signals are coupled to the read-out electrode where they cancel, resulting in a zero output signal
...
Using the simplified model of Figure 5
...
When V1 5 2V2 5 Vi, the output current Iout is directly proportional to the
capacitance difference C1 2 C2
...
Its phase is either 1π/2 or 2π/2 according to the direction of
the displacement
...
An alternative read-out scheme is shown in Figure 5
...
Two adjacent plates
are supplied with two sinusoidal voltages with phase difference π/2
...
6A
...
(5
...
When the electrode arrives just above the right plate, the phase is π
...
108
Sensors for Mechatronics
Figure 5
...
To calculate the phase of the output current in dependence of the displacement
we define the co-ordinates as in Figure 5
...
The centre of the moving plate runs
from x 5 0 to x 5 p
...
Suppose the input
^
^
voltages are V1 5 Vsinωt and V2 5 Vcosωt
...
(5
...
With Figure 5
...
(5
...
The phase angle satisfies the relation
x
ϕ 5 arctan
p2x
ð5:14Þ
ð5:15Þ
The phase varies with displacement in a slightly non-linear way (Figure 5
...
Stray
fields cause further deviations from linearity, but even with guarding the relation is
essentially nonlinear
...
Capacitive displacement sensors can also be configured in a cylindrical configuration, as in Figure 5
...
The principle is the same, but a cylindrical set-up is more
compact, has less stray capacitances and therefore a better linearity
...
The sensor exhibits extremely good linearity (better than 0
...
Capacitive Sensors
109
Figure 5
...
The rotational version of the LVDC is called RVDC (rotational variable differential capacitor)
...
Angular sensitivity is obtained using triangularly shaped electrodes
...
2)
in Section 5
...
The lower limits of linearity, stability and accuracy of these precision sensors
are set by the air humidity: water vapour in the air may condensate in edges and
small gaps of the construction (capillary condensation), thereby locally replacing
air (with dielectric constant of about 1) by liquid water (with εr % 80, see
Table 5
...
Even at temperatures above dew point, water vapour may condensate
due to contamination: hygroscopic particles attract water molecules and act as condensation nuclei
...
5
...
2
Multiplate Capacitive Sensors
The measurement range of the linear capacitive sensors discussed so far is limited
to approximately the width of the moving plate (Figures 5
...
7)
...
Figure 5
...
It consists of an array of
sections similar to the one in Figure 5
...
When the moving plate approaches the
end of one section, it simultaneously enters the next section
...
When the moving plate travels along four successive sections,
the phase of the voltage on this plate changes from 0 to 2π (Figure 5
...
This is
repeated for each group of four electrodes
...
An unambiguous output is obtained by keeping track of the number of passed cycles, using an
incremental counter
...
9B are actually four s-shaped curves from
Figure 5
...
Phase differences can be measured with high resolution,
down to 0
...
By periodically repeating the structure a large range is obtained
110
Sensors for Mechatronics
Figure 5
...
Segmented electrode
Guarding
Revolving vane
Common electrode
Guarding
Figure 5
...
combined with high resolution
...
01 mm
...
10)
...
The challenge of the designer is to obtain the highest possible resolution over a
fixed range of 2π rad
...
Evidently, guard electrodes are indispensable here
to reduce stray fields
...
5
...
3
Silicon Capacitive Sensors
Silicon micromachining technology offers the possibility to construct extremely
small capacitive sensors
...
Instead of
adding piezoresistors to the spring element, the flexible membrane is opposed to a
fixed flat electrode, building a miniaturized flat-plate capacitor
...
Advances in the technology of MEMS have
resulted in the realization of microsensors for other quantities as well, for instance
acceleration
...
These technologies are highly attractive for accelerometers, rate gyroscopes and
(gas) pressure sensors but less for force sensors because of the susceptibility to
mechanical damage of the tiny movable parts
...
Capacitive sensors for other measurands are also considered to be
implemented in MEMS technology, e
...
the angular sensor discussed in Ref
...
From a technological point of view, however, a capacitive sensor is more difficult to realize compared to its resistive counterpart
...
Further, the spacing between the plates should be
made small, to obtain a reasonable capacitance and sensitivity, and the alignment
of the two electrodes is also a critical processing step
...
The support layer and top layer can be made from silicon or glass
...
The layers
are connected using special techniques
...
11 shows some examples [11À13] of
integrated capacitive pressure sensors (vertical scale much larger than horizontal
scale)
...
11B the electronics and the membrane
are made from separate wafers, to enhance technological freedom: the processes for
etching membranes and deposition of electronic circuitry are not fully compatible
...
A large variety of alternative structures have been proposed over the last three
decennia
...
A structure without separate top
layer is described in Ref
...
Both capacitor plates are constructed on the membrane chip using surface micromachining
...
Here,
too, a reference capacitor (insensitive to pressure) has been integrated
...
A larger (initial) capacitance may be realized by reducing the gap distance
between the plates
...
The alternative is to
112
Sensors for Mechatronics
Circuit chip
Glass plate
Reference gap
Electrodes
Membrane
Electronics
Bonds
Electronics
Support
Support chip
Membrane
Figure 5
...
Source: (A) After Refs [11] and [12]; (B) After Ref
...
increase the effective surface area
...
The sensor is made up of two processed wafers, put
together face-to-face and resulting in a narrow gap between them
...
5 μm) as the remainder of the top wafer
...
In this way a relatively large area combined with a narrow gap is achieved,
and hence a larger capacitance and sensitivity can be obtained than with other
techniques
...
A few decennia ago it was
shown that the complete system can be integrated on silicon, resulting in a small,
easy-to-mount device [17]
...
19 (a piezoresistive accelerometer): they consist of a seismic
mass suspended on flexible beams
...
The mass moves due to an inertial force, resulting in a change in distance between
the plates, and this causes the capacitance to change
...
Together with the MEMS
sensor, additional electronics and signal processing, for instance voltage regulators
or an ASIC (application-specific integrated circuit) and a temperature sensor for offset compensation can be housed in a small package [19]
...
A larger (initial) capacitance might be realized by a
dielectric support structures (see the preceding section on pressure sensors)
...
This is realized in MEMS
Capacitive Sensors
113
Figure 5
...
technology, allowing the construction of so-called comb structures
...
12
shows the basic configuration
...
The more fingers, the larger the
surface area and the higher the capacitance
...
The
same structure is also used for capacitive actuators, so-called comb drives
...
3
Interfacing
In high-resolution sensors and microsensors the capacitance changes that have to be
measured can be extremely small (down to fractions of a femtofarad or 10215 F)
...
We discuss four major interface methods for capacitive sensors (Figure 5
...
2
...
4
...
For each of these methods we give a brief analysis (see Appendix C for the transfer of operational amplifier configurations)
...
13A) is:
Vo
1
C1
1 C2 2 C1
5 2
5 U
Vi
2 C1 1 C2
2 C1 1 C2
ð5:16Þ
In a single sensor configuration, C1 5 C 1 ΔC and C2 5 C, hence
Vo
ΔC
ΔC
U 12
%2
Vi
4C
2C
ð5:17Þ
114
Sensors for Mechatronics
Figure 5
...
The transfer is frequency independent but nonlinear
...
A proper measurement of the bridge output voltage requires a differential amplifier with high input impedance and high
common mode rejection ratio
...
13B and C: the first for single mode operation and the second for differential mode operation
...
20), which is linear, and the output is zero in the initial state (equal
capacitances)
...
13C
is left out
...
The
resistance R prevents the circuit from running into overload but causes the transfer
to fall off with decreasing frequency from about f 5 1/2πRCf
...
When the maximum capacitance change is small, the feedback capacitance Cf
should be chosen small too, for a reasonable gain of the circuit (as follows from
Eq
...
20))
...
In integrated capacitive sensors these stray capacitances are very small, allowing a small feedback capacitance,
hence high gain
...
Neither the amplitude drift nor the frequency instability of the
oscillator affects the zero stability since they are common to both differential sensors
...
The output appears to be very sensitive
for deviations from the required 180 phase difference, a fact that can be used to
create a sensitive capacitance-to-phase converter [20]
...
13D
...
An advantage of the oscillator method is
easy signal processing with a microprocessor: the frequency can be determined by
simply counting the number of clock pulses during one cycle of the oscillator signal
...
A detailed analysis of a circuit based on this principle can be found in [21]
...
This interface has a sensitivity of 100 Hz/fF and a resolution of about 0
...
An interface circuit that combines the advantages of a time signal output and
high linearity is given in Figure 5
...
The unknown capacitance is periodically charged and discharged with currents I1
and I2
...
At that moment the switches
turn over and the capacitance is discharged until the lower hysteresis level is
116
Sensors for Mechatronics
reached
...
The method yields accurate
results because the frequency depends only on these fixed levels and the charge
current
...
We mention
some of these works
...
[22] an interface circuit based on a three-phase time sequence is
described, applied to a differential capacitive sensor pair
...
Hu et al
...
13C, with switchable feedback capacitances and a rectifier
...
13C) the transfer (gain) can be adopted to the needs,
maximizing signal-to-noise ratio
...
A resolution of 0
...
In Ref
...
The feedback capacitance, a reference capacitance and the voltage gain can be programmed to optimize circuit
performance
...
Finally, we mention an advanced version of the circuit in Figure 5
...
In
this circuit, two capacitors instead of just one are periodically charged and discharged, resulting in a periodic signal of which the duty cycle is related to the
capacitance to be measured
...
04%
...
4
5
...
1
Applications
Capacitive Sensors for Position- and Force-Related Quantities
Capacitive sensors are suitable for the measurement of all sorts of position-related
quantities: displacement, rotation, speed, acceleration and tilt
...
Most of these sensors are based on Eq
...
1), indicating the
relation between the capacitance value and a geometric parameter (e
...
effective
surface area and plate distance)
...
2 Typical Specifications of Various Capacitive Sensors
Type
Range
Resolution
t
...
Gain
(KÀ1)
Tmax
( C)
Bandwidth
(Hz)
LVDC
RVDC
Acceleration
(feedback)
Tilt
2
...
5
...
01) μm
0
...
01
1024
300
80
applications with high demands (for instance extreme temperatures)
...
Furthermore, extremely small capacitance
changes (down to 1 fF) can be measured with simple interface circuits
...
As with all displacement sensors, capacitive displacement sensors can be
modified to make them suitable for the measurement of angular rate, acceleration,
force, torque, mass and pressure
...
Table 5
...
Using the circular multiplate capacitor discussed in Section 5
...
2, angular position and angular speed can be determined with high accuracy, as has been demonstrated in many papers, for instance in Refs [26À28]
...
A micromachined contact-free angle
sensor was already mentioned in Section 5
...
3 [10]: this angle sensor combines an
inductive principle for the transduction from angle (with respect to a fixed magnetic field) to the deflection of a polysilicon micromass and the capacitive measurement of this deflection
...
[29] with a balanced capacitive read-out circuit
...
In some of these applications the sensor on the axis is purely passive, which means
that no power supply on the axis is needed
...
The capacitive mass sensor in Ref
...
The capacitive force sensor in Ref
...
14
...
At zero force, all
four capacitances C1 2 C4 are equal
...
14 3D force sensor layout with elastic dielectric: (A) and (B) cross section; (C) top
view
...
The interface should be able to distinguish between these force
components
...
4
...
Selected
measurands are distance, displacement, thickness, rotation, strain, force, level and
flow
...
Capacitive sensors offer the possibility of highly accurate distance or displacement measurements, as in controlled xÀy tables
...
[35]
...
In this work
the bending of the touch probe (a thin stylus) is determined by capacitive means
...
3 mm, with an accuracy of 1 μm
...
For a non-conductive coating on a conductive plate, the capacitive method is suitable to measure the thickness of such a coating
...
[36], proposing
a capacitive probe and giving an analysis of the various sources of errors
...
2
...
An alternative solution is given in
Ref
...
The sensor consists of two printed circuit boards
(PCBs) each provided with an array of electrodes (transmitter and receiver), able to
slide linearly over each other as in an optical encoder
...
Although realized with simple technology (e
...
PCBs, copper electrodes and coating), the resolution of the sensor
appears to be about 126 nm, over a range of 20 mm
...
An example was given in Figure 5
...
A modified version is presented in Ref
...
The main advantage of this
design is that no electrical connections to the rotating part are needed
...
[39]: the
measurement of tyre strain
...
When the tyre is loaded, the resulting strain causes the distance between
these wires to increase
...
The paper describes how to measure this capacitance change
...
13D), but instead of an LC-oscillator, an
RC-oscillator is chosen
...
Another approach to measure tyre strain using a capacitive method is described in Ref
...
The authors have fabricated a particular
strain gauge, consisting of a pair of interdigitated flat electrodes on a flexible polyimide carrier
...
As mentioned before, capacitive sensors can also be applied for force and pressure measurements
...
The sensor consists of two rubber layers sandwiched between (three) conductive sheets
...
The sensor is flexible, light-weight and
easy to carry
...
Thus far we have used the geometric factor G in Eq
...
5) as the basis for a
capacitive measurement
...
Measuring liquid level in a tank is an obvious example
...
15A)
...
A partly filled capacitor can be conceived as two
capacitors in parallel: one filled with the liquid up to the upper level (CL), and one
with air from the level to the top of the plates (CA)
...
Obviously, this
method holds only for non-conducting liquids
...
15 Capacitive level measurements
...
[43]
...
15B, the influence
of several parameter variations can be eliminated [44]
...
15C)
...
[45] such a solution is presented, resulting in a resolution of 0
...
Further, Ref
...
The capacitive method makes it possible to detect water drops on a windscreen:
a rain sensor
...
To be less sensitive to temperature variations and other possible common
mode interferences, a differential structure is preferred: one capacitor is exposed to
water, the other is not and serves as a reference capacitor [47]
...
Pavlov et al
...
The interface is
based on the oscillation method and with special signal processing it is also possible
to extract particular features of the passing person, for instance high or low speed and
direction
...
[49] discuss a capacitive method to detect the presence of a
person on a car seat
...
The sensor configuration enables the discrimination between an adult
and a child, and between persons and objects (for instance bottles with water)
...
[50]
...
The measured impedance parameters are compared with the model parameters, from which information about the occupancy is
derived
...
[51]; large flat electrodes are integrated in the floor and walls of a 2 3 2 m room
...
One of the many ways to measure flow velocity of a substance moving through
a pipe is correlation: two sensors placed a distance d apart from each other measure
some property of the flowing substance, for instance reflection (scattering), acoustic noise or thermally induced temperature variations
...
An implementation using a capacitive principle is found in Ref
...
Two ring-shaped electrodes are mounted
at the outside of the pipe, a distance d apart and a third electrode just midway
between them
...
The flow velocity is
found from the cross correlation of the two capacitance signals
...
A varying magnetic flux in a (ferromagnetic) material
Capacitive Sensors
121
produces eddy currents (see Chapter 6), which in turn create a voltage difference
across the material
...
To be able to measure in this way, the needles must make electrical
contact, so any possible isolating coating should be removed at the contact places
...
[53] the needles are replaced by conductive pads acting as pick-up electrodes: the voltage is coupled capacitively to the measurement instrument
...
This section clearly shows that the capacitive sensing principle can be applied in
numerous situations
...
References and Literature
References to Cited Literature
[1] J
...
Hasted: Aqueous dielectrics (Series: Studies in chemical physics)
...
[2] D
...
Kauzmann: The structure and properties of water; Oxford University
Press, London, 1969
...
Chr: Heerens: application of capacitance techniques in sensor design, J
...
E Sci
...
, 19 (1986), 897À906
...
W
...
[5] M
...
W
...
370
...
1
...
A
...
H
...
L
...
Instrum
...
, 40(6)
(1991), 897À901
...
N
...
C
...
Meijer: A low-cost, smart capacitive position sensor, IEEE Trans
...
Meas
...
[8] K
...
Klaassen, J
...
L
...
E
...
A
...
E
...
), From electronics to microelectronics, North-Holland Publishing Company, 1980, pp
...
[9] X
...
Li, G
...
M
...
W
...
Instrum
...
, IM-45 (1996),
516À520
...
R
...
Schellin: A novel silicon surface micromachining angle sensor,
Sens
...
[11] C
...
Sander, J
...
Knutti, J
...
Meindl: A monolithic capacitive pressure sensor with
pulse-period output, IEEE Trans
...
122
Sensors for Mechatronics
[12] Y
...
Lee, K
...
Wise: A batch-fabricated silicon capacitive pressure transducer with
low temperature sensitivity, IEEE Trans
...
[13] A
...
-E
...
A
...
Carlson, B
...
Holwech: An
integrated capacitive pressure sensor with frequency-modulated output, Sens
...
[14] S
...
Moe, K
...
T
...
Lund, J
...
Furuberg,
M
...
Fallet, R
...
Bernstein: Capacitive differential pressure sensor for harsh
environments, Sens
...
[15] C
...
Mastrangelo, X
...
C
...
1, pp
...
[16] T
...
Fragiacomo, O
...
V
...
Actuators A, 154 (2009), 35À41
...
B
...
Instrum
...
, IM-37(4) (1988), 569À571
...
Rodjegard, C
...
Enoksson, G
...
Actuators A, 123À124 (2005), 50À53
...
Rodjegard, C
...
Malmstrom, G
...
Andersson: Frequency and temperature
characterization of a three axis accelerometer; Proceedings Eurosensors XIX,
Barcelona, Spain, 11À14 September 2005, MP27
...
F
...
P
...
Regtien: Capacitance-to-phase angle conversion for the
detection of extremely small capacities, IEEE Trans
...
Meas
...
[21] C
...
Marioli, E
...
Taroni: A 15 ppm resolution measurement system for capacitance transducers, Meas
...
Technol
...
[22] A
...
Hou, S
...
P
...
Actuators A, 119 (2005), 113À119
...
L
...
M
...
E
...
Actuators A, 125 (2006), 329À334
...
Bracke, P
...
Puers, C
...
Actuators A, 125 (2005), 25À33
...
M
...
J
...
Instrum
...
, IM56(1) (2007), 153À157
...
Fabian, G
...
Instrum
...
, IM-47(1) (1998), 280À285
...
Brasseur: A capacitive 4-turn angular-position sensor, IEEE Trans
...
Meas
...
[28] P
...
Fulmek, F
...
Zdiarsky, G
...
Instrum
...
, 51(6) (2002), 1145À1149
...
E
...
Akin: A planar gyroscope using a standard surface micromachining
process; Proceedings Eurosensors XIV, 27À30 August, Copenhagen, Denmark,
pp
...
[30] J
...
Turner: The development of a thick-film non-contact shaft torque sensor for
automotive applications, J
...
E Sci
...
, 22 (1989), 82À88
...
Falkner: A capacitor-based device for the measurement of shaft torque, IEEE Trans
...
Meas
...
[32] R
...
Wolffenbuttel, J
...
Foerster: Noncontact capacitive torque sensor for use on a
rotating axle, IEEE Trans
...
Meas
...
Capacitive Sensors
123
[33] A
...
Al Aish, M
...
Actuators A, 151 (2009), 113SÀ117S
...
G
...
F
...
Lanceros-Mendez: Capacitive sensor
for three-axis force measurements and its readout electronics, IEEE Trans
...
Meas
...
[35] S
...
Li, M
...
Kaiser, F
...
K
...
Sci
...
, 9 (1998), 1365À1368
...
J
...
G
...
A
...
Sci
...
, 9 (1997), 1028À1033
...
Kim, W
...
[38] V
...
Ghisla, D
...
Taroni: Capacitive angular-position sensor with
electrically floating conductive rotor and measurement redundancy, IEEE Trans
...
Meas
...
[39] R
...
Todorokib: Wireless strain monitoring of tires using electrical capacitance changes with an oscillating circuit, Sens
...
[40] R
...
Todoroki: Wireless flexible capacitive sensor based on ultra-flexible
epoxy resin for strain measurement of automobile tires, Sens
...
[41] R
...
Keating, A
...
Hiraoka: Rubber-based strain sensor fabricated using photolithography for intelligent tires, Sens
...
[42] L
...
Zhang, Q
...
[43] F
...
J
...
C
...
Meijer: Liquid-level measurement system based on a
remote grounded capacitive sensor, Sens
...
[44] H
...
Instrum
...
, 58(10) (2009), 3762À3768
...
N
...
C
...
Meijer, M
...
Instrum
...
, 46(2) (1997), 644À646
...
K
...
Tiruthani: A capacitive displacement sensing technique
for early detection of unbalanced loads in a washing machine, Sensors, 9 (2009)
9559À9571, doi:10
...
´
[47] P
...
Menil: Temperature influence on a differential capacitive rain sensor performances, Sens
...
¨
¨
[48] V
...
Ruser, H
...
Trankler, J
...
[49] B
...
Zangl, T
...
Brasseur: Seat occupancy detection based
on capacitive sensing, IEEE Trans
...
Meas
...
[50] A
...
Hammerschmidt, D
...
Actuators A, 152 (2009), 1À4
...
N
...
M
...
Kerkvliet, G
...
M
...
Sci
...
, 21 (2010) doi: 10
...
[52] H
...
Zangl, E
...
Brasseur: Petriu: flow-velocity measurement for bulk granular solids in pneumatic conveyor pipes using random-data correlator architecture, IEEE
Trans
...
Meas
...
[53] S
...
Meydan: A novel capacitive flux density sensor, Sens
...
124
Sensors for Mechatronics
Literature for Further Reading
[1] L
...
Baxter, R
...
Herrick: Capacitive sensors: design and applications; IEEE Press
Series on Electronics Technology, 1996; ISBN 0780311302
...
A
...
H
...
L Carroll: Investigation of a capacitance-based displacement transducer, IEEE Trans
...
Meas
...
¨
[3] A
...
Sjolund: Analysis of the performance of the capacitive displacement
transducer, IEEE Trans
...
Meas
...
[4] G
...
Jankauskas, J
...
LaCourse, D
...
Limbert: Optimization and analysis of a capacitive contactless angular transducer, IEEE Trans
...
Meas
...
6 Inductive and Magnetic Sensors
Inductive sensors employ variables and parameters like magnetic induction B, magnetic flux Φ, self-inductance L, mutual inductance M or magnetic resistance Rm
...
First we review various magnetic quantities and
their relations
...
Special attention is given to transformertype sensors
...
6
...
1
...
1A)
...
For each configuration of conductors carrying
an electric current the field strength in any point of the surrounding space can be
calculated by solving the integral equation (6
...
A current I through a long,
straight wire produces a magnetic field with strength H 5 I/2πr at a distance r from
the wire
...
The field lines form concentric circles around the wire so the vector direction
is tangent to these circles (Figure 6
...
Only for structures with a strong symmetry, simple analytical solutions can be
obtained
...
The space is subdivided in small (triangular) areas and for
each area the equations are solved numerically
...
As an illustration Figure 6
...
The FEM programme also shows the numerical values of the field quantity in each point of the space enclosed by a specified
boundary
...
DOI: 10
...
00006-6
© 2012 Elsevier Inc
...
126
Sensors for Mechatronics
Figure 6
...
Figure 6
...
Evidently a stronger field strength can be obtained by increasing the current
...
Each turn
carries the current I, thus contributing to the field strength
...
The product n Á I
(expressed as ampere-turns) is a measure for the strength of such a magnetic
source
...
By definition the flux is:
ZZ
Φ5
BUdA
ð6:2Þ
S
In words the flux is the inner vector product of the magnetic induction vector
and a surface patch dA, integrated over the total area S for which the flux is
Inductive and Magnetic Sensors
127
calculated (Figure 6
...
In particular for a homogeneous field that makes an angle
α with the normal on a flat surface A, the flux is:
Φ 5 BUAUcos α
ð6:3Þ
When the surface is in parallel to the field (α 5 π/2), there is no flux through
that surface
...
The magnetic field strength of (permanent) magnets is expressed in terms of
magnetic induction B (so in Tesla) rather than of H
...
01 to 1 T
...
The movement results in a potential difference, the induction voltage,
across the conductor and satisfies the equation
Vind 5 2
dΦ
dt
ð6:5Þ
which is the induction law of Faraday
...
In a closed loop, the induced voltage causes a current
equal to Vind/R, where R is the resistance of the wire loop
...
(6
...
At constant flux, the induced voltage is zero
...
(6
...
6
...
2
Permeability
The magnetic quantities H and B are related by the equation
B 5 μH 5 μ0 μr H
ð6:6Þ
The quantity μ is the (magnetic) permeability; μ0, the permeability of free
space, equals 4π Á 1027 Vs/Am by definition
...
For vacuum μr 5 1, for gases
and many nonferrous materials it is very close to 1
...
Table 6
...
128
Sensors for Mechatronics
Table 6
...
2
2
...
9
0
...
The non-linearity of μr is employed in, for instance, fluxgate sensors
(Section 6
...
3)
...
1
...
This holds not only for wires (where it is used for the generation of electric currents) but also for bulk material (as the iron cores of transformers and electric
machines)
...
They produce unwanted heat, so
normally they are minimized by, for instance, increasing the resistance of the bulk
material
...
g
...
Eddy current can only flow in the plane of the plates, but cannot
cross the boundary between two adjacent plates
...
3
...
6
...
4
Magnetic Resistance (Reluctance) and Self-Inductance
The analogy between the description of magnetic circuits and electrical circuits is
demonstrated by the equations in Table 6
...
Equation (6
...
The electrical conductivity σ 5 1/ρ
opposes the magnetic permeability μ
...
(6
...
Equation (6
...
(6
...
The
latter is also called reluctance
...
(6
...
In an electric circuit consisting of a series of elements, the current through each
of these elements is the same
...
