Design and Development of the URE06 Rear · PDF file3 Summary This internship covers the...
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Internship Report Coach: dr. ir. I.J.M. Besselink (TU/e) Supervisor: Prof. dr. H. Nijmeijer (TU/e) Technische Universiteit Eindhoven Department Mechanical Engineering Dynamics and Control Group Eindhoven, November, 2009 Design and Development of the URE06 Rear Suspension C. OZTURK DC 2010.021
Transcript of Design and Development of the URE06 Rear · PDF file3 Summary This internship covers the...
Internship Report
Coach: dr. ir. I.J.M. Besselink (TU/e)
Supervisor: Prof. dr. H. Nijmeijer (TU/e)
Technische Universiteit Eindhoven
Department Mechanical Engineering
Dynamics and Control Group
Eindhoven, November, 2009
Design and Development of the
URE06 Rear Suspension
C. OZTURK DC 2010.021
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Contents Summary ........................................................................................................................................................................ 3
Sign conventions ............................................................................................................................................................ 4
1. Introduction .......................................................................................................................................................... 6
1.1. Objective ...................................................................................................................................................... 6
1.2. Outline .......................................................................................................................................................... 6
2. Background information ....................................................................................................................................... 7
2.1. Camber angle ............................................................................................................................................... 7
2.2. Toe angle ...................................................................................................................................................... 8
2.3. Roll center height ......................................................................................................................................... 9
2.4. Anti-squat ................................................................................................................................................... 10
2.5. Anti-rise ...................................................................................................................................................... 11
2.6. Tyre-road contact point motion and wheel centre motion ....................................................................... 12
3. The existing rear suspension of the URE05 ......................................................................................................... 13
3.1. Kinematic suspension model ..................................................................................................................... 13
3.2. Kinematic characteristics of the rear suspension of the URE05 ................................................................ 14
4. Kinematic suspension design .............................................................................................................................. 23
4.1. Requirements and constraints on the rear suspension of the URE06 ....................................................... 23
4.2. Design of the rear suspension of the URE06 .............................................................................................. 23
4.2.1. Initial concept .................................................................................................................................... 24
4.2.2. Final concept ..................................................................................................................................... 26
4.2.3. The kinematic characteristics of the rear suspension of the URE06 ................................................. 27
5. Force Analysis for the Worst Case Scenarios ...................................................................................................... 32
5.1. Acceleration ............................................................................................................................................... 33
5.2. Braking ....................................................................................................................................................... 34
5.3. Cornering .................................................................................................................................................... 35
5.4. Bump .......................................................................................................................................................... 36
5.5. Resultant forces ......................................................................................................................................... 37
6. Conclusion and recommendations ..................................................................................................................... 39
6.1. Conclusions ................................................................................................................................................ 39
6.2. Recommendations ..................................................................................................................................... 39
References ................................................................................................................................................................... 40
Appendix ...................................................................................................................................................................... 41
A. URE06 Suspension Coordinates ...................................................................................................................... 41
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Summary This internship covers the design and development of the new rear suspension for the URE 05 FSAE for
University Racing Team. The kinematic characteristics of the rear suspension of the URE05 have been
investigated and according to this kinematic analysis the new rear suspension is designed. Hereby, the
challenge is found in satisfying the compromising demands from the suspension system. A higher
camber gain for the outer wheel during cornering is the essential aim of the design while keeping the
structural stiffness high and the centre of the gravity low. In order to obtain an optimal suspension
system, a double-wishbone suspension is proposed. After many iterations, the optimum configuration is
obtained.
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Sign conventions In order to eliminate any misunderstandings, a sign convention is provided in Figure 1 which is based on
the international norm ISO 8855 [1].
Figure 1: Sign Conventions
The definitions are given in Figure 1.
Wheelbase [l]: the distance between the center of the tyre-road contact point of the two wheels on the
same side of a vehicle along the x-axis.
Track [b]: the distance between the centers of the tyre-road contact points of the two wheels of an axle.
Tyre inclination angle [γ]: is positive when the tyre is inclined by positive rotation around the x-axis of
the vehicle.
Camber angle: is the angle between the vertical axis of the wheel and the vertical axis of the vehicle
when viewed from the front or rear. The camber angle is defined positive when the top of the wheel is
further out than the bottom and the camber angle is defined negative when the bottom of the wheel is
further out than the top. It should be also noted that for the front and rear left tyre, the camber angle is
opposite to the inclination angle. For the front and rear right tyre, it has the same sign.
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Toe angle: is the angle of the two front wheels or two rear wheels relative to each other when the
vehicle is viewed from a top view. If the front of the wheels points inward towards the car so that the
front of the wheels are closer together than the back of the wheels then the wheels are in the toe-in
position. If the front of the wheels point away from the car so that the fronts of the wheels are further
apart than the back of the wheels then the wheels are in the toe-out position.
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1. Introduction
1.1. Objective
In this internship, a rear suspension for the University Racing Team of Eindhoven University of
Technology (TUE) will be designed. While developing the rear suspension, the drawbacks of the existing
multi-link rear suspension of URE05 are taken into account. This year new tyre data is available, which
provides valuable information for designing the new rear suspension. At the end of the internship, the
kinematic design of the rear suspension is obtained and some load cases will be analyzed.
1.2. Outline
In chapter 2, the background information which is necessary to develop a suspension is provided.
Camber angle, toe angle, tyre-road contact point motion, anti-squat percentage, anti-rise percentage
and roll center height are explained in this chapter.
The existing rear suspension of URE05 is analyzed in chapter 3. Therefore, a kinematic suspension model
is developed. The characteristics of the existing rear suspension, e.g. roll centre and anti-effects, are
obtained and the results are given in this chapter.
The design considerations and results of the new design are discussed in chapter 4. A comparison is
made with the multi-link suspension of URE05 vehicle.
Force analysis is made for the worst case scenarios which include severe acceleration, severe braking,
severe cornering and bump in chapter 5. The new rear suspension is compared with the existing rear
suspension.
This report ends with conclusions and recommendations for further research as given in chapter 6.
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2. Background information In order to design a rear suspension, there are crucial features that should be investigated and taken
into account throughout the design. These are camber angle, toe angle, tyre-road contact point motion,
wheel center motion, anti-squat, anti-rise and roll center height.
2.1. Camber angle
Camber is one of the most useful alignment adjustments that can be made to the cars. The definition of
the camber angle is made under the sign convention part. In Figure 2, a negative camber angle is
depicted [2].
