Executive Summary:
The dynamics of motor
vehicle motion is an important field of study as it relates to safety, accident
investigation and general ground vehicle performance. Aircraft are free to fly
in the air, while ships can move freely on the water surface. In the same way,
the road vehicle is free to move, by steering its wheels, and shares
similarities with aircraft and ships, in the sense that its movements are
unrestricted. From the viewpoint of dynamic motion, the similarity lies in the
fact that these three moving bodies receive forces generated by their own
movement that are used to accomplish the desired movement. Aircraft depend on
the lift force caused by the relative motion of its wings and the air; ships
rely on the lift force brought by the relative motion of its body and the
water; and ground vehicles rely on the wheel lateral force created by the
relative motion of the wheels and the road. For the study of vehicle dynamics
and control, a typical vehicle mathematical model is assumed. This vehicle
model has wheels that are steerable: two at the front and two at the rear,
which are fitted to a rigid body. Passenger cars, trucks, 1 bus, and
agricultural vehicles all fall into this category. At first sight, it may seem
that there are no common dynamics among these vehicles, but by applying a
simple four-wheeled vehicle model, as in Fig. 1.1, it is possible to obtain
fundamental knowledge of the dynamics of all these vehicles. In the vehicle
mathematical model, which is presented in Fig. 1.1, the wheels are regarded as
weightless, and the rigid body represents the total vehicle weight. The
coordinate system is fixed to the vehicle, the x-axis in the longitudinal
direction, the y-axis in the lateral direction, and the z-axis in the vertical
direction, with the origin at the vehicle center of gravity. Generally, when a
vehicle is traveling in a straight line, the heading direction of the wheel
coincides with the traveling direction. In other words, the wheel traveling
direction is in line with the wheel rotational plane. However, when the vehicle
has lateral motion and/or yaw motion, the traveling direction can be out of
line with the rotational plane.
Chapter
One
Vehicle
Design and Manufacturing
1.
Introduction
Ground vehicles can be divided into two main categories: vehicles that
are restricted by a track set on the ground (e.g., the railway vehicles) and
vehicles that are unrestricted by tracks, free to move in any direction on the
ground by steering the wheels (e.g., road vehicles). Aircraft are free to fly
in the air, while ships can move freely on the water surface. In the same way,
the road vehicle is free to move, by steering its wheels, and shares
similarities with aircraft and ships, in the sense that its movements are
unrestricted. From the viewpoint of dynamic motion, the similarity lies in the
fact that these three moving bodies receive forces generated by their own
movement that are used to accomplish the desired movement. Aircraft depend on
the lift force caused by the relative motion of its wings and the air; ships
rely on the lift force brought by the relative motion of its body and the
water; and ground vehicles rely on the wheel lateral force created by the
relative motion of the wheels and the road. In the above described manner, the
dynamics and control of the three moving bodies are closely related to their
natural function, whereby for an airplane, it is established as flight
dynamics, a ship as ship dynamics, and a vehicle, similarly, as vehicle
dynamics. The vehicle studied in this book, is a vehicle, similar to the
airplane and ship that is capable of independent motion on the ground, using
the forces generated by its own motion.
1.2
Design
Introducing a new model of automobile generally takes three to five
years from inception to assembly. Ideas for new models are developed to respond
to unmet pubic needs and preferences. Trying to predict what the public will
want to drive in five years is no small feat, yet automobile companies have
successfully designed automobiles that fit public tastes. With the help of
computer-aided design equipment, designers develop basic concept drawings that
help them visualize the proposed vehicle's appearance. Based on this
simulation, they then construct clay models that can be studied by styling
experts familiar with what the public is likely to accept. Aerodynamic
engineers also review the models, studying air-flow parameters and doing
feasibility studies on crash tests. Only after all models have been reviewed
and accepted are tool designers permitted to begin building the tools that will
manufacture the component parts of the new model.
1.3
The Manufacturing Process:
1.3.1
Components
- 1 The
automobile assembly plant represents only the final phase in the process
of manufacturing an automobile, for it is here that the components
supplied by more than 4,000 outside suppliers, including company-owned
parts suppliers, are brought together for assembly, usually by truck or
railroad. Those parts that will be used in the chassis are delivered to
one area, while those that will comprise the body are unloaded at another.
Fig 01: Components of Motor Vehicle
1.3.2
Chassis
2 The typical
car or truck is constructed from the ground up (and out). The frame forms the
base on which the body rests and from which all subsequent assembly components
follow. The frame is placed on the assembly line and clamped to the conveyer to
prevent shifting as it moves down the line. From here the automobile frame
moves to component assembly areas where complete front and rear suspensions,
gas tanks, rear axles and drive shafts, gear boxes, steering box components,
wheel drums, and braking systems are sequentially installed.
Fig
02: Workers install engines on
Model Ts at a Ford Motor Company plant. The photo is from about 1917.
The automobile, for decades the quintessential American industrial
product, did not have its origins in the United States. In 1860, Etienne
Lenoir, a Belgian mechanic, introduced an internal combustion engine that
proved useful as a source of stationary power. In 1878, Nicholas Otto, a German
manufacturer, developed his four-stroke "explosion" engine. By 1885,
one of his engineers, Gottlieb Daimler, was building the first of four
experimental vehicles powered by a modified Otto internal combustion engine. Also
in 1885, another German manufacturer, Carl Benz, introduced a three-wheeled,
self-propelled vehicle. In 1887, the Benz became the first automobile offered
for sale to the public. By 1895, automotive technology was dominated by the
French, led by Emile Lavassor. Lavassor developed the basic mechanical
arrangement of the car, placing the engine in the front of the chassis, with
the crankshaft perpendicular to the axles.
In 1896, the Duryea Motor Wagon became the first production motor
vehicle in the United States. In that same year, Henry Ford demonstrated his
first experimental vehicle, the Quadricycle. By 1908, when the Ford Motor
Company introduced the Model T, the United States had dozens of automobile
manufacturers. The Model T quickly became the standard by which other cars were
measured; ten years later, half of all cars on the road were Model Ts. It had a
simple four-cylinder, twenty-horsepower engine and a planetary transmission
giving two gears forward and one backward. It was sturdy, had high road
clearance to negotiate the rutted roads of the day, and was easy to operate and
maintain.
- 3 An
off-line operation at this stage of production mates the vehicle's engine
with its transmission. Workers use robotic arms to install these heavy
components inside the engine compartment of the frame. After the engine
and transmission are installed, a
Fig
03: Vehicle Installation
On automobile assembly lines, much of the work is now done by robots
rather than humans. In the first stages of automobile manufacture, robots weld
the floor pan pieces together and assist workers in placing components such as
the suspension onto the chassis.
Worker attaches the radiator, and another bolts it into place. Because
of the nature of these heavy component parts, articulating robots perform all
of the lift and carry operations while assemblers using pneumatic wrenches bolt
component pieces in place. Careful ergonomic studies of every assembly task
have provided assembly workers with the safest and most efficient tools
available.
1.3.3
Body
- 4
Generally, the floor pan is the largest body component to which a
multitude of panels and braces will subsequently be either welded or
bolted. As it moves down the assembly line, held in place by clamping
fixtures, the shell of the vehicle is built. First, the left and right quarter
panels are robotically disengaged from pre-staged shipping containers and
placed onto the floor pan, where they are stabilized with positioning
fixtures and welded.
5 The front and
rear door pillars, roof, and body side panels are assembled in the same
fashion. The shell of the automobile assembled in this section of the process
lends itself to the use of robots because articulating arms can easily
introduce various component braces and panels to the floor pan and perform a
high number of weld operations in a time frame and with a degree of accuracy no
human workers could ever approach. Robots can pick and load 200-pound (90.8
kilograms) roof panels and place them precisely in the proper weld position
with tolerance variations held to within .001 of an inch. Moreover, robots can
also tolerate the
Fig
04: Body Construction
The body is built up on a separate assembly line from the chassis.
Robots once again perform most of the welding on the various panels, but human
workers are necessary to bolt the parts together. During welding, component
pieces are held securely in a jig while welding operations are performed. Once
the body shell is complete, it is attached to an overhead conveyor for the
painting process. The multi-step painting process entails inspection, cleaning,
undercoat (electrostatically applied) dipping, drying, topcoat spraying, and
baking. smoke, weld flashes, and gases created during this phase of production.
