College of Engineering and Computer Science
Mechanical Engineering
Final Project Report:
FSAE Suspension
California State University, Sacramento
Mechanical Engineering 191
Senior Project
May 21, 2009
Team Members
John Murray
Bryan Rowley
Jarret Vian
Executive Summary:
Every year, California State University Sacramento (CSUS) offers its
students the opportunity to enter a Formula Society of Automotive
Engineers (FSAE) race car competition in which students must form
teams to design and build a complete race car. It is the goal of this project
to design and build a suspension system that could be used in a FSAE
racecar. The major requirement for the suspension is that it must meet all
of the FSAE rules, in order to be eligible to participate in the competition.
The rules dictate a minimum 2 inch total suspension travel, minimum 60
inch wheelbase, and minimum size requirements for the drivers cockpit.
An in depth design and analysis was performed on the suspensions
Geometry and subsequent handling performance characteristics. These
parameters were set up to provide a high performance, neutral handling,
and easily adjustable car. The parts and assemblies are designed with
performance, weight, simplicity, cost and manufacturability as the main
design goals. Steel is used extensively as a low cost high strength
material, while several parts also use aluminum where weight and
performance are critical. The reduction of parts in the overall assembly is
achieved by refining the suspension adjustment points to only those that
are necessary. The Budget for the system ended at under $1000 and was
able to utilize many of the previous year’s vehicles components to lower
cost. The fabrication was done on site using CSUS facilities and was
performed by members of the FSAE team. Testing was performed on the
system and it was determined to meet all of the project goals and
requirements. The stress results were well within material yield
requirements and the geometry results were within 7% of the designed
specifications.
2
Table of contents
ADVISORS: ............................................................................................................................................... 6
GLOSSARY: ............................................................................................................................................... 7
PROBLEM DESCRIPTION: .......................................................................................................................... 9
BACKGROUND: ............................................................................................................................................... 9
PROBLEM DEFINITION: .................................................................................................................................... 9
PURPOSE: ................................................................................................................................................... 10
PROJECT REQUIREMENTS: ..................................................................................................................... 11
RULES AND REGULATIONS: ............................................................................................................................. 11
PERFORMANCE:............................................................................................................................................ 12
DESIGN DESCRIPTION: ........................................................................................................................... 15
GEOMETRY: ................................................................................................................................................. 15
INITIAL DESIGN ANALYSIS: ..................................................................................................................... 17
WHEEL LOAD CALCULATIONS: ......................................................................................................................... 17
WHEEL TRAVEL: ........................................................................................................................................... 24
THE UPRIGHT:.............................................................................................................................................. 25
REDESIGN: ............................................................................................................................................. 40
HISTORY: .................................................................................................................................................... 40
THE FINAL DESIGN: ....................................................................................................................................... 41
MANUFACTURING: ................................................................................................................................ 43
A-ARMS ..................................................................................................................................................... 44
UPRIGHT AND HUB ASSEMBLY ......................................................................................................................... 46
ASSEMBLY INSTALLATION ............................................................................................................................... 47
TESTING: ................................................................................................................................................ 48
GEOMETRY TESTING: ..................................................................................................................................... 48
UPRIGHT TESTING: ........................................................................................................................................ 50
FUTURE TESTING PLANS: ................................................................................................................................ 56
DESIGN VERIFICATION ANALYSIS: .......................................................................................................... 57
CONCLUSION AND FUTURE PLANS: ........................................................................................................ 69
APPENDICES: .......................................................................................................................................... 70
3
Table of figures:
Figure 1: 2006-2007 CSUS 60° tilt test ............................................................... 13
Figure 2: 2004 Formula SAE Track Map ............................................................. 14
Figure 3: SusProg3D rear suspension ................................................................ 15
Figure 4: relevant Geometry for static loading .................................................... 19
Figure 5: Geometry Relative to Lateral Load Transfer ........................................ 21
Figure 6: Dimensions and Loads ........................................................................ 28
Figure 7: Resolved hub force and moment ......................................................... 29
Figure 8: Upright General dimensions and loads ................................................ 30
Figure 9: Mechanical trail sketch......................................................................... 31
Figure 10: Steering sketch .................................................................................. 31
Figure 11: Braking sketch ................................................................................... 32
Figure 12: Fatigue hand calculation .................................................................... 33
Figure 13: Spindle load, hand calculation ........................................................... 34
Figure 14: Geometric stress concentration chart ................................................ 35
Figure 15: Spindle corrected stress hand calculation.......................................... 35
Figure 16: Hub-Spindle FEA ............................................................................... 36
Figure 17: Original Upright Initial FEA................................................................. 37
Figure 18: Original upright second FEA .............................................................. 37
Figure 19: Original Upright Assembly ................................................................. 38
Figure 20: Exploded Original upright Assembly ................................................. 39
Figure 21: Original upright assembly, comparison .............................................. 40
Figure 22: Final upright assembly ....................................................................... 42
Figure 23: Spherical bearing housings ................................................................ 43
Figure 24: A-Arm Computer Model ..................................................................... 44
Figure 25: A-Arm Jig ........................................................................................... 44
Figure 26: A-Arm Welding ................................................................................... 45
Figure 27: Completed A-Arms............................................................................. 45
Figure 28: Fabricated upright .............................................................................. 46
Figure 29: Machined hub-spindles ...................................................................... 46
Figure 30: Installation of suspension assembly .................................................. 47
Figure 31: Track width testing ............................................................................. 48
Figure 32: Caster angle measurement................................................................ 49
Figure 33 ............................................................................................................. 50
Figure 34: Upright abrasion ................................................................................ 51
Figure 35: Strain gauges, installed...................................................................... 52
Figure 36: Soldering of strain gauge wires .......................................................... 52
Figure 37: Measuring strain ................................................................................ 53
Figure 38: Loading tire ........................................................................................ 54
Figure 39: Tire load reading ................................................................................ 55
Figure 40: Data logging flow chart ...................................................................... 56
Figure 41: Experimental camber data ................................................................. 57
Figure 42: Theoretical camber data .................................................................... 58
Figure 43: Camber vs. roll experimental ............................................................. 59
Figure 44: Camber vs. body theoretical .............................................................. 59
Figure 45: Strain gauge analysis ........................................................................ 60
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Figure 46: Rosette 1 ........................................................................................... 62
Figure 47: Rosette 2 ........................................................................................... 62
Figure 48: Rosette 3 ........................................................................................... 63
Figure 49: Extrapolated strain gauge stresses .................................................... 63
Figure 50: FEA of final upright assembly ............................................................ 64
Figure 51: FEA compared to rosette 1 ................................................................ 64
Figure 52: FEA stress compared to rosette 2 ..................................................... 65
Figure 53: FEA compared to rosette 3 ................................................................ 66
Figure 54: Susprog 3D pictorial........................................................................... 68
5
Advisors:
Dr. Timothy Marbach
California State University Sacramento Faculty Member
Ph.D., Mechanical Engineering
University of Oklahoma, Norman, OK
Office: RVR 4038
Office Phone: 916-278-6089
Email: marbacht@ecs.csus.edu
Research Interests:
Thermodynamics, Combustion and Energy Systems
Pat Homen
Office: RVR 1003/1005
Office Phone: 916-278-5956
Email*: homenp
Dr. Sprott, Kenneth S.
California State University Sacramento Faculty Member
Ph.D., Mechanical Engineering
University of California, Davis, CA
Office: RVR 4031
Office Phone: 916-278-6308
Email: sprottk@ecs.csus.edu
Research Interests:
Machine Design, Mechatronics, Robotics, Computer Aided Design
6
Glossary:
The following is a list of terms that will be discussed and referenced
throughout this project:

Ackerman Principle  During a turn the inner wheel follows a narrower
radius than the outer tire

Bell-crank  Mechanism that relates wheel motion to spring motion
(also known as a Rocker)

Bump Steer  Steering effect caused by changes in camber and toe
during vertical wheel movement

Caster Angle  Inclination of upright mounting points relative to wheel
centerline as viewed from the side of the car

Camber  Angle of the tire with respect to the road as viewed from the
front

Droop/Rebound  Negative displacement of the wheel and/or spring

Instant Center (Front/Rear)  Imaginary point in space at which the
upper and lower a-arm planes meet as viewed from the front (or rear)

