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Vehicle Fundamentals

 Forces acting on a vehicle
Newton’s second law for vehicle
traction

Ft: traction force
Ftr: resistance force
Mv: total mass
δ: mass factor
V: vehicle speed

 Vehicle Resistance
Vehicle resistance opposing its movement includes rolling resistance of the tires rolling resistance
torque Trf and Trr, aerodynamic drag Fw, and grading resistance (Mv g sinα)

 Rolling Resistance

Tire deflection and rolling resistance on a (a) hard and (b) soft road surface

The rolling resistant moment;

To keep the wheel rolling, a force F, acting on the center of the wheels, is required to
balance this rolling resistant moment
...


The equivalent force is called rolling resistance with a magnitude of

where P is the normal load, acting on the center of the rolling wheel When a vehicle is operated on
a slope road, the normal load, P, should be replaced by the component, which is perpendicular to
the road surface
...
Based on
experimental results, many empirical formulae have been proposed for calculating the rolling
resistance on a hard surface
...

Range of inflation pressure:

This equation predicts the values of fr with acceptable accuracy for speeds up to 128 km/h
...
This force is
referred to as aerodynamic drag
...

Shape drag: The forward motion of the vehicle pushes the air in front of it
...
In between, air molecules move at a wide range of speeds
...

Aerodynamic drag is a function of vehicle speed V, vehicle frontal area Af , shape of the vehicle, and air
density ρ
...


The aerodynamic drag coefficients for a few types of vehicle body shapes are shown in Figure
...
This grading force is usually called
grading resistance
...
The grade is defined as

In some literature, the tire rolling resistance and grading resistance together are called road resistance,
which is expressed as

When the road angle is small, the road resistance can be simplified as

 Dynamic Equation
In the longitudinal direction, the major external forces acting on a two-axle vehicle, include the
rolling resistance of front and rear tires Frf and Frr, which are represented by rolling resistance
moment Trf and Trr, aerodynamic drag Fω, grading resistance Fg (Mv g sinα), and tractive effort of the
front and rear tires, Ftf and Ftr
...
The dynamic equation of vehicle motion along the longitudinal direction
is expressed by

where dV/dt is the linear acceleration of the vehicle along the longitudinal direction and Mv is the
vehicle mass
...


where rd is the effective radius of the wheel
...


where fr is the coefficient of the rolling resistance, coefficient of road adhesion μ
...
In traction, the speed V is less than rω, therefore,
the slip of the tire has a positive value between 0 and 1
...
During braking, however, the tire slip would be
defined as

which has a positive value between 0 and 1
...
The maximum traction effort of a tire
corresponding to a certain tire slip is usually expressed as

where P is the vertical load of the tire and μ is the tractive effort coefficient, which is a function of tire slip
...


Behavior of a tire under the action of driving torque

For normal driving, the slip of the tire must be limited in a range less than 15–20%
...


 Power Train Tractive Effort and Vehicle Speed
Conceptual illustration of an automobile power train;

The torque on the driven wheels, transmitted from the power plant, is expressed as

where ig is the gear ratio of the transmission defined as ig=Nin/Nout (Nin; input rotating speed, Nout;
output rotating speed), i0 is the gear ratio of the final drive, ηt is the efficiency of the driveline from
the power plant to the driven wheels, and Tp is the torque output from the power plant
...
The
following are representative values of the mechanical efficiency of various components:
Clutch: 99%
Each pair of gears: 95–97%
Bearing and joint: 98–99%
The total mechanical efficiency of the transmission between the engine output shaft and drive wheels or sprocket
is the product of the efficiencies of all the components in the driveline
...
The translational speed of the wheel center (vehicle speed) can be
expressed as

 Vehicle Power Plant and Transmission Characteristics

Power Plant Characteristics
For vehicular applications, the ideal performance characteristic of a power plant is the constant power
output over the full speed range
...


Since the internal combustion engine and electric motor are the most commonly used power plants for
automotive vehicles to date, it is appropriate to review the basic features of the characteristics that are
essential to predicating vehicle performance and driveline design
...


A multigear transmission is usually employed to modify it, as shown in Figure

A single-gear or double-gear transmission is usually employed, as shown in Figure

Transmission Characteristics
The transmission requirements of a vehicle depend on the characteristics of the power plant and the
performance requirements of the vehicle
...

Manual Gear Transmission
Manual gear transmission consists of a clutch, gearbox, final drive, and drive shaft
...