2 Comparison Between the Electrical and the Magnetic Domain
Electrical Domain
1
UJ
σ
ð
V 5 EUdl
E5
H5
1
UB
μ
ð6:7Þ
ð
V 5 Re UI
1 l
U
σ A
HUdl
ð6:8Þ
ZZ
Φ 5 BUdA
ð6:9Þ
nUI 5 Rm UΦ
ZZ
I 5 JUdA
Re 5
Magnetic Domain
nUI 5
ð6:10Þ
Rm 5
1 l
U
μ A
ð6:11Þ
elements is the same
...
The self-inductance of a magnetic circuit with coupled flux is found as follows
...
Substitution
of Φ using Eq
...
9) yields Vind 5 ðn2 =Rm ÞUðdI=dtÞ and since V 5 L(dI/dt) the selfinductance is:
L5
n2
μA
5 n2 U
Rm
l
ð6:12Þ
So the coefficient of self-inductance (unit Henry, H 5 Wb/A) is proportional to
the square of the number of turns and inversely proportional to the reluctance
...
6
...
5
Magnetostriction
All ferromagnetic materials exhibit the magnetostrictive effect
...
In the absence of an external field the magnetic domains (elementary magnetic dipoles) are randomly oriented
...
The effect is
not strong: materials with a large magnetostriction (for instance Terfenol-D) show
130
Sensors for Mechatronics
a sensitivity of about 5 μstrain per kA/m, with a maximum strain between 1200 and
1600 μstrain at saturation [3]
...
This effect is used in magnetostrictive
force sensors, discussed in Section 6
...
6
...
2
Magnetic Field Sensors
This section presents various sensors for the measurement of magnetic field
strength or magnetic induction
...
g
...
Such sensors are discussed in Section 6
...
The
sensors described in this section are: coil, Hall sensors, fluxgate sensors and magnetostrictive sensors
...
This sensor operates at
cryogenic temperature (liquid helium or liquid nitrogen) and is used mainly in medical applications and for material research
...
Most research on magnetic field sensors is focussed on Hall sensors and fluxgate
sensors, in particular to reduce dimensions and fabrication costs, by applying
MEMS technology and integration with interface electronics (see further
Section 6
...
Sometimes innovative concepts are introduced, but the application to
mechatronic systems requires further development
...
[4]
...
In force equilibrium the displacement is a measure for
the external magnetic field
...
3) and (6
...
A magnetic or inductive sensor can be based on a change in each of these parameters,
resulting in an induction voltage equal to
dΦðtÞ
@AðtÞ
@μðtÞ
@HðtÞ
5 nU μH
1 AH
1 μA
VðtÞ 5
dt
@t
@t
@t
ð6:14Þ
The remainder of this section deals with three types of magnetic field sensors:
the coil, Hall sensors, fluxgate sensors and magnetostrictive sensors
...
Inductive and Magnetic Sensors
6
...
1
131
Coil
The most straightforward method for the transduction from magnetic field to an
electric voltage is a coil: Eq
...
5) relates the induced voltage in a coil to the magnetic flux
...
Static fields can nevertheless be measured, just by rotating the coil
...
Disadvantages
of the method are movable parts, the need for brushes to make electrical connection
to the rotating coil and for an actuator to procure rotation
...
2
...
In 1856 W
...
5 on magnetoresistive sensors)
...
Only after the discovery of the Hall effect in 1879, by
the American physicist E
...
Hall, could the Gauss effect be explained
...
The Hall effect is caused by the Lorentz forces on moving charge carriers in a
solid conductor or semiconductor, when placed in a magnetic field (Figure 6
...
The force Fl on a particle with charge q and velocity v equals:
Fl 5 qðv 3 BÞ
ð6:16Þ
The direction of this force is perpendicular to both B and v (right-hand rule)
...
The charge carriers experience an electric
Figure 6
...
132
Sensors for Mechatronics
force Fe 5 qE that, in the steady state, counterbalances the Lorentz force: Fe 5 Fl
...
When B is homogeneous and perpendicular to v
(as in Figure 6
...
Finally with
I 5 b Á d Á J and V 5 E Á b, the voltage across the Hall sensor becomes:
V5
1 IB
IB
U 5 RH U
nq d
d
ð6:18Þ
The factor 1/nq is called the Hall coefficient, symbolized by RH
...
Obviously the Hall voltage
is inversely proportional to the thickness d
...
3), explaining the name ‘Hall plate’ for this type of
sensor
...
3
...
The Hall coefficient is large in semiconductors, because the charge density
is much lower compared to that in conductors
...
This
results in a deviation of the Hall coefficient from that given in Eq
...
18)
...
8 to 1
...
Table 6
...
Hall plates can also be implemented in silicon
...
Currents that are generated in
this layer (by on-chip current sources) deflect in a magnetic field, resulting in a
voltage difference between two lateral points on the chip
...
The Hall coefficient can be tuned
to a desired value by the doping concentration (see some examples in Table 6
...
Here too the measured value of RH deviates strongly from the value according to
Table 6
...
3 Á 1010 cm23
n 5 1
...
7 Á 1023
23
...
8 Á 1024
50
2150
Inductive and Magnetic Sensors
133
Eq
...
18) because of the non-homogeneous velocity distribution of the charge
carriers
...
Such silicon Hall devices can be realized in bipolar, JFET as well in CMOS processes [6À9]
...
When applying Hall plates for the measurement of magnetic fields, some shortcomings should be considered
...
This results in an offset voltage: the Hall voltage is not zero at zero field
...
It can be compensated for by using a compensation voltage derived
from the current
...
1 and 1 mT, respectively
...
Various
methods have been proposed to eliminate this offset (see Section 3
...
Typical offset values range from 10 to
50 mT for standard silicon Hall-effect devices down to 10 μT for offset-compensated designs
...
The changing flux induces a voltage in the loop consisting of the connection wires and the voltage contacts
...
Such
errors are small in integrated Hall-effect sensors because of the small dimensions
of such devices
...
3, modulation (and in particular chopping) is an effective
way to circumvent offset
...
The chopping is realized by surrounding the Hall sensor
by a torroidal coil with a ferromagnetic core of high permeability, as a magnetic
shield
...
When the coil is activated such
that the core is saturated, the permeability is low, and hence the shielding effect is
also low; the sensor receives almost the total external field to be measured
...
The
sensor is provided with a piece of material with high permeability; the magnetic
field to be measured is locally concentrated in this material and the Hall sensor is
positioned in that region of concentrated field lines
...
Depending on the material and the shape of the concentrators, a gain of more than
6000 can be achieved [12]
...
4 illustrates the effect of flux concentration
...
The method is also applicable in CMOS-type
Hall sensors, by deposition of thin layers of high permeability material nearby and
even on top of the chip [13]
...
134
Sensors for Mechatronics
Figure 6
...
Traditional Hall sensors are sensitive in one direction only, perpendicular to the
plate or chip
...
This solution is chosen in Ref
...
To achieve a low offset, spinning current Hall devices (manufactured in
CMOS technology) are used
...
Special technological knacks make it possible to create 2D and 3D Hall sensors in silicon (see for instance Refs [15,16])
...
To obtain sensitivity in the third direction, perpendicular to the plate, sensors are constructed with a vertical sensitivity [17]
...
Polycrystalline Hall sensors have been reported with a
sensitivity of 19 mV/T [18], or a plasma as sensitive material, resulting in a
10 mV/Gauss sensitivity [19]
...
The sensor in Ref
...
6
...
3
Fluxgate Sensors
Like the Hall plate, the fluxgate sensor measures magnetic field strength and is
therefore a suitable device in mechatronic systems, for instance as part of a displacement sensor (combined with a permanent magnet or an activated coil)
...
5C)
...
Hence the permeability of the core material changes with twice the excitation frequency, between values corresponding to the unsaturated and the (positive
and negative) saturated states
...
(6
...
Since the permeability varies periodically, so does this added field: it is modulated by the varying
Inductive and Magnetic Sensors
135
I
Excitation coil
B(t)
Excitation coil
Sense coil
H
I
(A)
H
Vind
Vind
Sense coil
(B)
Figure 6
...
permeability
...
(6
...
Assuming homogeneous and uniform fields, Φ 5 n Á μ Á H Á A, with A the cross section of the core and n the number of turns
...
Hence the output voltage of the
sensor is periodic, with an amplitude proportional to the magnetic field strength to
be measured
...
Frequency selective detection of the output (synchronous demodulation on the second harmonic of
the excitation frequency, see Chapter 3) makes the measurement highly insensitive
to interference
...
Since the actuating current produces an AC induction field B(t) and hence an
output voltage in the sense coil, the output is not zero at zero external field
...
A more elegant way is to employ a ring-shaped core (Figure 6
...
The excitation coil is
wound toroidally around the ring, whereas the sense coil fully encloses the ring,
with its radial axis in the plane of the ring
...
A field along the axis of the
sense coil disturbs this symmetry, resulting in an output voltage proportional to the
field strength
...
g
...
A further improvement of the sensor performance is obtained by the feedback
principle (see Chapter 3)
...
When the loop gain is sufficiently large the resulting induced field is zero, whereas the amplified sense voltage
serves as the sensor output (analogous to the feedback accelerometer in
Figure 3
...
Coils are relatively bulky components, and are not easy to miniaturize
...
A first step is to create coils on a PCB
...
A next step
towards further miniaturization is to implement the coils in IC-compatible or
micromachining technologies, combined with microstructured magnetic core material
...
Interfacing of fluxgate sensors (e
...
the actuation signal and the demodulation
method) is an important issue to achieve maximum results [33,34]
...
4 lists some maximum specifications of commercial fluxgate sensors
...
5 compares major properties of various magnetic field sensors discussed
so far
...
3
Magnetic and Induction Based Displacement
and Force Sensors
In this section we discuss various types of sensors based on induction or a change
in magnetic field strength
...
g
...
Table 6
...
)
Unit
Range
Resolution
Sensitivity
Noise
Excitation frequency
Bandwidth
Offset drift
Maximum temperature
1024
10210
10
10
0
...
5 Comparison of Various Magnetic Field Sensors
Property
Fluxgate
AMR
Hall (Si)
Unit
Range
Sensitivity
t
...
sensitivity
Linearity
Offset
t
...
offset
Bandwidth
1024
4 Á 104
30
1025
0
...
01
0
...
2
10À104
1023À1022
5
600
1022
10À100
10À100
106À5 3 106
100
0
...
3
...
6A)
...
When the field disappears, the reeds open
by their own elasticity
...
6B and C)
...
When the switch is closed, its resistance (the on-resistance)
should be as low as possible
...
The on-resistance is in the order of 0
...
Conversely the isolation resistance or off-resistance should be as high as possible; practical values are in the
order of 1012 Ω
...
2 ms turn-on time, 0
...
Further, the switch is susceptible to wear (life times in the order of 107
switches)
...
Finally the
switch shows hysteresis: the turn-on value exceeds the turn-off value
...
6
...
g
...
Figure 6
...
Table 6
...
3
...
7A
...
(6
...
A displacement Δx of the movable
part causes the reluctance Rm to change because the air gap width changes by an
amount of 2Δx
...
(6
...
Then at a
displacement Δx the self-inductance changes by
(
)
2Δx=l0
2Δx
2Δx 1 2Δx 2
...
A differential configuration gives some improvement (Figure 6
...
The sensitivity is doubled, whereas
the non-linearity is reduced to a second-order effect, as is shown in Eq
...
22):
L0
L0
4Δx=l0
2
5 L0
1 2 2Δx=l0 1 1 2Δx=l0
1 2 ð2Δx=l0 Þ2
(
)
4Δx
2Δx 2
5 L0
11
2?
l0
l0
ΔL 5 L2 2 L1 5
ð6:22Þ
The range of this sensor is limited to 2x0
...
8A: a coil with movable core
...
8B is better because quadratic terms cancel, as was demonstrated in the previous equations
...
The device
is not an ideal self-inductance: the wire resistance and the capacitance between the
Figure 6
...
Inductive and Magnetic Sensors
139
Figure 6
...
turns cannot be neglected
...
Due to these factors, the sensor impedance deviates remarkably from a pure self-inductance
...
3
...
6
...
3
Eddy Current Displacement Sensors
Eddy currents originate from induction: free-charge carriers (electrons in a metal)
experience Lorentz forces in a varying magnetic field, and cause currents to flow
in that material (Section 6
...
3)
...
The self-inductance of an isolated coil (not surrounded by any material) can be
approximated by Eq
...
12)
...
We distinguish two possibilities: a conductive object and a ferromagnetic object
...
(6
...
9)
...
These currents produce a magnetic field that counteracts the original
field from the coil (Lenz’s law)
...
When the object comes closer to the coil (where the magnetic field is
stronger), the eddy currents become larger, and so the self-inductance further
decreases
...
In conclusion the sensor impedance decreases upon the
approach of a conducting, non-ferromagnetic material
...
The reluctance of a
ferromagnetic material is Rm 5 l/μ0μrA, where l is the length of the (closed) flux
line in the magnetic structure (composed of the sensor, the target and the surrounding air) and A the cross section
...
Hence when a ferromagnetic material approaches a coil, the impedance of the sensor coil increases; the effect is stronger for materials with a high permeability μr
...
Figure 6
...
The sensor impedance is a rather complicated function of the distance: the frequency, the nature of the material and the orientation of the object have substantial
140
Sensors for Mechatronics
Figure 6
...
Sensor
x
Ia
B
Target (μ, σ)
Figure 6
...
influence on the sensor sensitivity
...
Figure 6
...
The network elements in this
model have the following meaning:
G
G
G
G
G
R1: copper losses of the coil (increases with frequency due to the skin effect)
R2: resistance of the object (depends on the conductivity and the frequency, the latter due
to the skin effect and the permeability)
L1: coil’s self-inductance
L2: measure for the counter-field produced by the eddy currents in the object (depends
strongly on the magnetic properties of the material)
M: measure for the coupling between sensor and object (hence dependent on the distance); another measure for the coupling is the coupling factor, defined by k2 5 M2/L1L2
...
[35] more detailed analysis of an eddy current displacement sensor is
given
...
In Ref
...
The measurement frequency of an eddy current sensor is in the order of 1 MHz
...
More specifications are listed in Table 6
...
Non-ferrous and isolating objects normally give no response; however,
by applying a thin conducting layer, for instance an aluminium foil, they can be
Inductive and Magnetic Sensors
141
Figure 6
...
detected as well, since eddy currents flow just near the surface of the conductor
(skin effect)
...
9) and differential coil
...
The coupling
between the two coils is determined not only by the sensor structure but also by
eddy currents induced in the object near the coils
...
Special designs have been developed to reduce the
dimensions
...
fluxgate sensors)
...
A
further step is the application of micromachining technology, for instance the LIGA
process [42], and the integration of the coils with the read-out electronics [43,44]
...
3
...
8) shows strong nonlinearity even when configured in balance
...
Figure 6
...
The coils have tapered windings in opposite directions
...
However when a ferromagnetic core (with high permeability) is inserted in the
hollow cylinder, the coupling between the coils is much stronger at the position of
the core
...
So the output voltage varies with core displacement
...
A better construction is the one shown in Figure 6
...
This device consists of
one primary coil and two secondary coils, positioned symmetrically with respect to
the primary, and wound in an opposing direction
...
The total output voltage of the two coils in series
is zero
...
12 Concepts of an
LVDT (A) with tapered
primary and secondary,
(B) with one primary and
two secondary coils and
(C) with complementary
tapered windings
...
13 Typical transfer characteristic of
an LVDT
...
The difference is a
measure for the distance from the centre position (Figure 6
...
Note that the output amplitude is equal for positive and negative displacements
...
The stroke of the construction in Figure 6
...
A shorter core would result in a much larger range but at the expense of linearity
...
12C
...
End-of-stroke non-linearity is further compensated for by additional turns at the extremities
...
Its
sensitivity is expressed in mV (output) per volt (input) per m (displacement), so in
mV V21 m21
...
e
...
A stainless steel housing guarantees proper shielding against mechanical and
chemical influences as well as against electrical and magnetic interference
...
To further
improve the performance, special constructions and compensation techniques have
been developed
...
[46]
...
The ratio of the two is independent on common interferences (more
or less similar to the post-processing method for a PSD in Chapter 7)
...
[47], with a range of 30 cm in two directions
...
[48]
...
7 presents selected
specifications of a typical commercial type LVDT
...
8 at the
end of this section lists some general characteristics of the LVDT
...
The principle of operation is
the same as for the LVDT
...
6
...
5
Resolvers and Synchros
Inductive sensors for the full range of 2π are the resolver and the synchro
...
The
coupling between primary and secondary coils depends on the angle between the
coils
...
14A) essentially consists of two fixed coils (stator)
making angles of π/2 and one rotating coil, the rotor
...
Both stator coils induce voltages in
the rotor coil; the two induced voltages add up in the rotor
...
7 Product Information of an LVDT (Novotechnik, Germany)
Electrical and mechanical data
Mechanical range
Required measuring force
Weight
Electrical range
Absolute non-linearity
Operating voltage
Signal out
Current consumption
Load impedance
Temperature coefficient
12 mm
4N
90 g
10 mm
6 0
...
14B)
...
(6
...
Instead of supplying the input voltage to the stator coils (so-called stator supply
mode), the input voltage can be supplied to the rotor coil as well (rotor supply
mode): in this case the stator coils provide two output signals from which the
mechanical angle can be derived
...
The output phase at the stator coils varies over a full period when
the rotor rotates over an angle of 2π/p, so the resolution is increased by a factor p
...
The three coils make
geometric angles of 120 and are supplied with three sinusoidal voltages which
also have phase differences of 120
...
Resolvers and synchros have a measurement range of 2π rad
...
The performance is mainly limited by the read-out
electronics, in particular the phase measurement circuitry
...
001 rad (3 min of arc or minarc), whereas a resolution down to 40 s of
arc can be achieved (1 5 60 min of arc 5 3600 s of arc)
...
[49], together with a compensation method to
reduce errors
...
01
...
We discuss only the linear
inductosyns here: the rotational version operates in the same way
...
15) consists of a fixed part, the ruler or scale, and a movable
part, the slider
...
The ruler acts as one elongated coil; its length determines the measurement
range
...
However, the geometric distance between the two parts of the slider is (n 1 1/4)
Figure 6
...
Inductive and Magnetic Sensors
145
Figure 6
...
of a geometric period p
...
The ruler receives the sum of two induced voltages, according to Eq
...
23)
...
Unlike the resolver, the inductosyns has
no iron, so the operating frequency can be higher: up to about 150 kHz
...
In this way an
almost infinite range can be achieved
...
Table 6
...
6
...
6
Magnetostrictive or Elastomagnetic Sensors
A magnetostrictive (or magnetoelastic or elastomagnetic) sensor is based on the
change of the magnetic flux in a magnetic material due to deformation
...
Basically two different magnetoelastic
sensor systems can be recognized: uni- and multidirectional
...
16A)
...
The
sensitivity is small: about 2
...
Furthermore, the output signal depends on
the temperature and on the frequency and amplitude of the supply voltage
...
Multidirectional devices use the effect that magnetic flux lines change direction
when a force is applied
...
Figure 6
...
The
core consists of a pile of ferromagnetic lamellae
...
When no load is
applied, the magnetic field lines of the primary coil (Figure 6
...
Upon an applied force, the permeability
of the magnetic material looses its isotropy, resulting in an asymmetric pattern of
field lines (Figure 6
...
In this situation field lines can intersect the secondary
coil, generating an output signal proportional to the force
...
It makes
up the magnetic joint between the primary and the secondary coils of a transformer
...
The transformer is configured in such a way that at zero torque the transfer is zero too
...
Figure 4
...
This in turn results in an induced voltage in
the secondary coil of the transformer, similar to the torque sensor in Figure 6
...
By a set of magnetoelastic transducers with proper configuring the magnetic cores
and the primary and secondary windings, a combined force and torque sensor can
be realized, with reasonably small crosstalk between the two measurands [52]
...
When taped on the curved surface of an axis the ribbon is stressed,
becomes anisotropic and exhibits magnetoelastic properties that can be used to
measure torque, similar to strain gauges
...
One such design consists of a rod made up of a magnetostrictive material (the fixed part, as the body of a linear potentiometer)
...
the wiper of the potentiometer)
...
The wave travels from the
coil towards each of the ends of the rod, where ultrasonic receivers measure
the travel times
...
Magnetostrictive-related hysteresis limits the accuracy,
but this can be reduced (up to a factor of 10) by a proper biasing of the magnetic
material [55]
...
17
...
It consists of an elongated soft magnetic core
Figure 6
...
Inductive and Magnetic Sensors
147
Figure 6
...
Magnet
Core
Saturation
Table 6
...
1À200 mm
0
...
1À5 V/mm
1À500 mV/(mm V)
1À10 mV/( V)
2π/rev
0
...
05 arcsec
À
50 μm
1029 m2/N
1% FS reproducibility
a
Tmax ( C)
300
500
500
60
50
120
70
Range in FS, so from 0 up to the indicated value, for various types
...
At the position of the magnet, the core is locally saturated, so the permeability
of the core at that position has a much lower value compared to the remainder of
it
...
The positiondependent reluctance can be measured in various ways
...
[56] this is accomplished by an LVDT-like configuration with primary and secondary coils, and in
Ref
...
In both
these cases the prototypes have a measurement stroke of about 20 cm
...
4
Applications
Inductive and magnetic sensors cover a wide application area
...
Eddy current sensing is also
used to detect defects in metal structures or for quality monitoring in production
...
Figure 6
...
148
Sensors for Mechatronics
Figure 6
...
G
G
G
Induction type: the moving magnet induces a voltage in a coil; the output is proportional
to the (relative) velocity
...
Transformer type: the transformation ratio varies with the position of the moving core
...
4
...
Modern integrated magnetic field sensors have a built-in interface: the output is a voltage or sometimes a
current or a frequency proportional to the applied magnetic field
...
It should be pointed out that though the overall sensitivity is
increased by the gain of the amplifier, the S/N ratio is decreased, or at best remains
the same when the amplifier noise is small compared to the noise from the sensor
...
The
conversion of this quantity into an electrical signal can be accomplished in similar
ways as for capacitive sensors (Figure 5
...
However while capacitors behave as
an almost ideal capacitance, this is not the case for coils: the wire resistance and
the capacitances between the turns are usually not negligible, making the impedance of a coil differ from just a pure inductance
...
The relaxation oscillator generates a pulse or square-shaped periodical signal with a frequency determined by the value of the self-inductance of
Inductive and Magnetic Sensors
149
the sensor
...
A completely different approach is given in Ref
...
6
...
2
Contact-Free Sensing Using Magnetic and Inductive Sensors
The magnetic displacement sensors in this section are based on a position-dependent magnetic field strength
...
(6
...
Generally the strength decreases with increasing distance from the source, in a way that depends on the pattern of magnetic field lines
(as represented in Figure 6
...
Magnetic field strength can be measured by any magnetic sensor, for instance a
Hall plate, a fluxgate sensor or a detection coil
...
Displacement measurements using a magnetÀsensor pair have a limited range, a
strong non-linearity (depending on the relative movement, Figure 6
...
Ferromagnetic construction parts in the neighbourhood of the sensing system may disturb the field
pattern
...
An important parameter is the switching distance, which depends on the
mechanical layout of the sensor but also on the dimensions and material of the
moving part
...
8)
...
Figure 6
...
One option is a
strip that is magnetized with alternating north and south poles (Figure 6
...
A magnetic field sensor moves along the strip, like the slider in a potentiometer
...
With two sensors spaced
(n 1 1/4) of a magnetic period (which can be as small as 200 μm), the direction of
movement can be determined as well
...
19 Two general
configurations for magnetic
Δx displacement sensors; the block
arrows show relative movement
between magnetic source and
sensor
...
20 Long range displacement sensing with magnetic sensors: (A) array of magnets
and single sensor, (B) array of sensors and single magnet and (C) sensitivity characteristics
...
Advantages of this type of sensor are its robustness and corrosion
resistance (strips of stainless steel)
...
It is possible to attach the strip to curved surfaces as well
...
5 μm
(over a limited range); maximum velocity of the sensor head is about 20 m/s
...
19B
...
20C)
...
Absolute linear encoders using a special code and read-out procedure are available, providing a measurement accuracy of 6 5 μm and a resolution down to 1 nm, over a range of over
25 m
...
10)
...
[60] to measure liquid level and liquid conductivity at
the same time, using two coaxially coils located above the liquid
...
Level and conductivity ranges are 0À30 cm and
4À10 S/m, respectively
...
4
...
10), contact-free distance measurement and
event detection (e
...
holes, edges and profiles, in metal objects)
...
Each time a tooth passes the sensor head, the interface electronics gets a count
pulse; the pulse rate is related to the rotational speed of the shaft
...
A miniaturized version of this tachometer is described in Ref
...
The (flat) coil measures
1 3 1 mm, and has 10 turns only
...
6 MHz
...
5 mm range [43]
...
As an example, Figure 6
...
In the neutral position (left) distances x1 and x2 are equal; when the bar rotates clockwise x1 decreases whereas x2
increases
...
In the eddy current angle sensor described in Ref
...
Linear Displacement and Velocity
When a conductor moves in a magnetic field, eddy currents are induced, affecting
the self-inductance of the coil that produces the magnetic field
...
A detailed analysis of
this concept is given in Ref
...
An alternative approach to measure velocity using eddy current sensors is
described in Ref
...
This method is based on correlation
(the same as described in Chapter 7 on optical sensors and Chapter 9 on acoustic
Figure 6
...
152
Sensors for Mechatronics
sensors)
...
The cross-correlation function of the two signals
shows a peak for a delay time equal to d/v
...
In practice a rail vehicle also makes common (vertical and sideways) movements
...
The presence of capacitances and the skin effect make the impedance of an
eddy current sensor frequency dependent
...
In general the
sensor can be modelled as a second-order system, of which the resonance frequency and the quality factor (or damping) are determined by the material properties, the thickness and the lift-off
...