Figure 2: Negative Camber Angle [2]
The handling qualities of a specific suspension design strongly depend on the camber angle. Basically, a
negative camber angle can provide a higher handling quality when compared to positive camber angle
since the negative camber improves grip for the outer wheel while cornering.
During cornering, load transfer occurs from the inner wheel to the outer wheel. Therefore, the outer
wheel is much more important for handling when compared to inner wheel. With negative camber
during cornering, the maximum lateral force on the outer wheel is increased since the outer tyre is
placed at a more optimal angle to the road. In other words, the fact that the inside edge of the contact
patch of the outer wheel will begin to lift during severe cornering will be minimized for outer tyre by
implementing a negative camber angle. This lifting effect is caused by body roll. As a result of the
negative camber, the contact patch area is maximized for the outer wheel. However, negative camber
results in an adverse effect on the inner tyre. The lateral force will be reduced, which is not significant
due to the load transfer to outer wheel.
On the other hand, when the maximum straight-line acceleration and braking is considered, the greatest
longitudinal force is obtained with zero camber angle, since in this situation there is no body roll. As a
result, tyre will not experience the lifting effect due to body roll and the highest grip for the tyre is
obtained when the camber angle is zero.
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Therefore, the characteristics of the camber angle should be taken into account when designing the rear
suspension. With independent suspensions such as the double wishbone and the multi-link design, it is
possible to have a zero camber angle for zero bump travel and a negative camber angle for positive
bump travel. Such a behavior provides a camber gain for the outer tyre while cornering because the
outer tyre will experience positive bump travel. These kinds of suspensions provide a good compromise
for conflicting characteristics of the camber angle.
2.2. Toe angle
Toe is an alignment parameter that describes how the wheels are oriented with respect to each other.
The definition of the toe angle is made under the sign convention part. In Figure 3, the toe-in is depicted
[3].
Figure 3: Toe-in [3]
Toe has an influence on the handling behavior of a car on corner entry. It is harder for a vehicle to turn
into a corner with more toe-in on a pair of wheels. Conversely, the more toe-out on a pair of wheels, the
easier the vehicle will turn into a corner. This phenomenon can be explained by the fact that the
radiuses of the arc of the inner and outer tyres, which are traced during cornering, determine the
easiness of the corner entry. For a pair of wheel with toe out, the inner tyre will have a smaller radius of
arc than the outer tyre has. This provides easiness in corner entry. However, for a pair of wheel with
toe-in, the inner tyre will have a larger radius of arc than the outer tyre has. In this situation, it is difficult
to make the car turn since the inner tyre is moving against the outer tyre. When the car is already in a
turn, weight transfers to the outer tyre and the effect of the inner tyre diminishes. Due to this load
transfer, toe mainly affects corner entry [4].
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Moreover, the understeer behavior of the vehicle is affected by the toe-angle. When the amount of toe-
in is increased on a pair of wheels, the lateral force during cornering is also increased. If the lateral
forces on the rear wheels are increased, the vehicle will have an understeer tendency, which means the
stability is increased. Therefore, more toe-in on the rear wheels will result in a higher understeer
tendency of the vehicle. Conversely, more toe-out on the rear wheels will result in less understeer
tendency.
It is not desirable to have bump steer, which is the term for the tendency of a wheel to have a change in
the toe angle with bump travel. Bump steer has mainly adverse effects during braking and acceleration.
For braking and acceleration, it is important to have the highest possible longitudinal force. If there is
bump steer, lateral forces will occur during acceleration and braking due to bump travel. This will lead to
a decrease in the longitudinal force since the total amount of the force can be obtained between tyre
and road is limited by friction and shared between the longitudinal forces and the lateral forces. So, the
higher the lateral forces, the smaller the longitudinal forces that can be obtained.
Furthermore, toe increases tyre wear since the tyres are moving against each other and scrubbing over
the ground. The outside edges of the tyres will be deformed with toe-in and toe-out tends to increase
tyre wear on the inside edges of the tyres. Therefore, if a negative camber angle is used on the wheels
which causes the inside of the tyres to wear more than normal, the implementation of toe-out to these
wheels should be considered carefully since the combination of excessive negative camber and toe-out
can quickly wear the inside of the tyre.
These considerations should be taken into account while designing the rear suspension.
2.3. Roll center height
The roll center is defined such that when a lateral force is applied to the vehicle body at the height of
the roll centre, this lateral force will not produce any body roll of the vehicle [2]. With different
suspension designs it is possible to obtain the same roll center.
In Figure 4 , the roll center of a double wishbone suspension is depicted.
Figure 4: Roll Center of a Double Wishbone Suspension [2]
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The roll center of a double wishbone is found as follows. The lines from the left and right instant centers
to their respective tyre contact patch center points are drawn. The kinematic roll center height is
obtained at the point where these two lines intersect.
There are several advantages and disadvantages of a high roll centre. One of the advantages is that with
higher roll center, it is possible to use a less stiff torsion stabilizer (anti-roll bar) or less body roll will be
obtained with the same stiffness. Another advantage is that reduced lateral displacement of the center
of the gravity will be obtained, which is beneficial for roll-over. On the other hand, as the roll center
height is increased, the lateral motions of the tyre contact patch on vertical deflections of the
suspension will also increase. This behavior affects the directional stability adversely. Another
disadvantage is that high roll center may give rise to jacking effects at high lateral accelerations.
As mentioned above a high roll centers require less stiff anti-roll bar. However, focusing only on this
aspect during design may lead to the problem of jacking effect at the end of the design. The jacking
effect occurs due to redistribution of the lateral force, which tend to lift the vehicle center of gravity
above the static location. The jacking effect is observed in all cars if the roll axis of the car is above the
ground and the jacking forces will increase as the roll axis gets higher. Therefore, these compromises
should be taken into account for designing the rear suspension.
The front roll center is mostly located at ground level, which is also the design policy of Ferrari [5]. The
rear roll center is preferred to be located above the ground.
2.4. Anti-squat
Anti-squat is the amount of longitudinal forces that is transmitted through the rear suspension links
during acceleration. It can be thought as the counterpart for acceleration, as jacking forces are to
cornering. It is expressed in terms of percentage. In Figure 5, the anti-squat is depicted [2].
