Today, we have to consider different demands to make a successful and reliable concept design of modern suspension systems. Beside package and lightweight construction especially the real scopes of a suspension system, kinematics and compliances are getting more and more important to fulfill all the technical needs coming from the automotive market. In particular, the development of suspension system for sport utility vehicle (SUVs) has to satisfy various demands and strong characteristic criteria coming from the on-road and off-road driving conditions. In this paper, the main kinematics and compliance effects for an independent SUV suspension system will be explained and illustrated: Explanation of different load cases coming from the individual purpose of a sport utility vehicle (off road & on road) - Illustration of the K&C influences coming from the use of active systems to control roll and pitch angles or the individual wheel loads - Development of an analytic approach to solve the kinematic and compliance needs. - Simulation description and results to verify the suspension design. - Analysis of vibration problems resulting from suspension concepts.

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Kinematics and Compliance of Sports Utility Vehicle
Sumit Jain1
, Kuldeep Sharma2
1
(Department of Mechanical Engineering / Jaipur Engineering College and Research Centre, India)
2
(Training & Placement officer, Professor / Jaipur Engineering College and Research Centre, India)
Abstract: Today, we have to consider different demands to make a successful and reliable concept design of
modern suspension systems. Beside package and lightweight construction especially the real scopes of a
suspension system, kinematics and compliances are getting more and more important to fulfill all the technical
needs coming from the automotive market. In particular, the development of suspension system for sport utility
vehicle (SUVs) has to satisfy various demands and strong characteristic criteria coming from the on-road and
off-road driving conditions.
In this paper, the main kinematics and compliance effects for an independent SUV suspension system will be
explained and illustrated:
Explanation of different load cases coming from the individual purpose of a sport utility vehicle (off road & on
road)
- Illustration of the K&C influences coming from the use of active systems to control roll and pitch angles or the
individual wheel loads
- Development of an analytic approach to solve the kinematic and compliance needs.
- Simulation description and results to verify the suspension design.
- Analysis of vibration problems resulting from suspension concepts.
Keywords: Suspension design, Kinematics and Compliance, Simulation, Vibration Analysis, SUVs
1. INTRODUCTION
Vehicle dynamics is the study of all forms of transportation (trains, airplanes, boats, and automobiles).
However, vehicle dynamics as we know it is the study of the performance of the automobile in all of
its motions (ride, acceleration, cornering, and braking). The vehicles suspension plays a key role in
each of these motions. The study of a vehicle’s suspension can be broken into two major categories:
suspension kinetics and suspension kinematics. Suspension kinetics is a dynamic and a vibration
analysis on the vehicle and suspension systems. Suspension kinematics involves analyzing the motion
of the tires as the suspension compresses and extends.
Especially the On-Road needs can only be realized to a great extent by independent suspension
systems. Because of that a clear trend to this kind of suspension systems can be noticed for SUVs.
Therefore, this paper focuses on independent suspension systems only.
To develop SUV suspension systems several requests, have to be taken into account. Especially the
high center of gravity leads to demands for very high roll spring rates that are difficult to realize
because of the package boundaries resulting from larger wheel travel ways and the use of very large
wheels. But especially because of the rollover stability needs it is one of the major K&C targets to
realize an optimized vehicle body roll behavior.
For modern Sports Utility Vehicles an excellent self-steering behavior is appropriate to assure
handling characteristics that are comparable to passenger cars. For most SUVs it is possible to achieve
similar axle loads at front and rear axle. For the design of the self-steering effects the torque
distribution between front and rear axle has to be considered. Because of the high center of gravity
SUVs are curving with higher roll angles than normal passenger cars do. Since that the front axles are
designed to a small roll-understeer effect. Target for the rear axle is to realize a nearly neutral roll-
steering effect.