Instant Center (side)  Imaginary point in space at which the upper
and lower a-arm planes meet as viewed from the side

Instant Axis  Three dimensional line that connects the front view and
side view instant centers

Front View Swing Arm (fvsa)  Virtual swing arm that relates changes
in suspension geometry to wheel movement (related to IC and upright
mounting points) – affects lateral load properties

Side View Swing Arm (svsa)  Virtual swing arm that relates changes
in suspension geometry to wheel movement (related to IC and upright
mounting points) – affects longitudinal load properties

Jounce/Bump  Positive displacement of the wheel and/or spring

Kingpin Inclination (kpi)  Inclination of upright mounting points
relative to wheel centerline as viewed from the front
7

Motion Ratio  Relationship between spring movement and wheel
movement

Pull-rod  Rod that links the upper a-arm to the bell-crank

Roll  The angular roll of the chassis with respect to the ground

Roll Center  The point in space which the vehicle desires to roll
about

Roll Axis  An imaginary line that passes through the front and rear
roll centers

Scrub Radius  The distance between the intersection of the steering
axis and the wheel tire patch centerline and the ground

Short Long Arm (SLA)  The use of unequal length a-arms for the top
and bottom (also known as double wishbone and double a-arm)

Spindle  Shaft that connects the wheel to the upright and allows it to
spin freely

Tire Patch  Distorted area of tire in contact with the ground

Tire Vertical Rate  The effective spring rate of the tire

Toe  Relative angle of the wheels with respect to each other (in – the
wheels point toward each other, out – the wheels point away from each
other) as viewed from the top

Track Width  Distance between the right and left wheels when
viewed from the top

Upright  Main component of the suspension that connects the wheel,
pull-rod, and steering arm

Wheelbase  Distance between front and rear wheel centerlines as
viewed from the side
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Problem Description:
Background:
California State University, Sacramento (CSUS) participates in an annual
national competition between mechanical engineering departments from a
broad range of universities across the country. This program is organized
by SAE International (formerly Society of Automotive Engineers) and is
designed to give students the opportunity to fully design, analyze, build,
and test a fully functional formula style race car. Utilizing theories and
methods learned in classrooms students are charged with the tasks of
leaving the classroom and putting the skills learned to real life
applications.
The target market for the race car is the non-professional race car
enthusiast. The motivation for the project is that a fictitious manufacturing
company is hiring a design team to design and construct a complete race
car. With this type of project students are introduced to real life situations
related to engineering including concepts such as design, manufacturing,
and even organization and finances.
The design encompasses a series of rules and requirements along with
timely deadlines the students must meet in order to enter and compete in
the event. The rules and regulations are set by the SAE International
Collegiate Design Group and are intended to develop problem solving
skills similar to those needed in real world engineering problems and
ensure that students work in a safe and professional manner.
The students are given a full year to elect members to form and manage
teams or organizations, design, build, and fully test the race cars
capabilities. Prior to entering the competition the cars are put through a
series of rigorous inspections by a panel of industry professionals with real
life race car experience. Any decision with the design of the car must be
explained and fully justified by the design team. Once inspected the car is
put through a series of competitions that measure and test all levels of the
race car’s performance including skid pad, acceleration, autocross and an
endurance tests.
Problem Definition:
Designing a race car is a very detailed and very lengthy process and is
open to all forms of design ideas as long as the rules and regulations are
met. The team is required to design every aspect of the car from the
wheels to the seat and every decision must be justifiable and reasonable.
The students are given a budget which can vary depending on sponsor
support and are required to purchase all relative components and
9
materials to complete the car. The primary components that the team
must have in order to form a functional car are an engine, a chassis, a
suspension/steering system, and a braking system.
One of the most crucial components of a FSAE race car is the suspension
system as its benefits outweigh many other aspects of cars performance.
A car with a properly designed and tuned suspension system will
consistently reduce lap times and will provide a more effective use of the
engines power. Suspension systems also greatly affect a cars braking
and acceleration characteristics and can reduce the drivers fatigue while
improving their confidence allowing them to “push the envelope” at crucial
times.
Purpose:
The purpose of this project is to design and analyze and build a viable
suspension system that conforms to the rules and regulations of the
competition while meeting performance criteria at the lowest possible cost.
10
Project Requirements:
Rules and Regulations:
Before being allowed to enter the competition the cars are put through a
series of rigorous test and inspections by industry professionals that cover
every detail of the car from material selection to driver size to overall
dimensions. Some of these requirements are minor and failure to meet
them will result in a point penalty, while other requirements are crucial and
failure to comply results in disqualification from the competition. A very
detailed and extensive rulebook is given to each design team prior to
beginning the design phase and is used as a basis for packaging
requirements, material selection and design limitations. These rules are
meant to invoke creativity and ensure that the final race car is safe enough
for competition. A complete rulebook is available at the college however
the following is a list of the more important rules which directly affect this
project:
 The car must have a minimum wheelbase of 60 inches
 A shorter wheelbase has decreased stability so this requirement
allows a safer minimum level of control however too long of a
wheelbase requires a greater steering angle and is therefore harder
to turn
 The car must have at least 4 wheels with the front and rear not in a
straight line (front and rear must have different track widths)
 The goal of this design (and common practice) is to have a shorter
track length in the rear allowing it to follow a smaller turning radius
allowing easier maneuvering through sharp turns while maintaining
a wide and stable front end
 The smaller track portion must be at least 75% of the larger track
 This helps balance load transfer to a manageable level preventing
undesired driving characteristics
 The car must have a minimum ground clearance of 1 inch with a
loaded driver at all times.
 This ensures that the car never bottoms out at any point in the
course which prevents unpredictable and highly dangerous loading
conditions
 The suspension system must have a minimum of 2 inches of total
travel (1 inch jounce and 1 inch droop)
 This provides adequate wheel and suspension travel over a range
of movement which prevents the suspension from bottoming out
(different from the car bottoming out as described above) which can
produce undesirable and potentially uncontrollable vehicle
dynamics at high speeds
 The track width and center of gravity must combine to form an
appropriate rollover stability
11