6 As the body moves from the isolated weld area of the assembly line,
subsequent body components including fully assembled doors, deck lids, hood
panel, fenders, trunk lid, and bumper reinforcements are installed. Although
robots help workers place these components onto the body shell, the workers
provide the proper fit for most of the bolt-on functional parts using
pneumatically assisted tools.
Fig
05: Body of a Motor Vehicle
1.3.4
Paint
- 7 Prior to
painting, the body must pass through a rigorous inspection process, the body
in white operation. The shell of the vehicle passes through a brightly
lit white room where it is fully wiped down by visual inspectors using
cloths soaked in hi-light oil. Under the lights, this oil allows
inspectors to see any defects in the sheet metal body panels. Dings,
dents, and any other defects are repaired right on the line by skilled
body repairmen. After the shell has been fully inspected and repaired, the
assembly conveyor carries it through a cleaning station where it is
immersed and cleaned of all residual oil, dirt, and contaminants.
- 8 As the
shell exits the cleaning station it goes through a drying booth and then
through an undercoat dip—an electrostatically charged bath of undercoat paint (called the
E-coat) that covers every nook and cranny of the body shell, both
inside and out, with primer. This coat acts as a substrate surface to
which the top coat of colored paint adheres.
- 9 After the
E-coat bath, the shell is again dried in a booth as it proceeds on to the
final paint operation. In most automobile assembly plants today, vehicle
bodies are spray-painted by robots that have been programmed to apply the
exact amounts of paint to just the right areas for just the right length
of time. Considerable research and programming has gone into the dynamics
of robotic painting in order to ensure the fine "wet" finishes
we have come to expect. Our robotic painters have come a long way since
Ford's first Model Ts, which were painted by hand with a brush.
- 10 Once the
shell has been fully covered 1 V with a base coat of color paint
and a clear top coat, the conveyor transfers the bodies through baking
ovens where the paint is cured at temperatures exceeding 275 degrees
Fahrenheit (135 degrees Celsius).
Fig
06: Painting
The body and chassis assemblies are mated near the end of the production
process. Robotic arms lift the body shell onto the chassis frame, where human
workers then bolt the two together. After final components are installed, the
vehicle is driven off the assembly line to a quality checkpoint.
After the shell leaves the paint area it is ready for interior assembly.
1.3.5
Interior assembly
- 11 The
painted shell proceeds through the interior assembly area where workers
assemble all of the instrumentation and wiring systems, dash panels,
interior lights, seats, door and trim panels, headliners, radios,
speakers, all glass except the automobile windshield, steering
column and wheel, body weather strips, vinyl tops, brake and gas pedals,
carpeting, and front and rear bumper fascias.
- 12 Next,
robots equipped with suction cups remove the windshield from a shipping
container, apply a bead of urethane sealer to the perimeter of the glass,
and then place it into the body windshield frame. Robots also pick seats
and trim panels and transport them to the vehicle for the ease and
efficiency of the assembly operator. After passing through this section
the shell is given a water test to ensure the proper fit of door panels,
glass, and weather stripping. It is now ready to mate with the chassis.
Fig 07: Interior Design
1.3.6
Mate
- 13 The
chassis assembly conveyor and the body shell conveyor meet at this stage
of production. As the chassis passes the body conveyor the shell is
robotically lifted from its conveyor fixtures and placed onto the car
frame. Assembly workers, some at ground level and some in work pits
beneath the conveyor, bolt the car body to the frame. Once the mating
takes place the automobile proceeds down the line to receive final trim
components, battery, tires, anti-freeze, and gasoline.
- 14 The
vehicle can now be started. From here it is driven to a checkpoint off the
line, where its engine is audited, its lights and horn checked, its tires
balanced, and its charging system examined. Any defects discovered at this
stage require that the car be taken to a central repair area, usually
located near the end of the line. A crew of skilled trouble-shooters at
this stage analyze and repair all problems. When the vehicle passes final
audit it is given a price label and driven to a staging lot where it will
await shipment to its destination.
1.4
Quality Control
All of the components that go into the automobile are produced at other
sites. This means the thousands of component pieces that comprise the car must
be manufactured, tested, packaged, and shipped to the assembly plants, often on
the same day they will be used. This requires no small amount of planning. To
accomplish it, most automobile manufacturers require outside parts vendors to
subject their component parts to rigorous testing and inspection audits similar
to those used by the assembly plants. In this way the assembly plants can
anticipate that the products arriving at their receiving docks are Statistical
Process Control (SPC) approved and free from defects.
Once the component parts of the automobile begin to be assembled at the
automotive factory, production control specialists can follow the progress of
each embryonic automobile by means of its Vehicle Identification Number
(VIN), assigned at the start of the production line. In many of the more
advanced assembly plants a small radio frequency transponder is attached to the
chassis and floor pan. This sending unit carries the VIN information and
monitors its progress along the assembly process. Knowing what operations the
vehicle has been through, where it is going, and when it should arrive at the
next assembly station gives production management personnel the ability to
electronically control the manufacturing sequence. Throughout the assembly
process quality audit stations keep track of vital information concerning the
integrity of various functional components of the vehicle.
This idea comes from a change in quality control ideology over the
years. Formerly, quality control was seen as a final inspection process that
sought to discover defects only after the vehicle was built. In contrast, today
quality is seen as a process built right into the design of the vehicle as well
as the assembly process. In this way assembly operators can stop the conveyor
if workers find a defect. Corrections can then be made, or supplies checked to
determine whether an entire batch of components is bad. Vehicle recalls are
costly and manufacturers do everything possible to ensure the integrity of
their product before it is shipped to the customer. After the vehicle is
assembled a validation process is conducted at the end of the assembly line to
verify quality audits from the various inspection points throughout the
assembly process. This final audit tests for properly fitting panels; dynamics;
squeaks and rattles; functioning electrical components; and engine, chassis,
and wheel alignment. In many assembly plants vehicles are periodically pulled
from the audit line and given full functional tests. All efforts today are put
forth to ensure that quality and reliability are built into the assembled
product.
Fig
08: Stress of a Vehicle
1.5
The Future
The development of the electric automobile will owe more to innovative
solar and aeronautical engineering and advanced satellite and radar technology
than to traditional automotive design and construction. The electric car has no
engine, exhaust system, transmission, muffler, radiator, or spark plugs. It
will require neither tune-ups nor—truly revolutionary—gasoline. Instead, its
power will come from alternating current (AC) electric motors with a brushless
design capable of spinning up to 20,000 revolutions/minute. Batteries to power
these motors will come from high performance cells capable of generating more
than 100 kilowatts of power. And, unlike the lead-acid batteries of the past
and present, future batteries will be environmentally safe and recyclable.
Integral to the braking system of the vehicle will be a power inverter that
converts direct current electricity back into the battery pack system once the
accelerator is let off, thus acting as a generator to the battery system even
as the car is driven long into the future.
The growth of automobile use and the increasing resistance to road
building have made our highway systems both congested and obsolete. But new
electronic vehicle technologies that permit cars to navigate around the
congestion and even drive themselves may soon become possible. Turning over the
operation of our automobiles to computers would mean they would gather
information from the roadway about congestion and find the fastest route to
their instructed destination, thus making better use of limited highway space.
The advent of the electric car will come because of a rare convergence of
circumstance and ability. Growing intolerance for pollution combined with
extraordinary technological advancements will change the global transportation
paradigm that will carry us into the twenty-first century.
1.6
Virtual Four-Wheel Vehicle Model
For the study of vehicle dynamics and control, a typical vehicle
mathematical model is assumed. This vehicle model has wheels that are
steerable: two at the front and two at the rear, which are fitted to a rigid
body. Passenger cars, trucks, 1 buses, and agricultural vehicles all fall into
this category.At first sight, it may seem that there are no common dynamics
among these vehicles, but by applying a simple four-wheeled vehicle model, it
is possible to obtain fundamental knowledge of the dynamics of all these
vehicles. In the vehicle mathematical model, which is presented in the wheels are
regarded as weightless, and the rigid body represents the total vehicle weight.