Figure 5: Anti-squat [2]
In Figure 5, h and l represent, respectively, height of the center of gravity and wheel base. The anti-
squat is calculated as follows;
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(2.1)
The anti-squat percentage is determined by calculating the height of the intersection point of a line
extended from the wheel center through the side view rear instant center which intersects a vertical line
drawn up through the center of the front tyre. If the height of this intersection point is at the same
height of the center of gravity, the suspension is said to have 100 % anti-squat.
Different percentages of anti-squat can be applied depending on the suspension design. For higher
percentages of anti-squats, the weight transfer under acceleration will be taken by the suspension rods
rather than the springs. For instance, at 100 % anti-squat, all of the longitudinal load transfer is carried
by the upper and lower control arms and none of the additional loads are carried by the springs. On the
other hand, for lower percentages of anti-squat, the longitudinal load transfer is mostly taken by
springs. For example, if no anti-squat is present, all rearward longitudinal load transfer will be taken by
the springs. In this case, during the first few milli-seconds of load transfer, a percentage of the increased
vertical load will be absorbed through spring compression rather than being applied directly to the tire
contact patch [4].
2.5. Anti-rise
The anti-rise percentage on the rear is of importance when braking. It defines the amount of the
longitudinal braking force which is transmitted through the suspension links which suppresses the lift of
the rear of the vehicle. In Figure 6, the anti-rise is depicted [7].
Figure 6: Anti-rise [7]
In Figure 6, h and l represent, respectively, height of the center of gravity and wheel base and p is the
brake force distribution. The anti-rise is calculated as follows;
���� − ���� = �� (�)�/(�(���)) × 100% (2.2)
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The anti-rise percentage is determined by calculating the height of the intersection point of a line
extended from the tyre-road contact point through the side view rear instant center which intersects a
vertical line drawn up through the center of the front tyre. If the height of this intersection point is at
the same height of the center of gravity, the suspension is said to have 100 % anti-rise. It should be also
noted that the anti-rise percentage is strongly depending on the brake force distribution. For higher
brake force distributions, the amount of the anti-rise is increased. An extreme example of anti-rise is
pro-rise, which corresponds to a value larger than 100%. This is applied to the rear swing arm of
motorcycles to increase traction during acceleration [7].
Anti-rise percentage is directly related to the anti-squat percentage, therefore, it not possible to change
it completely independently.
2.6. Tyre-road contact point motion and wheel centre motion
Tyre-road contact point motion is representative for directional stability of a vehicle. It is desirable not
to have tyre-road contact point lateral motion for positive and negative bump travel. The lateral motion
of the tyre-road contact point is strongly dependent on the roll center height. If the roll center is high
above the ground, the lateral motion of the contact point will be larger. This impairs the directional
stability. The fore-aft motion of the contact point is related with the anti-lift percentage. Similarly, the
fore and aft motion of the wheel centre motion is dependent on the anti-squat and anti-rise percentage.
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3. The existing rear suspension of the URE05 The current rear suspension implemented in URE05 is a multi-link (5-link) suspension. With this
suspension type, the designer has a large kinematic design freedom. The main difference between the
layout of the double wishbone and multi-link suspension is that the upper and lower A arms are coupled
in a double wishbone suspension and are decoupled from each other in a multi-link suspension design.
As a result, the rods forming the upper A-arm and lower A-arm in the double wishbone will not define a
plane anymore in multi-link suspension. This modification will eliminate the bending forces and
moments on the rods and the forces will be reacted along their own lengths in tension and compression
only.
The multi-link suspension design has several advantages and disadvantages. A large kinematic design
freedom can be obtained. High longitudinal and lateral stiffness is achievable. Bending forces and
moments are not present in the connection rods. On the other hand, the complexity of the design is
increased with a large number of suspension parts and it is more difficult to adjust suspension
parameters. Furthermore, when compared to double wishbone design, a multi-link suspension is slightly
heavier.
Taking into account these advantages and disadvantages, the multi-link suspension was selected for
URE05.
3.1. Kinematic suspension model
A kinematic multi-body analysis is necessary in order to analyze the behavior of the rear suspension of
the URE05 and to have a baseline for the development of the new suspension. There are several tools in
the industry for this purpose, such as ADAMS/Car. In this internship, MATLAB is used to create a
kinematic multi-body model. This model is developed in SIMMECHANICS, which is the multi-body
toolbox of MATLAB/Simulink.
In the kinematic multi-body analysis, the bump movement of the suspension is investigated. By this
analysis, it is possible to evaluate the characteristics of the rear suspension e.g. roll centre, anti effects.
In this model the rear suspension is constructed such that the upright is connected to the chassis with
connection rods (suspension rods) and ball joints at the both ends of each rod. As a result, the
movement of the upright is defined.
With this kinematic model, the multi-link suspension is modeled and the connection of the upright to
the chassis with six connection rods determines the kinematic behavior of this multi-link suspension.
These six rods consist of 4 connection rods, 1 tie rod and 1 push rod. The main constraint on the
locations of these rods is the available space. It is also possible to model a double wishbone suspension
with this model by selecting the same coordinates for the 2 rods for upper A-arm and 2 rods for lower A-
arm at the upright side. In Figure 8, the block diagram representing the multi-link suspension layout is
depicted.
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Figure 7: URE05 suspension rods
Figure 8: Block Diagram of a Multi-link Suspension Layout [7]
As it is observed from Figure 8, there is a steer rack block in the block diagram. With the kinematic
model it is possible to steer the rear wheels. However, since the rear wheels are not steered in the
racing car, the rear steering property of the model is not used, which means that the steer rack block is
not used throughout this internship.
3.2. Kinematic characteristics of the rear suspension of the URE05
As explained before, it is important to investigate the kinematic characteristics of the existing
suspension in order to improve it. In section 2, these characteristics are explained in detail and the
necessary equations required for calculations are given there. Now the results of these characteristics
for URE05 will be provided as obtained with the kinematic model.
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Camber angle change
Figure 9: Camber Angle Change of URE05
When Figure 9 is inspected, it can be seen that positive bump travel leads to a slight negative camber
angle and negative bump travel (rebound) leads to slight positive camber angle for URE05. This behavior
is favorable. As explained in section 2.1., it is beneficial to have negative camber during cornering for the
outside wheel since the lateral force is increased. During cornering, the outside wheel experiences a
positive bump travel and the inside wheel experiences a negative bump travel due to load transfer.