 This factor (the higher the better) determines the willingness of the
car to tip over and is a rather critical factor as rollovers can be
catastrophic
A chassis template must pass unobstructed through the chassis of the
car (see figure 23 in appendix A-2)
 This template is new to 2009 and allows adequate room for the
drivers legs and provides a greater crush zone and forces teams to
creatively package their designs
All spherical bearings and rod ends must be in double shear
 Double distributes the load over two faces instead of one making
the joint much stronger and is an effective strategy in preventing
failure
All fasteners must meet/exceed SAE grade 5 (metric grade 8.8)
 This guarantees the quality and durability as well as consistency of
fit for the fasteners since the suspension is under constant heavy
loading
All critical bolts, nuts and other fasteners must contain positive locking
mechanisms (thread compounds and lock washers are excluded)
 Racecars are very dynamic and very cyclic and constant load
changes can cause fasteners to reverse and cause the system to
fail
All lock nuts must have a minimum of two threads protruding
 This ensures that the lock nut is fully engaged and fully locked
preventing reversal and potential failure
Performance:
The rules and regulations above are designed to make the race car safe
and effective and are the priority requirement of the project however in
order to win the competition the car must perform to the highest levels
possible while conforming to the rules. The competition includes static
and dynamic tests including breaking, accelerating, turning, endurance
and even fuel economy.
 The static testing that applies to the suspension system is the 60
degree test where the vehicle (loaded with the tallest driver) is placed
on a table and is tilted to and angle of 60 degrees from horizontal in
either direction as viewed from the front or rear of the car.
12
Figure 1: 2006-2007 CSUS 60° tilt test
During this test the car cannot tip in anyway requiring the use of the
support straps on the upper side of the platform. This test measures
the cars stability factor or ‘willingness to tip’ and is the combined effect
of the track width’s and center or gravity location given by the following
formula:
Higher values mean a more stabile car with a recommended value of
greater than 1.2.
 The dynamic testing is done through actual driving competitions and
includes skidpad, acceleration, autocross and endurance tests.
Average track data provided from the rulebook is used in calculations
and geometry configurations and is summarized below:
 Straights: No longer than 200 feet with hairpins on each end or no
longer than 150 feet with wide turns on each end
 Constant Turns: ranges from 75 to 148 feet in diameter
 Hairpin Turns: Minimum of 29.5 feet outside diameter
 Slaloms: Cones in a straight line with 25 to 40 feet of spacing
 Miscellaneous: Track contains chicanes, multiple turns, decreasing
radius turns, etc. The minimum track width is 11.5 feet
13
With the given data a maximum lateral and longitudinal accelerations are
taken as 1.4g’s and are used as a built in safety factors as the likelihood of
the car actually seeing these accelerations is unlikely. The maximum
bump force is taken as 2g’s acceleration.
Figure 2: 2004 Formula SAE Track Map
This is a representative track map taken at the 2004 CSUS FSAE
competition (2009 track may differ) and gives an appropriate scale of the
track length and degree of difficulty showing a large array of turns that the
car must handle appropriately. The rulebook specifies a standard run is
approximately ½ mile with average speeds of 25 to 30 mph and top
speeds in excess of 60 mph depending on vehicle tuning but these
numbers provide an adequate basis of selecting a start point for
calculations.
14
Design Description:
Geometry:
Choosing the design parameters is a balance of calculations and
educated guesses as to the actual parameters of the car itself. Since the
overall parameters of the car are, at the time of design, largely unknown
the design must be able to perform well within a predicted range of
parameter. Once decided upon these parameters were turned into usable
geometry and mounting points, with the help of a program called
SusProg3D. Figure 3. Illustrates the initial parameter design of the rear
suspension, and also shows the ICs and the Roll center.
Figure 3: SusProg3D rear suspension
 Track width:
The determination of the track width is a balance between the cornering
stability of the car, and size of the track that it must drive through.
 Front Track:
48 inches from front left wheel centerline to front right wheel centerline.
 Rear Track:
45 inches from rear left wheel center to rear right wheel center. This
shorter wheel base in the back decreases lateral stability slightly, but
pays off in maneuverability around the cones on the track.
 Car Length:
The length of the car determines many of the weight transfer
characteristics. Our suspension has 63 inches from front wheel centerline
15
to rear wheel centerline. This gives us a stable car that is nimble and
maneuverable around the track.
 Roll center Heights:
The roll centers have been staggered front to rear in an attempt to balance
the car. Since there is more weight in the rear of the car the roll center for
the rear is placed vertically closer to the CG. In the front the roll center is
a little vertically farther away from the CG. This is an attempt to balance
the moments acting on the front and rear suspensions during cornering.
 FVSA Lengths front and rear
The rate of change of wheel camber during deflection is determined by the
length of the Virtual swing arms that the wheels rotate about. As the
swing arm gets longer the wheels camber changes
 SVSA
The rear of the car has a little bit of anti-squat characteristics built into its
geometry. This is accomplished by slanting the mounting points of the Aarms, so that a line drawn through them points towards the CG of the car
instead of horizontal. This will keep the camber from changing drastically
on the rear tires during acceleration thus maximizing the tires contact
patch with the road.
16
Initial Design Analysis:
Wheel load Calculations:
The following is a list of vehicle parameters were chosen for this design:
Chosen Car Data:
Total Car Weight:
450.00
lb.
Driver Weight:
165.00
lb.
Weight of Front Sus. (Wuf):
50.00
lb.
Weight of Rear Sus (Wur):
Resulting Sprung Weight
(Ws):
50.00
lb.
515.00
lb.
Height of W (h):
13.00
in.
1.08
ft.
Height of Wuf (Rlf):
10.25
in.
0.85
ft.
Height of Wur (Rlr):
10.25
in.
0.85
ft.
Height of Ws (hs):
13.53
in.
1.13
ft.
Front Part of Wheelbase (a):
37.80
in.
3.15
ft.
Rear Part of Wheelbase (b):
25.20
in.
2.10
ft.
Ride Rate, Front
175.00
lb./in.
Ride Rate, Rear
200.00
lb./in.
Roll Center Ht, front (Zrf):
(1.28)
in.
(0.11)
ft.
Roll Center Ht, rear(Zrr):
(0.58)
in.
(0.05)
ft.
Front Track (tf):
48.00
in.
4.00
ft.
Rear Track (tr):
45.00
in.
3.75
ft.
Wheelbase (l)
63.00
in.
5.25
ft.
Shock Inst. Ratio, front (If):
0.83
(unit-less)
Shock Inst. Ratio, rear (Ir):
0.89
(unit-less)
Tire Vertical Rate (Kt):
Total Combined Weight (W):
760.00
lbs./in.
615.00
Front Spring Rate:
300.00
17
lbs.
lbs./in.
Rear Spring Rate:
Required Installation Ratio, Front:
Required Installation Ratio, Rear:
300.00
0.87
0.95
lbs./in.
Developing the total wheel loads during a dynamic situation is very difficult
and virtually impossible without onboard data logging of an existing car, or
rather sophisticated software. Since this is a first time design without any
of the previous mentioned abilities this design will be looked at in static
‘worst case’ scenarios only. Some major assumptions must be made
(Milliken 665) in order to begin this type of analysis and are outlined as
follows:
1. All conditions are considered Steady-State and therefore road
conditions, velocities, and all measurable quantities are assumed
constant. In reality the suspension geometry continually changes
due to road condition changes and input factor changes which
would require extensive dynamic analysis.
2. The chassis is assumed to be infinitely rigid. Real vehicle frames
twist and flex and those changes must be included in the
calculations however in this design they have been left out
3. The law of superposition applies to all load conditions meaning that
static loads can be calculated separate from load transfer and then
added at the end to determine the total load
These assumptions and all following calculations are outlined and
demonstrated in reference 1.
The process of calculating the total wheel loading is done using the
superposition method explained above. The static wheel loading is
calculated using the total weight of the car plus driver to which all
appropriate load transfers are added (whether positive or negative) to
determine the total load for a given scenario. First the static loads will be
calculated as they are independent of track and acceleration conditions.
Given a 60/40 split with zero lateral offset the total weight of the vehicle is
appropriately split between each respective:
Front & Rear Wheelbase Portions
a = L(. 4)
b = L(. 6)
W b
W a
W1 = W2 = ( )
W3 = W4 = ( )
2 L
2 L
Where:
W = Total Vehicle Weight
L = Wheelbase
W1 , W2 , W3 , W4 = Respective Wheel Load
18
Figure 4: relevant Geometry for static loading
s
The following is a summary of designs values:
Static Load Front Wheel:
123.00
lbs.
Static Load Rear Wheel:
184.50
lbs.
Since the center of gravity is located closer to the rear of the car the rear
wheels carry more of the static weight.