Pressure is usually measured by an intermediate elastic element: its deformation
is proportional to the applied force or pressure
...
In Ref
...
The deflection is sensed by
a flat coil (made on a PCB) and by force feedback using a second coil the deflection is compensated, according to the general feedback principle explained in
Chapter 3
...
In this application the object is scanned by moving one
or more eddy current sensors over the area of interest
...
Material defects (e
...
cracks and corrosion) are detected based on a change in local conductivity or permeability
...
With an array of sensors the scanning can be
limited to just one direction, a useful solution when the resolution requirements are
not very high
...
A particular example is
the use of eddy current sensing for metal tag recognition [70]
...
Flat coiled eddy current sensors are also suitable for imaging roughness and
defects in metal surfaces
...
Section 1
...
4)
...
[41])
...
The principle of this technique is shown in Figure 6
...
The object
under test is magnetized by an external magnet
...
In case of a surface defect (e
...
hole and crack) the permeability at
that location is low, and this causes the magnetic flux to bulge out of the material
...
Note that the defects create field lines perpendicular
to the surface, so sensing in this direction is recommended
...
The MFL technique is still widely studied, aiming at better resolution and a
more accurate localization and characterization of defects
...
For instance in Ref
...
A completely different application of a magnetic field sensor is found in
Ref
...
Goal is to create an image of steel objects embedded in concrete
structures
...
The pattern of the magnetic field reflects the shape
of an embedded steel object
...
An optimized layout of the sensor
setup and advanced signal processing are required to obtain an image of reasonable
quality, but the method enables the visualization of objects at a depth up to10 cm
...
4
...
Real accelerometers make use of a seismic mass: when accelerated, the inertial force causes a deformation of an elastic
element connected to the mass
...
[73] is based
on an LVDT with a magnetic fluid as movable core
...
22 Principle of magnetic flux leakage for NDT: (A) measurement setup and (B)
simulation example with two defects in the plate under test: left at the top side, right at the
bottom side
...
In this sensor the inertial force on the fluid is in equilibrium with the magnetic
force
...
[74]
...
When tilted the magnetic core
is displaced over a distance determined by the tilt angle and the magnetic forces
...
Pressure and force are likewise determined by an elastic intermediate
...
For instance the bending of a conductive membrane affects the reluctance of a magnetic circuit composed of this membrane and one or more coils
...
A strain sensor in
which the coil itself acts as a deforming element is presented in Ref
...
The coil
is embedded in a flexible epoxy, and the change in coil shape causes its self-inductance to change
...
The magnetic sensor can be of any type
...
[77]
...
The magnetic angular sensor presented in Ref
...
The (integrated) device comprises four Hall sensors, a flux concentrator
and an analogue signal processing circuit
...
Fluxgate sensors have a high sensitivity, and are therefore suitable for measuring
the Earth’s magnetic field (e
...
as part of a compass)
...
Research is aiming at the increase of overall performance, a
lower price and reduced dimensions
...
[79] for satellite navigation, [80] spacecraft and [81] land navigation
...
T
...
J
...
1996; ISBN 0-7503-0015-9
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Ripka (ed
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Lynch (ed
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Vol
...
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Ciudad, C
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Lopez, P
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Ide: A multilayer eddy current microsensor for non-destructive
inspection of small diameter pipes; Transducers ’95 À Eurosensors IX, Stockholm,
Sweden, 25À29 June 1995, pp
...
´
[42] P
...
Kluser, R
...
S
...
Actuators A, 110 (2004), 93À97
...
A
...
A
...
Hediger, Ch
...
S
...
Actuators A, 68 (1998), 257À262
...
A
...
A
...
Bayadroun, S
...
Bernasconi, R
...
Popovic:
First integrated inductive proximity sensor with on-chip CMOS readout circuit and
electrodeposited 1 mm flat coil, Sens
...
[45] E
...
Herceg: Evolution of the linear variable differential transformer; in: Handbook of
measurement and control, Chapter 3; Schaevitz Engineering, Pennsauken NJ, USA,
1972
...
C
...
B
...
Seksena: A self-compensated smart LVDT transducer, IEEE
Trans
...
Meas
...
[47] Y
...
Hasebe, C
...
Yamada: New type linear variable differential transformer position transducer, IEEE Trans
...
Meas
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[48] P
...
McDonald, C
...
Sci
...
, 9 (1998), 563À569
...
Mingji, Y
...
Jibin, L
...
Livingstone, G
...
Sci
...
, 10 (1999),
1292À1295
...
K
...
Koul, C
...
Bhat, I
...
Kaul, A
...
Tickoo: Use of a ‘look-up’
table improves the accuracy of a low-cost resolver-based absolute shaft encoder, Meas
...
Technol
...
[51] M
...
Ben-Brahim, M
...
Alhamadi, A High: Precision resolver-to-DC
converter, IEEE Trans
...
Meas
...
[52] J
...
Instrum
...
, 46(4) (1997), 807À810
...
Dahle: The Torductor and the Pressductor; ASEA Res
...
: O
...
, 5 (1959), 32À37
...
Hardcastle, T
...
Actuators A, 81 (2000), 121À125
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Seco, J
...
Martın, J
...
Pons, A
...
Jeminez: Hysteresis compensation in a magnetostrictive linear position sensor, Sens
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[56] O
...
Hinz, N
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Actuators A, 25À27 (1991), 277À282
...
Legrand, Y
...
-Y
...
-P
...
Actuators A, 106 (2003), 149À154
...
A
...
A
...
Hediger, Ch
...
S
...
Actuators A, 68 (1998), 257À262
...
de Cos, A
...
M
...
Actuators A, 112 (2004), 302À307
...
Yin, A
...
Peyton, G
...
Denno: Simultaneous noncontact measurement of
water level and conductivity, Trans
...
Meas
...
[61] J
...
Ding, Y
...
Li: A novel eddy current angle sensor for electrohydraulic
rotary valves, Meas
...
Technol
...
1088/0957-0233/19/1/015205
...
T
...
Gomes de Almeida: The use of eddy currents on the measurement of
relative acceleration, Sens
...
[63] T
...
[64] W
...
Yin, A
...
Peyton, S
...
Dickinson: Simultaneous measurement of distance and
thickness of a thin metal plate with an electromagnetic sensor using a simplified
model, IEEE Trans
...
Meas
...
158
Sensors for Mechatronics
[65] Y
...
Nakane, T
...
Hasuike: Simultaneous measurement of the resistivity and permeability of a film sample with double coil, IEEE Trans
...
Meas
...
[66] N
...
Kroupnova, Z
...
P
...
Regtien: Application of eddy-current imaging in
multi-sensor waste separation system; Proceedings of the International Conference &
Exhibition on Electronic Measurement & Instrumentation, ICEMI’95, Shanghai,
China, 3 January 1996, pp
...
[67] B
...
Dutoit, P
...
Besse, A
...
Friedrich, R
...
Popovic: Demonstration of a new principle for an active electromagnetic pressure sensor, Sens
...
[68] H
...
Moineau, G
...
Actuators A, 45 (1994), 183À190
...
-Y
...
Le Bihan: Multisensor probe and defect classification in eddy current
tubing inspection, Sens
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[70] F
...
Huez, A
...
Sci
...
, 11 (2000), 367À374
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Wilson, Gui Yun Tian: Pulsed electromagnetic methods for defect detection
and characterization, NDT&E Int
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[72] D
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Benitez, S
...
Gaydecki, V
...
Instrum
...
, 57(11) (2008), 2437À2442
...
Baglio, P
...
Savalli: Ferrofluidic accelerometers; Eurosensors XIX,
Barcelona, Spain, 11À14 September 2005
...
Olaru, D
...
Dragoi: Inductive tilt sensor with magnets and magnetic fluid, Sens
...
[75] H
...
Ashworth, J
...
Milch: Force measurement using inductively coupled sensor, Rev
...
Instrum
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[76] J
...
Butler, A
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Vigliotti, F
...
Verdi, S
...
Walsh: Wireless, passive, resonant-circuit,
inductively coupled, inductive strain sensor, Sens
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[77] Ph
...
Passeraub, P
...
Besse, S
...
De Raad, R
...
Popovic: High-resolution
miniaturized inductive proximity sensor: characterization and application for stepmotor control, Sens
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[78] C
...
Racz: Novel analog magnetic angle sensor with linear output, Sens
...
[79] J
...
G
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Brauera, F
...
Actuators A, 120 (2005), 71À77
...
Forslund, S
...
Ivchenko, G
...
Edberg, A
...
Sci
...
, 19 (2008) doi:10
...
[81] K
...
Lee, Y
...
Kim, J
...
Yun, J
...
Lee: Magnetic-interference-free dual-electric
compass, Sens
...
Literature for Further Reading
Books
[1] P
...
): Magnetic sensors and magnetometers; Artech House Publishers, Boston,
London
...
Inductive and Magnetic Sensors
159
[2] P
...
Tipek (eds
...
[3] R
...
Popovic: Hall effect devices; Institute of Physics Publishing, Bristol, Philadelphia
...
7503
...
5
...
Ripka: Review of fluxgate sensors, Sens
...
´
´
[5] M
...
Ripka, A
...
Actuators A, 106
(2003), 38À42
...
Boero, M
...
-A
...
S
...
Actuators A, 106 (2003), 314À320
...
C
...
C
...
Lo: The role of new materials in the development of magnetic sensors
and actuators, Sens
...
[8] V
...
Berkman, L
...
Klymovych, A
...
Marussenkov,
M
...
7 Optical Sensors
Most displacement and force sensing systems operating on optical principles consist of three basic parts: a light source, a light sensor and the transmitting medium
...
An optical displacement sensor is constructed
in such a manner that a change in distance between two sensor parts or between
one sensor part and a moving object results in a change in transmission, reflection,
absorption, scattering or diffraction of a beam of light
...
Other modalities are not often encountered in mechatronics
...
Since light is a wave, one can also make use of
travel time (or ToF), phase shift and interference
...
The transmission properties of such fibres can be modulated by various physical properties, for instance temperature, humidity, bending, strain and
concentration of chemicals put in contact with the fibre
...
First we discuss in this chapter the major optical variables and parameters
...
The subsequent section deals with methods on
how to build up sensing systems for the measurement of position and displacement,
using such components
...
Section 7
...
Finally Section 7
...
Appendix A
...
7
...
Their output is used to control proper operation of the system, for instance to perform a
specified action (i
...
movement and rotation) or to maintain a specified condition
Sensors for Mechatronics
...
1016/B978-0-12-391497-2
...
All rights reserved
...
1 Basic configuration of
an optical sensing system
...
1 Overview of Optical Emitters and Receivers, Modulation Types and Possible
Accessories
Emitters
Modulation
Receivers
Accessories
Light bulb
(Gas) Laser
Laser diode
LED
Transmission
Reflection
Absorption
Scattering
Refraction
Polarization
Dispersion
Photo resistor
Photovoltaic cell
Photo diode
Photo transistor
PSD
Line scan camera
Matrix camera
Lenses
Mirrors
Reflectors
Filters
Fibres
Collimators
(i
...
position and force)
...
1
...
The light travels through a medium (usually air but may include parts of
the construction) from transmitter to receiver
...
Various properties of the light
can be affected by the measurand
...
1
...
Clearly the large number of combinations gives the designer much freedom in choosing the best solution
for the intended application
...
Therefore it is important to include the (optical and any other) sensing
system from the very beginning in the design process of the mechatronic system
...
7
...
1
Light Emitters
The next list gives commonly used emitters for the application in displacement and
force transducers, with a general characterization
...
Optical Sensors
163
The major types of light emitters are:
Thermal light bulb: A very cheap and easy to get optical source, also available in small
dimensions (for instance a bicycle taillight)
...
LED (light-emitting diode): A cheap and widely used light source for numerous applications (e
...
illumination, displays and remote control)
...
Semiconductor laser (laser diode): Low power types having appearance and dimensions
similar to LEDs, but whose physical operation is different; well known from CD and
DVD players, laser pointers and laser printers
...
Solid-state laser: Much more expensive device, suitable for large optical power
...
Gas laser: Much more expensive device, suitable for large optical power
...
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
Many other types of lasers exist, mainly intended for other applications, such as
cutting, drilling and welding
...
Important parameters to be considered when designing a sensor system are the output intensity or power versus input current (sensitivity), output intensity versus wavelength (spectral sensitivity) and output intensity versus
angle of divergence (directivity diagram)
...
Some manufacturers offer the possibility to search in their database by particular specifications as
164
Sensors for Mechatronics
required by the designer, for instance by power range or wavelength
...
Finding exactly what is needed for a particular application is still time consuming
...
Figure 7
...
Intensity versus forward current: Figure 7
...
The maximal intensity of a
LED ranges from a few mW/sr up to several W/sr, depending on the type
...
A
laser diode (Figure 7
...
Here, too, the intensity drops with increasing temperature,
mainly because of the decreasing quantum efficiency at higher temperatures
...
2C
...
2)
...
The optical bandwidth is the wavelength interval at 50% relative
intensity
...
Figure 7
...
Optical Sensors
165
Table 7
...
2D is an example of the directivity diagram
...
The diagram combines the directivity of two types: a narrow beam and a wide
beam type
...
Note that laser
diodes have also a relatively wide beam angle (due to the short optical path the
light travels in the device)
...
Other important parameters to consider when choosing a light source are the temperature sensitivity of
the peak wavelength (about 0
...
7
...
2
Light Sensors
Commonly used optical sensors and their general characteristics are:
G
G
G
G
G
G
G
Photoresistor: small; cheap; sensitive to visible and IR light; no directional sensitivity;
slow (large response time, see Chapter 4)
...
Photo transistor: similar to photo diode, somewhat slower
...
Position sensitive diode (PSD): radiometric properties as photo diode; 1D and 2D position
sensitive (see Section 7
...
3)
...
CMOS camera (area scan): higher resolution compared to CCD camera; somewhat worse
noise performance
...
The market
offers a gradually increasing number of cameras with built-in image pre-processing
...
Current research
166
Sensors for Mechatronics
aims at increasing the resolution (number of pixels) and the speed (measured in either
pixel acquisition time or frame rate)
...
CMOS cameras have higher resolution because there are no charge buffers on the
chip as with CCD
...
Cameras will
not be discussed further in this book: the reader is referred to textbooks on this subject and the information provided by the manufacturers
...
3AÀD shows typical characteristics of photo diodes: voltageÀcurrent
characteristics, sensitivity and temperature characteristics and the spectral sensitivity
...
VoltageÀcurrent characteristic: Figure 7
...
In the absence of light, the voltageÀcurrent
relation (uppermost curve) is the same as for a normal pn-diode: an exponentially
increasing current with forward voltage and a small leakage current (the dark current) when reversed biased
...
As can be seen in Figure 7
...
The open voltage (represented by the circles on the V-axis) increases as well
with irradiance but in a non-linear way
...
3 Typical characteristics of photo diodes: (A) currentÀvoltage characteristic, (B)
sensitivity characteristic of a silicon photo diode, (C) dark current versus temperature and
(D) spectral sensitivity of a Si, a GaAs and an InGaAsP diode
...
3B)
...
Current readout is easily accomplished using an operational amplifier in currentto-voltage converter arrangement (Section 7
...
1)
...
3A
...
This is
exactly why the reverse current of a pn-diode is not zero
...
At room temperature the leakage current
of a silicon diode is very small, some 10 pA, but since a photo diode has an essentially larger active area, its dark current is also much larger, and moreover, it
increases exponentially with temperature (Figure 7
...
Spectral sensitivity: Assuming a quantum efficiency of 100%, each incident photon creates one electronÀhole pair, if the photon energy is larger than the bandgap
energy Eg (to generate a free electron):
Eg 5hUυ
ð7:1Þ
where υ is the frequency and h Planck’s constant
...
Silicon has a bandgap equal to 1
...
The lower boundary of the spectrum is
set by the absorption of the light before it has reached the pn-junction
...
The result is a spectral band that strongly depends on the materials
...
3D
gives the spectral sensitivities of three photo diodes: Si, GaAs (both sensitive in the
visible part of the spectrum) and a special diode for large wavelengths
...
7
...
3
Position Sensitive Diode
A PSD is a light sensitive diode which is not only sensitive to the intensity of the
incident light but also to the position where the incoming light beam hits the diode
surface
...
4 shows, schematically, the configuration of a lateral silicon PSD
...
An incident light beam
can penetrate through the top layer, down to the depleted region around the pnjunction where it generates electronÀhole pairs
...
Due to the electric field across the junction, the electrons are driven to the positive side, the holes move to the negative side of the
junction
...
168
Sensors for Mechatronics
Figure 7
...
Figure 7
...
It is used to explain how the
current division depends on the position of the light beam
...
The division over the two contacts is determined by the resistances from this
point on to the two end points (Ra and Rb)
...
(7
...
Thus x is the position of the light beam relative to the centre (x 5 0)
...
4A equals L /2 1 x and b
equals L 2 a, so
0
1
1 xA
Iph
Ia 5 @ 2
2 L
ð7:4Þ
0
1
1
xA
Ib 5 @ 1
Iph
2 L
Apparently the difference between the two output currents, Ia 2 Ib equals
22xIph/L and is linearly dependent of x and Iph
...
In order to obtain such an output, Ia 2 Ib is divided by
Ia 1 Ib 5 Iph, resulting in
Ia 2 Ib
2x
5
Ia 1 Ib
L
ð7:5Þ
So to perform an intensity-independent position measurement, the PSD should
be connected to an electronic interface for three signal operations: addition, subtraction and division (see Section 7
...
2)
...
This is one of the reasons why researchers have designed PSDs with on-chip (analogue) signal processing to accomplish intensity-independent output signals according to Eq
...
5) [1,2]
...
4A the position of the light beam can be determined
only in one direction
...
Its operating principle is exactly the same as for the 1DPSD
...
In the central part (about 70% of the total length or area) the linearity
is better than 1%, whereas at the edges the linearity error rises significantly: this
should be considered when operating the device in that area
...
A 2D-PSD measures 1 3 1 to 4 3 4 cm
...
Devices with larger size
are difficult to realize in silicon
...
For instance PSDs made from hydrogenated amorphous silicon (a-Si:H) have been realized with a range of 10 3 10 cm and comparable sensitivity [3]
...
Most PSDs are made of silicon, hence their spectral sensitivity is comparable
with normal silicon photo diodes: most LEDs and laser diodes match well in this
respect with the PSD
...
Nonhomogeneous background light causes a shift of this point, resulting in a measurement error
...
(7
...
A more in-depth analysis
of the effect of environmental illumination sources is given in Ref
...
In general there is just one light spot (from a laser) of which the position can be
detected
...
The PSD can be used for contact-free displacement measurements
...
2
...
170
Sensors for Mechatronics
7
...
2
...
4
...
We distinguish two possible modes: the direct
and the indirect mode
...
5A and B show the general setup according to the
direct mode
...
Comparing Figures 7
...
4
...
Assuming a homogeneous light beam over the complete beam angle in
the configuration of Figure 7
...
2D
...
These parameters should have sufficient
stability to be able to distinguish their changes from displacement-induced intensity
changes
...
The output quantity is the
difference or (better but more complicated to implement) the ratio of both sensor
Figure 7
...
Optical Sensors
171
signals
...
The final accuracy is limited by changes in the difference
of sensor parameters
...
5C shows the indirect mode, suitable for contact-free distance measurements
...
The
source casts a light beam on the target which scatters this light in all directions (diffuse reflection; we disregard here specular reflection for simplicity)
...
4
...
Actually the object acts as a secondary
light source, in the same way we see the moon by the sunlight scattered from
its surface
...
The inverse square law (7
...
If, on the other hand, the target is smaller (as shown
in Figure 7
...
The irradiance (incident power per unit area) of the target decreases with the square of the
distance from the source (because the surface area is constant)
...
For this part the inverse square law also applies, so in total the sensor output drops
with the fourth power of the distance between source and target (see Appendix
A
...
3 for a more general derivation):
Io %
1
x4
ð7:7Þ
Note that the output depends also on the angle of the object’s surface relative to
the optical axis of the source
...
Clearly the design of a proximity sensor must be such
that the object always intersects the whole beam, in other words, a narrow beam is
preferred
...
(7
...
(7
...
Nevertheless they are useful for a quick check during the design process
...
4 gives a more general proof of these relationships
...
5C and D special
devices are available, in which the emitter and receiver are mounted in a single
housing
...
The optical axes make a fixed angle; as can be seen in
Figure 7
...
The useful range of the sensing system is somewhat smaller: both the
lower and the higher limits of the detection range are set by the configuration
geometry and by the directivity characteristics of the devices: xa , x , xb
(Figure 7
...
172
Sensors for Mechatronics
Figure 7
...
All considerations given for this type of linear displacement sensors hold for
angular sensors too
...
The contact-free distance sensors discussed here are simple and cheap
...
01 μm) can be obtained [7]
...
For instance changes in the target reflectivity, the intensity
of the emitter and the sensitivity of the receiver all contribute to a change in the
output signal
...
6B, where the upper curve refers to a surface with a relatively high reflectivity and the lower (dotted) one to a more absorbing surface
...
Instead of a
single receiver, a pair or a quad (four diodes arranged in a 2 3 2 matrix) is used
...
Displacement information is
derived from the actuators controlling the beam position
...
Similar concepts
are used in CD-players to keep the reading head exactly on the right track on the
disc
...
For this purpose
special optical sensors have been constructed with a wide range of specifications
...
Indirect mode systems have a smaller range, because only part of the
scattered light will return to the sensor
...
Up to here only sensors in reflection mode have been discussed
...
A simple configuration is given in Figure 7
...
Optical Sensors
173
Figure 7
...
Light transmission is modulated by the tapered slot in the moving mask: a very
cheap and simple linear displacement sensor suitable for applications with low
demand on accuracy
...
The dimensions of the slot are chosen such that
the whole displacement range is covered from 0% to 100% transmission
...
A high
sensitivity (but small range) is obtained by a configuration with a narrow slot in the
moving mask and a fixed slot in front of the receiver (Figure 7
...
By shaping the
slot in a particular way, an arbitrary transfer function can be obtained, for instance
a logarithmic or a parabolic relationship between displacement and transmission
...
7
...
2
Triangulation
A triangle is completely determined by three parameters (sizes or angles), a property that is used to find an unknown distance
...
8 is an
unknown distance
...
Figure 7
...
With one fixed distance d, one fixed angle α and one measured distance y (on a
PSD or diode array) the unknown distance can be calculated
...
It carries an omnidirectional light transmitter,
viewed by a PSD (or a line camera)
...
This creates a sharp image on the PSD only if the
spot is far away (which in most practical situations is indeed the case)
...
From Figure 7
...
8 Triangulation principle with a PSD
...
9 Triangulation applied to contact-free distance measurement: (A) direct mode and
(B) indirect mode
...
Figure 7
...
A light beam from a laser
source casts a spot on a suitable, well-defined point at the movable target
...
A displacement of the target causes a
displacement of the projected light spot on the sensor
...
Clearly each target position xt corresponds to a spot position yt on the PSD
...
9B) we arrive at
y5fU
x tan α 2 d
x 1 d tan α
or x 5 dU
y tan α 1 f
f tan α 2 y
ð7:10Þ
Optical Sensors
175
Figure 7
...
25
...
10 shows the effect of the parameter α on the range and on the transfer
characteristic
...
25 rad
...
In
general the transfer is non-linear; only for α 5 π/2 (the optical axes of the source
and the sensor are perpendicular) the transfer is linear: y/f 5 x/d; the range is rather
small
...
In practice a compromise must be made with respect to range and inaccuracy by
non-linearity
...
4 on applications
...
For a PSD this is not very relevant because it responds to the optical centre
of intensity, which lies on the main axis of the light beam
...
A more serious problem is the low S/N
ratio due to poorly reflecting surface materials, a slanting angle of incidence or
simply a too large distance
...
When using a diode array instead of a PSD, the light spot may simultaneously
activate several adjacent elements of the array
...
While designing a displacement sensing system often a trade-off
has to be made between a (1D or 2D) PSD and a (line or matrix) camera
...
3
176
Sensors for Mechatronics
Table 7
...
Note that numerical data are typical; higher values for
resolution and speed are available
...
2
...
They convert,
through an optical intermediate, the measurement quantity into a binary signal,
representing a binary coded measurement value
...
Optical encoders are composed of a light source, a light sensor and a coding
device (much the same as the general setup in Figure 7
...
The coding device consists of a flat strip for linear displacement or disc for angular displacement, containing a pattern of alternating opaque and transparent segments (the transmission
mode) or alternating reflective and absorbing segments (the reflection mode)
...
11
...
In the transmission mode the encoder consists either of a translucent
material (e
...
glass, plastic and mylar), covered with a pattern of an opaque material (for instance a metallization), or just the reverse, for instance a metal plate with
slots or holes
...
An absolute encoder gives instantaneous information about the absolute displacement or the angular position
...
12 gives examples of absolute encoder
devices in transmission mode
...
11A
...
Optical Sensors
177
Figure 7
...
Figure 7
...
Obviously the maximum resolution of an absolute encoder is set by that of the
least significant bit (LSB) track; evidently it is the outer track of an angular
encoder
...
Special integrated circuits including photo diodes and built-in compensation have been developed to maintain the performance also with high resolution
encoder discs [10]
...
12A,
upper track)
...
For this reason most encoders use the Grey code, which requires
also the minimum number of tracks at a given resolution but is monostrophic: at
each LSB displacement only one bit will change at a time, as can be seen from the
linear encoder in the lower track of Figure 7
...
Serious disadvantages of an absolute encoder are its limited resolution, the large
number of output sensors and the consequently high price
...
13 shows a typical
example for linear displacement
...
13 Incremental linear
encoder scale with coded
markers
...