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The rollover stability of vehicles is influenced by a lot of different effects. This paper focuses on the
kinematics and compliance effects on the rollover stability. Beside the distance between the center of
gravity and the roll center of an axle system also the position of the roll center as function of the
wheel travel is essential for the rollover stability of a Sports Utility Vehicle.
1.1.KINEMATICS CONCEPT
For modern Sports Utility Vehicles an excellent self-steering behavior is appropriate to assure
handling characteristics that are comparable to passenger cars. For most SUVs it is possible to achieve
similar axle loads at front and rear axle. For the design of the self-steering effects the torque
distribution between front and rear axle has to be considered because of the high center of gravity
SUVs are curving with higher roll angles than normal passenger cars do. Since that the front axles are
designed to a small roll-understeer effect. Target for the rear axle is to realize a nearly neutral roll-
steering effect Main target for the camber design is to compensate the roll angle at the outer curve
wheel.
As SUVs mostly have higher roll angle gradients than common passenger cars, it is useful to have a
higher camber change at wheel travel than at normal passenger cars. By using active stabilizers, it is
possible to limit the body roll angle gradient. Since that also a smaller gradient of the camber change
within the kinematic design is needed for the use of active roll control systems. By this an active
stabilizer bar makes also the camber curve of a strut suspension acceptable for SUVs.
1.2.SUSPENSION STIFFNESS AND DAMPING
The suspension stiffness is one of the most important parameters when considering the vertical
performance of the vehicle. It is generally best to have a moderate spring rates. This is because low
spring rates reduce the tire deflection which increases the tire grip; however, it also allows for
increased body motions (in roll and in pitch) which are harmful to the overall handling performance of
the vehicle. The opposite is true for high spring rates. Therefore, there should be a compromise
between implementing high and low suspension stiffness’. Also, according to Maurrie Olley the
following set of rules should be followed when designing a suspension system for the comfort of the
passenger, and they are:
 Front suspension should have a 30% lower ride rate than rear suspension.
 Pitch and bounce frequencies should be close together; bounce frequency should be 1.2 times
the pitch frequency.
 Neither the bounce nor the roll frequency should be greater than 1.3Hz.
The reason for this is that the front of the vehicle will ride over the bump (or disturbance) first
creating an excitation in the front suspension, and then seconds later the rear suspension will ride
over the bump creating an excitation in the rear suspension. If the two suspension rates are
identical the phase lag between the front and the rear suspensions will create an undesirable motion
in pitch. There have been studies that have shown that the driver/passenger is/are very
uncomfortable in pitch motion, it tends to cause neck muscle strains. Therefore, by increasing the
suspension rate in the rear suspension allows for the rear of the vehicle to “catch up” to the front of
the vehicle (Figure: The front and the rear suspension amplitudes as a function of time).

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Fig 1. Oscillation of a vehicle passing over a road bump
It can be seen from the figure above that there exists a phase lag between the front and the rear
excitations, and that by having a rear suspension rate higher than the front suspension rate allows for
the rear excitation to catch up to the front excitation.
1.3.SPRUNG AND UN-SPRUNG MASS
The mass of the vehicle is an important parameter in the analysis of the vertical dynamics of the
vehicle. The mass of the vehicle is one of the main parameters in which will decide the deflections of
both the front and the rear tires, and the suspension units when they are excited. The mass of the
vehicle is divided into two parts the sprung mass and the un-sprung mass. The sprung mass consists of
everything the suspension units have to support, and these include the chassis, and the engine. The un-
sprung mass consists of everything the tires have to support, and these include the front and rear axles.
Typically the sprung mass is of an order of magnitude greater than the un-sprung mass. Therefore, the
following formula can be used to calculate the sprung mass and the un-sprung mass based on the mass
of the vehicle
1.4.INSTANT CENTER AND ROLL CENTER POSITION
The instant center is the point the wheel rotates about relative to the vehicle chassis. It is a function of
the geometry of the suspension system. The instant center is important because it defines the position
of the roll center. The roll center position is a position where the lateral forces developed at the wheels
are transmitted to the vehicle sprung mass. This point will affect the behavior of both the sprung and
un-sprung mass and thus effects the vehicles cornering characteristics. The roll center is defined as the
point in the transverse vertical plane where the lateral forces may be applied to the sprung mass
without producing any suspension roll. The definition of roll center derives from the fact that a vehicle
will possess a roll axis (Figure: The roll axis of the vehicle).
Fig 2. The roll axis of the vehicle