Now the various load transfers will be calculated and applied to the static
loads but some new assumptions must added that affect the amount of
calculations and are as follows:
1. Neglect banking due to track conditions – the track used in
completion is a flat asphalt track without any sizable banks that
would affect the calculations
2. Neglect crests, dips, and grades – again due to the flat asphalt
track in question these changes in loading can be ignored
3. No aerodynamic loading – this car is an open chassis and will not
have any sizeable down force attributes that would affect the
loading on the car
4. No engine torque reaction – due to the design of independent rear
suspension this torque is felt by the chassis and not the suspension
allowing it to be ignored
19
With these assumptions the load transfers that are required for
consideration are longitudinal (breaking/accelerating) and lateral
(cornering) load transfers. The longitudinal transfer is the most simple of
the two will be examined first. This transfer is dependent on the
accelerations given to the car and as discussed above will be taken as
1.4g’s as both acceleration and braking. Since the system was designed
with anti-squat geometry and since the car will have a 60/40 split the
longitudinal transfer will be greater in breaking than in acceleration and
therefore will be the focus of the calculation and is as follows:
Longitudinal Weight Transfer:
h
∆Wx = WAx
L
Acceleration (+)
Braking (-)
Where:
Ax = Longitudinal Acceleration
h = Hight to Center of Gravity
L = Wheelbase
W = Total Vehicle Weight
This equation is derived by equating the moments about the centerline of
one wheel (equal for the two since it is relative to the center of gravity
height) and applying the acceleration at the center of gravity. A summary
of the vehicle results are below and are given as the static loads plus the
transfer (positive for front and negative for rear since the roll is about the
center of gravity and will push on the front axle and lift on the rear axle):
Forward Weight Transfer,
Braking Acceleration
177.67
This number is reflective of the total weight transfer (lbs) that is applied to
the front axle and is split between the two wheels.
The more difficult and effective weight transfer is the lateral load transfer
and occurs when the vehicle travels through a corner and the transfer is a
result of the tires cornering force opposing the centrifugal force trying to
push the car off the track. The equations to calculate the front and rear
lateral load transfers (they require different calculations because they
have different track widths) are below:
20
Lateral Load Transfer:
∆Wf = Ay
W Hk f
b
, front load transfer
[
+ Zrf ]
tf kf + kr L
∆Wr = Ay
W Hk r
a
, rear load transfer
[
+ Zrr ]
tr kf + kr L
Where:
Ay = Lateral Acceleration
H = Distance from inclination to C. O. G.
Zrf , Zrr = Front & 𝑅𝑒𝑎𝑟 𝑅𝑜𝑙𝑙 𝐶𝑒𝑛𝑡𝑒𝑟 𝐻𝑖𝑔ht
t f , t r = Front & 𝑅𝑒𝑎𝑟 𝑇𝑟𝑎𝑐𝑘 𝑊𝑖𝑑𝑡ℎ𝑠
Figure 5: Geometry Relative to Lateral Load Transfer
A complete derivation of these equations can be found in (Milliken 679)
and can be summarized by taking the sum of the moments about the cars
roll axis. These values are usually calculated as change in weight per unit
acceleration however this design uses the 1.4g acceleration so the load
transfers are calculated and summarized below:
21
Load Transfer,
front (DWf)
114.83
Load Transfer,
rear (DWr)
126.25
These values relate the load that is transferred from the inside tires to the
outside tires along the roll axis (which for zero lateral offset is the center of
gravity).
Both of the load transfers calculated up to this point have been assuming
uni-directional acceleration when in reality the car will at some point brake
while turning thus putting both lateral and longitudinal accelerations into
play. The way this is accounted for an analyzed is based on experimental
data which does not exist yet for this vehicle due to the fact that it is a first
time design. The solution is to use reference based experimental data
from g-g diagrams that plot a vehicles relative accelerations at any point
during a lap run. Upon examining g-g diagrams found in figure 22 for a
rear wheel drive vehicle the values for combined lateral and longitudinal
accelerations are 1.2g’s lateral and 0.5g’s longitudinal. These values
were estimated with the idea of overshooting what the car will actually see
on the track as a built in factor of safety since the actual accelerations
cannot be found until the car is built and tested. Applying these
accelerations together and comparing them to each of the previous load
transfers a ‘worst case’ scenario was chosen based on which of the three
produced the highest wheel loads. This worst case scenario was during
the combined accelerations.
22
Since the load transfer and static wheel loads have been calculated the
resulting total wheel loads are the sum of the static loads and transfers.
The results are defined as:
Lateral Load Transfer Only (1.4g's)
Wheel Loads
Front Outside:
Front Inside:
Rear Outside:
Rear Inside:
237.83
8.17
310.75
58.25
Longitudinal Load Transfer Only (1.4g's Braking)
Wheel Loads
Front Outside:
Front Inside:
Rear Outside:
Rear Inside:
211.83
211.83
95.67
95.67
Combined Lateral and Longitudinal Load Transfers (1.20g's Ay and 0.50g's Ax)
Wheel Loads
Front Outside:
Front Inside:
Rear Outside:
Rear Inside:
253.15
56.3
260.99
44.56
Here the max loads applied are highlighted in red corresponding with the
worst case scenario loading which is to be applied to the components in
the finite element analysis section to be discussed later.
The method used to calculate these loads was through the use of an excel
spreadsheet as this gave the ability to iterate calculations over different
values of the suspension geometry as changing the geometry weighs
heavily on the calculated results especially the ride rates and roll center
heights. Appendix A-3 shows screenshots of the spreadsheet used as it
contains several other calculations that were used to derive terms used in
the equations above.
23
Wheel Travel:
Along with wheel loads the wheel travel was calculated as a ratio of wheel
center rate (the effective spring rate of the wheel at its center including the
tire vertical rate) and load transfers in order to determine if the suspension
was going to bottom out and violate the design criteria stated previously.
Using the worst case scenario loading described above the results of the
wheel travels are summarized below:
Wheel Travel
Front Outside:
Front Inside:
Rear Outside:
Rear Inside:
0.66
-0.66
0.63
-0.63
Wheel Travel
Front Outside:
Front Inside:
Rear Outside:
Rear Inside:
0.51
-0.51
0.44
-0.44
Wheel Travel
Front Outside:
Front Inside:
Rear Outside:
Rear Inside:
0.74
-0.38
0.38
-0.70
Here it can be seen that the wheels do not travel more than the minimum
that the suspension must move verifying that the design will not bottom
out and meets the design criteria.
24
The Upright:
 Background:
The upright is the main assembly of components that connects the a-arms
to the rim. Without it and the functions that it provides, double-a-arm
suspension would not be as we know it to be today.
Considerations:
 Design Limitations
 Packaging - One goal when designing an upright is to minimize the drag
on the car by arranging the packaging in a way that keeps it out of the air
flow currents the vehicle encounters while racing. The most practical way
to achieve this goal is to design the upright to fit inside the rim.
 Time - There was a limited amount of time to design the upright. We had
one semester allotted to complete this project, which also included at least
four other classes and a job. This meant that we had to make decisions
as time went by and build on them, even if, in hindsight, they could be
improved upon.
 Budget - The budget for the whole suspension system is approximately
$2,000. When all parts, manufacturing, and time costs are taken into
consideration, this is a limit that needs to be in the forefront of our
thoughts at all times. In order to meet our budget, we had to think ahead
and plan to design a system that would cost less than our limit.
 Manufacturing Processes - Our school has a wide variety of
manufacturing processes available to students who are working on their
senior projects. They include, but are not limited to, MIG and TIG welding,
shearing, braking, pressing, turning, milling, drilling, torching, and CNC
machining. Some are more available than others. Some of us have
experience with some of the tools and less with others. With the time and
money limitations in mind, we chose manufacturing processes that would
meet our needs.
 Material Selection
 Low Cost - Our budget was the main factor in the cost section of the
material selection portion of our project. We wanted to have materials that
were light-weight and strong because we wanted our car to have those
characteristics. The problem was that our budget did not allow us to
choose that route. We compromised and came up with materials that fit
within our budget.
25
 Easy to Machine - The last thing that we want is to discover that there are
problems with machining the parts that we have chosen. In order to meet
this requirement, we chose materials that are relatively easy to machine.
 Widely Available - Widely available parts generally cost less because of
the law of supply and demand. Since we had to keep our budget in mind
at all times, we chose materials that were widely available in order to keep
the costs as low as possible.
 Easy to Weld - One of the manufacturing processes that we needed to