14 Linear incremental encoder with fixed scale and moving mask
...
In the angular type these slots are arranged radially along the
circumference of the optical disc
...
The output of
the sensor changes alternately from low to high when the encoder is displaced relative to the sourceÀsensor system, generating a number of pulses equal to the number of light-dark-light transitions
...
The reference position is marked by an extra
slot in the disc or scale
...
At very
large scales, this could take too much time; therefore, long scales have multiple
markers, which are coded to make them distinguishable from each other
...
13 the markers are identical but positioned on different distances
...
If the incremental encoder is used in the same way as the absolute encoder (one
sensor for each line) its resolution would not be much better: the size of the sensor
should not exceed the width of one slot
...
14
...
The light transfer changes periodically from a minimum to a maximum value
and back for each displacement over the pitch of the optical pattern
...
14), whereas the minimum light transfer is zero over
the whole area of the mask (position x1)
...
15 Output currents versus displacement (A) without offset, (B) and (C) transfer of
each mask with offset and (D) difference between the two signals
...
However due to mechanical tolerances and not perfectly
collimated light the minimum transfer is not completely zero
...
In the ideal case the sensor output changes linearly with the displacement or
rotation over half a grating period
...
15
...
Unfortunately real encoders show some deviations from the ideal behaviour
...
15A can be shifted upwards or
the amplitude decreased, due to misalignment of the scale and the masks, resulting
in a position as in Figure 7
...
Adding a second moving grating and sensor offers
some improvement
...
15B and C)
...
15D): the (common) offset is eliminated and zero crossings define
darkÀlight transitions in a more reproducible manner
...
They are useful for unidirectional displacements and as (absolute) velocity sensors, but fail when position information is
required after displacement in an arbitrary direction
...
16 clarifies how to
solve this problem
...
A displacement results in two triangular signals according to
Figure 7
...
16A and B)
...
16 Determination of displacement direction using two optical encoders
...
16C)
...
From these two signals d1 and d2 the direction of the movement
can simply be deduced
...
So code 11 is followed by 10
...
By
driving a pair of flipflops, information about the direction is easily achieved
...
When the relation between displacement and output is known, this information can
be used to find intermediate positions between the maximum and the minimum
values of the triangle
...
In practice the output versus displacement is not a nice triangle as given in
Figure 7
...
Better
interpolation accuracy is obtained when the output is first converted into a sinusoidal shape
...
Another way is the arctan method: the
quotient of two quadrature signals is a tangential function, so by taking the arctan
of this function the displacement is obtained
...
A relation between signal errors and resulting position errors is given in Ref
...
A method to further
reduce the interpolation error is the generation of higher harmonics as ‘in-between’
quadrature signals [12]
...
16),
Optical Sensors
181
´
Figure 7
...
Incremental encoder employing (A) the Vernier effect and (B) the Moire effect
for increased resolution
...
15) and interpolation all in one
...
The intrinsic resolution of an incremental encoder is set by the number of slots
per unit distance or rotation
...
Two identical scales
with patterns having a slightly different pitch cause, when superimposed, alternately light and dark zones along the encoder scale, with a synthetic period L
(Figure 7
...
Similarly two scales with the same pitch but making a small angle cause also
white and dark zones (Figure 7
...
When the scales shift a distance of one pitch
relative to each other, the dark zone shifts over a complete synthetic period
...
The configuration behaves as an optical
displacement amplifier
...
The zones have an extension that allows the use of normally sized sensors
...
16,
using two sets of sourceÀsensor pairs
...
A special design based on this concept is described in Ref
...
The Vernier concept can also be applied in absolute encoders, to enhance their
intrinsically lower resolution
...
[14], dealing with an
absolute angular encoder used to control a servo motor
...
6 can be achieved, instead of 45
with a conventional three-bit code disc
...
4 Maximum Specifications of Optical Encoders
Encoder Type
Range (FS)
Resolution
Tmax ( C)
Incremental lineara
Incremental angulara
Absolute linear
Absolute angular
1 cm to 3 mb
2π
1 cm to 3 m
2π
80 lines/mm
18,000 lines/2π
1 μm
14 bit
100
80
a
80
Without interpolation
...
b
incremental encoder without interpolation), the mask tolerances, the misalignment
and the eccentricity of the code patterns
...
4 shows ultimate specifications of
several encoder types
...
Many other code patterns have been proposed to reduce instrument
complexity, increase accuracy or enhance applicability (see further section 7
...
Instead of a collimated light beam (to fully cover the coded area), a
scanning light beam (as used for reading bar codes) is a useful alternative [15]
...
It is also easier to
read codes with a non-regular format, for instance pseudo-random codes
...
The scanning may slow down the system, but for many applications, such as navigation, this
is not a serious limitation
...
2
...
The resulting
amplitude (or intensity) varies with the phase difference between the two waves
...
At equal amplitudes of the individual waves, the total intensity doubles when
the waves are in phase (constructive interference), and drops to zero when in antiphase (destructive interference)
...
The wave form of monochrome light (i
...
light with just one wavelength) is
described by:
Aðx; tÞ 5 Ao cosðωt 2 kxÞ
ð7:11Þ
where Ao is the wave amplitude (for both the electric and the magnetic field components), ω 5 2πf is the angular frequency of the wave, k 5 2πn/λ is the wave
Optical Sensors
183
number and x the co-ordinate in the direction of propagation
...
In the remainder of the
text we assume n 5 1, because most applications are in air having a refraction index
very close to 1
...
Both waves fall simultaneously on the same sensor, so the wave functions are added:
Atot 5 A1 cosðωt 2 kx1 Þ 1 A2 cosðωt 2 kx2 Þ 5 AðxÞ cosfωt 2 φðxÞg
ð7:12Þ
where
AðxÞ 5
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
A2 1 A2 1 2A1 A2 cos kðx1 2 x2 Þ
1
2
ð7:13Þ
and
tan φðxÞ 5
A2 sin k
A1 1 A2 cos kðx1 2 x2 Þ
ð7:14Þ
Equation (7
...
A flat wave transfers optical (electromagnetic) energy into the direction of propagation x that amounts to Sx 5 Ey Á Hz, a quantity that is proportional to the square
of the wave function
...
(7
...
So the sensor output satisfies:
2
Id 5 AðxÞ 5 A2 1 A2 1 2A1 A2 cos kðx1 2 x2 Þ 5 Io ð1 1 m cos kΔxÞ
1
2
ð7:15Þ
with
m5
2A1 A2
A2 1 A2
1
2
ð7:16Þ
Apparently the sensor output changes sinusoidally with the path difference Δx
...
18)
...
This is why the factor m is called the interference visibility
...
18 Sensor output as a function of the relative displacement: (A) m 5 1,
(B) m 5 0
...
whose displacement has to be measured
...
According to Eq
...
15) this results in an output signal proportional to the intensity, which varies with the optical path difference hence with the displacement of the object
...
18 shows that the output varies periodically with displacement; the
unambiguous measurement range is just half a wavelength (for red light about
300 nm)
...
The first is to count
the number of darkÀlight transitions during the movement starting from some reference position, as with the incremental encoder
...
2
...
This corresponds to a wavelength λmix equal to
λmix 5
2λ1 λ2
λ1 2 λ2
ð7:18Þ
also called the synthetic wavelength
...
424 mm, resulting in an
unambiguous displacement range of 0
...
Interference is only visible with two monochromatic, coherent light beams
...
The emitted light beam is split up into
two separate beams, for instance using a semi-transparent mirror
...
19 shows
such a system, known as the classical interferometer or Michelson interferometer
...
19 Classical interferometer configuration
...
20 MachÀZehnder
interferometer configuration
...
The two light beams arrive at the sensor via different
paths: one runs from the source, via MS and MR and back through MS to the sensor;
it has a fixed length
...
Evidently all optical components should be accurately aligned to achieve a proper
operation
...
19 is the
optical feedback towards the source, which may introduce instability of the output
frequency
...
20 such feedback is eliminated by using
an extra beam splitter
...
Originally designed for the investigation of the
properties of transparent samples, it can also be used for displacement measurements
...
There are two receivers, which can act in balance mode: when one has maximum output, the other has minimum output
...
The simplest interferometer is the FabryÀPerot configuration (Figure 7
...
It is
essentially an optical cavity made up from two semi-transparent mirrors in parallel
...
21 FabryÀPerot
interferometer configuration
...
22 Interferometric scale (after Heidenhain)
...
The sensor receives light that
has travelled a number of path lengths in the cavity
...
When the pitch of an incremental encoder is made smaller, in the order of the
wavelength, the light is refracted at the grating
...
Figure 7
...
The instrument comprises two scales moving relatively to each other, at about 1 mm apart
...
The non-transparent scale has a pattern of small
grooves, with pitch p; this is the step grating
...
Light that falls on such a grating will be partly diffracted, resulting in diffracted beams of order 0, 61, 62
...
Optical Sensors
187
The 0th-order wave front passing the transparent grating hits the step grating,
where it is diffracted again in three directions 0, 11 and 21
...
However when the step grating is
shifted over a distance x, the diffracted wave front shows a phase shift equal to
φ 5 2πnp/λ (n is the order of diffraction)
...
The design is made in such a way that the diffracted beams interfere when entering back to the scanning scale: for each of the
three directions the phase difference of the interfering waves is 2p
...
Interferometry is mainly applied for linear displacement measurements
...
Rotation measurements by interferometry
require additional optics, for instance a prism assembly [16,17]
...
In these cases the small displacements of a
membrane [18], a cantilever [19] and a seismic mass [20], respectively, are measured by an interferometric principle
...
As an interferometer has a very high sensitivity to displacement parameters, it
requires a rigid setup and careful adjustment of the optical components
...
An interferometer, therefore, needs a
very stable source, to minimize phase noise in the output signal
...
The range of an interferometer runs from several cm up to several tens of metres
and depends on the maximal number of subsequent fringes (lightÀdark transitions)
that can be counted
...
The accuracy depends
largely on the accuracy and stability of the wavelength (the displacement between
two consecutive counts)
...
For
small variations of these parameters, an approximation for the wavelength change
is [21]:
Δλ
5 0:9U1026 UΔt 2 0:3U1026 Δp 1 1028 ΔH
λ
ð7:19Þ
denoting the relative change in wavelength around atmospheric conditions
...
An example: the wavelength of a heliumÀneon
188
Sensors for Mechatronics
laser in vacuum is λ0 5 0
...
In air with temperature t 5 20 C, pressure
p 5 1013 hPa and 50% humidity λ 5 0
...
The relative accuracy of a non-compensated interferometer in a conditioned
room is not much better than 10 μm per metre (hence 1025), mainly due to pressure
dependency
...
Some types of errors can be reduced using two waves with different wavelengths and assuming the errors are common to both waves [22]
...
2
...
The ToF method is based on measuring the time interval between
the emission of a light pulse and the arrival time of the reflected pulse
...
000 km/s in air
...
The measurement of short distances calls for fast electronics to obtain a reasonable resolution
...
When the incident laser light makes an angle with
respect to the target’s normal, the light is reflected away from the receiver
...
The same can be done for an absorbing target
surface
...
3
7
...
1
Interfacing
LEDs and Photo Diodes
LEDs and photo diodes are the most frequently used electro-optical components in
mechatronic applications
...
The simplest circuits are with discrete resistors and transistors, but they have rather poor stability
...
23A presents an interface circuit
for controlling a LED
...
23 Interface circuit for a LED, with resistor and voltage source: (A) circuit, (B)
adjustment by resistor, (C) adjustment by a voltage; dots represent the bias points
...
The exact value follows from the voltage-to-current characteristic of the device and the load line:
I 5 ðE 2 VÞ=R
ð7:20Þ
Figure 7
...
23C the resistance R is fixed, and the current is adjusted by the voltage
E
...
In Figure 7
...
In the first case the circuit is loaded by a system with
zero input resistance (in Figure 7
...
For a finite
value of the resistance, the output voltage is given by the intersection of the diode
characteristic and the line V 5 Ip Á R, as shown in Figure 7
...
Clearly only current readout provides an output voltage that varies linearly with
the photo current
...
These conditions cannot be met easily just by a resistor
...
Figure 7
...
Figure 7
...
Figure 7
...
190
Sensors for Mechatronics
In both circuits the operational amplifiers are configured in feedback mode; this
makes the voltage difference between the two input terminals zero
...
25A is equal to E, forcing a current
E/R flowing through resistor R
...
By varying E the radiant flux varies accordingly
...
25B the operational amplifier is configured as a current-to-voltage
converter
...
The resistor R in
series with the positive input terminal serves for compensation of the bias current
of the operational amplifier, which flows also through the feedback resistor (see
Appendix C)
...
This can easily be achieved using the circuit of Figure 7
...
The modulation frequency (the carrier) should be
chosen such that interference signals can easily be separated from the signal by filtering (Appendix C)
...
3
...
1
...
Figure 7
...
The currents Ia and Ib from the PSD are converted into voltages Va and Vb,
respectively, using simple IÀV converters configured with operational amplifiers
...
All mathematical operations according to Eq
...
5) are performed by a microprocessor
...
In that case the system takes the most
advantage from the full resolution of the ADCs
...
26 Signal processing
circuit for a PSD triangulation
system
...
27 PSD interface
(analogue) with stabilized input
Vo(x) radiant power
...
2
...
At large distances the output signal may drop below the acceptable noise level
...
To extend the measurement range, the source intensity could be controlled in
such a way that the PSD receives the highest possible radiant power, irrespective of
the distance
...
Figure 7
...
The output of the summing amplifier is compared with a reference voltage Vref
...
Within the operating range of the control
circuit, the summing voltage equals the reference voltage
...
Since the intensity of the incident
beam is fixed by this feedback, the output signal is that of the differential amplifier,
and the (analogue) division can be omitted, which is an important advantage of this
approach
...
4
Applications
This section presents various applications of optical sensors in mechatronics
...
However we
will not discuss these applications further here; the reader is referred to the extensive literature on computer vision
...
A colour camera is a suitable transducer, but when no spatial
information but just colour is needed, a simple set of three diodes with colour
filters will do as well
...
5
...
5 Applications of Optical Sensing
Application
Primary Quantity
Methods
Linear distance (1D)
Medium- and long-range
distance
Short-range distance
Distance
Velocity
Velocity; displacement
Angle
Intensity; triangulation;
encoder; interferometry; ToF
Fibre optic
2D scanning
Doppler; correlation
Differentiation
Encoder; interferometry
3D co-ordinates
Distance
Distance
Distance
Deformation
Probing; triangulation
Passive
Active/passive
3 modi; active
Elastic element; interferometry
Proximity (1D)
Roughness, flatness
Linear velocity
Linear acceleration
Rotation; angle; angular
rate
Object shape (2D, 3D)
Ranging (2
...
4
...
Optical sensing allows the measurement of these quantities without making contact with the moving object
...
The major principles are, in the order of increased accuracy, reflectance, triangulation and interferometry
...
2
...
The
small-sized electro-optical components can easily be mounted on or integrated into
the mechatronic system
...
Since reflectance depends on the reflectivity of the object, operation is restricted
to environments with invariant objects
...
This problem was recognized in the early days of robotics when designing
a controlled gripping systems (see for instance Ref
...
To become independent
of the reflectivity and the orientation of the objects to be handled, special algorithms and sensor configurations have been developed [24]
...
If objects are completely unknown, as is the case of
navigation in an unknown environment, sufficient tolerances should be allowed in
the obtained distance data using reflection methods
...
28 Optical position measurement in feedback configuration; (A) far and (B) close by
...
Adding one or more receivers to compensate for the effect of unwanted changes makes reflection-based systems less sensitive
to the surface properties and may even allow uncalibrated operation [25,26]
...
[27], where the relative position of transmitter and
receiver is adjusted such that the maximum intensity is received
...
Feedback is an even more powerful solution
but has higher system complexity
...
28 shows an example of such a system
...
The position of this mirror is controlled such that the two sensors receive equal radiation (position x1 in Figure 7
...
The corresponding angle
of the mirror is φ1
...
This
difference is used to drive the mirror to rotate to an angle φ2 where the photo currents become equal again
...
By feedback the requirements to the source and the sensors are reduced
significantly, as explained in Chapter 2
...
o
...
and the detector comprises four receivers arranged in a square (a quad)
...
Another application is found in contact-free measurement of profiles
...
All aforementioned examples use the change in irradiance with distance between
source and sensor (usually a 1/x2 relation)
...
The absorption coefficient of air is
rather low; some materials show a much larger absorption and can be used to create
194
Emitter
Sensors for Mechatronics
Emitter
Receivers Figure 7
...
Receivers
(A)
(B)
a distance sensor based on light attenuation
...
[28]
...
The intensity of the light that arrives at both ends of
the fibre is measured by two photo diodes
...
(7
...
Similar to the PSD the difference of the photo currents is a measure for the position of the light source
...
Distance measurements over a very short range can be performed using optic
fibres
...
29
...
The light diverges within a short distance from the exit end, so the
irradiance at the entrance face of the receiving fibre depends on the distance x, in a
similar way as in the arrangements of Figures 7
...
6
...
The sensitivity characteristic depends on the
angle of divergence, the stand-off distance and the angles between the fibre ends
and the flat target
...
[7]
...
Using modulation techniques and proper filtering the equivalent
noise can be as low as 1 nm/OHz [29]
...
[30], for example
...
Distance measurements based on reflectance have a limited range, due to the
inverse power laws given by Eqs (7
...
7)
...
In the triangulation system shown in Figure 7
...
Commercial triangulation systems are available in a compact housing that
includes laser, one or two PSDs, optical components and interface electronics to
generate an output independent of the intensity, according to Eqs (7
...
10),
(Figure 7
...
The instrument either contains a display or provides an electrical output
...
Optical Sensors
195
Figure 7
...
Size reduction of the optical system is another issue to increase the versatility of
distance measurement systems based on triangulation
...
[31], where the LIGA process
(German: Lithographie, Galvanoformung und Abformung) is applied to realize the
required optical structure
...
However the repeatability error is
less than 3 μm
...
[32]
...
Speckles are randomly distributed light and dark areas on the surface; this speckle pattern changes
with the distance from the laser to the surface
...
[32] uses this dependency
...
In this way the movement of the target is transformed to that of
the actuator
...
The system enables displacement measurements over a range of 500 mm with sub-micron resolution
...
5 m up to 10 km, with an inaccuracy ranging from a few mm for shortrange types to a few cm for the long-range types
...
Besides simple distance measurements, the principle is
also applicable for range finding and imaging; such systems comprise a rotating
scanning mirror for 1D or 2D scanning of the reflective object
...
Very high resolution is needed in applications
like roughness measurements and profile measurements
...
In Ref
...
The roughness measurement is based on the scattering of a light beam
incident normal to the surface; the height measurement follows the standard
196
Sensors for Mechatronics
triangulation method
...
With this system roughness can be measured over a range
from 5 to 100 nm; the height range amounts to 6300 μm
...
An
example of this application is found in Ref
...
In the application a light strip is projected under an angle of 30 onto the sheet
(moving at a maximum speed of 15 m/s)
...
Using a special algorithm the resolution is increased to an equivalent of
0
...
Position or displacement sensors which are intended for a very particular application may be redesigned to serve other applications in mechatronics and quality
inspection
...
In Ref
...
Experiments showed the feasibility
(and limitations) of this application
...
A particular application area is the exploration of an (unknown) environment or
object reconstruction for recognition purposes
...
4
...
Linear Velocity and Acceleration
Velocity can be derived from distance information by taking the time derivative of
the displacement signal
...
So, in principle, any displacement sensor can be taken as the starting point of a velocity or acceleration measurement
...
A better option is to select a measurement principle that produces an output signal that is directly related to the speed or acceleration of the
object under test, without the need of a differentiating operation
...
g
...
The method is rather inaccurate, because slip and wear of the wheels
introduce measurement errors
...
The basic operation of
the correlation method using optical sensors is presented in Figure 7
...
Two sets of a transmitterÀreceiver pair in reflection mode are mounted at the
moving vehicle, a distance d apart in the direction of the movement
...
31 Velocity
measurement using cross
correlation
...
While moving the output signals will show a random component according to the varying scattering of the surface
...
The time delay between
these signals can easily be derived by cross correlation: the cross-correlation function shows a maximum for a time difference equal to d/v, from which the velocity
is calculated
...
The S/N ratio is adversely affected by vibrations or other movements (i
...
roll
and pitch) of the vehicle, misalignment of the optics and surface characteristics
...
Various solutions
have been proposed to overcome such difficulties
...
[38] a system is presented that makes use of optical fibres transmitting the light from two laser diodes
towards the moving surface
...
Using a special correlation technique, the speed of the
moving surface was measured up to 30 km/h, with an error of 9%
...
We mention just some of them here
...
The moving object
is illuminated by environmental lighting (so not necessarily coherent light)
...
When the object moves with velocity v in the plane of the grating, the output of the detector contains a frequency component equal to kv/p, with k the optical
magnification
...
[39] a velocimeter is described that uses this principle; the
grating has been replaced by a CCD camera, acting simultaneously as detector and
spatial filter device
...
Experiments revealed velocity errors of less than 0
...
Various optical velocimeters are based on self-mixing interferometry
...
When particular conditions with respect to
198
Sensors for Mechatronics
phase and amplitude of the returning light are fulfilled, the laser beam shows power
fluctuations that are more or less saw-tooth shaped
...
One of the advantages of
self-mixing interferometry is a more compact arrangement of the optical parts and
simple alignment
...
At constant distance between the target and the laser head, the power
fluctuations have a more or less constant amplitude
...
At
moderate velocities the Doppler frequency is rather high; for instance, using a laser
with wavelength 680 nm and normal incidence (φ 5 π/2), the Doppler frequency at
a velocity of 1 m/s equals 2
...
Accurate determination of this frequency is
hampered by the presence of the speckle effect, which introduces multiplicative
noise to the signal [40]
...
In particular fluctuations in
the angle φ and variations in the height above the ground may give large errors, as
can be seen in Eq
...
23)
...
[41]: two lasers are pointing to the ground,
with incident angles of 618 with respect to the ground normal
...
Experiments with the two-laser configuration showed a mean standard deviation less than 0
...
A well-known application of the optical ToF principle (Section 7
...
6) is found
in laser guns that measure car speed
...
Typical range and accuracy are 5À500 6 2 km/h
...
Such an accelerometer
comprises a mass and a spring element (see also Chapter 8 on piezoelectric sensors)
...
This deformation can
be measured in various ways, for instance by optical means
...
Configurations with optical fibres in reflection
mode (Figure 7
...
A particular solution is proposed in Ref
...
Here the (small) displacement is
measured by an incremental encoder using the Moiree effect (according to
Figure 7
...
One grating is fixed to the housing; the other grating, making a small
angle with respect to the first, is connected to the seismic mass
...
Due to the small angle even small displacements of the mass result
in a measurable displacement of the Moiree pattern
...
16
...
The
resonance frequency of the mass-spring combination (here 20 Hz) limits the bandwidth, as is further explained in Chapter 8 on piezoelectric sensors
...
4
...
Accurate measurement of angular
displacement is mostly performed by encoders, either absolute or incremental
(Section 7
...
4)
...
29A: the transmission from transmitting to
receiving fibre is modulated not only by a vertical displacement but also by rotation
of the target as well
...
The market offers various ready-to-use inclinometers,
covering ranges from 61 to 690 , with excellent linearity
...
At the pivot of the pendulum
some means of displacement sensing is connected, which gives an output signal
that is related to φ
...
Application of a feedback loop (Chapter 3) reduces errors due to,
for instance, a strong non-linear relationship between angle and measured
displacement
...
29 is also sensitive to angular displacement of
the reflecting surface
...
[43]
...
The configuration combines a high angular sensitivity and a negligible sensitivity to normal displacements
...
A small
hemispherical compartment with the liquid is mounted on top of a silicon wafer in
which a quad diode structure is deposited
...
Light from an LED, mounted on top of the structure,
travels through the liquid with the bubble and arrives at the diode structure, at a
position that depends on the place of the bubble and hence on the tilt angle
...
Angular rate information could be obtained by counting the number of zero
transitions in the output signal of an incremental encoder (Figure 7
...
However incremental encoders have a limited slew rate
(maximum speed), above which the transitions cannot be detected correctly
...
Low-cost angular rate sensors or tachometers are realized simply by mounting
one or more segments of a reflective material, such as aluminium foil, along the circumference of the rotating shaft or on the head of the shaft (Figure 7
...
In case of
a reflective shaft one should take an absorbing material, like black paint or black
paper
...
The measured angular
speed equals 2πn 5 4πf/p rad/s and can be determined by digital processing
...
At lower
speeds a larger number of intensity changes per revolution is required, to minimize
the quantization error, being 1/p s21
...
Commercial optical tachometers are available in various sizes
and ranges, up to 12,000 rpm
...
6), for instance the starting torque, the
Figure 7
...
Table 7
...
108 rev
...
33 Bellows couplers to obviate parallel and angular misalignment
...
As tachometer the maximal rotation (or slewing) speed should be kept in mind
...
When proper alignment of encoder and rotating shaft is difficult to realize, special accessories can be applied, for instance bellows couplings, available in numerous implementations (angular, axial, parallel; Figure 7
...
A special interferometric arrangement allows the measurement of angular speed,
utilizing the Sagnac effect
...
Actually there are two light waves, one travelling clockwise
through the loop, the other counter-clockwise
...
The intensity is maximal when the travel times are
equal, which is the case in an inertial system in rest
...
The range of such a system is about 660 , whereas a thermal drift of 10 per
hour can be expected
...
The rotational
acceleration sensor described in Ref
...
One disc is
elastically coupled to the other, to transform angular acceleration into angular displacement (according to the law of inertia)
...
This shift is measured by a PSD
...
4
...
In many applications a further task is to track the said object or a
specific point on that object when it is moving around
...