However, the trend depicted in Figure 9 is not sufficient. According to new tyre data, - 2 degree camber
angle for the outside wheel is the optimum camber angle for cornering in order to have the highest
possible lateral forces. From Figure 9, it can be seen that it is not possible to satisfy this demand with the
current rear suspension configuration.
It is possible to implement some static camber angle to the suspension in order to increase the amount
of negative camber during cornering. However, with this modification the static camber angle will lead
to lateral forces occurring in straight forward movement, which is not desirable since the highest
possible longitudinal force is decreased.
The chassis roll should be also taken into account while cornering. The suspension geometry determines
the roll angle, which strongly depends on the centre of gravity height and the roll stiffness of the
suspension. Another factor playing an important role in the roll attitude is the tyre since the vertical
stiffness of the tyre also affects the roll angle.
With lower roll stiffness a larger roll angle is obtained. This behavior has some impacts on the maximum
achievable lateral acceleration. It has been found that lower roll stiffness leads to a lower vertical
stiffness at the wheel centre during cornering, which in turn causes a reduced vertical tyre force
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fluctuation on uneven roads. As a result, the transmittable lateral forces by the tyre are increased, which
means that the lateral acceleration is also increased [7].
Figure 10: Inclination Angle with respect to Chassis Roll
In Figure 10, the inclination angle change with respect to chassis role is depicted. It is observed from
figure that, for a positive chassis roll there will be a positive inclination angle at the wheel and vice
versa. This behavior, for instance, is obtained on the left wheel while the vehicle is cornering to the
right. In this case, the left wheel will be the outer wheel and the chassis roll angle will be negative for
that wheel. So, the inclination angle change will be in the negative direction, which means that there will
be a camber loss. This situation is not desirable for the maximum achievable lateral forces.
The camber gain will be one of the requirements while designing the new suspension. Besides, the
camber loss due to chassis roll should be diminished with new suspension design.
-3 -2 -1 0 1 2 3-3
-2
-1
0
1
2
3
chassis roll angle [deg]
inclin
ation a
ngle
[deg]
URE05
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Toe angle change
Figure 11: Toe Angle Change
The characteristics of the toe angle are explained in section 2.2. in detailed. In Figure 11, the toe angle
change of URE05 is depicted for bump travel. As it is observed from the figure, there is a slight deviation
of toe angle from 0 degree over a wheel travel of -30 mm to 30 mm. In other words, the bump steer
behavior is close to zero, which is preferable since the lateral forces occurred by the bump steer is kept
small.
The wheels will generate a small toe out with positive bump travel. This is the situation which occurs on
the rear outer wheel while cornering and while acceleration. Besides, the wheels will generate toe-in
with negative bump travel and this is the situation of the inner wheel while cornering and the rear
wheels while braking.
This behavior of the toe angle with bump travel is not favorable. For instance, when the vehicle is about
to exit the corner, it will accelerate. In this case, the rear wheels will become more toe-out, which in
turn shift the vehicle into more oversteer tendency. As a result of this behavior, it becomes more
difficult for the vehicle to be stable in straightforward acceleration. However, since the amount of the
toe-out is small, it does not have a dramatic effect on the oversteer tendency of the vehicle.
Actually, the reverse effect of the toe angle is preferable so that the positive bump travel will generate
toe-in and the negative bump travel will not lead to any bump steer. As a result, the vehicle will be more
stable while leaving the corner. However, it should be always taken into account that bump steer should
be small in order to avoid lateral forces during bump travel.
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Roll center height
Figure 12: Roll center height change with bump travel
As mentioned in section 2.3, there is a compromise between having a high roll centre height and low roll
center height. High roll centre height brings the possibility of reduced body roll, but increases the jacking
effects.
From Figure 12, it is observed that the roll centre height for the rear suspension of the URE05 is almost
constant throughout the wheel travel and moderate so that jacking effects will not be present. Besides,
the lateral displacement of the tyre-road contact point is directly linked to the roll center height.
Relatively low roll center height results in a less lateral displacement of the tyre-road contact point.
However, it is still possible to increase the roll center height of the rear suspension a little bit more in
order to have less body roll.
-30 -20 -10 0 10 20 305.4
5.6
5.8
6
6.2
6.4
6.6
6.8
7Roll Center Height
wheel travel [mm]
roll
cente
r heig
ht
[mm
]
URE05
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Anti-squat
Figure 13: Anti-squat
As mentioned in section 2.4, the anti-squat percentage on the rear is important when the vehicle is
under acceleration. The required formulas for the anti-squat are given in section 2.2.4.
For the calculations:
The center of gravity height, h = 260 mm
The wheelbase, l = 1600 mm
In Figure 13, the anti-squat behavior of the rear suspension of the URE05 is depicted. The static value of
the anti-squat is set to be approximately 35%. When the Figure 13 is inspected, it is observed that the
anti-squat behavior of the suspension is not good in terms of progressiveness. It is more desirable to
have an anti-squat behavior which is increasing with increasing wheel travel so that during acceleration
the anti-squat value of the rear suspension will increase with positive bump travel. As a result of higher
progressiveness, there will be an increase in the amount of the forces transferred via suspension rods.
This results in a better performance during acceleration since the traction is increased on the rear
wheels.
-30 -20 -10 0 10 20 3024
26
28
30
32
34
36
38
40
42
44Anti-squat
wheel travel [mm]
Anti-s
quat
[%]
URE05
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Anti-rise
Figure 14: Anti-rise
The anti-rise behavior of a suspension is explained in section 2.5. It is important while braking on the
rear suspension. Similar to anti-squat, for calculations the following parameters are used;
The center of gravity height, h = 260 mm
The wheelbase, l = 1600 mm
The fore/aft brake force distribution, p = 0.8
In Figure 14, the anti-rise behavior of the rear suspension of URE05 is depicted. The static value of the
anti-rise is set to be around 12.5 %. When the figure is examined, it is observed that the behavior of the
suspension is quite linear. A higher value is desirable but this is not possible since the anti-rise behavior
is strongly linked to the anti-squat value.
-30 -20 -10 0 10 20 3010
10.5
11
11.5
12
12.5
13
13.5
14
14.5
15Anti-rise
wheel travel [mm]
Anti-r
ise [
%]
URE05
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Tyre-road contact point motion
Figure 15:Longitudinal tyre-toad contact point motion
Figure 16: Lateral tyre-road contact point motion
It is observed from Figure 15 that when the bump travel is positive, the tyre moves backwards in the
longitudinal direction of the vehicle. And when the bump travel is negative, the tyre moves forwards in
the longitudinal direction of the vehicle.