The coordinate system is fixed to the vehicle, the x-axis in the longitudinal direction,
the y-axis in the lateral direction, and the z-axis in the vertical direction,
with the origin at the vehicle center of gravity. With this coordinate system,
the vehicle motion has six independent degrees of freedom:
1. vertical motion in z direction,
2. left and right motion in y direction,
3. longitudinal motion in x direction,
4. rolling motion around x-axis,
5. pitching motion around y-axis,
6. yawing motion around z-axis.
These can be divided into two main groups. One group consists of 1, 3,
and 5 motions, which are the motions generated without direct relation to the
steering. Motion 1 is the vertical motion caused by an uneven ground/road surface
and is related to the vehicle ride. Motion 3 is the longitudinal, straight-line
motion of the vehicle due to traction and braking during acceleration or
braking. Motion 5 is the motion caused by either road unevenness, acceleration
or braking and is also related to the vehicle ride. Motions 2 and 6, the yaw
and lateral movements, are generated initially by steering the vehicle. Motion
4 is generated mainly by motions 2 and 6 but could occur due to road unevenness
as well. As described earlier, the vehicle studied in this text can move freely
in any direction on the ground, by steering the vehicle. The main behaviors
studied here are motions 2, 4, and 6, which are caused by the steering of the
vehicle.
Fig
09: Vehicle dynamics model.
Chapter
Two
Motion
and Force
2.
Control of Motion
For normal vehicles, motions are controlled by the driver. The lateral,
yaw, and roll motions of the vehicle are generated by the driver’s steering and
depend on its dynamic characteristics. This doesn’t mean that the driver is
steering the vehicle meaninglessly. The driver is continuously looking at the
path in front, either following his target path, or setting a new target path
to follow. The driver is observing many things, such as the current position of
the vehicle with reference to the target path and the current vehicle motion.
The driver is also predicting the imminent vehicle behavior. Based on this
information, the driver decides and makes the suitable steer action. In this
manner, the vehicle generates its motion in accordance to a target path that is
a given or path set by the driver. The vehicle that is capable of free motion
within a plane, without direct restrictions from preset tracks on the ground,
only produces a meaningful motion when it is acted on by suitable steering
control from the driver. The primary interest now lies on the inherent dynamic
characteristics of the vehicle itself. This becomes clear from the motion of
the vehicle to a certain steering input. Next is to study this vehicle’s
characteristics when it is controlled by a human driver. Finally, the aim is to
explore the vehicle dynamic characteristics that make it easier for the driver
to control the vehicle.
2.1
Tire and side-slip angle
Generally, when a vehicle is traveling in a straight line, the heading
direction of the wheel coincides with the traveling direction. In other words,
the wheel traveling direction is in line with the wheel rotational plane.
However, when the vehicle has lateral motion and/or yaw motion, the traveling
direction can be out of line with the rotational plane is the wheel looked at
from the top, where (a) is when the traveling direction is in line with the
rotation plane, and (b) is when it is not.
(a)
(b)
Fig
10: Vehicle
tire in motion.
The wheel in (b) is said to have side slip. The angle between the wheel
traveling direction and the rotational plane, or its heading direction, is
called the side-slip angle. The wheel is also acted on by a traction force if
the wheel is moving the vehicle in the traveling direction, or braking force if
braking is applied. Also, a rolling resistance force is always at work. If the
wheel has side slip, as in (b), a force that is perpendicular to its rotation
plane is generated. This force could be regarded as a reaction force that
prevents side slip when the wheel produces a side-slip angle. This is an
important force that the vehicle depends on for its independent motion.
Normally, this force is called the lateral force, while the component that is
perpendicular to the wheel rotation plane, is called the cornering force. When
the side-slip angle is small, these two are treated as the same. This force
corresponds to the lift force, explained in fluid dynamics, which acts on a
body that travels in a fluid at an attack angle, as shown in. There are many
kinds of wheels, but all produce a force perpendicular to the rotation plane,
when rotated with side slip. The schematic comparison of the lateral forces, at
small side-slip angles, for a pneumatic tire wheel, a solid rubber-tire wheel,
and an iron wheel. From here, it is clear that the magnitude of the force
produced depends on the type of wheel and is very different. In particular, the
maximum possible force produced by an iron wheel is less than 1/3rd of that
produced by a rubber tire wheel. Compared to a solid rubber-tire wheel, a
pneumatic tire wheel produces a larger force. For independent motion of the
vehicle, the force that acts on a wheel with side slip is desired to be as
large as possible. For this reason, the traveling vehicle that is free to move
in the plane, without external restrictions, is usually fitted with pneumatic
tires. These are fitted for both the purpose of vehicle ride, and for achieving
a lateral force that is available for vehicle handling. In the following
chapter, the pneumatic tire is called the tire, and the mechanism for
generating a lateral force that acts on a tire with side slip is explained.
Fig
11: Lifting force.
2.2
Deformation of tire with side slip and lateral force
Generally, forces act through the contact surface between the tire and
the road. A tire with lateral slip is expected to deform in the tire contact
surface and its outer circumference: (a) shows the front and side views of the
tire deformation; (b) shows the tire contact surface and outer circumference deformation
viewed from the top. At the front of the surface, the deformation direction is
almost parallel to the tire’s traveling direction. In this part, there is no
relative slip to the ground
Fig
12: Lateral forces for several wheels.
A B
Fig
13: Tire deflection with side slip.
When the tire slip angle is small, the whole contact surface is similar
to this and the rear end of the contact surface has the largest lateral
deformation. When the tire slip angle gets bigger, the front of the surface
remains almost parallel to the tire traveling direction. The deformation
reduces near the center of the contact patch, and the lateral deformation
becomes largest at certain point between the front and rear of the surface.
After this maximum, the tire contact surface slips away from the tire
centerline and the lateral deformation does not increase. As tire slip angle
gets even larger, the point where lateral deformation becomes maximum moves rapidly
toward the front. When the slip angle is around 10–12_, the contact surface
that is parallel to the tire travel direction disappears. The contact surface
deformation is nearly symmetric around the wheel center and consists of nearly
all the slip regions. The lateral deformation of the tire causes a lateral
force to act through the contact surface, which is distributed according to the
deformation. This lateral force is sometimes called the cornering force when
the side-slip angle is small. By looking at the tire lateral deformation, the
resultant lateral force may not be aligned with center of the contact surface.
Thus, the lateral force creates a moment around the tire contact surface
center. This moment is called the selfaligning torque and acts in the direction
that reduces the tire slip angle.
2.2.1
Tire camber and lateral force
The angle between the tire rotation plane and the vertical axis is
called the camber angle. If a tire with a camber angle of f is rotated freely on
a horizontal plane, as shown in Fig. 2.5, the tire makes a circle with the
radius of R=sin f and origin at O. If the circular motion is prohibited for a
tire with camber angle, and the tire is forced to travel in a straight line
only, a force will
Fig
14: Tire with camber angle and camber thrust.
act on the tire as shown in the figure. This force, due to the camber
between the tire and the ground, is called camber thrust.
2.2.2 Tire Cornering Characteristics
The
characteristics of the tire that produce lateral force and moment, as elaborated
in Section 2.2, are defined as the cornering characteristics. In this section,
the tire cornering characteristics will be examined in more detail.
2.3 Fiala’s theory
The mathematical
model proposed by Fiala is widely accepted for the above analysis of the
lateral force due to side slip of the tire. It is commonly called Fiala’s
theory and is related to the tire cornering characteristics. It is one of the fundamental
theories used by many people for explaining tire cornering characteristics. Here,
based on Fiala’s theory, the tire cornering characteristics will be studied
theoretically. The tire structure is modeled. A is a stiff body equivalent to
the rim. B is the pneumatic tube and sidewall that can deform elastically in
both vertical and lateral directions. C is the equivalent thin tread base
joined to the sidewall at both sides. D is equivalent to the tread rubber. The tread
rubber is not a continuous circular body, but consists of large numbers of independent
spring bodies around the tire circumference. When a force acts in the lateral
direction at the ground contact surface, the tire will deform in the lateral
direction. The rim is stiff and it will not be deformed, but the tread base
will have a bending deformation in the lateral direction. Moreover, the tread
rubber will be deformed by the shear force between the tread base and ground
surface. shows this kind of deformation in the lateral direction. Assuming that
the tread base deforms equally at the front and rear ends of the ground contact
surface, the line that connects these points is the centerline for the tread
base and is defined as the x-axis. The y-axis is perpendicular to the x-axis
and positioned at the front end point. The x-axis is parallel to the tire rim centerline
and also the tread base centerline before deformation.