The latter approach is characterized by the presence of a light
source with known position (in the system’s co-ordinate frame), and that this position is used to reconstruct the position of the object
...
It should be mentioned that active lighting systems
may also comprise a camera (e
...
line, matrix and 2D-PSD)
...
The reconstruction process combines knowledge about that light source and the image of the
reflected light
...
The
reader is referred to the extensive literature
...
7 compares both concepts with
respect to some important design considerations
...
Since the transmitter usually takes the most of
the available power, the choice between putting the transmitter or the receiver on
the (moving) object is an important issue
...
The latter has the advantage that the object
to be tracked is completely free from wiring and power sources
...
When the design is based on the direct mode, again various options are open:
transmitter on the moving object and receiver somewhere in the environment or
vice versa
...
Of all possible combinations practical applications can be found
...
Therefore first a search is performed, in which the environment is scanned by either
the transmitter or the receiver, until the receiver gets a proper signal back
...
Further details of the system design strongly depend on
the specific application
...
A first application is the 3D tracking of the end-effector of a robot
...
However errors in the mechanical construction and the
Table 7
...
Measuring the TCP with
respect to the robot co-ordinate frame may provide data for compensation for
such errors
...
The light is perceived
by a set of cameras (2D-PSD, matrix CCD), positioned at fixed, known locations,
together covering the full work space of the robot
...
The working range is set by the viewing field of the
cameras
...
The principle
of feedback may be applied to enhance accuracy and increase the working range
...
In this application a 2D-PSD camera is a good choice
because only a single light spot has to be detected
...
Encoders on the axes of the platform provide the information about the light source position
...
In all cases the system, once
set up, must be calibrated to obtain the highest accuracy
...
The pattern can be a light spot, a line (when emitting a light plane), a
cross hair or any known pattern
...
An algorithm to obtain the
required information is described in Ref
...
Tracking systems are also used in rehabilitation, to study the movement of people
...
A set of (retro)reflecting pads or spheres is positioned on specific
locations on the body (e
...
arms, legs, head, shoulders and feet)
...
To increase the S/N ratio, the light is first filtered, so the
camera actually sees mainly the reflection from the markers
...
Accuracy requirements are not severe; processing speed is a more
important issue since fast movements must be tracked and analysed
...
Takatsuji et al
...
It comprises a retroreflector mounted on the stage and four lasers that track
204
Sensors for Mechatronics
the position of the retroreflector
...
7
...
4
Object Shape
The shape of an object is characterized by the co-ordinates of its outer surface
...
The accuracy requirements are set by
the application
...
Identification and (global) characterization are
less demanding applications
...
The applicability of the
method is almost unlimited
...
[48]
...
Light source and detector
(a quad photo diode) are positioned just at the outer edge of the blade
...
An illustration of object characterization using distance sensing with fibre optics
is the (on-line) measurement of tool wear [49]
...
A
group of fibres in the bundle transmits the light towards the object; another group
transmits the reflected light to the sensor unit
...
29
...
In this application the intensity method is satisfactory, because the setup
is fixed, the distances are short and the environmental conditions are more or less
constant
...
We discuss two
other methods: probing and triangulation
...
The touch probe consists
of a ball-shaped touching point with well-known dimensions and which is connected to the end of a stylus
...
Next the movement is controlled in such a way that the point
follows the surface of the object, thereby just keeping contact between probe and
surface
...
Shape
information is reconstructed from the momentary positions of the stages and possibly corrected for the bending of the stylus
...
The ball is elastically attached to
the end of the stylus, so when the probe touches the object, the ball is displaced
somewhat in the direction of the reaction force
...
A
set or a bundle of fibres is fixed to the stylus, with their ends just above these mirrors
...
29A, the ball movement is measured in
two directions normal to the stylus
...
In less demanding applications, or when touching is not possible or allowed, triangulation is a suitable method to obtain shape information
...
9 should be extended by a scanning
mechanism to cover the whole area of the object to be investigated
...
The method is also referred to as ranging
...
Optical range finding (some call it 2
...
Navigation
by ranging is discussed in the next section
...
3A)
...
Needless to say this is a rather slow acquisition
process
...
3B
...
The line is created either by a special
optical lens or by a fast-rotating mirror and is viewed by a matrix camera
...
If the object itself is moving, as on a conveyer belt, such scanning
mechanism may be unnecessary
...
34 shows the basic setup of a line scan
range finder
...
34 Optical range finder for object
recognition using line scanning
...
The projected line follows the shape of the object; this pattern is viewed by a camera
...
In
general not all points of the object are illuminated, and not all illuminated points
may be viewed by the camera
...
When this is not acceptable for the application, a second triangulation system can be used operating under a different angle
...
This solution is proposed in, for instance,
Ref
...
Evidently the two scans should be complementary to build up a complete image of
the object
...
[53]; in this
example, elliptical mirrors are used, which allows dynamical reconfiguration of the
geometry
...
Finally we mention a laser range finder that uses a multifaceted pyramidal mirror
...
The system, of which design details can be found in Ref
...
Much research is being done to monitor the condition of buried pipes
...
Pipe robots carrying various sensors travel through the pipes
under test, collecting important data about the pipe’s condition (i
...
obstacles, corrosion, leaks and mechanical defects)
...
As an example of an optical test system for small pipe diameters we refer to
Ref
...
This work concerns an optical system that measures the inner surface of
a 10 mm pipe
...
The system enables the detection of surface defects as small as 0
...
Mechanical scanning is relatively slow and forms the major limitation of the
acquisition time, in particular for a 2D scanning mechanism
...
One solution to speed up scanning of the other
dimension is an array of transmitters sending a set of parallel lines to the object
under test
...
This solution is only suitable in cases where no
high resolution in the scanning direction is required
...
[56]
...
The cross section of each line has a
bell-shaped intensity distribution and the lines overlap partly
...
Optical Sensors
207
By controlling this ratio, the peak value shifts across the object under test, over a
distance about equal to the line separation
...
Based on this principle an acquisition time of 6 μs was obtained,
with a spatial resolution of 1 μm over a scanning area of 22 3 24 mm
...
Since the distances involved in such applications are much larger than in
the previous examples, triangulation is not a suitable technique
...
2
...
Moreover to keep the
sensor dimensions small, a feedback approach (with tracking) is recommended
...
[57]
...
Another application area concerning acquisition of shape information is the
determination of a height profile (or depth profile), for instance in seam tracking
for automatic welding
...
[58], where methods for recognition of electronic components on a PCB are
studied
...
g
...
Also
here the object (PCB with components) is illuminated from two sides to eliminate
shadow effects
...
From the obtained range data, the
shape of the relevant parts in the image is reconstructed and parameterized [59] to
match them with the corresponding parameters of standard electronic components
...
Several researchers
have proposed methods to reduce the resolution by using special image-processing
algorithms
...
[60], where the shape of trees is determined using triangulation, and in Ref
...
As objects are normally resting on a base, the bottom side is not accessible to
the triangulation system
...
Recovering the full shape of irregular objects, like agricultural products, is
not possible in this way
...
The sensing system consists of a
ring with a large number of transmitters and receivers located alternately around
the ring and pointing inwards
...
When an object resides in the ring, some of the receivers are
in the ‘shadow’ of the object and will not receive light whilst the others do
...
When the object
moves through the ring (just by falling) a 3D image of the total shape is obtained
...
208
7
...
5
Sensors for Mechatronics
Navigation
Movement is change in position; hence, it can be measured by any position sensor,
provided such sensor has an adequate range and response time
...
A
simple optical navigation method is tracking a marked path
...
An LED or other light emitter casts a light
beam down to the floor and two detectors on either side pick up the reflected light
...
When the vehicle starts to deviate from the track, either the left or the right detector
receives more light, from which a control signal is derived
...
Similarly the movement of
a free mobile robot can be tracked by some contrasting 2D pattern on the floor,
using sensors detecting darkÀlight transitions or even an onboard camera viewing
the floor [65]
...
At two positions of the vehicle (front and rear)
the random intensity variations are measured; the speed follows from correlation of
the two random signals [38]
...
Beacons for the determination of absolute position can be either passive or
active
...
The transmitters and receivers are located on the vehicle
...
Important design considerations
are the directivity (or the scanning area) of the transmitter/receiver, the location of
the beacons and the identification of beacons (the vehicle must be able to recognize
the active beacons)
...
35 shows a robot
with a multi-sensor navigation system [66]
...
Coarse navigation of
this robot is performed by fixed cameras looking to optical markers on the robot
...
36)
...
Then the robot must be located at
a point P lying on the crossings of the two circles c1 through (B1,B2,P) and c2
through (B2,B3,P)
...
The sensing system on the robot consists of a rotating photo
diode (four turns/s), connected to an encoder that provides information on the angle
of the optical axis with respect to the robot co-ordinates
...
35 MART optical navigation system: (A) mobile assembly robot and (B) details of
optical navigation system (University of Twente, The Netherlands)
...
36 High precision positioning
of the mobile robot MART
...
The light from the beacons contains a unique code to
distinguish them, which is decoded by the sensing system
...
005 over a distance range from 1 to 10 m
between robot and beacon [66]
...
In many applications this is not the case, for instance when
AGVs have to navigate in a complex area with many large obstacles or in corridors
...
A solution could be a higher position of the beacons (for instance
on the ceiling of a hall), thus increasing the working range of the beacons
...
de Cecco [67] gives a
solution to this problem, based on a special optical scanning system able to accurately measure angles as well, resulting in a position accuracy better than 2 mm in
a range of 10 m
...
When an extra
d
...
f
...
From the
output of both 2D-PSD cameras the three co-ordinates xp, yp and zp of the light
spot can be calculated, as illustrated in Figure 7
...
The focal point of the left camera coincides with the origin of the reference
frame, so the light spot has co-ordinates (xd1,yd1,2F1), which satisfy:
xp
yp
zp
5
5
xd1
yd1
F1
ð7:24Þ
The second PSD camera is rotated over angles φ and θ around the z- and y-axis,
respectively
...
(7
...
With Eqs (7
...
26) the position
of the light spot can be expressed in terms of the output co-ordinates of both PSD
cameras, their focal lengths and the geometrical parameters of the system
...
37 3D optical
localization system with two
2D-PSD cameras
...
Integrating the output of an accelerometer provides linear velocity
...
Most optical gyros, for instance the one discussed in Section 7
...
5,
are based on interferometry
...
[68]
...
4
...
In this sense in principle the displacement
sensing methods discussed in previous sections of this chapter are candidates in the
selection process of a force measurement method
...
An applied torque results in a twist of the object (for instance a shaft) over an
angle φ
...
To obtain a high sensitivity the distance between the end points should
be large
...
A simple solution is to transfer the rotation at the one end by a mechanical extension to near the other end (Figure 7
...
When the object angle is still too small an elastic element with known compliance
can be inserted, as drawn in Figure 7
...
The torque is reconstructed from the relative angle between two end points of the rotational spring element
...
In such an application contact-free sensing is required, which can be realized by optical means
...
[69] this method is used for torque measurements on a wood cutting machine
...
38 are provided with optical markers on the circumference,
viewed from the side by a pair of photo diodes
...
Another particular application of an optical force measuring system is the online measurement of 2D force on a pen for the purpose of signature verification
[70]
...
A small mirror, mounted on the end
Figure 7
...
212
Sensors for Mechatronics
side of the ink channel, modulates the direction of a laser beam, falling on a quad
photo diode
...
Since the transfer from force via mirror displacement to the
photo currents is rather complex, the device needs be calibrated
...
Very small deformations are best measured by interferometric methods, since
this principle enables displacement measurements with very high resolution
...
Electrostriction is electric field-induced strain: deformations are in the sub˚
¨
Angstrom to sub-micron range
...
The paper reports a
displacement resolution of less than 1025 nm, and operates in a frequency band
from 3 to 20 kHz
...
A particular kind of force sensor is a
tactile sensor, mainly encountered in robotics applications
...
Many optical techniques have been developed to obtain information on
the displacement of the individual elements (taxels)
...
A common problem is the resolution: in order to realize
high resolution, the taxels should have small dimensions and be densely packed
...
39A
...
In the variable transmission type, the displacement is measured by
mechanical modulation of the intensity of a light beam, a method already published
in 1983 [72]
...
3 cm
...
The principle of variable contact surface is already addressed in Section 3
...
2,
where the contact area is measured by resistive means, but optical readout is also
an option
...
Upon an applied force the bulbs
are impressed and the contact area with the glass plate increases (Figure 7
...
Figure 7
...
Optical Sensors
213
This change in area is measured optically by a camera viewing the back side of the
plate [74,75]
...
However it
makes the sensor rather bulky and unsuitable for incorporating in a robot gripper
...
A more flat construction can be achieved by crossing optical fibres
...
The crossing points act as
taxels, and the fibres perform the scanning
...
These fibreoptic tactile sensors have a potentially high resolution but more research is required
to fully profit of this property
...
Details on the construction and performance of fibre-optic tactile sensors are given in Refs [77À79]
...
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...
Piezoelectricity can also be applied to construct acoustic transducers;
this is the subject of Chapter 9
...
1
8
...
1
Piezoelectricity
Piezoelectric Materials
Piezoelectricity is encountered in some classes of crystalline materials
...
3): the positions of the positive and negative charges in the crystal
are displaced relative to each other, causing a net polarization or change in intrinsic
polarization
...
1 shows a simplified 2D representation of this effect
...
1A the structure is fully symmetric: the centre of gravity of all positive charges coincides with that of the negative charges (the whole crystal is electrically neutral)
...
1B), the
centre of positive charges has shifted downwards, resulting in a non-zero polarization
...
1C), the centre of positive charges
has shifted upwards, resulting in a non-zero polarization in the other direction
...
Evidently Figure 8
...
Crystal structure, addition of dopants and other treatments of the material substantially determine the piezoelectric properties; for instance Ref
...
The surface charge per unit area (C/m2) is proportional to the applied stress (N/m2),
the charge (C) is proportional to the applied force (N)
...
The construction behaves as a flat-plate
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...
The piezoelectric
Sensors for Mechatronics
...
1016/B978-0-12-391497-2
...
All rights reserved
...
1 Piezoelectricity; larger circles represent positive charges, the smaller negative charges
...
3); this
property is used in piezoelectric actuators
...
Natural piezoelectricity was discovered already in 1880 by the brothers Curie, in
several crystalline materials [2]
...
It has a rather low but stable piezoelectricity: about 2 pC/N
...
However they can be made piezoelectric by poling: the material is
heated up to the so-called Curie temperature, where the dipoles obtain high mobility
...
After slowly cooling down the
dipoles maintain their orientation, giving the material its piezoelectric properties
...
The orientation of the dipoles slowly tends to
a disordered state, resulting in a negative exponential decay in sensitivity over time:
SðtÞ 2 Sðt0 Þ
t
5 cUlog
Sðt0 Þ
t0
ð8:1Þ
where S(t) and S(t0) are the piezoelectric sensitivities at time t and the end of the
polarization treatment time t0
...
For this reason the poled
material is aged artificially, before being applied as a transducer
...
Clearly the decay goes
faster at higher temperatures
...
In 1969 Kawai discovered that some polymers can be made piezoelectric by poling under particular conditions [3,4]
...
The material is available in sheets with various thicknesses (6À100 μm), with conducting
material deposited on its surface for connection purposes
...
Poling is performed during
stretching (in one or both directions), to obtain reasonable piezoelectricity
...
Since shortly after
the material became commercially available, the material has been successfully
applied as a transducer in the thermal, mechanical and acoustical domains [5,6]
...
The thin sheets can be glued on top of a silicon wafer that contains
part of the interface electronics
...
This material is available as a solution
...
Polymer-on-silicon technology
opens up the possibility for the creation of smart (integrated) sensing devices, for
the detection of pressure, force, sound and thermal energy (the latter due to the fact
that PVDF is pyroelectric as well) [8,9]
...
Another development concerns the deposition of thin film ceramics
...
The primary output quantity of a piezoelectric sensor is charge
...
3
we will show two basic schemes to convert that charge into a voltage: with a very
high load impedance (open terminals) and with an almost zero load impedance
(short-circuited terminals)
...
1
...
In
this book we use the two-port description, which is analogous to the description of
electrical two ports (Figure 8
...
Two pairs of variables are involved: two input
variables and two output variables
...
2)
...
For a
linear electric network we can express the two voltages V1 and V2 as a linear function
of the two currents I1 and I2:
V1 5 Z11 I1 1 Z12 I2
V2 5 Z21 I1 1 Z22 I2
ð8:2Þ
Figure 8
...
222
Sensors for Mechatronics
or, in matrix notation:
V1
Z11 Z12
I
5
U 1
V2
Z21 Z22
I2
ð8:3Þ
In this description the matrix elements have a clear physical meaning: they represent electrical impedances
...
For systems with no internal energy sources Z12 5 Z21
...
The input impedance is the ratio between input voltage and input current; likewise, the output impedance is the ratio between output voltage and output current
...
We distinguish two cases: open- and short-circuited terminals
...
2 is:
Zio 5 Z11
ðat open output: I2 5 0Þ
2
Z12
Zis 5 Z11 1 2
Z11 Z22
ðat short-circuited output: V2 5 0Þ
ð8:4Þ
ð8:5Þ
For the output impedance we find:
Zoo 5 Z22
ðat open input: I1 5 0Þ
Z2
Zos 5 Z22 1 2 12
Z11 Z22
ðat short-circuited input: V1 5 0Þ
ð8:6Þ
ð8:7Þ
Apparently input characteristics depend on what is connected at the output and
vice versa
...
The maximum power transfer occurs for a load impedance equal to
pffiffiffiffiffiffiffiffiffiffiffiffiffi
ð8:9Þ
ZL 5 Z22 1 2 κ2
Now we consider a piezoelectric sensor as a two-port network, analogous to the electrical system in Figure 8
...
In Chapter 2 we defined the relation between stress T and strain S:
T 5 cS
ðN=m2 Þ or
S 5 sTð2Þ
ð8:10Þ
Piezoelectric Sensors
223
Similarly the relation between dielectric displacement D and electrical field
strength E is given by
D 5 εUE
ðC=m Þ
2
1
UD
or E 5
ε
ðV=mÞ
ð8:11Þ
where ε is the dielectric constant or permittivity (F/m)
...
A two-port model of a piezoelectric
system is shown in Figure 8
...
The two-port equations of this system are, in general
S 5 f1 ðT; DÞ
E5 f2 ðT; DÞ
ð8:12Þ
and for linear systems in particular
S 5 sD UT 1 gUD 1
0
1
E5 2 gUT 1 @ T AUD
ε
ð8:13Þ
that is, Eqs (8
...
11) extended by the parameter g (m2/C or V m/N)
...
13) is the constitutive equation of the piezoelectric system
...
From a physical point of
view sD is the compliance at open electrical terminals (ΔD 5 0), and εT is the permittivity at open mechanical terminals (ΔT 5 0)
...
At open electrical terminals the voltage generated by an applied force is E 5 2 gT, which explains the name piezoelectric voltage
constant for g
...
For instance the material’s stiffness is higher at short-circuited
electrical terminals than when these terminals are open
...
3 Two-port model of a piezoelectric
system
...
1 The Four Piezoelectric Parameters
Parameter
Definition
Unit
d
e
g
h
D/TjE or S/EjT
D/SjE or T/EjS
E/TjD or S/DjT
E/SjD or T/DjS
C/N 5 m/V
C/m2 5 N/V m
V m/N 5 m2/C
V/m 5 N/C
which, for linear systems, becomes:
S 5 sE UT 1 dUE
D5 dUT 1 εT UE
ð8:15Þ
where sE is the compliance at short-circuited electrical terminals (ΔE 5 0) and d
(C/N or m/V) is the piezoelectric charge constant
...
Other possible combinations of the electrical and mechanical quantities result in
other material parameters, for instance εS: the permittivity at clamped state
(ΔS 5 0)
...
Table 8
...
The definitions are given
as A/BjC, with A the quantity affected by B at constant C
...
Relations between these four piezoelectric parameters follow from the respective
constituent relations that define them (see for instance Refs [11,12])
...
Hence there is a relation between the various piezoelectric parameters
...
The relations between sD and sE, respectively
between εS and εT can be derived from the constitutive equations as follows:
sD 5 sE Uð1 2 κ2 Þ
ð8:17Þ
εS 5 εT Uð1 2 κ2 Þ
ð8:18Þ
where
κ 2 5 g2
εT
sD
ð8:19Þ
Piezoelectric Sensors
225
is the piezoelectric coupling constant of the material (compare the coupling constant for an electrical two port in Eq
...
8))
...
Just as in the case of the electrical system, the piezoelectric constant κ2 denotes the maximal fraction of
(mechanical) energy stored in the crystal that can be converted into electrical
energy (see for instance in Ref
...
Note that κ2 differs from the overall
efficiency
...
Many piezoelectric materials are anisotropic
...
As an example Eq
...
21) shows the permittivity
matrices for quartz and ferroelectric Rochelle salt, respectively:
0
ε11
@ 0
0
0
ε11
0
1
0
0 A
ε33
0
and
ε11
T@ 0
ε13
0
ε22
0
1
ε13
0 A
ε33
ð8:21Þ
Hence the dielectric properties of quartz can be described by only two parameters: ε11 and ε33 (apparently ε11 5 ε22), whereas for Rochelle salt (NaKC4H4O6
...
Now the relationship between E and D is described with three linear equations:
Dx 5 εxx Ex 1 εxy Ey 1 εxz Ez
Dy 5 εyx Ex 1 εyy Ey 1 εyz Ez
ð8:22Þ
Dz 5 εzx Ex 1 εzy Ey 1 εzz Ez
or in matrix notation:
Di 5 εij UEj
ð8:23Þ
where i, j are the directions x, y and z in a given co-ordinate system
...
Each of the
six force components may result in a dielectric displacement in three directions
...
3; k 5 1
...
Applied, for instance, to the displacement in
x-direction (1-direction), this results in
D1 5 ε11 E1 1 ε12 E2 1 ε13 E3 1 d11 T1 1 d12 T2 1 d13 T3 1 d14 T4 1 d15 T5 1 d16 T6
ð8:26Þ
Similar equations can be derived for D in the y- and z-directions, D2 and D3
...
Many of them are zero, due to
the particular crystal structure
...
As
an example, for quartz, d12 5 2 d11, d25 5 2 d14 and d26 5 22d11, due to the specific crystal structure of this material
...
18]:
0
d11
@ 0
0
2 d11
0
0
0
0
0
d14
0
0
0
2 d14
0
1
0
22d11 A
0
with the numerical values d11 5 2
...
7 3 10212 C/N
...
Figure 8
...
In all these
examples the electrical output (voltage or current) is measured in the direction of
the polarization vector (3-direction), so the components of the matrix are all of the
form d3i
...
4A the applied force is in the polarization direction
...
This mode of operation is
called longitudinal, since the mechanical and electrical directions are the same
...
4B a force is applied perpendicular to the direction of polarization:
this is the transversal mode of operation
...
Figure 8
...
Finally in Figure 8
...
Table 8
...
Note
that the numerical values of all piezoelectric parameters depend on temperature, on
Figure 8
...
In all these cases the electrical output is taken over the z-direction
(thick lines in (A) to (C) represent the electrodes)
...
2 Comparison of Piezoelectric Properties PZT, Quartz and PVDF
Parameter
Symbol
PZTa
Quartz
PVDF
Density (kg/m3)
Curie temperature ( C)
Compliances (m2/N)
ρ
ΘC
sE33
sE11
εT33/ε0
εT11/ε0
g33
g31
g11
g14
g15
d33
d31
d11
d14
d15
7
...
65 3 103
550
9
...
8 3 10212
4
...
5
1
...
e
...
e
...
06
0
...
3 3 10212
0
...
a
Data for a modified form of leadÀzirconateÀtitanate; small modifications have a large effect on most piezoelectric
properties
...
Detailed data are found in for
instance Ref
...
Piezoelectric coefficients of PVDF and a measurement method
for obtaining numerical values can be found in Ref
...
(8
...
8
...
2
...
The elasticity of the spring element determines the sensitivity of
such sensors
...
Such a large displacement, however, could
unintentionally affect the structure in which the force has to be measured
...
Although force is the primary quantity that is
measured by a piezoelectric sensor, other quantities such as pressure, strain and
acceleration can easily be measured as well, using a proper construction
...
The surface charge produced by
an applied force might be neutralized easily by charges from the environment (airborne charges), by current leakage (due to a non-zero conductivity of the dielectric)
or just by the input resistance of the connected electronics (discussed further in
Section 8
...
This makes the sensor behave as a high-pass filter for input signals,
impeding pure static measurements
...
There are various
causes for this temperature effect
...
Secondly a temperature change may
induce crystal deformation and hence an electrical output as well
...
Fortunately as long as these changes are slow, they would not
limit the applicability because of the previously discussed intrinsic high-pass
character
...
A consequence is that the crystals become preloaded
...
5 shows
in a very schematic way some basic constructions
...
5A) the force to be measured is directly transferred
to the piezoelectric crystal
...
Usually the case acts as the ground terminal
...
The total force on the membrane À that is the pressure times
Piezoelectric Sensors
Plate
Crystal
(A)
229
Preload
Base plate
Mass
Housing
Crystals
Crystals
(B)
Clamp
Mass
(C)
Mass
Crystals
(D)
Figure 8
...
the active area of the membrane À is mechanically transferred to the crystal
...
For applications where pressure has to be measured in a vibrating or otherwise moving environment, special pressure sensors are designed with a compensating crystal, to
minimize the acceleration sensitivity
...
Here, also, the mass is fixed by a preload onto the
crystal
...
5B shows a compression mode accelerometer
...
One electrode is connected to the common surface of the crystals, the other
to the housing
...
Moreover some compensation for common interferences is achieved
...