When the Figure 16 is inspected, it is seen that with negative bump travel the tyre-road contact point
shifts to inward. However, for positive bump travel the contact point first shifts to outward till a certain
value of bump travel which is 0.6 cm. Then, the contact point starts to shift inwards again.
From Figure 15 and Figure 16, it is seen that there is a slight tyre-road contact point motion.
Lateral displacement of the tyre-road contact point is important in terms of track width change and it is
directly related to roll center height. It is desirable not to have big changes in the track width with bump
travel since track width change will impair the traction.
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Vertical force (spring rate) and forces on suspension rods
Figure 17: Vertical Force with respect to bump travel
Figure 18: Forces on the rods with bump travel
In Figure 17, the force at the wheel center during bump travel bump travel is depicted. This is the so
called spring rate at the wheel center. From the experiences of last year, this characteristic is found out
to be satisfactory.
In Figure 18, the forces on the rods are depicted for bump travel. The labeling of the rods is given in
Figure 7. The magnitudes of the forces on rods are not problematic since there is not any buckling
problem. However, there is a free play problem for the ball joints, which is most likely due to excessive
forces. This problem should be taken into account for new design.
-30 -20 -10 0 10 20 30-3000
-2000
-1000
0
1000
2000
3000
4000Vertical Force
wheel travel [mm]
vert
ical fo
rce [
N]
URE05
-30 -20 -10 0 10 20 30-6000
-4000
-2000
0
2000
4000
6000
8000
wheel travel [mm]
rod f
orc
e [
N]
p1
p2
p3
p4
p5(tierod)
p6(push)
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4. Kinematic suspension design It is important to determine the requirements and constraints for the new suspension. Therefore, the
pro and cons of the rear suspension of URE05 are analysed and based on this evaluation the parts that
need to be improved are determined.
The kinematic suspension model which is explained in section 3.1 is used for designing the new rear
suspension.
4.1. Requirements and constraints on the rear suspension of the URE06
When the kinematic behavior of the rear suspension of URE05 is examined and the experienced
problems of last year are taken into account, the following requirements are aroused:
1. The negative camber gain during cornering is not sufficient. According to the new tyre data,
during cornering -2 degree of camber angle provides the highest possible lateral force.
Therefore, the new rear suspension should provide higher negative camber gain during
cornering for the outer wheel.
2. The toe behavior of the rear suspension needs to be changed so that the vehicle will be more
stable after leaving the corner. In other words, there should be more toe-in on compression.
3. The roll center height can be increased so that less stiff torsion stabilizer can be used for the
same body roll with last year or less body roll will be obtained with the same stiffness as last
year. However, jacking effects should be taken into account.
4. Anti-squat behavior of the rear suspension should be less degressive so that the vertical forces
on the tyre contact patch during the first mili-seconds of the acceleration can be increased,
which provides better traction at the first mili-seconds of the acceleration.
5. Low centre of gravity
6. When the rear suspension of the URE05 is inspected, it is observed that some of the pickup
points on the chassis side are not stiff enough since these points are floating points in the space
and are not exactly on the rear frame. These pickup points should be shifted to the rear frame
so that the forces on the suspension rods will directly transferred to the chassis, which will
increase the stiffness.
7. Easy set-up adjustment. Any adjustment on the camber angle should not affect the toe behavior
of the vehicle.
While developing the new rear suspension, tight space constraints should be kept even. For the URE06
the rear end is shifted to the front by 40 mm, which makes the space constraint more important.
Cooperation is necessary with the other team members in order to obtain an optimal vehicle including
the mounting of the engine, differential support and drive-shaft as well as the locations of the
suspension rods.
4.2. Design of the rear suspension of the URE06
After determining the requirements and constraints, a literature survey has been done in order to see
which suspension type fits the requirements best. The suspension of the other racing teams have been
24
investigated and it has been found out that for the requirements the double-wishbone suspension is
suited best and it is the most common suspension design for racing cars these days.
In order to determine the exact coordinates of the pickup points, an iterative method has been used. In
total 81 design iterations have been made. After each iteration, the kinematic behavior of the rear
suspension is examined and modifications are made where necessary. At the same time the rear frame,
the rocker and the spring were also redesigned. At each iteration the demands coming from the rear
frame, the rocker and the spring are also taken into consideration.
4.2.1. Initial concept
In Figure 19, the initial concept is depicted.
Left Side View
Top View
Rear View
Isometric View
Figure 19: Initial URE06 rear suspension concept
As it can be seen from Figure 19 that p1 and p2 form the lower A-arm, p3 and p4 form the upper A-arm
and p5 is the toe link. In side view, the rods are labeled and in top view the chassis and the upright side
are shown.
Firstly, the pickup points of the upper A-arm and the lower A-arm on the upright side are determined to
be on the same vertical line when looked from the side view. Besides, the toe link is located such that
the lower A-arm pickup point on the upright side and the pickup point of the toe link on the upright side
will be on the same horizontal line in x direction when looked from the top view. As a result of this
configuration, any change in the static camber as applied at the upper A-arm connection will not affect
the toe angle of the wheel.
25
Figure 20: Movement of the A-arms with bump travel
As mentioned above, one of the requirements is the camber gain during cornering. First of all, the
kinematics of the camber angle change during bump travel should be understood. The camber change
with bump travel is strongly depending on the arcs that are drawn by the upper and lower A-arms. As it
is observed from Figure 20 that when the wheel is moved upwards (positive bump travel), the pickup
point of the upper A-arm on the upright side gets more close to the chassis when compared to the
pickup point of the lower A-arm on the upright side. As a result of this motion, the upper side of the
wheel is tilted to the chassis, which in turn changes the camber angle so that during cornering it is
possible to obtain negative camber on the outer wheel. Therefore, in order to obtain maximum camber
gain with bump travel the pickup point of the upper A-arm is tried to be kept as high as possible on the
upright side and it will be more inwards on the rear view (closer to the chassis) when compared to the
pickup point of the lower A-arm on the chassis. With this kind of configuration, the arcs drawn by the A-
arms will provide the maximum camber gain. It should be noted that the camber gain is mostly
influenced by the angle and length of the upper A-arm because the lower A-arm is subjected to tight
space constraints. On the other hand, the location of the upper A-arm pick-up points can be selected
more freely.