The number of the gear ng is known, the factor Kg can be determined as

and each gear ratio can be obtained by

For passenger cars, to suit changing traffic conditions,
the step between the ratios of the upper two gears is
often a little closer than that based on upper
equations
...
They consist of a torque converter and an automatic gearbox
...


The major advantages of hydrodynamic transmission :
• When properly matched, the engine will not stall
...

• Together with a suitably selected multispeed gearbox, it provides torque–speed characteristics that
approach the ideal
...
The variation of the capacity factor with speed
for a typical engine
...
That is,

The matching procedure begins with specifying the engine speed and engine torque
...


For a particular value of the input capacity factor of the torque converter, Ktc, the converter speed ratio, Csr,
and torque ratio, Ctr, can be determined from the torque converter performance characteristics
...


Continuously Variable Transmission
A continuously variable transmission (CVT) has a gear ratio that can be varied continuously within a certain
range, thus providing an infinity of gear ratios
...


 Vehicle Performance
The performance of a vehicle is usually described by its maximum cruising speed, gradeability, and
acceleration
...
The
tractive effort and resistance equilibrium can be expressed as

The maximum speed of the vehicle can be written as

where np max and ig min are the maximum speed of the engine (electric motor) and the minimum gear
ratio of the transmission, respectively
...
For heavy commercial vehicles or
off-road vehicles, the gradeability is usually defined as the maximum grade or grade angle in the whole
speed range
...
While the vehicle drives on a road with a large grade, the gradeability of
the vehicle can be calculated as

Acceleration Performance
The acceleration performance of a vehicle is usually described by its acceleration time and the distance
covered from zero speed to a certain high speed (zero to 96 km/h or 60 mph, for example) on level
ground
...
The mass factor can be written as

where Iω is the total angular moment of the wheels and Ip is the total angular moment of the rotating
components associated with the power plant
...
In the case where these values are not
known, the mass factor, δ, for a passenger car would be estimated using the following empirical relation:

From equation a=dV/dt, the acceleration time, ta, and distance, Sa, from low speed V1 to high speed V2 can
be written, respectively, as

 Operating Fuel Economy
The fuel economy of a vehicle is evaluated by the amount of fuel consumption per 100 km traveling
distance (liters/100 km) or mileage per gallon fuel consumption (miles/gallon), which is currently used
in the U
...
The operating fuel economy of a vehicle depends on a number of factors, including fuel
consumption characteristics of the engine, gear number and ratios, vehicle resistance, vehicle speed,
and operating conditions
...
The typical fuel economy characteristic of
a gasoline engine is shown in Figure
...


Calculation of Vehicle Fuel Economy
Vehicle fuel economy can be calculated by finding the load power and the specific fuel consumption
of the engine
...
The total fuel consumption within a total distance, S, at a constant cruising speed, V, is obtained by

The Figure shows an example of the fuel economy characteristics of a gasoline vehicle at constant
cruising speed on level ground
...
This figure also indicates
that with a high-speed gear (small gear ratio), the fuel economy of the vehicle can be enhanced due to
the reduced engine speed at a given vehicle speed and increased gear ratio
...
It indicates that the engine has a much lower operating efficiency in low gear
than in high gear
...


It should be noted that because of the complexity of vehicle operation in the real world, fuel consumption at
constant speed cannot accurately represent fuel consumption for a vehicle under real driving conditions
...
The drive cycles are usually represented by the
speed of the vehicle along with the relative driving time
...
S
...


Basic Techniques to Improve Vehicle Fuel Economy
The effort to improve the fuel economy of vehicles has been an ongoing process in the automobile industry
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In urban driving, a significant amount of energy is consumed in braking
...
The brake pad is pressed against the brake plate, thus developing
a frictional torque on the brake plate
...


Braking Distribution on Front and Rear Axles
The Figure shows the forces acting on a vehicle during braking on a flat road
...
j is the deceleration of the vehicle during braking, which can be easily expressed as

where Fbf and Fbr are the braking forces acting on front and rear wheels, respectively
...

The braking forces of the front and rear axle should be proportional to their normal load, respectively; thus, one
obtains

In vehicle design, the actual braking forces on the front and rear axle are usually designed to have a fixed linear
proportion
...
With β being the actual braking force on
the front and rear axle, this can be expressed as

Thus, one obtains

Figure shows the ideal and actual braking force distribution curves (labeled I and β curves)
...
This point
represents one specific road adhesive coefficient, μ0
...
The figure shows the top view of a two-axle vehicle acted upon by the braking force and the
inertia force

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