5C and D contains four crystals mounted on a rectangular post
...
The absence of moving parts allows a piezoelectric sensor to be mounted in a
robust package and hermetically sealed
...
6 gives an impression of the real
construction of the two accelerometer types shown in Figure 8
...
In both cases the main axis is in the vertical direction, where the sensitivity has a
maximum value
...
Commercial sensors have a non-zero sensitivity in directions perpendicular to the
main axis, due to construction tolerances (not well-aligned crystals) or the cross sensitivity of the crystal itself
...
For instance when d15 in the shear type is responsible for maximum output (in the
1-direction), the values of d12 and d13 should be zero, since these forces normal to the
crystal may not generate an electrical output in that direction
...
When two or all three components of a force or acceleration vector have to be
measured, multi-axis sensors should be applied
...
6 Schematic drawing of piezoelectric accelerometers; left: compression type; right:
¨
three-crystal shear type (Bruel & Kjaer)
...
7 Three-axis piezoelectric accelerometer
consisting of three stand-alone single axis sensors
...
7
...
More recently
MEMS tri-axial accelerometers have flooded the market, mainly for consumer products (e
...
cameras and games)
...
Typical sensitivities are 10À100 mV/g, and are 10À50 g in weight
...
2
...
2
...
At the upper
side of the spectrum it is limited by the resonance frequency
...
8 shows the
useful frequency range of a standard type piezoelectric accelerometer
...
Piezoelectric Sensors
231
Figure 8
...
Table 8
...
001
1À104
100
0
...
A piezoelectric accelerometer consists of a base plate, a seismic mass and a
(preloaded) crystal
...
The natural frequency of the system (i
...
the resonance
frequency for α 5 0) equals:
rffiffiffiffi
k
ωo 5
m
ð8:30Þ
The damping constant of a piezoelectric accelerometer is usually very small; in
that case the (damped) resonance frequency ωres in Figure 8
...
A
high resonance frequency requires a small mass m and a large stiffness k
...
The resonance frequency of commercial accelerometers
range from 1 to 250 kHz: the smaller the size, the higher the resonance frequency
...
The
smallest commercial accelerometers have a weight of 0
...
Table 8
...
4 shows some maximum ratings
...
4 Maximum Ratings of Piezoelectric Sensors
Type
Range (FS)
Sensitivity
Tmax ( C)
Acceleration
Force
Pressure
103À106 m/s2
102À106 N
107À108 Pa
0
...
When mounting a sensor on an object, the latter is loaded mechanically, resulting in a
change of acceleration a and resonance frequency ωa
...
(8
...
These equations allow quick assessment of the loading effects when applying an
accelerometer
...
3
Interfacing
The primary signal of a piezoelectric sensor is charge Q
...
This simple impedance model can be
extended by a resistance Rs, modelling leakage currents (Figure 8
...
The charge signal can be measured in two different ways
...
Hence the interface circuit consists of a voltage amplifier
...
The
voltage across this capacitor is proportional to the charge
...
Piezoelectric Sensors
233
Figure 8
...
Figure 8
...
Figure 8
...
It will be
shown that the cable capacitance can have a substantial influence on the signal
transfer of the system, due to the capacitive character of the sensor
...
9B
...
First we consider the
voltage readout (Figure 8
...
The transfer of this circuit is given by
Hv 5
jωRp Ce
jωRp ðCe 1 Cc Þ
Vo
Ce
5 AU
5 AU
U
Q=Ce
1 1 jωRp ðCe 1 Cc Þ
Ce 1 Cc 1 1 jωRp ðCe 1 Cc Þ
ð8:32Þ
where Rp 5 Rs//Rc (parallel connection) and A 5 1 1 R2/R1, the gain of the noninverting amplifier
...
11A): for frequencies satisfying ωRp(Ce 1 Cc)c1 the transfer equals Ce/
(Ce 1 Cc), so it is frequency independent
...
Hence the total signal transfer depends on the length of the cable
...
The interface circuit of Figure 8
...
Due to the virtual
ground of the operational amplifier the voltage across the sensor and the cable is
kept at zero: neither the cable impedance nor the input impedance of the amplifier
influences the transfer, and hence can be ignored
...
11 Transfer characteristics of the interface circuits in (A) Figure 8
...
10B
...
Without resistor Rf, Z1 5 1/jωCe and
Z2 5 1/jωCf, hence the output voltage equals Vo 5 2 (Ce/Cf)(Q/Ce) which, indeed,
does not depend on cable properties
...
Here
the input current is generated by the piezoelectric sensor and equals dQ/dt, that
is the time derivative of the piezoelectrically induced charge Q
...
Unfortunately the integrator does not only integrate the input charge, but also
the unavoidable offset voltage and bias current of the operational amplifier
...
This results in a transfer given by
Hq 5
Vo
2 jωRf Ce
Ce
jωRf Cf
5
52 U
Q=Ce
1 1 jωRf Cf
Cf 1 1 jωRf Cf
ð8:33Þ
Just as in Eq
...
32), this transfer has a high-pass characteristic (Figure 8
...
When using a high quality operational amplifier
(low offset, low bias current), the value of the cut-off frequency can be chosen
down to 0
...
A true static measurement of acceleration or force, however, is
not possible
...
4
Applications
Piezoelectric force sensors and accelerometers are available for a wide range of
applications
...
If only little space is available for mounting a commercial device, single piezoelectric
crystals could be used, taking note of the polarization direction, the orientation of
Piezoelectric Sensors
235
the electrical contact surfaces and a proper interfacing
...
In this section we present some examples of special designs of piezoelectric sensors
for various applications
...
4
...
2)
...
However the flexibility of PVDF allows the material to bend easily, so it can serve
as a membrane, resulting in a much higher pressure sensitivity
...
[15]
...
The sensor is applied in pneumatic and hydraulic systems, for pressures up to 200 kPa and temperatures up to 125 C and is resistant to a wide range of chemicals
...
e
...
As outlined in preceding sections, the sensor element is also pyroelectric, so it
responds to temperature changes as well, and shows a high-pass characteristic that
depends on the temperature-dependent loss factor (resistance) of the membrane
...
In Ref
...
Clearly the small thickness of PVDF as
well as its flexibility makes this sensing material an excellent candidate for this
task
...
Many examples can be found in literature illustrating the versatility of PVDF as a
means to measure pressure and obtain pressure images
...
[17]
describes a system for measuring the dynamic (normal) pressure between a car’s tyre
and the ground, and in Refs [18,19] the material is used for automatic verification of
hand-written signatures
...
4
...
5
...
However proposals for alternative designs aiming at even better performances or for particular applications appear on a regular basis in scientific literature
...
236
Sensors for Mechatronics
Soon after its discovery piezoelectric PVDF was recognized as being a
suitable sensing material
...
An early attempt to create a PVDFbased accelerometer is found in Ref
...
An angular acceleration sensor can be created as well, as shown in
Ref
...
By a special geometric arrangement of four piezoelectric elements
(PVDF) and two seismic masses, an angular sensitivity of about 0
...
By suspending a seismic mass on a sheet of PVDF, a very sensitive accelerometer has been achieved, to be used for very low frequencies as a replacement for a
geophone [22]
...
8) amounts to 265 Hz for a particular choice of the parameters; the sensitivity is almost constant up to 100 Hz
...
In this case the piezoelectric material is one of a sandwich of thin layers deposited on a silicon substrate [23]
...
The seismic mass is formed by selective etching of the
substrate, resulting in a mass-spring system similar to the one shown in
Figure 4
...
The structure is sensitive in three directions, 22 pC/g for transversal
and 8 pC/g for in-plane acceleration
...
[24], providing guidelines for the
design of devices with specified properties
...
[25], in which the PZT is deposited in a
thick layer (typically 50 μm), on an alumina substrate
...
They also serve as
seismic mass
...
The reversibility of the piezoelectric effect provides solutions with a combination
of actuation and sensing
...
[26] such a combined piezoelectric sensorÀactuator
system is used to reduce vibrations that may occur in precision mechatronic systems,
in this example a waver stepper
...
With a proper design of the control loop, the amplitude of the dominant vibration mode is reduced by a factor of 7
...
4
...
In particular the piezoelectric polymer PVDF has
attracted much attention
...
One drawback of
the material is the charge leakage (preventing the measurement of static images)
...
e
...
Like other tactile sensors discussed in preceding chapters, piezoelectric tactile
sensors too are used for two important tasks: contour recognition and improving
gripper control [31,32]
...
[32] a study on a thick (1 mm) piezoelectric tactile
sensor is presented
...
8, with a resonance
frequency of 6
...
In applications where dynamic performance matters (for
instance as an active rate of force sensor described in Ref
...
A common problem in tactile sensing for contour measurement is the low spatial
resolution
...
Piezoelectric ceramics and polymers are also applied in the acoustic domain
...
The integration of polymer technology and silicon technology offers interesting
prospects for future developments of compact, high-resolution tactile sensors with
integrated electronics
...
F
...
Alkoy, R
...
Newnham: Piezoelectric sensors and sensor materials,
J
...
, 2(4) (1998), 257À272
...
Gautschi: Piezoelectric sensorics; Springer-Verlag, Berlin, 2002; ISBN 3540 422
595; Chapter 2
...
Kawai: The piezoelectricity of PVDF, Jpn
...
Appl
...
, 8 (1969), 975À976
...
Fukada, T
...
[5] H
...
Gallantree, R
...
, 39 (1976), 189À200
...
R Gallantree: Review of transducer applications of polyvinylidene fluoride, IEE
Proc
...
[7] D
...
[8] A
...
S
...
van der Spiegel, P
...
Bloomfield, J
...
Dario: Design
and fabrication of a silicon-P(VDF-TrFE) piezoelectric sensor, Thin Solid Films, 181
(1989), 245À250
...
C
...
Hammes: Infrared matrix sensor using PVDF on silicon, PhD thesis, Delft
University of Technology, The Netherlands, 1994
...
Schiller, D
...
Polla, Integrated piezoelectric microactuators based on PZT thin
films, Proc
...
Conf
...
154À157
...
Holland, E
...
Eernisse: Design of resonant piezoelectric devices; Res
...
I
...
Press, 1969, ISBN 0-262-08033-8
...
Wersing: Applications of piezoelectric materials: an introductory review; in:
N
...
): Piezoelectric materials in devices, N
...
[13] A
...
[14] E
...
Nix, I
...
Ward: The measurement of the shear piezoelectric coefficients of polyvinylidene fluoride, Ferroelectrics, 67 (1986), 137À141
...
V
...
K
...
Actuators,
A, 142 (2008), 48À55
...
Akitegetse, C
...
Farzaneh: Measuring bending stress on an ice/aluminium
composite beam interface using an embedded piezoelectric PVDF (polyvinylidenefluoride) film sensor, Meas
...
Technol
...
[17] R
...
Meas
...
[18] P
...
229À233
...
Wang, Y
...
Yao, J
...
Jiao, M
...
Meas
...
´
[20] B
...
Clot, E
...
J
...
Actuators, A, 33 (1992), 111À114
...
Marat-Mendes, C
...
Dias, J
...
Marat-Mendes: Measurement of the angular acceleration using a PVDF and a piezo-composite, Sens
...
[22] B
...
F
...
M
...
Mohamed, A
...
Prugger: A PVDF transducer for low-frequency
acceleration measurements, ISA Trans
...
[23] K
...
Enoksson, R
...
Stemme: Highly sensitive triaxial silicon accelerometer with integrated PZT thin film detectors, Sens
...
[24] Q
...
Wang, Z
...
Yang, F
...
Smolinski: Analysis of thin film piezoelectric microaccelerometer using analytical and finite element modeling, Sens
...
[25] D
...
Marioli, A
...
Actuators, A, 87 (2001), 131À138
...
Holterman, Th
...
A
...
, 14 (2004), 15À34
...
Dario, A
...
Vivaldi, P
...
Pinotti: Tendon actuated exploratory finger with
polymeric, skin-like tactile sensor, Proceeding of International Conference Robotics
and Automation, St
...
, March 1985, pp
...
[28] R
...
Dario, D
...
C
...
1845À1856
...
J
...
M
...
Rob
...
, 9(3)
(1993), 313À318
...
Dario, R
...
de Rossi, L
...
Wang, P
...
Pinotti: Touch-sensitive polymer
skin uses piezoelectric properties to recognise orientation of objects, Sens
...
,
(1982), 194À198
...
S
...
Dario, M
...
[32] H
...
Tzou, S
...
Rob
...
, 4(6) (1987), 719À741
...
F
...
K
...
O
...
Ultrason
...
Freq
...
Literature for Further Reading
Some Books and Articles on Piezoelectric Materials, Sensors,
and Applications
[1] A
...
): Piezoelectric transducers and applications; Springer, Berlin, 2004,
ISBN 3-540-20998-0
...
Setter (ed
...
Setter, Lausanne, 2002,
ISBN 2-9700346-0-3
...
Gautschi: Piezoelectric sensorics; Springer-Verlag, Berlin, 2002, ISBN 3540 422
595
...
F
...
Alkoy, R
...
Newnham: Piezoelectric sensors and sensor materials,
J
...
, 2(4) (1998), 257À272
...
Caliano, N
...
Iula, M
...
Actuators, A46À47 (1995), 176À178
...
T
...
Courrech: Mechanical vibration and shock measurement; Bruel & Kjaer
Corporation, Denmark, 1994, ISBN 87-87355-34-5
...
Asch: Les capteurs en instrumentation industrielle
...
´
¨
[8] I
...
Gautschi: Piezoelektrische Meβtechnik; Springer-Verlag, Berlin, 1980
...
van Randeraat, R
...
Setterington (eds
...
[10] B
...
R
...
Jaffe: Piezoelectric ceramics; Academic Press, London, 1971
...
In combination
with a controllable sound source, acoustic sensors can be used for measuring various other physical parameters, for instance distance, velocity of fluids, material
properties, chemical composition and many more
...
g
...
In mechatronics they mainly fulfill the task of non-contact measurement of distances and derived quantities
...
Many
acoustic sensing systems are based on the measurement of the travel time or ToF,
that is the time it takes for an acoustic wave or signal to travel a certain path
x 5 vUt
ð9:1Þ
This path is made dependent on the physical parameter to be determined, for
instance a distance
...
Acoustic sensing has some advantages over optical sensing:
G
G
G
the output is much less sensitive to smoke, dust, vapour, etc
...
We start the chapter with an overview of acoustic parameters and properties
...
In the ensuing section various methods for contact-free distance measurements are
given
...
9
...
The most common waves are longitudinal waves
and shear waves
...
Some sensors utilize surface acoustic waves (SAW)
...
DOI: 10
...
00009-1
© 2012 Elsevier Inc
...
242
Sensors for Mechatronics
substance is deposited on the surface of a device on which the waves are travelling:
the SAW’s velocity is influenced by the concentration of the absorbed matter
...
The selectivity is greatly determined by the chemical interface
...
Since
the quality of an acoustic measurement strongly depends on the acoustic properties
of the medium, we present here an overview of the major acoustic characteristics of
air
...
9
...
1
Sound Intensity and Pressure
Any piece of vibrating material radiates acoustic energy
...
Sound intensity is the
rate of energy flow through a unit surface area; hence intensity is expressed as W/m2
(compare the optical quantity flux)
...
The intensity is the time-averaged product of
these two parameters
...
The relation between intensity and pressure in the free field (no reflections) is simply given by the equation
I5
p2
ρv
ð9:2Þ
where p is the pressure (in RMS value), ρ the density and v the speed of sound
...
Often sound power, pressure and intensity are expressed in dB, which means
relative to a reference value
...
For example for the intensity at 2 m away from a sound source of P 5 1 mW at
the ground, the surface area of the hemisphere is about 25 m2 (half of 4πr2), so the
intensity in dB amounts 10 log(I/Iref) 5 76 dB
...
Most sensors do not measure sound intensity, but sound pressure only
...
9
...
2
Sound Propagation Speed
In general the propagation speed of sound in a material is given by the equation
va 5
rffiffiffi
c
ρ
ð9:3Þ
Acoustic Sensors
243
where c is the stiffness (modulus of elasticity) and ρ the specific mass of that material
...
Substitution of numerical values for air yields:
va 5 331:4ð1 1 1:83U1023 ϑÞ m=s
ð9:5Þ
with ϑ the temperature in C
...
The influence of air humidity is relatively small
and is only relevant when high accuracy is required
...
Hence
ToF is easier to measure, but consequently the measurement time is longer
...
Acoustic velocity differs from particle velocity u
...
9
...
3
Acoustic Damping
An acoustic wave is attenuated by molecular absorption of sound energy and by
scattering: the wave gradually looses energy when propagating
...
The attenuation or damping coefficient α
comprises two effects: absorption loss and scattering loss
...
In gases the second term dominates, hence α 5 a Á f 2: the attenuation of the
wave increases with squared frequency
...
For air it means that acoustic attenuation is affected by the air humidity
...
1 shows some values of damping in dry and humid air
...
1 Attenuation Coefficients for Air [1]
Medium
Frequency (Hz)
α (dB/m)
Dry air
10% RH
90% RH
106
105
105
160
18
42
Table 9
...
3
103
1
...
2 3 103
2
...
5 3 103
5
...
5 3 103
2
...
7 3 103
5
...
8 3 103
3
...
4 3 103
1
...
5 3 106
3
...
5 3 107
3 3 107
4
...
1
...
For a sound wave that propagates only in one direction, the acoustic impedance Z is found to be:
Z5
p pffiffiffiffiffiffiffi
5 ρUc 5 va Uρ
u
ð9:8Þ
Table 9
...
Clearly air has a very
low acoustic impedance; liquids and solids are much ‘harder’ materials
...
Similar to light waves which show reflection
and refraction on the interface of two media with different optical properties (i
...
refractive index, dielectric constant and conductivity), sound waves are also
reflected at the interface of two media with different acoustic properties
...
The amount of reflected or
transmitted energy can be expressed in terms of the acoustic impedances
...
In the special case of a wave perpendicular to the boundary plane, the ratio
between reflected and incident power (the reflection ratio) is given by
R5
Z1 2 Z2 2
Z1 1 Z2
ð9:9Þ
Acoustic Sensors
245
Figure 9
...
Z1 is the acoustic impedance of the medium of the incident wave, Z2 that of the
medium behind the boundary plane
...
On the other hand
when the impedances show a strong difference, the power transmission is small
...
First an airborne
sound wave that arrives at a solid object reflects in the same way as light on a mirror
...
Secondly transmission from an acoustic ‘soft’
material to an acoustic ‘hard’ material is poor
...
Since many systems consist of a source and a detector,
the power loss occurs twice, resulting in a low S/N ratio in acoustic sensing
systems
...
2
Acoustic Sensors
9
...
1
General Properties
Commonly used acoustic sensors belong to one of the following types:
G
G
G
G
piezoelectric
electrostatic
electromagnetic and
magnetostrictive
...
The transduction effects are reversible, which means that
an acoustic transducer might be used as a source (transmitter) as well as a sensor
(receiver)
...
We will now derive an approximated expression for the spatial distribution of
the acoustic power emitted by an ultrasonic transducer
...
1)
...
2 Axial pressure
distribution for D 5 15 mm and
wavelength (A) 8 and
(B) 1
...
Each element dS of the disc surface acts as a point source for acoustic waves
...
At places where the sound waves are (partly) out of
phase, the sound intensity is low; at places where the waves are in phase, the sound
intensity is high
...
For simplicity we will consider two special cases: the pressure along the main
axis of the transducer (φ 5 0), and the pressure at a distance r far from the centre,
for arbitrary angle φ
...
This is just the result of integrating the contributions to the pressure from all surface patches dS
...
2 shows
a picture of the relative pressure along the acoustic axis for two cases: D 5 15 mm,
λ 5 8 mm and D 5 15 mm, λ 5 1
...
Close to the emitter the pressure shows
strong pressure variations with distance
...
Extreme values of p(x) in Eq
...
10) occur for
!
Â
Ã
1
D2
2 λ k 1ð1=2Þ
xextr 5
2 4λ½k 1ð1=2Þ
k 5 0; 61; 62; ?
ð9:11Þ
The maximum for the largest value of x is found for k 5 0 and amounts:
xM 5
D2 2 λ2
4λ
ð9:12Þ
At frequencies for which the wavelength is small compared with the dimension
of the transmitter, the near field covers a range which is roughly D2/4λ
...
2A with D 5 15 mm, λ 5 8 mm (40 kHz in air)
shows that the near field ranges about 6 mm only
...
An important sensor characteristic is the directivity diagram, representing the
sound pattern in the far field
...
Imagine a sphere (or circle)
with radius r around the centre of the transmitter
...
78]
21
πD
πD
sin φ
sin φ
pðr; φÞ 5 2pðrÞJ1
λ
λ
ð9:13Þ
where p(r) is the pressure at distance r, λ the wavelength of the sound signal, D the
plate diameter and J1(πD sin φ/φ) is an order 21 Bessel function
...
The width of the main lobe follows from Eq
...
13)
...
73]
sin φ % 1:22U
λ
D
ð9:14Þ
Apparently the ratio D/λ determines the direction selectivity of the transducer: a
narrow beam is achieved by a large ratio (Dcλ)
...
(9
...
Figure 9
...
2)
...
For a narrow beam
248
Sensors for Mechatronics
Figure 9
...
Movable plate
Movable plate
Dielectric
Sound
Figure 9
...
Fixed charge
Fixed plate
Fixed plate
(A)
(B)
(required for optimal S/N ratio), the transducer should be large compared to the
wavelength
...
Since actual transducers may have shapes that differ from the circular piston
model, the pressure field patterns have much more complicated shapes; see for
instance Ref
...
By special design the beam angle can be made smaller, resulting
in so-called focussed probes [2, chapter 5]
...
9
...
2
Electrostatic Transducers
An electrostatic (or capacitive) ultrasonic transducer consists of two flat conductive
plates, one fixed to the housing, the other movable relative to the fixed plate,
together constituting a flat-plate capacitor (Figure 9
...
For this construction the
equations V 5 Q/C and C 5 ε0εrA/d apply (Chapter 5)
...
Sound waves (moving air particles) bring the plate
into motion
...
To obtain a high sensitivity the plate is made very thin and flexible, resulting in an enhanced acoustic
Acoustic Sensors
249
coupling to the air (see Section 9
...
4 on acoustic impedance)
...
The necessity of
an external high voltage is the major drawback of the electrostatic transducer
...
Such electret (or electret condenser) microphones
for air-coupled applications operate mainly in the audible range (20 HzÀ20 kHz)
...
A voltage difference V between the plates results in a force equal to
F 5 εS
V2
d2
ð9:15Þ
with S the surface area of the plates and d the gap distance
...
Should the
plate move linearly proportional to an applied AC voltage (to generate the proper
sound waves), the capacitor should be biased with a DC voltage higher than the
amplitude of the AC voltage
...
15) also shows that the sensitivity of the
emitter increases with decreasing initial plate distance
...
4B), accomplished by, for instance, a grooved plate or other
isolating structures like a grid or a net [4]
...
This multi-mode vibration explains the large
deviations in the directivity diagrams of real electrostatic transducers as compared
to those given in Figure 9
...
Moreover the layout of the structure strongly determines the frequency characteristics of the transducer [5]
...
Like many other sensors ultrasound transducers can also be manufactured using
silicon technology
...
It acts as the movable (vibrating) electrode of a capacitor-like structure [6,7]
...
Silicon membrane sensors have a smaller bandwidth,
due to (multi-mode) resonance frequencies of the mechanical structure
...
9
...
3
Piezoelectric Transducers
A piezoelectric acoustic transducer consists of a piece of piezoelectric material
(Chapter 8), configured as a flat-plate capacitor (Figure 9
...
An AC voltage
250
Sensors for Mechatronics
Matching cone
Matching layer
Base plate
Figure 9
...
Piezoelectric
material
(A)
Electrodes
(B)
applied to the crystal causes the material to vibrate, resulting in the generation of
acoustic energy
...
Hence the transducer might be used in transmitter mode and in receiver mode, similar to the electrostatic transducer but without
the need of a biasing DC voltage
...
As
explained in Section 9
...
4 the transfer is governed by the acoustic impedances of
the materials involved
...
Also for a liquid or solid medium, power loss can be considerable
too
...
In such applications a coupling gel between the transducer and the
(solid) object under test is essential
...
However efficiency is not the only characteristic of
interest: bandwidth and beam shape are equally important parameters
...
Advanced models of the acoustic
arrangement, based on transmission lines, are required to find an optimal solution
for a particular application
...
The first
is usually applied for liquid and solid contacts (Figure 9
...
Two essential parameters of such a layer are the acoustic impedance and the thickness
...
According to very simple models, the optimum value
is the harmonic mean of these two values, but in practice other values appear to be
more effective [2, chapter 4]
...
Having found the optimum
impedance value, the next problem is finding a material having that particular
impedance
...
Acoustic Sensors
251
Figure 9
...
To overcome the enormous mismatch in airborne applications, the transmission
efficiency is improved by placing a precisely shaped piece of an acoustically soft
material on the front side of the ceramic element, for instance a tiny horn as shown
in Figure 9
...
A horn or cone also affects the frequency range as well as the radiation field of the transducer [1, p
...
Most commercial low-cost piezoelectric
transducers are provided with such a horn
...
2), making it
an attractive material for ultrasound applications
...
Other piezoelectric materials are being studied for their suitability as acoustic transducer, for instance porous films with artificially electric
dipoles [11]
...
The resonance frequency is determined by the dimensions of the crystal and, to a
lesser extent, by the matching elements
...
Many acoustic detection systems use tone burst signals
...
6
...
This has important consequences for the determination of the ToF measurement, as will be explained in Section 9
...
9
...
4
Arrays
As shown in Section 9
...