Fig15: Tire
structural model.
2.4 Effects
2.4.1 Effects of
Vertical Load and Road Condition
The effect of
tire vertical load on lateral force is also shown in. The tire vertical load
has almost no effect on lateral force at very small side-slip angles. The
different saturation levels of lateral force become more obvious with larger side-slip
angles. The mathematical model shows that the tire load only affects lateral
force in the region where there is relative slip between the tread rubber and
the ground. When this region occupies the majority of the contact surface, i.e.,
side-slip angle is large, the lateral force approaches the product of m and W, and
so, the effect of W is remarkable. Figure
shows the effect of the tire vertical load effect on lateral force. Next is to
study the effect of the tire vertical load on the tire cornering stiffness.
when the tire load is small, the cornering stiffness increases together with
the tire load, but after a certain limit, it seems to decrease. The cornering
stiffness, divided by the corresponding tire load, is called the cornering
stiffness coefficient. This cornering stiffness coefficient decreases with tire
load almost linearly, In relation to tire load, cornering stiffness could be
approximated as a parabolic that passes through the origin. Cornering stiffness
increases with tire load to a peak value and beyond that it decreases. Tires
are normally used in the region where cornering stiffness increases with
vertical load. The dependence of tire cornering stiffness on tire load for a
real tire. The approximation to a parabolic is verified. Usually, the effect of
the tire vertical load is expressed in the form of mW: The friction coefficient
between the tread rubber and ground, m; is expected to have an effect similar
to the tire vertical load. The effects of the road surfaces on the cornering
force as it changes with side-slip angle. From the figure, it can be seen that
the friction coefficient has almost no effect on lateral force at small
side-slip angles, but has a more obvious effect as side-slip angles get larger.
The effect of friction coefficient on the lateral force is very similar to the
vertical.
Fig 16: Effects
of road surface on lateral force.
2.4.2 Tire Pressure
Effects
From analysis of
the mathematical model, it is clear that the tire lateral force becomes larger
with a smaller tread base displacement under a constant force. From Equation, y
becomes smaller with smaller a3l2=ð2kÞ: If k, the spring constant of the spring
support, is large, and the tread base bending stiffness, EI, is also large,
then the tread base displacement is small. Since spring constant, k, depends on
tire air pressure, it is expected that cornering force also increases with tire
pressure. However, the increase of tire pressure reduces the contact surface
length, l, and Eqn (2.15) shows that the lateral force decreases with a
decrease in contact length. Figure 16 is a good example of the relationship
between lateral force and tire pressure. The increase of tire pressure
contributes to the increase of k and an increase in the lateral force is
expected; however, the reduction of the contact length, l, due to the increase
of the tire pressure decreases the lateral force. Eventually, it is interesting
to see that the lateral force is almost constant with the variation in the tire
pressure in this case. The above point is shown in more detail by the relation
of the cornering stiffness to the tire pressure. If the vertical load is
relatively low, the decrease in contact length contributes more than the
increase of k as the tire pressure increases. In this case, the cornering
stiffness decreases with an increase in tire pressure. On the other hand, if the
vertical load is relatively high, the effect of the increasing k is dominant
compared with the decrease in the contact length and the cornering stiffness
increases with the tire pressure. However, with even higher vertical loads, the
excessive increase of the tire pressure has a greater effect on the contact
length reduction and the cornering stiffness decreases with the increase of the
tire pressure
2.4.3 Tire Shape
Effects
The tread base
bending stiffness, EI, is decided by the tire shape. If the tire material and
the construction are given, the shape effect is dominated by the moment of
inertia, I, of the tread base. This is generally larger for a larger tire. For
tires with the same radius, it is larger for flatter tires with larger width. Therefore,
low profile tires are desirable for obtaining larger cornering force. The
cornering stiffness increases when b is larger and d is smaller. Figure 17 is
an example of the relationship between the cornering stiffness and the tread
depth, which corresponds to the tread rubber thickness. From this figure, the
increase in cornering stiffness is seen for a tire with smaller d, i.e., with
worn tread.
Fig 17: Effect
of tire slit depth on cornering stiffness.
2.4.4 Braking and
Traction Force Effects
The effects of
tire parameters and vertical load on the lateral force have already been
studied. During braking or traction, the tire is acted on by the vertical load that
supports the vehicle weight and the longitudinal force at the contact surface that
accelerates or stops the vehicle. These forces also affect the lateral force. Based
on the classical Law of Friction, and as shown in Fig.18, the lateral force, F,
and traction force (or braking force) T, acting on a tire, must always satisfy
the following equation.
Fig 18: Friction
circle.
In other words,
the resultant of the horizontal, in-plane, forces that act on the contact surface
between the tire and the ground cannot exceed the product of the tire load and
the friction coefficient. This means that the resultant force vector is
restricted to be inside a circle with radius mW: This circle is called the
friction circle. If there is a longitudinal force, either traction force or
braking force, acting on the tire, the maximum cornering force, for a large
side-slip angle, is given by,
and, if T ¼ 0,
then the above is the same as in Eqn (2.25). The relation of lateral force, F0,
to side-slip angle, when traction or braking force is zero, is given by the
line O–A0 in Fig. 2.25. The relation of lateral force to side-slip angle, when
traction (or braking) force, T, is at work, is given by line O–A in the same
figure. If the reduction ratio of lateral force due to traction (or braking)
force is assumed to be the same at any side-slip angle.
2.5 Self-aligning torque
The theoretical
analysis with the mathematical model shows that when the sideslip angle is
small, the self-aligning torque increases linearly with side-slip angle, but
when side-slip angle is large, the self-aligning torque approaches saturation
and reaches its peak at a certain value. After this point, the self aligning torque
decreases with side-slip angle. Figure 19 is a typical example of the relation
between self-aligning torque and side-slip angle of a real tire. In Fig 19, the
effect of tire load on self-aligning torque is shown together with the side
slip. The effect of tire load on lateral force is small at small sideslip angles,
and large at large side-slip angles. In comparison, the effect of tire
load on
self-aligning moment is large at any side-slip angle. One of the reasons for
this is that the load effect occurs in the region where there is relative slip between
the contact surface and the tread rubber, and self-aligning torque itself also
has a greater contribution from the lateral force acting at both the ends of the
contact surface. Another reason is that the contact surface length increases with
tire load and the moment produced by the acting lateral force increases too. This
could be verified from Eqn. where the third order or more term of l is included
in the equation. If the tire pressure is increased, as seen from the previous
discussion, the lateral force increases in some cases and the self-aligning
torque also increases. However, on a real tire, self-aligning torque decreases
if the tire pressure is increased. It is thought that while even though the
lateral force increases with tire pressure, the contact surface length decreases
with tire pressure. This has a large effect on self-aligning torque.
Self-aligning torque increases if the tire pressure is decreased, but beyond a
certain limit, the self-aligning torque does not increase with decreasing tire
pressure. It is thought that if the tire pressure is too small, the decrease in
lateral force has a larger effect than the effect of increasing the contact surface length. Self-aligning
torque is the moment of the lateral force around the vertical axis that passes
through the contact surface center. The relationship between xn ¼ M=F and j:
The result shows that xn decreases dramatically when side-slip angle becomes
larger.
2.6 Camber thrust
From Eqn (2.36),
it is expected that the camber thrust of a tire is proportional to the camber
angle when the side-slip angle is zero. The relationship between the camber
angle and camber thrust of a normal tire. This example shows that the camber
thrust is proportional to the camber angle. The effect of tire load is also noted
in the same figure. As seen from the figure, the camber thrust coefficient,
which is the camber thrust per unit camber angle, increases almost linearly
with tire load. The tread base effective radius, R0 and depends on tire
vertical load, W, as in Eqn. The contact surface length also increases with tire
load. From Eqn, it is understood that camber thrust coefficient depends on tire
vertical load, and increases with tire vertical load. Moreover, from the same
equation, the camber thrust coefficient is equal to the product of the
cornering stiffness and l/(6R0). It can now be assumed that the camber thrust
coefficient has similar characteristics to the cornering stiffness. Since the
ratio of contact surface length l to effective radius R0, l/R0, is generally
about 0.3, the camber thrust coefficient is normally less than 1/10th of the
cornering stiffness. So far, the camber thrust and lateral force produced by
side-slip angle have been considered. However, the normal tire that is fitted
to a real vehicle usually has both side-slip angle and camber during its travel.