Furthermore, the roll center height is also important kinematic characteristic of the suspension. The rear
view instant center determines the height of the roll center which is explained in section 2.3. The
coordinates of the pickup point of the p1 and p4 on the chassis side is located with an intention of
optimal roll center height.
Moreover, the forces on the rods are very important. As it can be seen on the top view of Figure 19, the
pickup point of the tie rod on the upright side is located as far backwards as possible. Such a
configuration also increases the lateral stiffness of the rear suspension.
The pickup point of the tie rod on the chassis side is determined in order to obtain as less as possible toe
changes on bump. The kinematic behavior of the tie rod should be known for this purpose. If the tie rod
26
path originates from the rear view instant center, there will be zero bump steer. In other words, the
center of the arc followed by the tie rod ball joint must be coincident with the suspension rear view
instant center [6].
Finally, the coordinates of the pickup points of the p2 and p3 on the chassis side are determined
according to the desired anti-squat percentage. Furthermore, these pickup points are shifted to the roll-
hoop so that the stiffness problem of the URE05 has been solved because with this concept the forces
on p2 and p3 will directly transferred to the chassis instead of using a separate subframe.
4.2.2. Final concept
Left Side View
Side View
Top View
Top View
Rear View
Rear View
Figure 21: The final concept
As it is seen from Figure 21, there are several differences between the initial concept and final concept.
27
Firstly, the pickup points of the upper A-arm and lower A-arm on the upright side are separated from
each other so that p1, p2, p3 and p4 become individual suspension rods. With this alteration, the rear
suspension becomes multi-link suspension but the characteristics of the suspension are very close to a
double-wishbone. As a result of this concept, the bending moments and forces are eliminated from the
suspension rods. With a double wishbone suspension, the lower and upper A-arms form a triangular
plane in the space. When these planes are loaded from the pickup points through ball joints, the forces
on the plane will not be distributed along the suspension rods, which create bending moments and
forces on the suspension rods. However, in multi-link suspension since all the suspension rods are
separated, the forces coming from the pickup points will be along the rods, which means that the rods
can be either in compression or tension but not bending.
Another alteration is that the pickup points of p1 and p4 are shifted to the front of the car in the positive
x direction. This is not ideal; however, these points are shifted due to space constraints coming from
rear frame. With this change, the forces on the suspension rods are increased, especially on p1 and p4.
However, the shifting of the pickup points is performed with in the limitations such that the rods can
handle the increase in the forces.
For other pickup points, there are minor changes in order to obtain the optimum suspension
characteristics.
4.2.3. The kinematic characteristics of the rear suspension of the URE06
The spring stiffness is kept same as the URE05 as 61000N/m. The stiffness at the wheel center for the
URE05 is 85000N/m and for the URE06 is 44000N/m. In appendix A, the suspension coordinates is
provided.
Camber Angle Change
Figure 22: Camber angle change comparison
-30 -20 -10 0 10 20 30-2
-1.5
-1
-0.5
0
0.5
1
1.5
2camber angle change
wheel travel [mm]
cam
ber
[deg]
URE05
URE06
28
Figure 23: Inclination angle comparison
It is observed from Figure 22 that camber gain for positive bump travel is much larger for the URE06
when compared to the URE05. As mentioned in 4.1, one of the requirements is that the camber angle of
the outer wheel needs to be -2 degree to obtain the highest lateral force. With the rear suspension of
URE 06, this will be possible when also introducing a static camber angle.
Furthermore, the negative camber loss on the outer wheel due to chassis rolls during cornering is
diminished, which is depicted in Figure 23. This behavior will contribute to achieve the first requirement.
Toe angle
Figure 24: Toe angle comparison
-3 -2 -1 0 1 2 3-3
-2
-1
0
1
2
3
chassis roll angle [deg]
inclin
ation a
ngle
[deg]
URE05
URE06
29
Like the URE05, the toe angle change of the wheels with bump travel is close to zero, which means that
there is almost no bump steer. As a result, the requirement of zero bump steer is satisfied.
When the Figure 24 is inspected, it is observed that the toe behavior of the rear suspension has been
reversed and for negative bump travel the wheels will have a slight toe out and for positive bump travel
the wheels will have a slight toe in for URE06. This behavior leads the car to more over-steer tendency
during braking, which is not desirable but since the amount of the toe-out is very small, it will not lead to
any problem. And during acceleration, which means that the wheels experience negative bump travel,
after leaving the corner the car will get into more under-steer tendency so that the straight forward
stability is increased. As a result second requirement is satisfied.
Roll center height
Figure 25: The roll center height comparison
As it is observed from Figure 25, the roll center height of URE06 is increased when compared to URE05.
The static value is almost 15 mm. With higher roll center, it is possible to use a less stiff anti-roll bar for
URE06. The roll center height is still low so that jacking effects are not a problem, however, this has not
been proved and this comment is made with engineering intuition. As a result, third requirement is
satisfied.
-30 -20 -10 0 10 20 305
10
15
20Roll Center Height
wheel travel [mm]
Roll
Cente
r H
eig
ht
[mm
]
URE05
URE06
30
Anti-squat
Figure 26: Anti-squat comparison
It is observed from Figure 26 that the static value of the anti-squat percentage of the rear suspension of
URE06 is almost close to the URE05 and it is approximately 36%. Here, the important behavior of the
anti-squat percentage of the URE06 is that it is less degressive when compared to URE05 so that with
increasing bump travel the loss on the anti-squat percentage will be less. This behavior provides better
traction during acceleration. As a result, fourth requirement is also satisfied.
Anti-lift
Figure 27: Anti-lift comparison
-30 -20 -10 0 10 20 3024
26
28
30
32
34
36
38
40
42
44Anti-squat
wheel travel [mm]
Anti-s
quat
[%]
URE05
URE06
-30 -20 -10 0 10 20 304
6
8
10
12
14
16Anti-lift
wheel travel [mm]
Anti-lift
[%]
URE05
URE06
31
From Figure 27, it is seen that anti-lift percentage of the vehicle is decreased somewhat. It is desirable to
have a higher value but this is not possible since the anti-lift percentage is directly linked to the anti-
squat value. The anti-lift percentage is 6% at zero wheel travel.
Tyre-road Contact Point Motion
Figure 28: Longitudinal tyre-toad contact point motion comparison
Figure 29: Lateral tyre-road contact point motion comparison
In Figure 28, the longitudinal tyre-road contact point motion is depicted. It is observed that the behavior
of URE06 is very close to the URE05. The longitudinal tyre road contact point motion is directly related
to the anti-lift. Since the anti-lift percentage has not been changed much when compared to URE05, the
longitudinal motion stays almost same with URE05.