implement in order to achieve the goals of this project is welding. In order
to weld the parts together and achieve desirable qualities, we chose
materials that are easy to weld.
 Strong - A light weight race car is a desirable item to have when racing.
The materials needed to be strong enough to withstand the loading that
we would put on them, while light enough to maintain the race car’s
desirability. Strong materials generally tend to be lighter than weak
materials under the same loading conditions, so we chose materials that
would meet the strength requirements of our loading conditions.
 Familiarity - There are doctors who have studied material science and are
familiar with a plethora of available materials. Our time limitations and
manufacturing processes required us choose materials that we were
generally familiar with. Any questions that we might have when we run
into problems would have a higher probability of a known solution in the
resources available to us.
 Choose - We chose AISI 4130 Steel, Normalized and 6061-T6 Aluminum
as our materials. These both met the requirements listed above.
 Factor of Safety
 Too Large - We want to design a light weight suspension system. A large
factor of safety would mean that larger parts and more material would be
needed to carry the loads that the suspension system would see during a
race. We chose a factor of safety that was reasonable.
 Too Small - One of the unfortunate risks of racing is death. Death is
something that racers try to avoid at all costs. A factor of safety, by
nature, is implemented in the context of our project to ensure that the
design is safe enough to keep the racer from meeting death. By designing
a system that could tolerate larger loads than expected, we have done our
part to keep the racer out of harms way.
 FOS - We chose a factor of safety of 1.5
26
 Analysis Techniques
 Hand Calculations - Hand calculations are based on tried and tested
techniques that match results of many tests with the formulas created by
theory. They are essential as a design-check for any computer modeling
done on or for the system.
 COSMOS Works - We have Solid Works on the computers available to us.
The finite element analysis tool that is integral with Solid Works is
COSMOS Works. We chose to use this design test tool because it
worked seamlessly with our 3-d design models.
 Good Engineering Practice
 Spindle and Hub - Inherent to the design of the spindle and hub part are
steps in the shaft. One of the problems with steps in shafts is the stress
concentrations located at each step. One of the best ways to reduce the
stress concentrations is to create the largest radius possible at each step.
 Upright Ends - The ends of the upright are where the a-arms connect to
the upright. One of the rules for the 2008 competition is that the
connections need to be in double-shear. Double-shear is stronger than
the previously allowed single shear. Our design will foster double-shear in
all connections.
 Brake Caliper Bracket - There are many different ways to design the brake
caliper bracket. The actual design incorporates flowing curves that allow
reduction of stress concentrations. The brake caliper bracket will hold the
loads that will be incident upon it.
 Forces:
 Tire
The wheel loads found through SusProg 3d and the formulas that pertain
to the design of suspension systems were used to calculate the forces that
the front outside tire would experience in a worst-case scenario. Figure 6
shows the location of the lateral force, FL, and the vertical force, FT, that
act on the tire as a result of the wheel loading. The lateral force was
calculated by multiplying the vertical force by the coefficient of static
friction between the road and the tire. The vertical force was calculated by
summing the static weight, load transfer, and the force that would result if
the tire were to hit a bump that would accelerate the tire twice the
acceleration of gravity.
27
Figure 6: Dimensions and Loads
Spindle and Hub
The moment at each step in the spindle shaft was found by taking the
moments at each location due to the forces found on the tire. Figure 6
shows the location of the two moments used to calculate the stress
concentrations in the spindle shaft.
To aide in running the computer analysis to make sure the finite element
analysis matches the hand calculation, the sum of the moments was taken
about the smaller step in the shaft to find the load to apply to the face of
the hub as shown in Figure 7.
28
Figure 7: Resolved hub force and moment
Upright Ends
The forces on the ends of the top and bottom arms were found through a
static analysis of the part configuration. Figure 8 shows the forces used to
calculate the reactions at the ends of the top and bottom arms of the
upright.
29
Figure 8: Upright General dimensions and loads
Steering Arm
The forces on the steering arm are a result of a couple of factors. These
factors include pneumatic trail and mechanical trail as seen in Figure 9.
Pneumatic trail results from the tendency of the tire to distort as it rolls.
The distortion creates a longer tire patch that is no longer centered directly
under the vertical center of the rim. Pneumatic trail is the distance
between the center of the tire patch and the vertical center of the rim.
Mechanical trail is an inherent trait based on the geometry of the
suspension system. Quantitatively, it is the distance between the point on
the ground that is created when a line is drawn from the top to the bottom
a-arm mounting point and extended to the ground and the vertical center
of the rim.
30
Figure 9: Mechanical trail sketch
The force on the steering arm is calculated as a counter-acting moment to
the sum of the moments created by the mechanical and pneumatic trail.
Figure 10 shows that the moments act around the vertical centerline of the
rim.
Figure 10: Steering sketch
Braking
The forces due to braking are transmitted from the tire to the brake caliper
mount and the upright. Figure 11 shows the braking force on the tire
creates a moment about the horizontal center of the rim. That moment is
transmitted through the parts assembly to the brake caliper mount. The
resultant force on the brake caliper mount is found by summing the
moments about the horizontal centerline of the rim.
31
Figure 11: Braking sketch
Hand Calculation Analysis:
Spindle and Hub
The moments found at each of the steps on the shaft were used in a
fatigue analysis of the shaft. First, the fatigue life of the 6061-T6
Aluminum was found as shown in Figure 12. The number of cycles was
calculated based on the perceived number of cycles that the spindle and
hub would see before and during the race. The maximum stress was
found by drawing a vertical line from the number of cycles on the x-axis to
the line on the graph, then by drawing a horizontal line from the point on
the graph where the vertical line met to the y-axis.
32
Figure 12: Fatigue hand calculation
The spindle was sized based on the maximum allowable stress based on
the fatigue life of the spindle and hub. A diameter was assumed as shown
in Figure 13. The stress concentration factor was found on the chart in
Figure 14. The nominal stress was found by dividing the maximum
allowable stress by the stress concentration factor. Since the nominal
stress based on the bending stress calculation for the shaft was less than
the allowable stress, the shaft was hollowed via a reverse-calculation to
find the inner diameter of the shaft.
33
Figure 13: Spindle load, hand calculation
34
Figure 14: Geometric stress concentration chart
A calculation was conducted as shown in Figure 15 to make sure that the
stress concentration in the larger step in the spindle and hub shaft was
less than the max allowable stress when the shaft inner and outer
diameters were factored into the equation.
Figure 15: Spindle corrected stress hand calculation
35
COSMOS Works Analysis:
Spindle and Hub
A finite element analysis was conducted on the spindle and hub assembly
to ensure that the hand calculations match the computer results. Figure
16 shows the location of the forces and the result of the analysis. The
result computer analysis was very close to the result of the hand
calculations.
Figure 16: Hub-Spindle FEA
Upright
After the upright was designed using the guidelines in the considerations
portion above, a finite element analysis was conducted on the upright
because it would be difficult to determine by hand the stresses on the
upright as a result of the loading. The loads as they were applied to the
upright based on the calculations in the above portion of the report are
shown in Figure 16.
The results of the first analysis are shown in Figure 17. The max stress
was on the circular line where the bolt met the upper part of the bottom
upright end. The stress was less than the maximum allowable stress. The
blue color in the picture represents areas of low stress levels. Low stress
is a result of over-building a part. In our application, over-building a part is
not desirable because it adds unnecessary weight to the racecar.
Removal of material will remove some of the blue. This was facilitated by
thinning the wall of the upright center
36
Figure 17: Original Upright Initial FEA
The result of the second analysis is shown in Figure 18. Mesh control was
used to find an accurate location and value of the maximum stress in the
part. The maximum stress is now located where the bearings meet the
inside of the upright center. The upright center could not get any thinner
because of distortion during welding.