In this case, the tire is simultaneously acted on by the lateral force and the
camber thrust and it is regarded that they act independently. The lateral force
due to both side-slip angle and camber angle, as shown by Ellis. The curves
showing the relationship between camber angle and lateral force, at different
side-slip angles, and the curves showing the relation of side-slip angle and
lateral force, at different camber angles, are both parallel to each other. This
shows that the lateral forces acting on the tire, produced by the camber angle and
the side-slip angle, can be treated individually and independently. In recent
years, low profile tires have become more popular, especially among passenger
cars. When this kind of tire cambers, the lateral distribution of the tire load
in contact plane could easily give larger tire loads at the inner side, and
smaller loads at the outer side. This kind of unequal distribution, compared to
the case of equal distribution, causes a decrease in the generated lateral
force at an axle. This is anticipated from the dependency of the lateral force
and
Fig 19: Effect
of camber angle on tire lateral force.
cornering
stiffness on the tire vertical load, which is shown by parabolic curves in Figs
2.17 and 2.19. The decrease of the lateral force due to a reduction in tire load
is larger than the increase of the lateral force due to a tire load increase. Consequently,
even in cases where the camber angle is added so that the camber thrust and the
lateral force caused by side-slip angle are in the same direction, the total
lateral force produced by the tire with both side-slip angle and the camber
anglemay be reduced. This is due to the decrease of lateral force caused by
tire load distribution changes, which in turn are caused by the camber angle.
Fig 20: Effects
of camber angle on lateral force of kart tire with small aspect ratio.
Chapter Three
Mathematical Analysis
3.0 Mathematical model
The tire
cornering characteristics from Fiala’s theory have been explained. The
mathematical model assumes that with side slip, the tire tread base deforms
elastically in the lateral direction toward the tire rim and, at the same time,
the tread rubber deforms elastically further more toward the tread base. The
effect of longitudinal force, such as traction and braking, could be considered
using the same mathematical model, but the model would become too complex.
Instead, how the tread rubber is fitted circumferentially to the stiff rim, and
the tread base is the only elastic part. This model allows elastic deformation
in both the longitudinal and lateral directions. The tread rubber, similar to
the previous model, is not a continuous circular body, but consists of a large
number of independent springs around the tire circumference. This type of tire
model is called the brush model. This tire model will be used to understand theoretically
the force generated by the tire in the longitudinal and lateral directions.
Fig 21: Tire
deformable in lateral and longitudinal directions.
3.1 Tire lateral force
during traction and braking
The tire is
rotating with an angular velocity, u; while traveling in a direction that forms
an angle of b to the rotation plane. The velocity component in the rotation
plane is taken as u. Three forces act upon this tire, namely the longitudinal
force, Fx, lateral force, Fy, and vertical force, Fz.
3.1.1 Braking
The front end
point of the tire contact surface centerline is taken as the origin of the
coordinate axes, with the x-axis in longitudinal direction, and the y-axis in
lateral direction. The point on the tread base directly on top of point O is
taken as point O0. After a fraction of time, Dt; the contact surface point
moves from O to P, and the point O0 on the tread base moved to P0. The
projected point P0 on x-axis is marked as P00.
Fig 22: Tire
forces in three directions.
The motion of
the vehicle for a given steer input is studied and the mechanics of vehicle
motion are explained. Only vehicle responses to a predetermined steering action
are studied in this chapter, steering in response to vehicle motion is studied
later in the book. There is an enormous amount of previous work that has
studied the vehicle response to a predetermined steering action. These studies
have established the fundamentals of vehicle dynamics. This chapter describes
these fundamentals, which are necessary for understanding of the independent
vehicle motion due to steering, i.e., the vehicle dynamics problem.
3.2 Vehicle Equation of
Motion
The first
chapter identified the vehicle motion degrees of freedom that should be considered
as lateral, yaw, and roll. However, to understand the basic characteristics of
vehicle motion, more simplicity is needed, provided the nature of the problem
is not lost. The transient phenomena of the vehicle, such as sudden acceleration
or deceleration are omitted, as is the case of a sudden large steer action.
With these preconditions, the vehicle can be assumed to be traveling at a
constant speed, and the roll motion can be neglected. If a vehicle travels at constant
speed, and without roll, the vehicle vertical height can be neglected and only
the lateral and yawing motions need to be considered. The vehicle is represented
as a rigid body projected to the ground. In describing the motion of the rigid
body, the definition of a reference coordinate frame is necessary. Depending on
particular body motion 47 characteristics, there could be many ways of defining
the coordinates for describing the body motion. Clever definition of a
coordinate frame can simplify the description of the body motion, so selection
of suitable coordinates for a particular body is important. Considering this, it
is sensible to first derive the fundamental vehicle equations of motion.
3.2.1 Equations
of motion with fixed coordinates on the vehicle
Consider the
vehicle moving in the horizontal plane. The vehicle longitudinal and lateral
directions are continuously changing with reference to a fixed coordinate frame
on the ground. If the vehicle is examined on-board, regardless of the direction
of the vehicle, the motion constraints are basically unchangeable. It is more
convenient to describe the vehicle motion by fixed coordinates on the vehicle
rather than by fixed coordinates on the ground. X–Yare the fixed plane
coordinates on the ground, and x–y are the fixed coordinates on the vehicle,
with x in the vehicle longitudinal direction, and y in the lateral direction.
The origin of the system is at the vehicle center of gravity, P. The yaw angle
around the vertical axis is taken as positive in the anti-clockwise direction.
The vehicle is considered to be moving in plane with some speed. The position
vector of point P, with reference to coordinate system X–Y, is defined as R.
The velocity vector _R .here, i and j are the respective unit vectors in x and y
directions. u and v are the velocity components of point P in the x and y
directions. Differentiating Eqn with time, the acceleration could be written as
a vector of point P, as below. Here, mean d=dt and d2=dt2:
Fig 23: Coordinate
axes for vehicle plane motion.
Fig 24: Time
derivative of unit vectors.
Chapter Four
Vehicle Dynamics
4.0 Vehicle Dynamic
Characteristics
The basic
characteristics of vehicle motion by looking at the vehicle steady-state
cornering. The results obtained so far can only be classified as the static
characteristics, in other words, the characteristics of the vehicle motion in
steady state. To understand the characteristics of vehicle motion in more
detail, the dynamic characteristics must be examined as well. Thus, continuing
from here, the vehicle’s transient response to steer input will be analyzed
from different points of view to further understand the fundamental
characteristics of the vehicle motion.
4.1 Motion by Literal Force
Exerted on the Center of Gravity
When the vehicle
is traveling on a banked road for example, a component of the vehicle weight
will act as a lateral force at the center of gravity. This section will look at
the vehicle motion when the lateral force, Y, acts at the center of gravity.
4.2 Vehicle motion due
to a step change in lateral force
In order to
study the vehicle motion due to the lateral force, Y, the vehicle response to
an idealized form of lateral force will be looked at. Generally, one ideal form
of lateral force in this kind of situation is a step change. Consider the lateral
force acting on the center of gravity of a vehicle traveling on a straight
line. If this disturbance force acts for a long enough time, even if the Y0 value
is small, the vehicle will eventually deviate away from its original path. The
vehicle motion in this case is more conveniently expressed with coordinates fixed
on the vehicle itself
Fig 25: Lateral
force exerted on CG.