1 the beam width of a sound emitter is determined by its
lateral dimensions and the frequency of the emitted sound signal
...
7)
...
In other points, as in Q, the
waves (partly) cancel
...
Similarly the sensitivity angle of an acoustic transducer operating in receiver mode
can be narrowed using an array of such receivers
...
By controlling the delay
252
Sensors for Mechatronics
Figure 9
...
Figure 9
...
times the main sensitivity axis can be varied over a limited angle
...
Due to improved technology phased arrays are gaining
interest for acoustic ranging and imaging [16À19]
...
In general at an increasing deflection angle the amplitude of the side lobes
(Figure 9
...
9
...
A measurement based on distance-dependent attenuation (as with light) is
rather susceptible to environmental influences and the absorption properties of the
objects involved
...
8)
...
The travelled distance x follows
directly from the ToF t, using the relation va 5 x/t (for direct travel) or va 5 2x/t for
echo systems (where the sound wave travels twice the distance)
...
Most popular are the burst (a number of
periods of a sine wave), a continuous wave with constant frequency (CW) and an
Acoustic Sensors
253
Figure 9
...
FM-modulated sine wave (FMCW or ‘chirp’)
...
Pulses and bandwidth limited Gaussian noise are other
possibilities
...
3
...
g
...
A transmitter emits a short burst, a
few up to about 10 periods of a sine wave, in the direction of an object
...
1), travels back and is received by the same
or a second transducer, which detects the moment of arrival
...
First there is noise of electrical and acoustic origin, which becomes important at larger distances, when the echo signal is low due
to divergence of the sound waves
...
A further cause of inaccuracy is the (unknown) orientation of the reflecting surface relative to the main axis of the transducers
...
Some but not all of these causes are typical for the burst method
...
9A)
the measured distance x0 is:
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a2
x 5
1 x2
4
0
ð9:16Þ
from which follows a relative error equal to
Δx 1 a2
% 2
x
8x
ð9:17Þ
254
Sensors for Mechatronics
Figure 9
...
So, for a distance x 3
...
A tilted reflecting surface (Figure 9
...
As an example, a 1% error occurs when the tilt angle is about 8
...
When in
this numerical example the half angles of both R and T are also 8 , the intensity of
the echo has dropped by a factor of 4
...
This limits the minimum detectable distance: there is a dead band or dead zone, equal to half the number of wavelengths (because sound is travelling twice the distance)
...
The response of a piezoelectric transducer on a burst (Figure 9
...
Actually this
effect occurs twice: first at the transmitter and a second time at the receiver
...
The most common detection method for the echo burst is a threshold applied to
the receiver signal
...
The threshold must be well above the noise level, to prevent noise being interpreted
as the incoming echo
...
10
...
Many methods have been published over the past years, all aiming at a higher
accuracy of the burst ToF measurement, despite noise and other interfering effects
such as temperature changes and air turbulence
...
These techniques yield typical errors below 1 mm, depending on the S/N ratio and the travelled distance but
need longer processing time
...
11 AM-signal: (A) time domain
and (B) frequency spectrum
...
Alternatively instead of the starting point of the echo signal, where
the S/N ratio is low, the arrival time of a point around the maximum amplitude
could be chosen as a measure for the ToF
...
1 mm [23]
...
Noise as the input signal is studied
in Ref
...
A comparison of various detection methods is presented in Ref
...
9
...
2
Continuous Sine Wave (CW)
The average output power of a burst is relatively small, and may result in a poor
S/N ratio, in particular at increased distances
...
Distance information is obtained from the phase
difference between the transmitted and the received waves
...
First emission and detection cannot share the same transducer,
hence two transducers are required, making the system larger and more expensive
...
Secondly the unambiguous measurement range is only one
period of the sound wave
...
4 μm
...
So for distance control over a short range, the CW method is preferred over
the burst method [31]
...
11A)
...
When
using piezoelectric transducers the carrier frequency should equal the resonance
256
Sensors for Mechatronics
Figure 9
...
frequency
...
11B)
...
It means that the period time of the ‘envelope’ is much
larger than the wavelength of the carrier
...
So for a ToF corresponding to one period (2π) of the envelope, the carrier has
shifted over ωc/ωs as many periods
...
The method has the advantage of
the continuous mode, but with enlarged range
...
(9
...
In Ref
...
Using a digital phase detection circuit, an accuracy of 2 mm over a 1
...
9
...
3
Frequency-Modulated Continuous Waves (FMCW)
The unambiguous range of the continuous mode can be increased by frequency
modulation of the sound wave
...
12 shows the transmitted and the received
signals (sometimes called a ‘chirp’, referring to the whistling of some birds)
...
Due to the time delay of the
reflected wave, its frequency in the same time frame is f(t) 5 fL 1 k Á (t 2 τ)
...
The distance to the reflecting surface follows from
x5
1
va
va τ 5 UΔf
2k
2
ð9:21Þ
Apparently this distance is directly proportional to the frequency difference and
unambiguous over a time tm as illustrated in Figure 9
...
The CWFM method combines the advantages of the first two methods: the transmitted signal is continuous
(favourable for the S/N ratio, uninterrupted distance information) and the range is
larger (determined by the frequency sweep)
...
Further since transmission is essentially continuous, two transducers are required for simultaneous transmitting and receiving
...
The sweep length should correspond to the largest distance to be measured, to guarantee sufficient time overlap
between the transmitted and reflected waves
...
Electrostatic transducers for low-cost applications have a rather limited frequency range, typically from 50 to 100 kHz, so just
one octave (a factor of 2)
...
This may be a disadvantage from the viewpoint of construction; however, as has been shown in
Section 9
...
1, the half angle is much smaller, contributing to a better S/N ratio of
the echo signal
...
(9
...
Usually this is
done by some correlation procedure, performed in the digital signal domain (see
for instance Refs [33,34])
...
However the procedure is essentially based on the multiplication of both
signals, followed by some filtering
...
(9
...
Now let the transmitted FM signal be:
xT ðtÞ 5 A cos½2πðfL 1 kUtÞt
ð9:23Þ
The reflected wave signal delayed over a time τ becomes:
xR ðtÞ 5 B cos½2πffL 1 kðt 2 τ Þgðt 2 τÞ
ð9:24Þ
258
Sensors for Mechatronics
1000
800
800
700
600
600
200
500
Amplitude
Amplitude
400
0
–200
400
300
–400
200
–600
100
–800
0
–1000
0
(A)
0
...
02 0
...
04 0
...
06 0
...
08 0
...
1
5
...
8
(B)
5
...
9
5
...
6
6
...
1
6
...
2
×10–3
Figure 9
...
The product of these two signals contains components with sum and difference
frequencies
...
Obviously for an accurate determination of this frequency all
other components due to the multiplication procedure as well as noise should be
sufficiently suppressed by some method of filtering
...
To get an impression
of a possible output Figure 9
...
The horizontal time scale corresponds to the delay time (or ToF)
...
13A the full scale is just the cycle period (100 ms)
...
006 s a
pronounced maximum is noticeable
...
13B this peak
appears to occur at 5
...
02 m (at a measured sound frequency of 343 m/s)
...
Whether burst mode or continuous mode should be applied strongly depends on
the requirements and the application
...
CWFM is less sensitive to noise but
requires more complicated interfacing and signal processing [35,36]
...
Acoustic Sensors
9
...
4
259
Other Signal Types
Common to all methods considered thus far is the accurate determination of the
time delay of an acoustic wave
...
Assuming the total transfer from
transmitter, acoustic medium and receiver is linear (which is the case in the majority
of the applications considered here), any signal containing some time-discriminating
parameter will do
...
However the bandwidth of most transducers is too small for handling such signals and, moreover, for air applications the
energy content is too low
...
The autocorrelation of
wide-band Gaussian noise is a narrow peak
...
Limitations of this method are
mainly of a practical nature: the noise signal and the transducers are always band
limited, while sampling, AD conversion, and the finite measurement time further
limit the resolution and accuracy of the digitally processed signals
...
The signal is a (sinusoidal) carrier modulated in phase or frequency by a binary coded signal
...
An example of an application of binary phase shift keying signals for acoustic distance measurement in air is given in Ref
...
9
...
Ultrasonic sensors are
extensively used in the processing industry for a variety of parameters [38], but
they can also be found in numerous other fields, such as transportation, medical
diagnostics, material research and so on
...
These tasks comprise movement control in production machines, obstacle
avoidance in traffic, navigation of AGVs, object recognition and inspection and
many more
...
When moderate distance accuracy is required, the interfacing can be kept simple
...
We review two main tasks: navigation and inspection
...
4
...
Application examples are mobile robots
(e
...
path finding and collision avoidance), aids for visually impaired people and
260
Sensors for Mechatronics
Figure 9
...
localization of tools in a work space
...
The easiest task is collision avoidance, because
the demands with respect to accuracy and speed are not severe
...
A simple anti-collision system
for robots and other vehicles like cars and wheelchairs consists of a number of
fixed transducers at the front or around the circumference of the vehicle
...
When the reflecting surface is not perpendicular to the main axis of the transducer, an error is introduced (compare Figure 9
...
As a consequence the range
data obtained by an acoustic scanning system show the typical behaviour as seen in
the sonar maps in Figure 9
...
Simulations of such errors are extensively discussed
in literature [39]
...
14 the transmitter/receiver combination rotates over an angle α with
respect to the surface normal, and the dots represent measurement points
...
Assume that
this happens only when the reflected beam falls within the half angle of the receiver
(an arbitrary choice because the threshold level may be adjusted to any other value)
...
14A range data lie on an arc spanning twice the half angle of the transducers
...
14B, the acoustic wave reflects
away from the receiver, so no echo is received
...
In Figure 9
...
As can be seen in Figure 9
...
Obviously in these cases
the detectivity depends greatly on the angle between the two surfaces
...
Similar to the optical system the ultrasonic counterpart may be disturbed too by
spurious signals from other sources or unwanted reflections
...
When such echoes interfere with the main echo, phase information is easily corrupted, even when the amplitude of the unwanted echo is small
...
15 Interfering
echo, causing a peak time
shift error [40]
...
In systems based on envelope detection such spurious echoes
may introduce large ToF errors, as shown in Figure 9
...
More advanced detection
methods are required to overcome this problem [40,41]
...
Typical working distances of low-cost
anti-collision systems range from tens of cm (limited by the dead zone) to a few m
...
There is an overwhelming number of papers on this topic, dealing
with many kinds of system concepts and signal processing algorithms
...
Navigation
with acoustic beacons is a low-cost alternative for the optical beacon systems discussed in Chapter 7
...
g
...
Three approaches can be
followed:
1
...
a rotatable T/R combination on top of the robot
3
...
An example of the first approach is presented in Ref
...
An obvious advantage
of a (mechanical) scanning system is the need for just one or a very few pair of
transducers; the scanning, however, is slow
...
16 Resolution improved
by convolution; scales in cm
(unpublished from laboratory
experiments by the author and
students)
...
Due to the relatively large wavelength of ultrasonic sound in air, the lateral resolution is rather low
...
Enhancement of
the lateral resolution without greatly increasing the number of transducers or their
directivity (which is limited anyway) can be achieved by more advanced signal
processing, for instance potential fields [44] (applied for wheel chair navigation)
and a one-transmitter three-receiver configuration [45]
...
This may potentially improve both the lateral and the radial resolutions of an echo-location system,
as is shown in Figure 9
...
This figure shows the outcome of an experiment with
two coffee cups placed on a flat table; the rotating piezoelectric transducers are
positioned in the origin
...
By deconvolution (using the known pulse response of the transducers) they
can be distinguished separately
...
[46] where
the information from the echo amplitude is also used to construct a sonar map
...
Such beacons can be transmitting, receiving or passive
...
From the signals received by the beacons the distance to the robot can
be derived
...
17)
...
Acoustic Sensors
263
Figure 9
...
In this example the
vehicle’s position is on one of the
two possible intersections of two
circles with radius equal to the
measured distances from the two
beacons
...
From these signals an onboard robot computer determines its distance from the beacons and subsequently
its 2D position
...
In a system with passive beacons the robot transmits and receives signals,
reflected by the beacons
...
They need no power supply and the only requirements are an
accurately known position and sufficient reflectivity for the signals
...
Navigation Tool for Visually Impaired Persons
This particular application of ultrasound sensing has attracted increased interest
over the last few decades
...
Fixing the acoustic transducers somewhere on
the body leaves the hands free; attaching the transducers on a person’s head allows
exploration of the environment in a more natural way
...
For this application it is important to not only avoid obstacles, but also to characterize or identify objects in the person’s immediate environment
...
The technical problems to overcome are similar to those encountered in robot
navigation
...
A completely different approach to many of these systems is still in the experimental phase, but there
is noticeable progress in performance
...
264
Sensors for Mechatronics
Transmitter
Direct path
Receiver
Figure 9
...
h
Indirect path
s
Localization of Tools
When a moving object is provided with a sound source, its position and orientation
can be determined by using a set of acoustic sensors located at fixed points in the
working space, similar to the beacon concept discussed earlier
...
A different approach, presented in Ref
...
Another example is the localization of surgical tools [57], where a
position accuracy of 40 μm is reported
...
They may cause phase errors
and a shift in the envelope top of the received signal (see Figure 9
...
Figure 9
...
Assume the sound frequency is 40 kHz, corresponding with a wavelength of
8 mm
...
e
...
On
the other hand at multiples of a full wavelength path difference (i
...
8 mm, 16 mm
and so on) constructive interference takes place
...
Since the amplitudes of the sound waves differ, interference is only partial, to an extent that depends on the angles with respect to the acoustical axis of the transducers and on the reflectivity of the surfaces
...
9
...
2
Inspection
General
Compared to 3D vision the technique of acoustic ranging suffers from a much
lower spatial resolution
...
1)
...
We discuss three particular
approaches: acoustic imaging in air as an alternative for imaging by vision, NDT
Acoustic Sensors
265
and inspection by touch using ultrasound-based tactile sensors
...
Acoustic Imaging
The goal of any imaging system is the acquisition of an electronic picture from
which information about an object’s size and shape can be inferred, preferably
including as many details as feasible
...
Since the spatial resolution of an acoustic distance measurement is
relatively low, some method of scanning is required to obtain detailed shape information
...
In general the
acquired image data are sparse and not accurate, which complicates recognition
...
Scanning can be performed in various ways
...
In a
robotics environment a robot can perform the scanning, thereby making use of the
many d
...
f
...
The encoders in the joints provide the orientation of the scanning range finder
...
Sideways
scanning enables the reconstruction of the circumference of an object, from the
position and orientation of the flat or curved sides [61À63]
...
In all these examples mechanical scanning is used
...
Usually such systems comprise an array of transducers with relatively large spacing [67]
...
An accuracy analysis of such an approach can be found in Ref
...
One
of the difficulties in such a system is to distinguish between multiple objects and
between various shapes returning similar echo patterns
...
For the classification of objects with known shape, the ‘signature method’ can
be applied [62,69,70]
...
Instead the system is taught to associate each object
class with a characteristic echo pattern
...
On the
other hand different but similarly shaped objects may result in echo patterns that
are also similar
...
[71]
...
NDT and Material Properties
Sound waves reflect at the boundary of two materials with different acoustic impedances
...
One of the applications is the detection
and localization of defects (e
...
voids and flaws) in a solid, even when invisible at
the outside
...
To a certain extent the size and shape of defects
can also be reconstructed from the echo pattern [72À74]
...
To achieve
high accuracy advanced signal processing is required
...
[78]
the thickness of a multilayered structure is measured with an accuracy less than
10 μm for the individual layers
...
[79], thickness and
hardness are simultaneously measured by a combination of acoustic and capacitive
sensing elements
...
1
...
It is a suitable method in
cases where the relation between the unknown parameter and the damping constant
is known, for instance by an acknowledged model or by calibration
...
We give just one example: the
measurement of bubbles in liquids [80]
...
By measuring these
parameters over a relevant frequency range, various liquid properties can be
deduced or evaluated
...
G
G
G
vibration measurements (example: a vibrating cantilever, phase detection of an 80 kHz
sound wave [81]);
seam tracking (example: short-range scanning with a MHz piezoelectric transducer with
focussing surface [82]);
respiratory air flow (example: two CW waves from piezoelectric transducers, with
slightly different frequencies [83]);
Acoustic Sensors
267
Figure 9
...
G
G
G
G
G
G
G
liquid level (examples: in bottles, 220 kHz piezoelectric sensors, burst mode [84]; as an
acoustic resonator [85]);
go/no-go decision on product quality (examples: quality of foundry pieces; signature
imaging and Artificial Neural Network (ANN) for identification [86]; defect detection in
food can production line: same method, according to Figure 1
...
The number of applications where a ToF measurement can be used is almost
unlimited, and the reader is referred to the vast amount of literature in books and
journals on NDT for further examples and inspiration
...
A tactile sensor consists of a matrix of force-sensitive elements (taxels)
...
So a tactile
sensor provides a pressure or deformation image of the object with which it is
brought into contact
...
4
...
In this section we focus on ultrasonic measurement of the deformation,
which is mostly based on the ToF method
...
Usually a piezoelectric material is used, allowing small dimensions of the
taxels
...
1
...
One of the first sound-based tactile matrix sensors is described in Ref
...
Figure 9
...
The elastic top layer of this 3 3 4 matrix is
responsible for the force-deformation transfer
...
The spatial
resolution is about 1 mm
...
268
Sensors for Mechatronics
A similar construction, but with the elastic layer in between transmitter and
receiver, is proposed in Ref
...
A completely different approach is described in
Ref
...
The basic assumption here is that touch is accompanied by ultrasound
...
The
authors expect the sensor also be sensitive to slip
...
Another type of tactile sensor, presented in Ref
...
Conclusion
This section on applications clearly demonstrates that the applicability of acoustic
(ultrasound) sensors is almost unlimited
...
Significant disadvantages are the low resolution
and the temperature sensitivity (due to the temperature dependence of sound speed)
...
For very high accuracy one should also consider the effect of humidity on
the speed of sound, and possible air turbulence, introducing noise
...
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Elsevier
32 Jamestown Road, London NW1 7BY
225 Wyman Street, Waltham, MA 02451, USA
First edition 2012
Copyright r 2012 Elsevier Inc
...
Details on how to seek
permission, further information about the Publisher’s permissions policies and our arrangement
with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency,
can be found at our website: www
...
com/permissions
This book and the individual contributions contained in it are protected under copyright by the
Publisher (other than as may be noted herein)
...
As new research and experience
broaden our understanding, changes in research methods, professional practices, or medical
treatment may become necessary
...
In using such information or methods they should be mindful of their own safety and the safety
of others, including parties for whom they have a professional responsibility
...
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing-in-Publication Data
A catalogue record for this book is available from the Library of Congress
ISBN: 978-0-12-391497-2
For information on all Elsevier publications
visit our website at elsevierdirect
...
Each copy is produced
to order and is limited to black ink
...
Preface
This book offers an overview of various sensors and sensor systems as required
and applied in mechatronics
...
The work is adapted from a course book on sensors for mechatronic systems, used by students in Electrical and Mechanical
Engineering of the University of Twente, The Netherlands
...
This information is obtained using sensors
...
For many other, newly defined applications, such a solution is not feasible, and a
sensing system should be assembled from obtainable or specifically designed subsystems
...
Sensors operate in at least two different physical domains
...
Moreover, it includes a
section devoted to sensor errors and error minimization that apply to most of the
sensors discussed in this book
...
These categories are resistive, capacitive, inductive and magnetic,
optical, piezoelectric and acoustic sensors
...
In subsequent sections, different types and constructions are given, together with the typical specifications and maximal ratings
for devices available on the sensor market
...
Where appropriate, a section is added on the interfacing of
the sensor
...
However, the reader is
assumed to have some background knowledge on physics and electronics
...
Moreover, readers who are not familiar with certain parts of physics
are briefly introduced into the subject
...
No references have been made
to web pages because this information source appears to be too volatile for citation
in a book
...
The author welcomes all kind of comments and suggestions that will result in an
increased quality of the work
...
L
...
Despite international
normalization of symbols for quantities and material properties, notations for physical quantities are not unambiguous when considering the various disciplines, which
each have their own system of notation
...
Further, where useful, relations between
quantities are listed as well
...
1
The Electrical Domain
A sensor produces an electrical output
...
1 displays the most important energetic quantities used in the electrical domain
...
Relations between
these variables are discussed in Chapter 6
...
2 shows the major properties for the electrical domain
...
The electric permittivity ε is the product of the permittivity of free space
(vacuum) ε0 and the relative permittivity (or dielectric constant) εr
...
Numerical values of ε0 and μ0 are:
ε0 5 ð8:85416 6 0:00003ÞU10212 ðF=mÞ
μ05 4πU1027 ðV s=A mÞ
The relative permittivity and permeability account for the dielectric and magnetic properties of a material
...
They are listed in Table A
...
The duty cycle is defined as the highÀlow ratio of one period in a periodic pulse
signal
...
A duty
cycle of 50% refers to a symmetric square wave signal
...
1 Electrical and Magnetic Quantities
Quantity
Symbol
Unit
Electric current
Current density
Electric charge
Dielectric displacement
Electric field strength
Potential difference
Magnetic flux
Magnetic induction
Magnetic field strength
I
J
Q
D
E
V
Φ
B
H
`
A (ampere)
A m22
C (coulomb) 5 A s
C m22
V m21
W A21
Wb (weber) 5 J A21
T (tesla) 5 Wb m22
A m21
Table A
...
3 Signal Variables
Signal Quantity
Symbol
Unit
Time
Frequency
Period
Phase difference
Duty cycle
Pulse width
t
f
T
φ
δ
τ
s (second)
Hz (hertz) 5 s21
s
rad (radian)
À
s
Appendix A
A
...
Changes in environmental or local temperature affect the mechanical and electrical performance of
mechatronic systems
...
Tables A
...
5 review the major thermal quantities
...
Its
value strongly depends on the flow type along the object and the surface properties
...
3
The Mechanical Domain
Quantities in the mechanical domain describe state properties related to distance,
force and motion
...
We will briefly resume the first two groups
...
The basic position quantities and their units and symbols are
listed in Table A
...
Table A
...
Some commonly used properties in the mechanical domain are listed in
Table A
...
Table A
...
5 Thermal Parameters
Thermal Property
Symbol
Unit
Thermal expansion coefficient
Heat capacitance
Specific heat capacity
Thermal resistance
Thermal conductivity
Coefficient of heat transfer
α
Cth
c
Rth
gth
h
K21
J K21
J kg21 K21
K W21
W m21 K21
W m21 K21
278
Appendix A
Table A
...
7 Force Quantities
Quantity
Symbol
Unit
Force
Tension, stress
Shear stress
Pressure
Moment of force
Power
Energy
F
T
τ
p
M
P
E
N
Pa 5 N m22
Pa
Pa
Nm
W 5 J s21
J5N m
Table A
...
A force (tension) results
in a deformation (strain): longitudinal forces cause translational deformation; shear
Appendix A
279
Figure A
...
o
...
in the
mechanical domain
...
The mechanical domain has six degrees of freedom (d
...
f
...
As an example, in Figure A
...
Note that in this example the
force causes a positive strain in z-direction and negative strain in the other two directions
...
In general a longitudinal force in the z-direction, Tz, causes the material to be
deformed in three possible directions (x, y and z), resulting in the strain components
Sz (usually the most important), Sx and Sy
...
Sometimes a longitudinal force
produces torsion
...
In general
the relation between tension and strain is described by
Sij 5 sijkl UTkl
ðA:3Þ
Tij 5 cijkl USkl
ðA:4Þ
or
with i, j, k, l equal to x, y and z
...
To simplify the notation the tensor indices ijkl
are substituted by engineering indices 1À6, according to the next scheme:
xx-1
yy-2
zz-3
yz 5 zy-4
xz 5 zx-5
xy 5 yx-6
So, Hooke’s law becomes:
Sλ 5 sλμ UTμ
ðA:5Þ
Tμ 5 cμλ USλμ
ðA:6Þ
or
280
Appendix A
with λ, μ 5 1
...
Apparently this compliance matrix contains 36 elements
...
(A
...
To get an idea of the practical values
Table A
...
Note that sij 5 sji
...
The remaining elements in the matrix are zero
...
A
...
4
...
The radiometric quantities are valid for the whole electromagnetic spectrum
...
35 , λ , 0
...
They are related to the mean, standardized sensitivity of the human eye and are applied in photometry
...
10 shows the
major radiometric and corresponding photometric quantities
...
The radiant intensity I (W/sr) is the emitted radiant power of a point source per
unit of solid angle
...
It includes
the total emitted energy in all directions
...
9 Matrix Elements of Compliancy for SiO2 and Si; Unit 10212 m2/N
a
SiO2
s11
s12
s13
s14
a
Si
12
...
79
21
...
50
s33
s44
s66
9
...
04
29
...
68
22
...
s44
12
...
10 Radiometric and Photometric Quantities
Radiometric Quantities
Power
Energy
Photometric Quantities
Quantity
Radiant flux
Symbol
P 5 dU/dt
Unit
W
Radiant
energy
Radiant
emittance
Irradiance
U
J
Es 5 dPs/dS
W/m2
Emitting power
per unit area
Incident power
per unit area
Radiant
Radiant power
intensity
per solid
angle
Power per solid Radiance
angle per unit
of projected
surface area
Ed 5 dPd/dS W/m2
Quantity
Luminous
flux
Luminous
energy
Luminous
emittance
Illuminance
Unit
lumen (lm)
Luminous
intensity
lm/sr 5 candela
(cd)
I 5 dP/dΩ
W/sr
L 5 dI/dSp
W/m2 sr Luminance,
brightness
lm s
lm/m2 5 lux
lm/m2 5 lux
lm/m2 sr 5 cd/m2
Figure A
...