Figure 18: Original upright second FEA
37
Final Assembly:
Front Upright
Using the parts designed based on good engineering practice and
analyzed with hand calculations and computer software, the final
assembly of the Original Upright design is shown in Figure 19 and the
exploded view is shown in Figure 20.
Figure 19: Original Upright Assembly
38
Figure 20: Exploded Original upright Assembly
39
Redesign:
History:
Upright Assembly
The previous upright design met the established criteria posed by design
limitations, material selection, factor of safety, and good engineering
practice for the suspension system. However, the upright had some
design flaws that were addressed before the start of production. A picture
of the original upright design is shown in Figure 21.
Figure 21: Original upright assembly, comparison
 Upright arms
The arms were designed to be constructed of steel square tubing.
The material selection design decision made them basic cantilever
beams. This left an undistributed stress concentration at the
location where the arms connected to the upright center.
 Upright ends
One requirement for the upright ends was that they be in doubleshear. Combined with the square tubing arms, this left little choice
when it came time to locate the bolt that would connect the upright
arms to the a-arms. This led to the design of the upright ends
where the bolt had to attach to a tapped surface. A nut could not
be incorporated into the design.
40
 Bearings
The upright center was designed to include two thrust needle
bearings. They met the design criteria, but it was later determined
that a single bearing that would also meet the design criteria. This
cut in half the number of bearings needed, and nearly cut in half the
money spent on bearings.
The Final Design:
The new finalized upright is shown in Figure 22. While the rest of the projects
assembly remained its original design. The following is a list of improvements
made to the upright assembly’s individual parts.
 Upright arms
The cantilever-style upright arms have been replaced with a sheet
metal structure that distributes the load and reduces stress
concentrations at the upright center.
 Upright ends
The upright ends now provide a place for a nut to be attached to
the bolts that connect the upright to the a-arms.
 Bearings
The space in the middle of the upright center has been adjusted to
accommodate a single bearing instead of the double-bearing
design. This also made it possible to use a smaller bearing and
spindle shaft.
41
Figure 22: Final upright assembly
42
Manufacturing:
This suspension system was manufactured in the CSUS tech shop and SAE
student work area by the FSAE student team members. While the suspension
system was used for this senior project, it was also built as part of the FSAE
Hornet Racing Club’s annual competition. This project bridged the gap between
the two groups, and fulfilled a need for each party involved.
The Hornet racing team, lead by Mike Bell, was responsible for funding the
required materials and manufacturing of the actual suspension parts, while under
the direct guidance of this project team.
One of the first and most daunting tasks of the manufacturing process was the
machining of all the small inserts, and housings required for the larger
assemblies. Many of the machined spherical bearing housings are displayed in
figure 23, after machining and prior to attachment to the A-Arms.
Figure 23: Spherical bearing housings
43
A-Arms
The construction of the a-arms for the suspension was a complex and
multi step process. The first step of the process was creating a
system to convert the computer model, shown in Figure 24, into the
actual part.
Figure 24: A-Arm Computer Model
After the bearing housings were machined on the lathe a jig, shown in
Figure 25, was constructed to hold each of the bearing housings in the
a-arm assembly. This jig was required both to place the bearing
housings in the correct locations, and to hold the there during and
immediately after welding When the bearing housings were fixed in
their proper place, the tubing material for the arms was cut and
ground to fit. Then, after all the test fitting and jigging, the arms were
welded to the bearing housings as shown in Figure 26.
Figure 25: A-Arm Jig
44
Figure 26: A-Arm Welding
After the arms were finished welding the a-arm was removed from the
jig and the plates between the arms were welded into place, as
shown in Figure 27. The final step was then to install the tree
spherical bearings into the bearing housings.
Figure 27: Completed A-Arms
45
Upright and hub assembly
The upright and hub-spindle assemblies were manufactured in the student
machine shops on the CSUS campus. The uprights were fabricated from .090
inch 4130 steed sheet, and solid 4130 round stock. This sheet metal was bent
into the upright arm shapes, per the project drawings. The upright center was
machined on a lathe to the drawing dimensions. Then the arms and the center of
the upright were assembled to the dimensions of the drawings, and welded
together, as shown in figure 28.
Figure 28: Fabricated upright
The hub-spindles, shown in figure 29 which are used for the
attachment of the wheels to the uprights, were machined on a lathe
out of 6160 T6 heat treated aluminum. These spindle shafts actually
had to be re-machined one time due to non-compliance with
tolerances.
Figure 29: Machined hub-spindles
46
Assembly Installation
Once all of the suspension components and sub-assemblies of the
suspension are manufactured, it was attached to the car frame. The
attachment of the suspension assembly was one of the most
important parts of manufacturing. All of the dimensions for the
general arrangement drawing of the suspension were used to locate
the a-arm mounts on the frame. Then these mounts were welded to
the frame and the arms bolted on. The location of the mounting
points is important it affects all aspects of the suspension system’s
geometry, and thus the suspensions performance.
Figure 30: Installation of suspension assembly
47
Testing:
Geometry Testing:
The majority of the project requirements determined by the rules and
regulations of the FSAE competition involved primarily the geometry of the
suspension. The requirements included wheelbase, track width, ride
height, and suspension travel. The method of testing incorporated some
primitive yet useful devices and instruments including a protractor and
bubble level. The test was designed to measure these required
geometries and verify that the manufactured system met the design
requirements.
The first step was to measure the vehicles various geometries including
wheelbase, track width (both front and rear), camber angle and castor
angle. The wheelbase and track widths were measured using a tape
measure as shown in figure 31 below.
Figure 31: Track width testing
The wheelbase was recorded at 61.5 inches while the front track width
was recorded at 49 inches and the rear track width was recorded at 45
inches.
The castor angle was measured at different points from minimum to
maximum steering angles however the repeatability of the measurement
proved to be unacceptable when using the bubble indicator as it need to
be held very steady while the wheels were turned which proved to be too
difficult. Instead the maximum values (or values at maximum turning
angle) were recorded using a large ‘stencil’ type device and level as
shown in figure 32 below.
48
Figure 32: Caster angle measurement
The values recorded were easily repeated and were recorded as an
average of 8 degrees.
The suspension travel along with minimum ride height was measured
using a scale and was measured from the lowest point of the frame with
respect to the ground. The car was ‘loaded’ by placing members of the
FSAE team on to the frame and through the use of steel bars as lever
arms. The goal was to get the suspension ‘maxed out’ in both directions
(bound and rebound) and measurements were taken throughout the
process. The minimum suspension travel was read at the lowest point
while the total travel was taken as the difference from the highest point to
the lowest point. The minimum clearance was recorded at 1.75 inches
while the total suspension travel was recorded at 2.625 inches.
A new requirement to the 2009 season as described in the problem
definition section describes the template referenced in appendix that must
be able to pass through the frame unobstructed. This was a simple
pass/fail test and was performed successfully.
49
Upright Testing:
Every engineering project requires the testing of a design and not just the
manufacturing of it. For this project testing was performed on the upright to verify
that it would be able to withstand the incident upon it during the actual operation
of the vehicle. Since stresses can’t be measured directly, strain gages were
used as a method of measurement allowing the determination of principle
stresses transformed from the measured strains. This data was then compared
to the original design analysis to verify the accuracy of the analysis.
 Strain gage installation
 The surface was de-greased to remove greases that may have
been imbedded deeper into the grain structure during the abrasion
process. This process is shown in Figure 33 below.
Figure 33
 It was abraded or sanded to a relatively fine surface roughness and
stripped free of all plating, paint, or any other defects on the
material. This was important because the gage must be mounted
on a very flat, smooth and clean surface. A picture of the abrasion
of a surface is shown in Figure 34 below.