4.3 Steady State
Condition
For a vehicle
with an US characteristic, the traveling condition and force equilibrium during
steady state. If the lateral disturbance, Y0; acts on the vehicle, the center
of gravity, P, will move and produce a side-slip angle of b > 0: Due to this
b; the forces of 2Kfb and 2Krb will be exerted on the front and rear tires. The
resultant force of these two forces acts at the NSP. The magnitude of the
resultant force is 2ðKf þ KrÞb and it acts in the opposite direction of Y0: If the
vehicle exhibits an US characteristic, the NSP is behind the center of gravity,
P, and the resultant force produces an anti-clockwise yaw moment around the point
P. If the vehicle motion is in steady state, a moment must act to balance this yawing
moment. This moment can only be produced by a force acting on the tire, so
there must be relative motion in lateral direction, other than b; between the
tire and the road surface. Here, the anti-clockwise yaw motion around point P produces
side-slip angles of lfr=V and lrr=V on the front and rear tires, respectively.
Two forces in an opposite direction to each other with the magnitude of lfKfr=V
and lrKrr=V are exerted on the front and rear wheels to balance the yaw moment
caused by the disturbance. This is why r in The centrifugal force, mrV; also
acts at the center of gravity in a direction opposite to Y0: These forces are
in the equilibrium so the vehicle is in steady-state cornering and heading outward
from the circular path. The vehicle with NS characteristic has the traveling
condition and force equilibrium. If the characteristic is NS, the NSP coincides
with point P, and the resultant force of the tire forces, 2ðKf þ KrÞb; acts at
the same position as Y0: This resultant force does not produce any moment around
the center of gravity and the vehicle has no yawing motion. There is no centrifugal
force acting at the center of gravity. This is why r is zero. The resultant
force of the tire forces is in equilibrium with the external force, Y0: Consequently,
the vehicle continues its transverse motion while producing a side-slip angle.
Fig 26: Steady
state of US vehicle.
Fig 27: Steady
state of NS vehicle.
The traveling
condition and force equilibrium for an OS vehicle. Here, the lateral force Y0
moves the center of gravity to produce a side-slip angle. This side-slip angle
generates forces of 2Kfb and 2Krb at the front and rear wheels, and the
resultant force acts at the NSP. If the vehicle characteristic is OS, the NSP
is in front of P, and the resultant force 2ðKf þ KrÞb produces a clockwise yaw
moment around the vehicle center of gravity. In steady state, there must be a
moment to balance this yawing moment. This moment is obtained from the front
and rear lateral forces, 2Kf lfr=V and 2Krlrr=V; produced by the clockwise
yawing motion of the vehicle. This is why r is negative. Then, the centrifugal
force, mrV; acts at the center of gravity in the same direction as Y0: When the
vehicle exhibits an OS characteristic, the steady-state cornering is in the
opposite direction to the case of US and the vehicle heads inwards of the
circular path.
Chapter Five
Geometrical
Analysis
5.0 Roll Geometry
Eberan’s
hypothesis of the roll center as the vehicle’s geometrical instantaneous rotation
center and assumption that this roll center is always fixed have long been
taken as the standard approach. This hypothesis is generally used due to its
simplicity. Based on this hypothesis, the roll mechanism of the 165 vehicle
will be studied with a constant lateral acceleration, which is caused by a
constant centrifugal force.
5.1.1 Roll Center and
Roll Axis
In general,
there are various types of suspension systems, from the simple rigid axle type
to the independent suspension that is common in passenger cars. The relative
vertical displacement or angular displacement between the sprung and unsprung
masses is dependant on the structure of the suspension system. The front and
rear wheel roll centers are also determined by the suspension system
configuration. The line that connects the front and rear roll centers is called
the roll axis. The roll center is the vehicle’s instantaneous rotation center
in the plane perpendicular to the vehicle’s longitudinal direction, which
contains the left and right wheels’ ground contact point. The wheels are
considered rigid in both up–down, left–right directions and the ground contact
point is fixed. The axle type suspension system. The vehicle body at points A1
and B1 can only have vertical displacement relative to the unsprang mass due to
the springs. Even if the sprung mass rolls, the unsprang mass including the wheels
is assumed rigid and thus, doesn’t move, the roll center is at point O. In other
words, when a rolling moment acts on the vehicle, the vehicle body will produce
a roll angle, f; relative to the wheels with respect to the point O.
A typical
independent type of suspension – often called the double wishbone suspension.
As its name implies, each wheel can move independently, relative to the vehicle
body. If the vehicle body is fixed, the instantaneous rotation centers of the
left and right unsprung mass relative to the vehicle body are the points O1 and
O2, respectively. The point O1 is the intersecting point of the extended lines
of A1–A2 and A3–A4, while the point O2 is the intersecting point of the
extended lines ofB1–B2 andB3–B4. Here, when the vehicle body rolls during cornering,
the wheel contact points with the ground,Aand B, are fixed and the unsprung
masses must roll around them. The points O1 and O2 move in the direction
perpendicular to O1A and O2B. O1 and O2 are the virtual points on the vehicle
body as well as on the unsprung masses. Consequently, the vehicle body instantaneous
rotating center, or the roll center is the intersection of the extended lines of O1A and O2B, which is the point O.
Fig 28: Roll
center for rigid axle suspension.
Based on this
way of thinking, the roll center for other types of suspension. It is clear
that the vehicle roll center position is dependant on the structure of the
suspension system. Usually, the suspension system and the vehicle are symmetrical
on the left and right, and the roll center is always on the symmetric axis. In
this case, it is the height of the roll center that is dependent on the
suspension system structure. The roll center is the vehicle instantaneous
rotation center, and its position can move during suspension movement. The
point O shown here is the roll centerwhen roll angle is zero; if the vehicle
rolls, the roll center will also move. If the roll angle is not large, the
movement of the roll center is small, and it is possible to assume that the
roll centers are fixed at point O. It is still possible to understand the
vehicle roll mechanism, even with a moving roll center. But the fixed roll
center concept is easier to understand and gives a good understanding of the
basic vehicle dynamics. Based on Eberan’s roll center hypothesis, the front and
rear roll centers are determined, and if the vehicle body is rigid, the
vehicle’s fixed roll axis is determined. The roll center at the front and rear
may not have the same height above the ground and the roll axis is not necessarily
parallel to the vehicle longitudinal axis. Furthermore, when vehicle motion is
accompanied by large roll angles, the fixed roll center and roll axis concepts
are not suitable anymore. In such cases, vehicle roll is usually dealt with as the
indeterminate problemof the vehicle’s four wheels.
5.1.2 Roll stiffness
and load transfer
Now, the vehicle
is assumed to have a constant lateral acceleration and centrifugal force acting
at the vehicle center of gravity. The center of gravity
Fig 29: Roll
axis.
Doesn’t normally
coincide with the vehicle roll axis, but is usually above the roll axis. The
centrifugal force acting at the center of gravity produces a rolling moment
around the roll axis resulting in a constant roll angle. If the vehicle body
rolls, the left and right vertical springs of the suspension system will be
stretched at one side and be compressed on the other side. This produces an
equilibrium moment to the rolling moment due to the centrifugal force. The
magnitude of the moment produced by the stretch and the compression of the
spring per unit roll angle is called the roll stiffness. Here, the respective
roll stiffness for the front and rear suspension systems is defined as Kff ;
Kfr; the roll center height from the ground as hf ; hr; the front and rear
tread as df ; dr; the distance between the vehicle center of gravity and the
roll axis as hs; and the distance between the front and rear axles to the
center of gravity as lf ; lr: The weight of the unsprung mass is small compared
to the weight of the sprung mass and could be neglected. In this case, the
vehicle weight is taken to be equal to the vehicle body weight, and written as
Ws: The vehicle lateral acceleration is taken as €y and the centrifugal force
acting on the vehicle is €yWs: Assuming that the vehicle is rigid, and the roll
angle is small, the rolling moment by the centrifugal force is €yWshs and the
roll moment by the vehicle weight due to tilting of the vehicle body is Wshsf;
the vehicle roll angle becomesThe centrifugal force, €yWs; acting on the
vehicle requires tire cornering forces to achieve equilibrium. Distributing the
€yWs force acting at the center of gravity to the front and rear wheels, the
forces €yWslr=l and €yWslf=l could be considered to act on the front and rear
wheels, respectively, where l ¼ lf þ lr: These forces are equal to the front
and rear wheel lateral forces. If the vehicle body rolls, the left and right
wheels at both front and rear axles will increase in load at one side and
decrease at the other side. This is called the load transfer due to roll.