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The roll axis is the instantaneous axis where the un-sprung mass will rotate relative to the sprung mass
when a pure couple (moment) is applied to the un-sprung mass. The roll center is the intersection of
the roll axis with the vertical plane at the front and rear of the vehicle. Typically, the roll center
position is located based on the suspension geometry and then the roll axis is located by defining a line
which connects the two roll centers together. The roll axis is also the instantaneous axis in which the
whole vehicle rotates with respect to the ground.
The amount of body roll depends on the height of the center of mass relative to the roll center position.
Therefore raising the roll center position closer to the center of mass is equivalent to increasing the roll
stiffness of the suspension. However, as the roll center position is increased (roll center height
measured from ground level is increased) the amount of jacking forces will increase. The jacking
forces are the forces that will travel through the suspension components to the vehicle body; it is the
force that is not absorb by the suspension system. Thus as the amount of jacking forces increase, the
amount of forces absorbed by the shock will decrease. Forces generated at the tire have two paths into
the vehicle: a flexible path and a stiff path. The stiff path is through the suspension components and
the flexible path is through the suspension spring
Fig 3. The effect of the jacking forces
Thus as the roll center is increased, the forces traveling through the stiff path will increase and the
forces traveling through the springs will decrease causing less spring compression. The jacking forces
will tend to lift the vehicle as it corners. Therefore, there should be a balance in roll center height
between suspension roll stiffness and the jacking forces seen by the frame. It is important to note that
the roll center is a fictitious point. Forces that are traveling from the ground to the chassis will not pass
through this point. The location of this point will not be able to determine the suspension roll stiffness,
nor will it be able to determine the magnitude of the jacking forces. This point is strictly there to give a
relative idea of the roll characteristics of the vehicle.
The roll center position is calculated differently for each type of suspension system. The procedure for
calculating the roll center position will be outlined for the double A-arm type of suspension only (if it
is desired to learn how to calculate the roll center position for a different suspension system, than it is
advised to look in vehicle dynamics text book). The first step is to locate the instant center. This is
accomplished by drawing a line that passes through each of the A-Arms when looking at the vehicle in
the front view. The intersection of these lines represents the instant center. The second step is to draw
a line form the center of the tires contact patch to the instant center. The point where the line drawn in
step two intersects the center line of the vehicle represents the roll center position (Figure Roll center
position of a double A-arm type of suspension).

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Fig 4. Roll center position of a double A-arm type of suspension
1.5.ROLL CENTER LOCATION
As the vehicle approaches a corner, the sprung mass distribution is transferred laterally from one
side to the other resulting in higher loads on the outside turning wheels. This transfer in the weight
distribution may cause the vehicle to roll depending on the roll moment acting on the vehicle. The roll
moment depends on the location of the roll center and the vehicle center of gravity, where the distance
between the roll axis and the center of gravity represents the roll moment arm. The longitudinal
position of the roll center is not considered due to the fact that it does not have a great impact on the
roll moment arm; the lateral location of the roll center on the other hand is given to be at the center line
of the vehicle. Therefore, only the vertical position of the roll center is considered when designing the
suspension geometry. By connecting the roll centers in the front and rear the vehicle roll axis is
formed. The orientation of the roll axis has a great impact on the oversteering and understeering
characterizes, designing the roll axis to be inclined towards the front of the vehicle results in
understeering, while oversteering is obtained when the roll axis is inclined towards the rear of the
vehicle.
1.6.ROLL STIFFNESS
As the vehicle approaches a corner, the sprung mass distribution is transferred laterally from one
side to the other resulting in higher loads on the outside turning wheels. This transfer in the weight
distribution may cause the vehicle to roll depending on the roll moment acting on the vehicle. The roll
moment depends on the location of the roll center and the vehicle center of gravity, where the distance
between the roll axis and the center of gravity represents the roll moment arm. The longitudinal
position of the roll center is not considered due to the fact that it does not have a great impact on the
roll moment arm; the lateral location of the roll center on the other hand is given to be at the center line
of the vehicle. Therefore, only the vertical position of the roll center is considered when designing the
suspension geometry. By connecting the roll centers in the front and rear the vehicle roll axis is
formed. The orientation of the roll axis has a great impact on the oversteering and understeering
characterizes, designing the roll axis to be inclined towards the front of the vehicle results in
understeering, while oversteering is obtained when the roll axis is inclined towards the rear of the
vehicle.
The roll stiffness is sometimes referred to as the roll rate. The roll stiffness of the suspension
system is the amount of roll moment needed to roll the suspension by one unit of rotation (degree
or radian). The roll stiffness of the suspension system is related to the ride rate through the
following equation.
𝐾 =
[(12) ∗ (𝑘𝑟) ∗ (𝑡)2]
2