50
Figure 34: Upright abrasion
 The surface of the part was then burnished or permanently marked
in the direction of layout application. This was done with a ball
point pen. A pen was chosen because a scribe or file would cause
a burr to pick up and could lead to stress concentrations and higher
errors of strain indication. The main focus behind proper gage
application was to minimize these errors.
 Surface conditioner was applied using a cotton swab applicator.
The process was repeated until the tip of the applicator no longer
showed dirt or grime.
 The surface was then neutralized to restore its pH balance. It was
important during this process to maintain a larger ‘clean’ area than
actually required for the gage itself in order to ensure that no
contaminates redeposit on the newly cleaned surface.
 After the surface was completely prepped the gage was then glued
very carefully using M-Bond 200 and catalyst to mount the gage to
the surface taking care to properly align the gage with the
burnished layout lines. It was extremely important during this stage
that neither the gage nor the surface were touched or
contaminated, and caution was used during the process not to
damage the gage itself. A picture of mounted strain gages is
shown in Figure 35 below. The strain gages are circled in red.
51
Figure 35: Strain gauges, installed
 The final part of the mounting process was the correct soldering of
the connecting wires using appropriate soldering techniques. The
wires were taped to the part to prevent movement in order to easily
solder the wires to the soldering tabs on the strain gage. A picture
of one of the wires being soldered to a tab on the strain gage is
shown in Figure 36 below
Figure 36: Soldering of strain gauge wires
52
 The gages were then hooked up electronically and were ready for
measurement. The instrumentation used to read the strain
measurements is shown in Figure 37 below. The opposite end of
the wires that were connected to the soldering tabs on the strain
gages were connected to the correct terminals on the
instrumentation.
Figure 37: Measuring strain
 Strain gage application
 The wiring from the strain gages was routed in a way that they
would be clear of all moving parts in the wheel and suspension
assembly. The lead wires were also made long enough to reach
the driver’s seat so that they could be connected to a data logger
allowing dynamic testing after the vehicle is completed.
 Since the vehicle was not finished the loads had to be applied
statically in a ‘test stand’ method. The loads were applied using a
lever arm to magnify the force seen at the wheel. Basically, a long
sturdy pipe with one end slid through the frame members and a
teammate literally sitting on the other end creating the desired load.
A picture of the application of static loading is shown in Figure 38
below.
53
Figure 38: Loading tire
 Digital scales were used to read the actual load applied to the
suspension system. The limit on the scales were 400lbs, so this
test was not able to load the suspension to the maximum loading
scenario that it would theoretically see in operation. However,
measurements were taken at three different loading scenarios and
were extrapolated to the desired data points from the collected
data. The material will only see linear-elastic deformation, so a
linear curve fit was used to fit the data. A picture of one of the
scales used is seen in Figure 39 below.
54
Figure 39: Tire load reading
 Strain gage measurement data
 Three rectangular rosettes were used to collect the strains and
were placed on three different faces of the upright. The data was
placed in an excel sheet. Excel was employed because of its ability
to handle formulas, and to present data in a user-friendly manner.
The data from the Excel sheet is shown in the table below. The
data recorded from the test is shown in the first four columns. The
load was the applied load read from the scale. The instrument
channel was specified by the port on the instrumentation that was
connected to each strain gage. The strain was the strain reading
taken by the instrumentation from each gage under the specified
load.
55
Future Testing Plans:
At the time that this report was written the FSAE car, that are
suspension system was a part of, was not yet completed. Although
the car was incomplete the suspension system was completed and
prepared for further dynamic testing, for the time that the car leaves
its current static state. The strain gauges, introduced earlier in this
paper, have been left in place and will be attached to the cars onboard data logger, shown in figure 40. This data logging computer
will sample the strain inputs from the gauges, and its internal
accelerometer, at a rate of 10 samples per second. This real-time
data sampling will allow us to extrapolate approximate wheel loads
and cornering forces during actual driving situations.
Figure 40: Data logging flow chart
56
Design Verification Analysis:
Geometry Analysis:
The camber test provided the largest usable, accurate and analyzable
data and was performed using the bubble level instrument made strictly
for camber measurements. Two tests were conducted to measure the
camber angle with respect to both wheel displacement and body roll. For
the wheel displacement test the camber angle was measured at several
increments of ‘frame displacement’ where by keeping the wheel stationary
and moving the frame the scenario simulated the wheel moving with
respect to the frame. A combination of weights, team members and lever
arms were used to push and pull the frame to different levels of
displacement while the camber angle was measured. Figure 41 below
shows a plot of camber angle versus wheel displacement.
Camber Angle vs Wheel Displacement
(Experimental)
Camber Angle (Degrees)
0.00
-0.50
y = -0.8085x - 1.2266
R² = 0.9633
-1.00
-1.50
Camber
-2.00
Linear (Camber)
-2.50
-3.00
-1.00
0.00
1.00
2.00
3.00
Wheel Displacement (Inches)
Figure 41: Experimental camber data
The data was plotted and a least squares linear curve fit was performed
and the resultant equation given was used as the rate of camber angle
change per inch wheel displacement. The regression value shows that
some some of the data has some error and it is believed that this error is
associated with either human interpretation of instrument scale or possibly
due to the spring and damper ‘resting’ back to a different position. This
data was collected in order to compare to the theoretical values that were
calculated by the susprog software (data referenced in appendix). Figure
42 below shows the theoretical data graphed over the designed inputs.
57
Camber Angle vs. Wheel Displacement
(Theoretical)
Camber Angle (Degrees)
1.00
0.50
y = -0.7564x - 0.5463
R² = 0.9969
0.00
-0.50
Camber
-1.00
Linear (Camber)
-1.50
-2.00
-2.00
-1.00
0.00
1.00
2.00
Wheel Displacement (Inches)
Figure 42: Theoretical camber data
This data when fit in the same manner as the experimental data gives an
equation and the slopes of the lines are very similar. This verifies that the
actual rate of camber change is close to the designed value.
To measure the rate of camber change per degree body roll a lever arm
was used to pry the frame and camber measurements were taken at
several values of body roll. The roll was measured with a protractor
mounted to the middle front portion of the frame (i.e. on centerline of the
vehicle) about which the car rolls durring a turn. The measured data was
compared similary as above against the design data taken from appendix
and is summarized in figures 43 and 44 below.
58
Camber Angle vs. Body Roll
(Experimental)
Camber Angle (Degrees)
1.00
0.50
y = 0.7857x - 1.5119
R² = 0.9973
0.00
-0.50
Camber
-1.00
Linear (Camber)
-1.50
-2.00
0.00
1.00
2.00
3.00
Body Roll (Degrees)
Figure 43: Camber vs. roll experimental
Camber Angle vs Body Roll
(Thoeretical)
3.50
Camber Angle (Degrees)
3.00
y = 0.7494x - 0.5621
R² = 0.9983
2.50
2.00
1.50
1.00
Camber
0.50
Linear (Camber)
0.00
-0.50
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
Body Roll (Degrees)
Figure 44: Camber vs. body theoretical
As the equations from the two figures show the values for camber change
per degree body roll are comparible. Both of the analysis are summarized
in table below.
59
Requirement:
Camber vs
Displacement goal
Camber vs Body Roll
goal
Experimental
(Actual)
Theoretical
Pass/Fail or %
Diff
-.7654 deg/in
-.8085 deg/in
6.89%
.7494 deg/deg
.7857 deg/deg
4.84%
As the data shows the rates of camber change are very close to the
theoretical values and when combined with the desired 8 degrees of
castor the geometrey is concluded to have met all design requirements
after fabrication.
Stress Analysis:
Figure 45: Strain gauge analysis
 The other six columns represent the transfer from the measured
strains to the Von Mises stress. They were calculated via the
following formulas:
60
𝛾𝑥𝑦 = 2𝜀𝑥𝑦 − 𝜀𝑥 − 𝜀𝑦
𝜀1 , 𝜀2 =
𝜀𝑥 + 𝜀𝑦
𝜀𝑥 − 𝜀𝑦 2
𝛾𝑥𝑦 2
∓ √(
) +( )
2
2
2
𝑉𝑜𝑛 𝑀𝑖𝑠𝑒𝑠 = 𝜎̅𝐻 =
𝜎1 =
𝐸
(𝜀 + 𝑣𝜀2 )
1 − 𝑣2 1
𝜎2 =
𝐸
(𝜀 + 𝑣𝜀1 )
1 − 𝑣2 2
1
√2
√(𝜎1 − 𝜎2 )2 + (𝜎2 − 𝜎3 )2 + (𝜎3 − 𝜎1 )2
 The maximum value that the scales could read was 400 lbs
however the values calculated in the design analysis required a
load of 759 lbs to be applied. In order to obtain the stresses for that
loading scenario the data was fit to a linear curve and the resultant
least squares fit equation was used to extrapolate to the higher
stress value from the lower loading conditions at each of the three
gage locations. The graphs for each are located in Figures 46-48
below. The values for the loads were plotted on the x-axis, and the