In Figure 29, it is observed that the lateral motion of the tyre-road contact point is increased. The lateral
motion of the tyre-road contact point is linked to the roll center height. As the roll center height is
increased, the lateral motion of the tyre-road contact point increases. However, still the lateral motion
of URE06 is very small so that it will not lead to any problem with traction.
32
5. Force Analysis for the Worst Case Scenarios In this chapter, firstly forces on the rear suspension of the URE05 and the URE06 are compared for
positive and negative vertical bump motion of the wheel. Then, a force analysis for the worst case
scenarios is performed and the results are provided.
Vertical forces (spring rate) and forces on the suspension rods
Figure 30: Vertical force comparison
As it is observed from Figure 30, the spring rate at the wheel center is decreased dramatically for URE06.
The spring rate for the URE05 is 85000 N/m and for the URE06 is 44000 N/m. This alteration is not
desirable and for further designs on the rear suspension, rocker design should be kept in mind.
Figure 31: Forces on the rods with bump travel
-30 -20 -10 0 10 20 30-3000
-2000
-1000
0
1000
2000
3000
4000Spring Rate at the Wheel Center
wheel travel [mm]
vert
ical F
orc
e a
t th
e W
heel C
ente
r [m
m]
URE05
URE06
-30 -20 -10 0 10 20 30-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
wheel travel [mm]
rod f
orc
e [
N]
p1
p2
p3
p4
p5(tierod)
p6(push)
33
When the Figure 18 and Figure 31 are compared, it is observed that the forces are more evenly
distributed among rods for URE06 when compared to URE05, which is beneficial in terms of the
suspension rods.
A force analysis is performed for the suspension rods for different worst case scenarios in order to see
the magnitude of the forces on the rods. There are four worst case scenarios, namely, severe cornering,
severe acceleration, severe braking and bump travel.
For the following scenarios, the parameters used are as follows;
Mass of the vehicle, m = 298 kg
Half length of the wheelbase, a = 0.8 m
Half length of the wheelbase, b = 0.8 m
Height of the centre of gravity, h = 0.26 m
Gravitational acceleration, g = 9.81 m/s2
Radius of the wheel, r = 0.26 m
5.1. Acceleration
Figure 33:Load transfer during acceleration
For this scenario, the acceleration ax is taken as 1g. In Figure 32, the forces acting on the wheel during
acceleration are depicted. In this scenario, the vehicle is accelerating in the positive x direction in a
straight line. In this situation, the wheel depicted in Figure 32 is the rear left wheel.
The required forces are calculated as follows:
�� = �∗� ! (5.1)
In Figure 33, the load transfer is shown. Note that a=b. When the moment about the contact point of
the rear wheel is taken;
Figure 32: Forces during acceleration
34
"# = $�%&�'& − ∆�)* ∗ (+ + -) + . ∗ +� ∗ ℎ − . ∗ 0 ∗ - = 0 (5.2)
∆�) ∗ (+ + -) = . ∗ +� ∗ ℎ (5.3)
∆�) = �∗� ∗�(�'&) (5.4)
�) = ∆12! + �∗%
3 (5.5)
Magnitude of the forces applied to the wheel center, which is depicted in Figure 32, are given in Table 1.
Magnitude
Fx [N] 1462
Fy [N] 0
Fz [N] 968
Mx [Nm] 0
My [Nm] 0
Mz [Nm] 0
Table 1: Forces applied to wheel center in acceleration
The resultant forces on the suspension rods are provided in Table 5 and Table 6.
5.2. Braking
Figure 34: Forces during braking
Figure 35: Load transfer during braking
For this scenario, the braking acceleration ax is taken as 1.5g and brake force distribution p is taken as
0.6. In Figure 34, the forces acting on the wheel during acceleration are depicted. In this scenario, the
vehicle is braking straightforward in the positive x direction. In this situation, the wheel depicted in
Figure 34 is the rear left wheel.
The required forces are calculated as follows:
35
�� = (1 − 4) ∗ �∗� ! (5.6)
#5 = �� ∗ � (5.7)
In Figure 35, the load transfer is shown. When the moment about the contact point of the rear wheel is
taken;
ΣM = $8∗9! − ∆Fz* ∗ (a + b) − m ∗ ax ∗ h − m ∗ g ∗ b = 0 (5.8)
∆�) ∗ (+ + -) = −. ∗ +� ∗ ℎ (5.9)
∆�) = ��∗� ∗�(�'&) (5.10)
�) = ∆12! + �∗%
3 (5.11)
Magnitude of the forces applied to the wheel center, which is depicted in Figure 34, are given in Table 2.
Magnitude
Fx [N] -877
Fy [N] 0
Fz [N] 968
Mx [Nm] 0
My [Nm] 228
Mz [Nm] 0
Table 2: Forces applied to wheel center in braking
The resultant forces on the suspension rods are provided in Table 5 and Table 6.
5.3. Cornering
Figure 36: Forces during cornering
In this scenario, the vehicle is taking a corner with acceleration ay of 1.5g and the vehicle is considered
to be on the edge of the roll over so that the inner wheels do not establish a contact with road.
36
Therefore, all the weight of the vehicle is taken by the outer wheels and all the lateral forces are applied
to the outer wheels. In this situation, the vehicle is making a turn to the right and the wheel depicted in
the Figure 36 is the rear left wheel.
�5 = �∗�B! (5.12)
∆�) = �∗%3 (5.13)
�) = ∆�) + �∗%3 (5.14)
Magnitude of the forces applied to the wheel center, which is depicted in Figure 36, are given in Table 3.
Magnitude
Fx [N] 0
Fy [N] -2193
Fz [N] 1462
Mx [Nm] -571
My [Nm] 0
Mz [Nm] 0
Table 3: Forces applied to wheel center in cornering
The resultant forces on the suspension rods are provided in Table 5 and Table 6.
5.4. Bump
Figure 37: Forces during bump
In this scenario, since the spring rates for the URE05 and the URE06 are not similar, two times the static
vertical load is applied to the wheel center in order to make a better comparison between the URE05
and the URE06. In this situation, the wheel depicted in Figure 37 is the rear left wheel.