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Roll stiffness as a function of ride rate
Note, the roll stiffness resulted will be in units of lb-ft/rad, the ride rate is in units of lb/in and the
track is in units of feet.
2. CALCULATION FOR ROLL GRADIENT
Weight on front wheels = 2040lb
Weight on rear wheels = 1360 lb
Total weight = 3040lb
Dimensions:
Wheel base = 9.5ft.
H1 (C.G. height from ground) = 1.5 ft
H2 (C.G. to roll axis) = 1.1ft
The cornering conditions is left hand turn where: α = -10deg. (roadway bank angle)
R (turning radius) = 600 ft.
V (Velocity) = 100 mph = 146.7 ft/sec.
Zrf (roll axis height, front-axle) = 0.25ft (above ground)
Zrr (roll axis height, rear-axle) = 0.625ft
We assume the roll rates:
KϕF = 70000lb.-ft/rad.= 122lb.-ft/deg
KϕR = 50000lb.-ft/rad.= 873lb.-ft/deg
Because we don’t yet know what the ride rates are, we also don’t know the roll rates (as they are
dependent on one another). We therefore have to assume roll rates values to start with. Also because
roll center locations can change with ride height and roll angles, we start with values at static design
positions.
Now, Lets calculate the Center of Gravity:
b = WF*l/WT = (2040 X 9.5) / 3400 = 5.7 ft.
a = l – b = 9.5 – 5.7 = 3.8 ft.
Next, the lateral acceleration values relative to the earth and the banked turn are calculated.
Aα = V2
/Rg = 146.72
/ (-600 X 32.2) = -1.11 g’s
AY = (Aα * cosα) – sinα = (-1.11 X cos(-10)) – sin(-10)
= -1.09 + 0.17 = -0.92 g’s
Here, Aα and AY is Horizontal lateral acceleration and Lateral acceleration in car axis system.
The effective weight of the car to the banking is:
W’ = W*(Aα (sinα) + cosα)= 3400(-1.11 sin(-10) + cos(-10))
= 3400 X 1.1776 = 4004 lb.
And, the effective front and rear axle weights are
W’F = (W’ b)/l = 4004*(5.7/9.5) = 2402 lb.
W’R = (W’ a)/l = 4004*(3.8/9.5) = 1602 lb.
The roll gradient is
Φ / AY = (-W * H2) / (KϕF + KϕR) = -3400*1.1/(70,000 + 50,000)
= -0.03117 rad/g or -1.78 deg/g
Here, Φ is body roll angle

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CONCLUSIONS
Kinematics and compliance of a Sports Utility Vehicle have to fulfil all needs coming from both
purposes On Road and Off-Road use.
Because of the high center of gravity special demands have to be solved to guarantee a save rollover
stability and an acceptable anti-dive mechanism. Since the definition of the instantaneous center line
also influences quite strongly the self-steering characteristics of the suspension serious investigations
have to guarantee the best possible compromise. Because of the high wheel loads and lateral forces
the characteristic requests for SUVs’ bushing elements are more demanding than for conventional
passenger cars. There is a clear trend towards a very soft longitudinal spring level of the suspension
system. But to fulfil the handling demands also a strong lateral wheel lead is necessary.
Analytic approaches can build a helpful basis for the K&C concept to understand different load cases.
To develop a comprehensive K&C design that considers all relevant load cases it is necessary to
verify and optimize the development process with numerical simulations.
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