10
...
the direction of the emitted light: it is the emitted power per unit area, per unit of
solid angle (W/m2 sr)
...
The amount of incident power Ed is expressed in terms of W/m2 and is called
the irradiance
...
A surface with (real) area S that is irradiated from a direction
perpendicular to its surface receives power equal to Ed Á S (W)
...
2)
...
282
Appendix A
Table A
...
10 the radiance L of a surface is defined following this idea: it is the
emitted radiant energy in a certain direction, per solid angle (to account for the
directivity) and per unit of projected area, that is per unit area when the emitting
surface is projected into that direction
...
All units have their counterpart in the photometric domain (right-hand side of
the table)
...
The radiometric
quantities in the table do not account for the frequency or wavelength dependence
...
The
total irradiance over a spectral range from λ1 to λ2 then becomes:
Ed 5
ð λ2
λ1
Ed ðλÞdλ
ðA:8Þ
To characterize optical sensors special signal parameters are used, related to the
noise behaviour of these components (Table A
...
Note that the signals can be expressed in voltage, current or power
...
The parameters D and NEP represent the lowest perceivable optical signal
...
This means that,
when specifying NEP, the modulation frequency, the sensor bandwidth, the temperature and the sensitive surface area should also be specified, as all these parameters are
included in the noise specification
...
Since noise power of a sensor is usually proportional
to the sensitive area A and the bandwidth Δf, the noise current and noise voltage are
proportional to O(AΔf); hence, NEPÃ 5 NEP/O(AΔf ) and DÃ 5 O(AΔf )/NEP
...
3 Cosine law of
Lambert
...
4 Derivation of the total radiant energy
from a unit surface with Lambertian emission
...
4
...
3)
...
Many surfaces scatter the incident
light in all directions equally
...
All radiant energy emitted from a surface A with radiant emittance Es has to
pass a hemisphere around that surface (Figure A
...
The area of surface element dS on the hemisphere, corresponding with a solid
angle dΩ equals:
dS 5 r 2 dΩ 5 r 2 sin φdφdϑ
ðA:9Þ
where r is the radius of the hemisphere
...
10
the radiant emittance from the emitting surface A in the direction of dS is:
dPs
5 L cos φdΩ
dA
ðA:10Þ
Since all radiant energy from A passes the hemisphere, the total radiant emittance of A equals the integral of dPs /dA over the full surface area of the hemisphere
...
So
284
Appendix A
2π π=2
ð ð
ZZ
Es 5
L cos φdΩ 5
hemisphere
L cos φ sin φdφdϑ 5 πL
0
ðA:11Þ
0
or the radiant emittance of a Lambertian surface equals π times the radiance of that
surface
...
4
...
Figure A
...
Light energy radiates from the source with emitting surface area S1 and radiance
Le (W/sr m2)
...
Further the light beam as received by the sensor makes an angle ϑ1 with the normal
on the emitting surface, and an angle ϑ2 with the normal on the receiving surface
...
Assume the source
dimensions being small compared to r
...
The emitter emits Le Á S1
W per steradian; hence, the part ΔPe of the emitted light falling on the sensor is:
ΔPe 5 Le S1 cos ϑ1 dΩ ðWÞ
ðA:13Þ
where S1 cos ϑ1 is the projected surface area of the source
...
(A
...
(A
...
Figure A
...
Appendix A
285
Figure A
...
Next we consider the indirect mode, where we distinguish between two different
situations
...
In the second situation the whole object falls within the light cone of the source
...
6 displays
the first situation and defines the various parameters
...
The target intercepts a light beam that makes an angle ϑs with the normal vector
nt on the target’s surface
...
The surface area S1 of the light spot on the object satisfies the equation:
2
S1 cos ϑs 5 Ωs rs ðm2 Þ
ðA:15Þ
where rs is the distance between the source and the target
...
(A
...
Part of the scattered light is
received by the detector with sensitive area Sd on a distance rd from the target
...
(A
...
7 The target falls completely within the
light cone of the source; light reflects from the
target to the sensor according to Figure A
...
Finally when substituting Eqs (A
...
17) into Eq
...
18) we find for the
optical power received by the sensor:
Pd 5
Sd cos ϑ1 cos ϑ2
UIs Ωs ðWÞ
2
πrd
ðA:19Þ
So the sensor output is inversely proportional to the square of the distance to the
sensor, as long as the object intercepts the whole light beam
...
Next we consider the situation where the whole object is illuminated by the
source, as can happen at large distances and with small objects (Figure A
...
The solid angle of the beam falling on the object is:
dΩs 5
St cos ϑs
ðsrÞ
2
rs
ðA:20Þ
where St is the area of the illuminated part of the object
...
Appendix B
Relations Between Quantities
B
...
Here we review the basic equations extended with the magnetic domain
...
According to the second law of thermodynamics the energy content of an infinitely
small volume of an elastic dielectric material changes by adding or extracting heat
dQ (J) and by work dW (J) exerted upon it
dU 5 dQ 1 dW ðJÞ
ðB:2Þ
The work dW is the sum of the different energy forms involved (here thermal,
mechanical, electrical and magnetic energy), so
dU 5 Θ dσ 1 F dx 1 V dQ 1 I dΦ ðJÞ
ðB:3Þ
When the heat is taken per unit of volume, this equation reads:
dU 5 Θ dσ 1 T dS 1 E dD 1 H dB ðJ=m3 Þ
ðB:4Þ
that is the change in internal energy when thermal, mechanical, electrical and magnetic energy is supplied to the system
...
Apparently in this equation only through-variables affect the system
...
288
Appendix B
We can generalize Eq
...
4) as
dU 5
X
Ai dBi ðJ=m3 Þ
ðB:6Þ
i
where Ai and Bi are conjugated pairs of variables
...
From Eq
...
6) it follows for the parameters Ai
Ai 5
@U
@Bi
ðB:7Þ
On the other hand the system configuration or the material itself couples the
conjugate variables of each pair
...
In general the intensive variable Ai and the extensive variable Bi within one
domain are linked according to
Ai 5 ci UBi
or
Bi 5 si UAi
ðB:9Þ
where ci is a (generalized) elasticity and si is a (generalized) compliancy
...
From Eqs (B
...
4) it follows that the system energy depends on all (generalized) parameters:
U 5 f ðAi ; Bi Þ;
i 5 1?n
ðB:10Þ
but since Ai and Bi are related by Eq
...
9) we can also write:
U 5 f ðBi Þ;
i 5 1?n
ðB:11Þ
So for small variations in the parameters Bi the variation in energy (as given in
Eq
...
6)) becomes:
dU 5
n
n
X @U
X
@U
@U
dB1 1 ? 1
dBn 5
dBi 5
Ai dBi
@B1
@Bn
@Bi
i
i
ðB:12Þ
Equation (B
...
However variables in one
domain are also linked to variables in another domain, resulting in cross effects,
the basis for transducers
...
Inversely parameter Bj depends on all parameters Ai
...
This can be proven by combining Eqs
(B
...
7):
@Ai
@2 U
@2 U
5 gij 5
5
5 gji
@Bj
@Bj @Bi
@Bi @Bj
ðB:16Þ
since the order of differentiation can be reversed
...
2
Application to Four Domains
The starting point is Eq
...
5) for the mechanical, electrical, magnetic and thermal
domains, which is repeated here in this order:
dG 5 2S dT 2 D dE 2 B dH 2 σ dΘ ðJ=m3 Þ
ðB:17Þ
The through variables can be written as
0
1
@GA
SðT; E; H; ΘÞ 5 2@
@T
0
E;H;Θ
1
@GA
DðT; E; H; ΘÞ 5 2@
@E
0
T;H;Θ
1
@G
BðT; E; H; ΘÞ 5 2@ A
@H
0
T;E;Θ
1
@G
σðT; E; H; ΘÞ 5 2@ A
@Θ
T;E;H
ðB:18Þ
290
Appendix B
Since we consider only small variations, the variables S, D, B, and Δσ are
approximated by linear functions, so
20
1
@S A
6@
6 @T
6
E;H;Θ
6
60 1
6
2
3 6 @@DA
6
dSðT; E; H; ΘÞ
6 @T
6 dDðT; E; H; ΘÞ 7 6
E;H;Θ
6
756 0 1
4 dBðT; E; H; ΘÞ 5 6
6
6 @B
dσðT; E; H; ΘÞ
6@ A
6 @T
6
E;H;Θ
6
60 1
6
6 @σ
4@ A
@T
0
1
@S A
@
@E
0
T;H;Θ
1
@@DA
@E
0
T;H;Θ
1
@@BA
@E
0
T;H;Θ
1
@@σ A
@E
E;H;Θ
0
1
@S A
@
@H
0
1
@S A
@
@Θ
T;E;Θ
0
1
@@DA
@H
T;E;Θ
0
1
@ @B A
@H
T;E;Θ
0
1
@ @σ A
@H
T;H;Θ
3
7
7
7
T;E;H 7
0 1
7
7
7 2
@D A
3
@
7
7 dT
@Θ
7 6
T;E;H 7
dE 7
7
0 1
7U6
4 dH 5
7
7
@ @B A
7 dΘ
7
@Θ
7
T;E;H 7
7
0 1
7
7
@σ A
5
@
@Θ
T;E;Θ
T;E;H
ðB:19Þ
Combining Eqs (B
...
19) results in
20
1
@2 G A
6@ 2
6 @T
6
E;H;Θ
6
1
60
6
6 @ @2 G A
2
3 6
dS
6 @E@T
6 dD 7 6
H;Θ
6
7 6
1
4 dB 5 5 6 0
6
6 @2 G
A
dσ
6@
6 @H@T
6
E;Θ
6
60
1
6
6 @2 G
4@
A
@Θ@T
E;H
0
1
@2 G A
@
@T@E
0
1
@2 GA
@
@2 E
0
H;Θ
1
@2 G A
@
@T@H
0
E;Θ
1
2
@@ GA
@E@H
T;H;Θ
1
2
@@GA
@H@E
0
0
T;Θ
1
2
@@GA
@Θ@E
T;H
0
1
T;Θ
2
@@ GA
@2 H
0
T;E;Θ
1
@2 G A
@
@Θ@H
T;E
0
1
@2 G A
@
@T@Θ
3
7
7
7
E;H 7
0
1 7
7
2
3
@@ GA 7 2
7
7 dT
@E@Θ
7
T;H 7 6 dE 7
7
0
1 7U6
7 4 dH 5
2
7
@ @ G A 7 dΘ
7
@H@Θ
7
T;E 7
7
0
1
7
7
@2 G A
5
@
2Θ
@
T;E;H
ðB:20Þ
The second-order derivatives in the diagonal represent properties in the respective domains: mechanical, electrical, magnetic and thermal
...
These derivatives are pair-wise equal, since the order of
Appendix B
291
Table B
...
(B
...
2 Symbols, Parameter Names and Units of the Effects in Table B
...
The derivatives in Eq
...
20) represent material
properties; they have been given special symbols
...
2
3
2
sE;H;Θ
S
6 H;Θ
6 D 7 6 d E;Θ
6 756 λ
4B5 6
4 αE;H
σ
d H;Θ
εT;H;Θ
mT;Θ
pT;H
λE;Θ
mT;Θ
μT;E;Θ
iT;E
3
2
3
αE;H
T
pT;H 7 6
7
E 7
7
iT;E 7U6
7 4 H 5
ρ T;E;H 5
c
ΔΘ
Θ
ðB:21Þ
The 16 associated effects are displayed in Table B
...
Some of these effects are mentioned in Figure 2
...
The parameters ε, cp and s correspond to those in Tables A
...
5
and A
...
Table B
...
292
Appendix B
Figure B
...
Figure B
...
B
...
5), (A
...
23))
...
These equations are:
Di 5 εij UEj 1 diμ Tμ
Sλ 5 djλ Ej 1 sλμ Tμ
Ej 5 β ij Di 2 gjμ Tμ
Sλ 5 giλ Di 1 sλμ Tμ
Di 5 εij UEj 1 eiλ Sλ
Tμ 5 2 ejμ Ej 1 cλμ Sλ
Ej 5 β ij Di 2 hjλ Sλ
Tμ 5 2 hiμ Di 1 cλμ Sλ
ðB:23Þ
representing in total eight material properties: the reciprocal pairs s-c and ε-β, and
four piezoelectric parameters (compare Table 8
...
These relations are
visualized in the Heckmann diagram for the electrical and mechanical domains
(Figure B
...
The circles represent the state variables, and the arrows represent the
material properties
...
One of them is the set given in Chapter 2, by Eq
...
10), yielding the most
practical material properties
...
2 shows the Heckmann diagram for three
domains, where the double arrows are left out for clarity
...
All
circuits are built up with operational amplifiers
...
In first instance the operational amplifier is considered to have ideal characteristics
...
C
...
1A
...
The model in
Figure C
...
The meaning of these circuit elements is as follows:
A: voltage gain (frequency dependent); A0: low-frequency voltage gain
Voff: input offset voltage
1
2
Ib and Ib : input bias currents through the plus and minus terminals
1
2
Ioff 5 jIb 2 Ib j: input offset current
2
1
Zc and Zc : common input impedances from either input to ground
Zd: differential input impedance (between the two input terminals)
Zo: output impedance
Further the common mode rejection ratio (CMRR) accounts for the suppression of
pure common mode signals relative to differential mode signals
...
For white
noise these error sources are specified in terms of V/OHz and A/OHz, respectively
...
1 the noise voltage can be modelled with a voltage source in series with
the offset voltage and the noise current by a current source in parallel to the bias current
...
Any deviation of these ideal values is reflected in the transfer properties of interface circuits built up with operational amplifiers
...
Table C
...
1 (A) Symbol of an operational amplifier, (B) modelling of some deviations from
the ideal behaviour
...
1 Selected Specifications of General Purpose Operational Amplifiers
Parameter
Type I
Type II
Type III
Unit
Voff
tc of Voff
Ib
Ioff
A0
Ri
CMRR
SVRR
ft
Slew rate
1
20
80 3 1029
20 3 1029
2 3 105
2 3 106
90
96
1
0
...
5
2À7
10À50 3 10212
10À20 3 10212
2 3 105
1012
80À100
80À100
1À4
3À15
0
...
Type III is
designed for high-frequency applications, with MOSFET transistors at the input
...
In the analysis that follows we distinguish two types of errors: additive and multiplicative errors
...
Multiplicative
errors are caused by the finite gain and the first-order frequency dependence of the
gain; in the analysis of the frequency dependence it is assumed that the DC loop
gain is much larger than unity: A0β c1
...
Knowing the input impedance
of an interface circuit, the error due to loading the sensor can easily be estimated
...
2
297
Current-to-Voltage Converter
Most AD converter types require an input voltage with a range from 0 to the ADC’s
reference voltage
...
The basic configuration that accomplishes this task is given in Figure C
...
Assuming the operational amplifier has ideal properties, the transfer of this IÀV
converter is simply Vo 5 2IiR and the input resistance is zero
...
The transfer including additive errors amounts:
Vo 52Ii R 1 Voff 1 Ib1 R
ðC:1Þ
To reduce the effect of bias current a current compensation resistance with value
R is inserted in series with the non-inverting input terminal (Figure C
...
The
transfer becomes:
Vo 5 2Ii R 1 Voff 1 Ioff
ðC:2Þ
which shows that current compensation reduces the error due to the bias current by
about a factor of 5 (see Table C
...
The transfer including multiplicative errors due
to finite gain A0 is:
Vo 5 2IR
A0
1
% 2Ii R 1 2
1 1 A0
A0
ðC:3Þ
which means that the scale error is about the inverse of the DC gain of the amplifier
...
2 Current-to-voltage converter: (A) without and (B) with bias current
compensation
...
Amplifiers with this transfer
have a constant gain-bandwidth product: in feedback mode, the overall gain
decreases as much as the bandwidth increases
...
1
...
Taking this into account the transfer
of the IÀV converter is:
Vo 5 2Ii R
1
1 1 jωτ A =A0
ðC:5Þ
Note that the bandwidth of the converter equals the unity gain bandwidth of the
operational amplifier
...
C
...
Voltage amplification is accomplished by either an inverting or a non-inverting amplifier configuration, depending on the required signal
polarity
...
3A shows a non-inverting amplifier with gain 1 1 R2/R1 and infinite input resistance
...
For R2/R1 5 0, the
configuration is called a buffer (Figure C
...
In the following formulas the feedback portion R1/(R1 1 R2) is abbreviated by β
according to the notation in Chapter 3
...
The transfer of the non-inverting amplifier including additive errors equals:
Vo 5
Vi
Voff
1
1 Ib2 R2
β
β
ðC:7Þ
The lower limit of the signal voltage range is set mainly by the offset voltage
and to a lesser degree the bias current
...
The transfer shows a scale error
(multiplicative error) due to the finite gain:
Appendix C
299
Figure C
...
Figure C
...
(C
...
Vo 5
Vi A0 β
Vi
1
%
12
β 1 1 A0 β
β
A0 β
ðC:8Þ
The scale error is the inverse of the loop gain A0β
...
(C
...
This relationship is shown in Figure C
...
Numerical example
...
01, so A0β 5 100; unity gain bandwidth
A0/τ A 5 106 rad/s, so the operational amplifier’s cut-off frequency is 1/τ A 5 100 rad/s
and the non-inverting amplifier bandwidth is 104 rad/s
...
5 shows a simulation1 of the transfer characteristic using a general purpose, low-cost operational amplifier for three gain factors: 1 (buffer), 100 and
1
Type μA741 (original design by Fairchild, 1968); simulated by PSpice (OrCAD Inc
...
5 Simulation with a low-cost operational amplifier
...
6 Inverting amplifier
...
Clearly the product of gain and bandwidth is constant
...
Finally the input resistance of the non-inverting amplifier is found to be:
Rin 5 Ri ð1 1 A0 βÞ 1 βR2 % A0 βRi
ðC:10Þ
which is sufficiently high in most applications
...
4
Inverting Amplifier
Figure C
...
Its voltage transfer is ÀR2/R1
and the input resistance amounts R1, a much lower value than in the case of the noninverting amplifier
...
With this bias current compensation, the
2
term Ib in Eq
...
11) is replaced by Ioff
...
The frequency-dependent gain is given by
Vo
R2
1
52
Vi
R1 1 1 jωτ A =A0 β
ðC:13Þ
Here, too, the product of gain and bandwidth is constant
...
4
...
Note that this value can be rather low, resulting
in an unfavourable load on the transducer
...
5
C
...
1
Comparator and Schmitttrigger
Comparator
A voltage comparator (or short comparator) responds to a change in the polarity of
an applied differential voltage
...
7A)
...
The comparator is frequently
used to determine the polarity in relation to a reference voltage
...
7 (A) Comparator, (B) Schmitttrigger
...
2 Specifications for Two Types of Comparators: Fast (Type I) and Accurate (Type II)
Type I
Voltage gain
Voltage input offset
Input bias current
Input offset current
Input resistance
Output resistance
Response time
Output voltage, high
Output voltage, low
A
Voff
Ibias
Ioff
Ri
Ro
tr
vo,h
vo,l
Type II
À
62 mV 6 8μV/K
5 μA
0
...
25 V
2 3 105
61 mV, max
...
300 nA
3 nA, max
...
3 μs
À
À
It is possible to use an operational amplifier without feedback as a comparator
...
However an operational amplifier is rather slow,
in particular when it has to return from the saturation state
...
2 gives the
specifications for two different types of comparators, a fast type and an accurate
type
...
They have an output level that is compatible with the levels
used in digital electronics (0 and 15 V)
...
C
...
2
Schmitttrigger
A Schmitttrigger can be conceived as a comparator with hysteresis
...
A
simple Schmitttrigger consists of an operational amplifier with positive feedback
(Figure C
...
The output switches from low to high as soon as Vi exceeds the
upper reference level Vref1, and from high to low as soon as Vi drops below the
lower level Vref2
...
However a large hysteresis will lead to huge timing
errors in the output signal
...
7B a fraction β of the output voltage is fed back to the non-inverting
input: β 5 R1/(R1 1 R2)
...
The voltage at the non-inverting input will be either βE1 or βE2
...
This remains a stable situation as long as Vi , βE1
...
The voltage difference between both input terminals decreases much faster
than Vi increases so, within a very short period of time, the output becomes
Appendix C
303
maximally negative E2
...
βE2, the output remains Vo 5 E2 , a new
stable state
...
In conjunction with the positive feedback even a rather slow operational amplifier
can have a fast response time
...
The switching levels can be adjusted by connecting R1 to an
adjustable reference voltage source Vref instead to ground
...
C
...
The reverse is also possible, by
differentiation, but this approach is not recommended because of an increased noise
level
...
8
...
The integrator runs into overload
because the constant offset voltage and bias current will be integrated too
...
The differentiator is unstable because of the (parasitic) second-order behaviour of the operational amplifier
...
Figure C
...
304
Appendix C
C
...
1
Integrator
Figure C
...
Taking into account the finite
gain of the operational amplifier A, the transfer function of this integrator is:
Vo
A
52
Vi
1 1ð1 1 AÞðR=Rf Þ 1 jωð1 1 AÞRC
ðC:17Þ
Assuming a frequency-independent amplifier gain: A 5 A0, the transfer function
becomes:
Vo
A0
R
1
% 2
52
Rf 1 1 jωRf C
Vi
1 1ð1 1 A0 ÞðR=Rf Þ 1 jωð1 1 A0 ÞRC
ðC:18Þ
The condition for the last approximation is valid for A0 c1 (which is always the
case) and A0R cRf (which is usually the case)
...
Numerical example
...
The component values should satisfy Rf/R 5 102 and
RfC 5 1/200π, accomplished by, for instance Rf 5 100R 5 100 kΩ and C 5 16 nF
...
10 shows the frequency characteristic for this design, based on a simulation
with an ideal and a real operational amplifier
...
C
...
2
Differentiator
The transfer of the basic differentiator, taking into account the finite gain of the
operational amplifier, is given by:
Vo
A
5 2jωRCU
Vi
1 1 A 1 jωRC
ðC:19Þ
Figure C
...
Appendix C
305
Figure C
...
(C
...
For A 5 A0 and A0 c1 this is:
Vo
A0
jωRC=A0
5 2A0
5 2jωRCU
Vi
1 1 A0 1 jωRC
1 1 jωRC=A0
ðC:20Þ
This corresponds to a first-order high-pass characteristic with cut-off frequency
at ω 5 A0/RC
...
For much
lower frequencies the transfer function is just 2 jωRC and corresponds to that of an
ideal differentiator
...
(C
...
Numerical example
...
1 at 1 rad/s
...
Suppose the amplifier properties are:
A0 5 105, unity gain bandwidth 105 rad/s
...
11 presents the calculated characteristic for this example
...
Figure C
...
e
...
Component values in this simulation are R 5 100 kΩ, C 5 1 μF
...
11 are due to different amplifier parameters A0 and τ A of the real
amplifier
...
Therefore the differentiating range should
be limited to some upper frequency, well below the cut-off frequency of the
306
Appendix C
Figure C
...
(C
...
Figure C
...
operational amplifier
...
13
...
(C
...
13 Modified or ‘tamed’
differentiator
...
14 Frequency characteristic of
the compensated differentiator according
to Eq
...
24)
...
Same values as for the uncompensated differentiator and
Rs 5 R/100
...
(C
...
14
...
The differentiation range runs from very low frequencies up to about 1000 rad/s
...
15 shows the effect of a taming resistor, here 100 Ω
...
Further note the big difference between an ideal operational amplifier and a real type
...
7
Filters
Removing unwanted signal components (noise, interference, intermodulation products, etc
...
Simple filters consist of passive components only
...
In such cases active filters (with operational
amplifiers) are preferred, providing independent choices for various filter parameters (input and output impedance, cut-off frequency, gain)
...
15 Simulation of a tamed differentiator with an ideal and a real operational
amplifier
...
16 Active band-pass filter
...
Figure C
...
Assuming ideal operational amplifier characteristics the transfer function is:
Vo
Z2
jωR2 C1
R2 jωR1 C1
1
52
52 52
Vi
Z1
ð1 1 jωR1 C1 Þð1 1 jωR2 C2 Þ
R1 1 1 jωR1 C1 1 1 jωR2 C2
ðC:25Þ
so a combination of gain (2R2/R1), low-pass filter (fl 5 1/2πR2C2) and high-pass
filter (fh 5 1/2πR1C1)
...
17 shows the transfer function (frequency characteristic) obtained by simulation with an ideal and a low-cost operational amplifier
...
6 nF
...
Appendix C
309
Figure C
...
16
...
18 Sallen-Key low-pass filter
...
18 shows a second-order low-pass filter of the ‘Sallen-Key’
configuration
...
The general transfer function of a Butterworth filter of
order 2n is:
Vo
1
5 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
V
i
1 1 ðω=ωc Þ2n
ðC:27Þ
For n 5 1 the Butterworth condition is C1/C2 5 (R1 1 R2)2/2R1R2
...
The cut-off frequency is fc 5 1/2πRC1
...
19
depicts a simulation of such a filter, with a cut-off frequency of 1 kHz (by making
R1 5 1 kΩ and C1 5 160 nF)
...
19 Transfer characteristic of the Butterworth filter from Figure C
...
Here, the influence of the finite unity gain bandwidth of the operational amplifier
is clearly visible and limits a proper filter function to about 20 kHz in this example
...
To obtain better selectivity, higher order filters
can be obtained by simply cascading (putting in series) filters of lower order
...
Note that the attenuation in the pass-band is also n times more compared to
that of a first-order filter
...
18 results in a slope of 236 dB/octave
...
L
Title: Sensors for Mechatronics
Description: Provides a clear and practical overview of sensor use in mechatronics for all levels of engineers and students
Description: Provides a clear and practical overview of sensor use in mechatronics for all levels of engineers and students