Defining the load transfer for the front and rear as DWf and DWr; respectively, the roll moment around
the roll center at the front and rear wheels in the plane perpendicular to the
vehicle longitudinal direction has to be in equilibrium,
5.2 Camber change and
roll steer
If the ground
contact point of the wheels is fixed, as the vehicle body rolls, the unsprang
mass, including the wheels, tilts relative to the ground. This gives the FIGURE
6.7 Transversal load transfer due to body roll.
5.3 Vehicle Body Roll
and Vehicle Dynamics
Camber change of
the wheel, which is measured relative to the ground and is due to body roll.
The vehicle roll also gives the wheels an up-and-down displacement relative to
the vehicle body. At such time, depending on the structure of the suspension
system, the wheels may produce some angular displacement in the horizontal
plane along with the up-and-down movement relative to the vehicle body. This is
called the roll steer. The camber change and roll steer are dependent on the
structure of the suspension system. The suspension system is designed with keen
consideration of these characteristics, often using them to affect the vehicle
dynamics or sometimes trying to avoid them completely. This chapter will skip
the detailed explanation of camber change and roll steer mechanism for various
suspension systems, and only look at the basic characteristics of camber change
and roll steer. The collective term for camber change and roll steer is
sometimes called the alignment change due to roll. In axle type suspensions,
the wheel doesn’t produce any camber change due to vehicle roll. The camber
change due to roll only occurs for independent suspension systems, where
depending on the suspension structure, there could be one of two cases: camber
change in the same direction as roll, which is called positive camber, or in the
opposite direction, negative camber. Independent
suspension systems are constructed by a linkage mechanism, and the vehicle roll
angle and camber change can be determined from geometrical analysis of the
linkage. The actual measured value and calculated value of the camber change
for a wishbone type suspension system. This relationship varies substantially with
the arrangement of the links, even for suspension systems of the same type.
From the figure, if the roll angle is not large, the camber change can be
considered as nearly proportional to the roll angle. As the roll angle becomes
large, this linear relation is lost, and nonlinearity appears. This is generally
for other types of suspension systems. The non-linear characteristic of the
camber change is one of the main factors that
Fig 30: Camber
change due to body roll.
Chapter
Six
Analysis
and simulation
6.0 Analysis
and simulation:
The
dynamic behavior of vehicles can be analysed in several different ways. This
can be as straightforward as a simple spring mass system, through a three-degree
of freedom (DoF)
bicycle model, to a large degree of complexity using a multibody system simulation package such as MSC ADAMS or Modelica. As computers have gotten faster, and software user
interfaces have improved, commercial packages such as CarSim have become widely used in industry
for rapidly evaluating hundreds of test conditions much faster than real time.
Vehicle models are often simulated with advanced controller designs provided as software in the
loop (SIL) with controller design software such as Simulink, or with physical hardware in the loop (HIL).
Vehicle
motions are largely due to the shear forces generated between the tires and road,
and therefore the tire model is an essential part of the math model. The tire
model must produce realistic shear forces during braking, acceleration,
cornering, and combinations, on a range of surface conditions. Many models are
in use. Most are semi-empirical, such as the Pacejka Magic Formula model.
Racing car games or simulators are also a form of vehicle dynamics
simulation. In early versions many simplifications were necessary in order to
get real-time performance with reasonable graphics. However, improvements in
computer speed have combined with interest in realistic physics, leading to driving simulators that are used for vehicle engineering using detailed models
such as CarSim.
It is
important that the models should agree with real world test results, hence many
of the following tests are correlated against results from instrumented test
vehicles.
Chapter Seven
Traubel Shooting of Vehicle
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Possible causes and remedies of mechanical
fuel pump.
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1. Fuel pump is unable to supply fuel.
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Possible cause
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Remedies
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1. Petrol tank and middle of the pump will be
protected.
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1. Remove the protection of fuel line.
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2. Diaphragm materials become so hard.
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2. Replace the diaphragm.
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3. If air is leaking by petrol and middle of the fuel
pump.
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3. Need to perfect lick in pipe in pipe line.
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4. If pump inlet is take off by the ridge.
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4. Need to clean pump inlet ridge.
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|
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2. If lick the fuel pump.
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|
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1. Housing screw is losing.
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1. Need to high the housing screw.
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2. Diaphragms become prude.
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2. Change the diaphragm.
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3. Connecting is losing.
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3. Need to tighten the connecting.
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4. Fitting thread is disappearing.
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4. Need replace the fitting.
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3. Pump is unable to supply sufficient fuel.
|
|
1. Connection of fuel line is losing.
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1. Need to tighten the fitting
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2. Diaphragm is weak.
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2. Need to replace the diaphragm.
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3. Fuel line is break.
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3. Replace the fuel line.
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4. Diaphragm spring is weak.
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4. Need to replace the diaphragm.
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4. Fuel pump creates sound.
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|
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1. Pump mounting is losing.
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1. Need to
tighten the mounting.
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2. Rocker arm became decay.
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2. Need to
replace the decky parts.
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3. Rocker arm spring is weak
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3. Replace
the rocker arm spring.
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5. Fuel pumps pressure & high volume.
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1. If gasoline is enter in the layer of
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1. Need to
replace diaphragm.
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diaphragm.
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2. If diaphragm is very tight to the
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2. Replace
the diaphragm.
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middle.
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3.
Flexibility of diaphragm become
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3. Replace
the diaphragm.
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disappear.
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4. If rocker
arm link become frozen
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4. Replace
the diaphragm.
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with the
diaphragm.
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5. Diaphragm
spring is very hard.
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5. Replace
the diaphragm.
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Struggle / Problem of the electrical
fuel pump & servicing possible cause.
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1. Pump supplies the un sufficient
fuel.
|
|
|
Possible cause
|
Remedies
|
|
1. Carburetor
float chamber middle
|
1. Need to
adjust the needle valve.
|
|
obstructed by
anything.
|
|
|
2.
Insufficient of petrol tank venting.
|
2. Need to
sufficient venting.
|
|
3. If pump
inlet obstructed by anything.
|
3. Need to
vapor the filter.
|
|
|
|
|
2. Pump is
completely unable to supply the fuel.
|
|
1.
Electricity is not label in pump.
|
1. Need to
supply electricity in pump.
|
|
2. Pump contact
point is become decay
|
2.Ndde to
adjusting the contact point or
|
|
or adjustment
is not is right position.
|
replacing the
contact point.
|
|
3. Petrol
tank of the middle pipe line is
|
3. Need to
remove the obstruction of pump.
|
|
obstruction
by anything.
|
|
|
|
|
|
3. Pump is
operate but fuel is not sufficient.
|
|
1. Leaking
air by the contact point of
|
1. Leak
proofs the contact point.
|
|
the petrol
tank and pipe line.
|
|
|
2. Leaking
air by the pump body joint.
|
2. Need to
leak proof joint.
|
|
3. Pump valve
obstructing by the ridge at
|
3. Need to
clean the pump.
|
|
the position
of open.
|
|
|
Possible causes and remedies of
carburetor main problems.
|
|
|
|
1. Flooding or leaking the
carburetor.
|
|
|
1. Carburetor
body become crack.
|
1. Replace
the crack body.
|
|
2. If main
body or fuel gasket is in
|
2. Replace
the gasket.
|
|
trouble.
|
|
|
3. Fuel level
or float setting is high.
|
3. Need to
adjust the float level.
|
|
|
|
|
2. Idle is not plain.
|
|
|
1. Idle speed
is so normal.
|
1. Need to
adjusting idle speed.
|
|
2. Idle fuel mixture
is not right.
|
2. Need to
adjust idle fuel mixture.
|
|
|
|
|
3.
Acceleration is weak.
|
|
|
1.