∆�) = �∗%3 (5.15)
�) = ∆�) + �∗%3 (5.16)
37
Magnitude of the forces applied to the wheel center, which is depicted in Figure 37, are given in Table 4.
Magnitude
Fx [N] 0
Fy [N] 0
Fz [N] 1462
Mx [Nm] 0
My [Nm] 0
Mz [Nm] 0
Table 4: Forces applied to wheel center in bump movement
The resultant forces on the rods are given in Table 5 and Table 6.
5.5. Resultant forces
URE05 Static position
[N]
Acceleration
[N]
Braking
[N]
Cornering
[N] Bump [N]
p1 1451 965 3772 5320 3417
p2 -69 432 -778 -4971 -162
p3 -28 353 -638 -8002 -65
p4 59 -699 1659 2660 140
p5(tie rod) -570 -43 -4112 -8286 -1343
p6(push rod) -1111 -1476 -604 -7801 -2575
positive values (tension) negative values (compression)
Table 5: Resultant forces for worst case scenarios for the URE05
URE06 Static position
[N]
Acceleration
[N]
Braking
[N]
Cornering
[N] Bump [N]
p1 935 915 3505 7125 1986
p2 249 -34 502 -2569 539
p3 -85 -1090 -123 1480 -145
p4 -371 -744 -95 1987 -818
p5(tie rod) -165 716 -2677 -6543 -330
p6(push rod) -874 -2174 -945 -3704 -1809
positive values (tension) negative values (compression)
Table 6: Resultant forces for worst case scenarios for the URE06
In Table 5 and Table 6, the resultant forces are depicted for different scenarios, respectively for the
URE05 and the URE06. The highest forces on each suspension rod are labeled with dark background and
positive values show that rod is under tension and negative values show that rod is under compression.
The first scenario (static) is the standstill situation and there is no force applied on the wheels. The
38
second one is acceleration with 1g, the third one is braking with 1.5g and the fourth scenario is
cornering with 1,5g. In the final scenario (bump), two times of the vertical static force is applied to the
wheel center. First four scenarios do not include bump travel, in other words, the bump travel is zero for
these scenarios. For the resultant forces,
When Table 5 and Table 6 are compared with each other, it is observed that the highest amount of the
forces on each suspension rods for the URE05 is almost same with the URE06. Since there was not a
problem with the suspension rods and ball joints of the URE05 when they were loaded, it is expected
not to have any problem with the suspension rods of the URE06 neither.
39
6. Conclusion and recommendations
6.1. Conclusions
The objective of this internship is to develop a new rear suspension for the URE06 FSAE vehicle. The
kinematic characteristics of the rear suspension of the URE05 have been investigated. For the new
design, several design iterations are performed in order to obtain superior kinematics for the new rear
suspension by taking into account the tight space constraints. Finally, a force analysis is performed on
the new rear suspension considering several worst case scenarios in order to check the forces acting on
the various suspension rods.
The next list summarizes the improvements of the rear suspension design:
• The negative camber gain during cornering is improved.
• The toe angle behavior with bump becomes better during acceleration and braking.
• Less stiff anti-roll bar can be implemented to the suspension.
• More progressive anti-squat behavior is obtained.
• The structural stiffness of the rear suspension is increased.
The type of the rear suspension of URE06 is very close to double-wishbone. However, in order to use the
advantage of the multi-link suspension, in which there are no bending forces and moments present in
the suspension rods, the upper and lower A-arm’s pickup points on the upright side are separated so
that instead of these A-arms, which form a triangular plane in space, the suspension system consists of
only individual rods.
6.2. Recommendations
There are several points that can be improved with the future designs.
It is better to use pull rod instead of push rod on the suspension since any deflection with pull rod on
the upright will contribute to the negative camber gain since it is pulling the upper part of the upright to
the chassis. However, in order to implement pull rod to the suspension, the mounting of the spring and
rocker should be considered at the early stages of the design. Otherwise, it might be impossible to
package the pull rod, the spring and the rocker due to space constraints.
The toe link could be made adjustable so that the kinematic behavior of the wheels can be changed. This
modification will allow obtaining optimum vehicle dynamic behavior for different race events. To
illustrate, for skippad event the toe behavior of the rear suspension could be altered in such a way that
the vehicle will have understeer tendency, which will increase the stability of the vehicle.
Another, improvement could be implementing an adjustable anti-squat percentage for the suspension.
As a result of this modification, 100 % anti-squat percentage can be obtained for the acceleration events
so that all the load transfer due to acceleration will be transmitted to contact patch through suspension
rods, which will improve the traction upon the application of the traction force.
40
References
[1] ISO 8855 Road vehicles Vehicle dynamics and road-holding ability Vocabulary.
[2] I. Besselink. Vehicle Dynamics, Lecture notes of the 4L150. Eindhoven University of Technology, 2008
[3] http://www.lancerevoclub.org/faq/img/toe.gif
[4] http://www.240edge.com/performance/tuning-toe.html
[5] http://www.formulastudent.de/academy/pats-corner/advice-details/article/pats-column-february/
[6] W. Rowley. An Introduction to Race Car Engineering. Rowley Race Dynamics ISBN10: 0973432004,
2003
[7] W. Lamers. Development and analysis of a multi-link suspension for racing applications, DCT
2008.077
41
Appendix
A. URE06 Suspension Coordinates
The mentioned coordinates are given for the rear left suspension. The vehicle is symmetric over the x-
axis. The coordinates of the right suspension are found by multiplying the y-coordinates with -1.
The rods are labeled in Figure 38.
Isometric View
Top View
Rear View
Side View
Figure 38: Suspension rod coordinates
42
d.rear.chassis.p1 = [0.105 0.178 0.117]; d.rear.chassis.p2 = [0.643 0.309 0.170]; d.rear.chassis.p3 = [0.643 0.308 0.340]; d.rear.chassis.p4 = [0.130 0.230 0.272]; d.rear.chassis.p5 = [-0.105 0.184 0.113];
d.rear.chassis.p6 = [0.1494 0.3440 0.3766];
d.rear.upright.p1 = [0.010 0.486 0.160]; d.rear.upright.p2 = [0.040 0.486 0.160]; d.rear.upright.p3 = [0.040 0.465 0.357]; d.rear.upright.p4 = [0.010 0.465 0.357]; d.rear.upright.p5 = [-0.105 0.486 0.160]; d.rear.upright.p6 = [0.075 0.470 0.185];
d.rear.upright.wc = [0.0000 0.5875 0.2550];