Accelerator pump link is not adjusting.
|
1. Need to
adjust accelerator pump link.
|
|
2. Check
valve of the accelerator is in
|
2. Need to
change the check valve.
|
|
|
|
4. Engine is in hard starting.
|
|
|
1. Engine
create flooding for miss use the
|
1. Use the
right starting process.
|
|
right
starting process.
|
|
|
2. Fuel level
of carburetor is not right.
|
2. Need to
adjusting the fuel level.
|
|
3. Adjustment
idle is not right.
|
3. Adjust the
low or high speed right.
|
|
4. Fuel inlet
valve is not adjusting
|
4. Need to
change middle valve.
|
|
righting
rightly.
|
|
|
5. Fuel pump
pressure is not right.
|
5. Need to
repair on change the fuel pump.
|
|
|
|
5. Stalling engine cold.
|
|
|
1. Mixture of
idle fuel is not right.
|
1. Need to
adjusting the idle fuel mixture.
|
|
2. Engine
idle speed is very slow.
|
2. Adjusting
the first idle.
|
|
3. Fuel
filter contain ridge, water and ice.
|
3. Clean the
filtering element.
|
|
4. Crankcase
ventilation is in trouble.
|
4. Need to
repair the trouble parts.
|
|
5. Leaking
air in fuel line.
|
5. Need to
lighting the fuel line.
|
|
|
|
|
6. Engine stalling in heat.
|
|
|
1. Despot is
not adjusting in rightly.
|
1. Adjusting
the despot.
|
|
2. Idle speed
is too slow.
|
2. Adjust the
float speed.
|
|
3. Idle fuel
mixer is not right.
|
3. Need to
adjusting idle mixture.
|
|
4. Head of
the idle screw is become
|
4. Need to
replace.
|
|
decay.
|
|
|
5. Fuel pump
is in trouble.
|
5. Repaire on
charge the fuel pump.
|
|
|
|
|
7. Acceleration or in high speed decreasing
the power.
|
|
1.
Accelerating carburetor circuit is in
|
1. Pump
connecting, plunger, valve checking.
|
|
trouble.
|
|
|
2.
Centrifugal mechanism of distributor
|
2. Need to
check the centrifugal mechanism
|
|
is in
trouble.
|
or replace
the centrifugal mechanism.
|
|
3. High speed
circuit of carburetor is in
|
3. Need to
service the carburetor.
|
|
trouble.
|
|
|
4. Air
cleaner jam.
|
4. Clean the
air cleaner.
|
|
5. Ignition
system is in trouble.
|
5. Need to
check the ignition system.
|
|
|
|
|
8. Reduced top Speed.
|
|
|
1. Fuel level
of carburetor is not in right
|
1. Adjusting
the float level.
|
|
level.
|
|
|
2. Fuel pump
pressure or volume is not
|
2. Need to
maintenance the fuel pump.
|
|
right.
|
|
|
3. The size
of main jet is narrow.
|
3. Need to
clean the main jet.
|
|
Possible causes and remedies of
diesel fuel system trouble.
|
|
|
|
1. Diesel fuel pump is unable to supply the fuel.
|
|
Possible cause
|
Remedies
|
|
1. Pump rack
jammed.
|
1. Rack free
by the adjusting.
|
|
2. Control
pawl, control plunger is unable
|
2. Need to
seat the position of troubling
|
|
to
maintaining.
|
parts of
governor liner and accelerator paddle.
|
|
|
|
|
2. Pump is unable to supply
sufficient fuel.
|
|
1.
Calibration of pump is not in right
|
1. Need to
calibrate the pump.
|
|
position or
inside barrel position of
|
|
|
plunger is
not right.
|
|
|
2. Fuel
return line is in obstruction.
|
2. Need to
remove the obstruction.
|
|
3. Fuel tank
bent is closed.
|
3. Cleaning
the fuel tank vent.
|
|
|
|
3. Control rack jammed.
|
|
|
1. Governor
linking, liver and calibrating
|
1. Necessary
to checking the governor
|
|
screw is not
in right position.
|
linkage,
liver & calibrating area.
|
|
2. Rack gear
& quadrant pinion are not
|
2. Need to
checking the rack gear and
|
|
in right
position.
|
quadrant
pinion.
|
|
|
|
|
5. Too high injection pressure.
|
|
|
1. Nozzle
opening is taken off by carbon.
|
1. Nee dot
clean the nozzle.
|
|
2. Nozzle
valve is not clean.
|
2. Need to
clean the nozzle.
|
|
3. Nozzle
valve is in decay.
|
3. Replace
the nozzle valve.
|
|
|
|
|
6. Too low injection pressure.
|
|
|
1. Nozzle
spring is weak.
|
1. Change the
nozzle spring.
|
|
2. Nozzle
spring has been broken.
|
2. Replace
the nozzle spring.
|
|
Trouble shooting and diagnosis of
Vehicle
|
|
|
1. Engine will not turn over.
|
|
|
1. Weak
battery.
|
1. Need to
charging the battery or replace the
|
|
|
battery.
Engine can be start by the jumper
|
|
|
battery or
cable.
|
|
2. Open
starting circuit.
|
2. Find the
open circuit & remove it.
|
|
3. Starting
motor drive is jammed.
|
3. Replace
the starting motor.
|
|
4. Engine
jammed.
|
4. Check the
engine for solving the problem.
|
|
|
|
|
|
Chapter
Eight
Conclusion
8.1 Conclusion
For a technical service
provider company O&M activities are very important as its service mostly
depends on the availability of its equipment & technology. AG Automobiles
Ltd is providing Maintenance and Trouble shooting service for vehicle where
uninterrupted is the key element to have success over its competitor. To
maintain properly it requires doing Maintenance activities very efficiently and
with minimum costing. Using Plant
Maintenance schedule can save cost and maximizes profit of CE.
The theme of this report
is relatively new in Bangladesh
and all over the world. During this
study it has been observed from the organizational point of view where it has
been implemented. The use of servicing schedule has shown tremendous potential
in developed countries worldwide. There are so many improvement and application
that can be offered through these ERP systems which of course would have direct
benefit for the organization.
The key findings of the
report include:
Ø To study maintenance
activities of vehicle.
Ø To study the standard
process required by AG Automobiles Ltd for the Maintenance activities and
incorporation which help to meet the requirement.
Ø To make an analysis on
the Maintenance activities through whole operation Systems
Ø To study Troubleshooting
of IC engines.
Ø The Status &
Performance of O&M team reflects from the service schedule
Ø Servicing schedule
integrated all the equipment, manpower & other resources of the
organization
Ø All the O&M
activities can be properly tracked using service schedule.
Ø Working in Servicing
schedule is user friendly
Ø Work become systematic
& different process has improved the O&M work
Ø Extra cost for the
O&M activities reduces
Ø Existing Manpower uses
the system besides their usual O&M job which increase additional work load
with pressure.
8.2 Recommendations
AG Automobiles being one
of the largest different vehicle suppliers to the customer’s vehicles in Bangladesh is
keep to stay competitive offers to its customers. With the set mission and
vision AG automobiles Ltd is committed to keep it up with quality for possible
maximum time to serve its customers. As its Quality Policy states, it is eager
to adopt new and advanced technologies to provide high and new age service to
the customers with satisfaction of its customer.
In line with these view the following recommendation
can be made for Covanta out of the study:
Ø Automated System to
Create Notification in servicing schedule for different Module for O&M
works due to fault.
Ø Automated closing of job
when fault rectified.
Ø Dedicated Team to monitor
the activity (updated & escalated) of SAP PM Schedule.
Ø Taking feedback from
Servicing Module for the OT & Man-hour to use for financial purpose.
Ø It can increase the
comfortable of using Servicing schedule.
Ø Severity of operation and
maintenance work can reduce critical and warning type by doing more efficiently
servicing work.
8.3 Appendix
m : vehicle mass
I : vehicle yaw moment inertia
l : wheel base
lf : longitudinal position of front
wheel(s) from vehicle center of gravity
lr : longitudinal position of rear
wheel(s) from vehicle center of gravity
Kf : cornering stiffness of front tire
Kr : cornering stiffness of rear tire
V : vehicle speed
d : front wheel steer angle
b : side slip angle
r : yaw rate
q : yaw angle
x : vehicle longitudinal direction
y : vehicle lateral direction and
lateral displacement
t : time
s : Laplace transform variable
8.4 Reference
01.
AG Automobiles Ltd. Abdullahpur, Uttara
Dhaka-1230.
02.
Masato Abe A Text Book of Vehicle Handling Dynamics
03.
R.S Khurmi, J.K Gupta
a Text Book of Thermal Engineering.
04.
www.madehow.com/Volume-1/Automobile.html
10.
ttp://www.ag+automobiles&sourceid=chrome&ie=UTF-8&q=ag+automobiles+bangladesh