Von Mises stress values were plotted on the y-axis. An equation of
the line is shown on each chart, as well as the R2 value for each.
The R2 value for each was above .98, which showed an accurate fit
of the line to the data.
61
Rosette 1
3,000
Von Mises Stress (psi)
2,500
y = 5.9793x
R² = 0.9812
2,000
1,500
1,000
500
0
0
50
100
150
200
250
300
350
400
450
350
400
450
Load (lbs)
Figure 46: Rosette 1
Rosette 2
4,000
Von Mises Stress (psi)
3,500
y = 8.452x
R² = 0.9892
3,000
2,500
2,000
1,500
1,000
500
0
0
50
100
150
200
250
Load (lbs)
Figure 47: Rosette 2
62
300
Rosette 3
1,000
Von Mises Stress (psi)
900
800
y = 2.0622x
R² = 0.9801
700
600
500
400
300
200
100
0
0
50
100
150
200
250
300
350
400
450
Load (lbs)
Figure 48: Rosette 3
 The chart shown in Figure 49 below contains the gage, and Von
Mises stress value for each strain gage location for the 759lb. load
applied at the tire.
Figure 49: Extrapolated strain gauge stresses
 CosmosWorks analysis data
 The forces obtained from the design analysis section of the project
were used to test the upright in CosmosWorks. This is the finite
element analysis tool in the 3-D design software SolidWorks. The
program output the 3-D model with colored regions that indicated
the levels of stress in the model. Figure 50 shows the upright as it
looked after the CosmosWorks test was completed. The probe tool
in CosmosWorks was used to select each location on the upright
where there was a strain gage in order to find the stress value at
each location.
63
Figure 50: FEA of final upright assembly
 Rosette 1 was on the face of the upper arm towards the rear of the
vehicle. The picture of the upright showing the location of the strain
gage and a picture of the value of the predicted Von Mises stress at
this location is shown in Figure 51.
Figure 51: FEA compared to rosette 1
64
 Rosette 2 was on the outer face of the upper arm. The picture of
the upright showing the location of the strain gage and a picture of
the value of the predicted Von Mises stress at this location is shown
in Figure 52.
Figure 52: FEA stress compared to rosette 2
 Rosette 3 was on the face of the upper arm towards the front of the
vehicle. The picture of the upright showing the location of the strain
gage and a picture of the value of the predicted Von Mises stress at
this location is shown in Figure 53.
65
Figure 53: FEA compared to rosette 3
 Comparison of experimental data to theoretical data
 The data for both the experimental and theoretical tests were
gathered and recorded. There was considerable error between the
experimental and theoretical data as seen in Figure 54, but it is
systematic.
 The stress values from the outer face of the upright arm show a
63% difference between theoretical and experimental. One of the
factors that could have a role in the discrepancy was that the strain
gage was located inside a heat affected zone from the welding that
took place to fabricate the upright. This should not have produced
much error, but could have affected the measurement and produce
different results from a theoretical test that assumes uniform
material. The model that was tested in CosmosWorks closely
approximates the actual part in size and shape.
66
 The stress values from the faces of the upper arm on the upright
towards the front and rear of the vehicle show a 94% and 95%
difference respectively. One of the factors that could have played a
role in the discrepancy was that they were also located inside a
heat affected zone from welding. Another factor is that the
theoretical model approximates a smooth transition between the
front and rear faces of the upper arm to the front and rear surfaces
of the upright center. In reality, the transition was not smooth. It
was in such a way that would produce a bending moment on each
face possibly causing the bulk of the larger percent difference
between the theoretical and experimental stress values than for
strain gage 2.
 The systematic nature of the data produced another possibility: the
loading of the upright was not completely understood. The
suspension was designed to be stiff, and an assumption was made
was that the suspension system would behave like a rigid structure.
This apparently was not a good assumption. An explanation of the
larger values of stress obtained in the experimental portion of the
testing process included the consideration that the suspension
actually behaved much differently than a rigid structure. When the
tire was in bump and load transfer, it moved upward. The a-arms
attached to the upright pivot at the frame. The distance between
the wheel and the frame decreases as the a-arms swing up as a
result of the upward motion of the tire due to the bump and load
transfer. The upper a-arm was shorter than the lower a-arm as
shown in Figure 55 below. This caused the distance between the
upper portion of the frame and the upper arm of the upright to
decrease more than the distance between the lower portion of the
frame and the lower arm of the upright. The difference caused a
bending moment on the upright that was not taken into
consideration during theoretical testing. This bending moment may
be source of the systematic error between the theoretical and
experimental data.
67
Figure 54: Susprog 3D pictorial
68
Conclusion and Future Plans:
This suspension system is a simple well performing design that
serves meets the performance and design requirements of a Formula
SAE race car. The fabrication and testing were successful and the
overall product is strong and well thought out. In the problem
description section a set of project requirements and goals were set
as the foundation for this project. Below is a table that summarizes
all of the requirements and gives comparisons (if applicable) to the
theoretical design data and the actual measured data.
Requirement:
Wheel Base
Unequal track length
Smaller track at least
75% of larger
Minimum 2" total
travel
Template must pass
through frame
Spherical bearings must
be in double shear
Material must not fail
Camber vs.
Displacement goal
Camber vs. Body Roll
goal
Experimental
Pass/Fail or % Diff
(Actual)
≥ 60"
61.5"
Pass
Front: 48" Rear: 45" Front: 49" Rear: 45"
Pass
Theoretical
94%
92%
Pass
3"
2.625"
Pass
Pass/Fail by design
Pass
Pass/Fail by design
Pass
See test and analysis section
Pass
-.7654 deg/in
-.8085 deg/in
6.89%
.7494 deg/deg
.7857 deg/deg
4.84%
In conclusion this suspension system meets and exceeds all the
design requirements, and performance characteristics needed to
build a competitive race car.
69
Appendices:
Appendices table of contents
A-1: Cost Report
A-2: Miscellaneous Diagrams
A-3: Excel Calculation Spreadsheets
A-4: References
70
A-2:
Cost Report
MATERIALS
BEARINGS
HARDWARE
TOTAL >>>>>
PREDICTED COST ACTUAL COST
1545
610
246
130
232
135
2023
875
71
A-3:
Figures:
Figure 22: G-G diagram
72
Figure 23: Chassis Template
73
A-4:
Excel Calculation Spreadsheets
74
75
76
77
78
79
80
81
82
LH wheel
0.00 roll
0.67 roll
1.33 roll
2.00 roll
2.66 roll
3.33 roll
4.00 roll
4.00 roll
RH wheel
0.00 roll
0.67 roll
1.33 roll
2.00 roll
2.66 roll
3.33 roll
4.00 roll
4.00 roll
camber caster caster
kpi
kpi wheel
axle
angle angle trail angle offset scrub tramp
in
-0.500 8.000 0.529 0.500 2.230 0.000 0.000
-0.047 8.000 0.531 0.047 2.230 -0.001 -0.005
0.416 8.020 0.538 -0.416 2.230 -0.001 -0.013
0.891 8.063 0.548 -0.891 2.230 -0.002 -0.025
1.381 8.130 0.562 -1.381 2.231 -0.002 -0.042
1.893 8.227 0.582 -1.893 2.231 -0.002 -0.063
2.434 8.362 0.610 -2.434 2.232 -0.001 -0.090
3.020 8.557 0.648 -3.020 2.233 -0.001 -0.125
toe
roll centre
offset height
fvsax
0.000 0.000 -1.668
-0.002 1.955 -1.656
-0.005 3.999 -1.585
-0.007 6.290 -1.449
-0.008 9.071 -1.235
-0.009 12.824 -0.912
-0.008 18.792 -0.405
-0.006 31.855 0.551
76.293
73.621
71.241
69.146
67.346
65.875
64.816
64.364
camber caster caster
kpi
kpi wheel
axle
angle angle trail angle offset scrub tramp
in
-0.500 8.000 0.529 0.500 2.230 0.000 0.000
-0.960 8.001 0.526 0.960 2.230 -0.001 0.005
-1.411 8.023 0.528 1.411 2.231 -0.002 0.005
-1.854 8.066 0.533 1.854 2.231 -0.003 0.002
-2.287 8.134 0.542 2.287 2.232 -0.005 -0.007
-2.707 8.232 0.557 2.707 2.232 -0.008 -0.021
-3.109 8.368 0.578 3.109 2.233 -0.011 -0.044
-3.478 8.562 0.610 3.478 2.234 -0.016 -0.078
toe
roll centre
offset height
fvsax
0.000 0.000 -1.668
0.002 1.955 -1.656
0.005 3.999 -1.585
0.007 6.290 -1.449
0.008 9.071 -1.235
0.007 12.824 -0.912
0.005 18.792 -0.405
-0.001 31.855 0.551
76.293
79.047
82.126
85.565
89.428
93.813
98.898
105.026
LH wheel
camber caster caster
kpi
kpi wheel
axle
toe
rc roll centre height
angle angle trail angle offset scrub tramp
in offset chassis ground
fvsax
1.500 bump
-1.749 8.003 0.522 1.749 2.231 -0.174 0.000 0.002 0.000 -2.371 -3.871
62.235
1.125 bump
-1.412 8.002 0.524 1.412 2.231 -0.117 0.000 0.001 0.000 -2.201 -3.326
65.595
0.750 bump
-1.092 8.001 0.526 1.092 2.230 -0.070 0.000 0.000 0.000 -2.027 -2.777
69.056
0.375 bump
-0.789 8.000 0.527 0.789 2.230 -0.030 0.000 0.000 0.000 -1.849 -2.224
72.620
Static
-0.500 8.000 0.529 0.500 2.230 0.000 0.000 0.000 0.000 -1.668 -1.668
76.293
0.375 droop
-0.225 8.000 0.530 0.225 2.230 0.022 0.000 0.000 0.000 -1.484 -1.109
80.081
0.750 droop
0.037 8.000 0.532 -0.037 2.230 0.035 0.000 0.000 0.000 -1.297 -0.547
83.992
1.125 droop
0.287 8.000 0.533 -0.287 2.230 0.039 0.000 -0.001 0.000 -1.106 0.019
88.035
1.500 droop
0.526 8.000 0.535 -0.526 2.230 0.034 0.000 -0.001 0.000 -0.912 0.588
92.217
Equivalent suspension travel due to chassis roll
RH
LH
0.00 roll
0.000
0.000
0.67 roll
-0.279
0.279
1.33 roll
-0.580
0.535
2.00 roll
-0.904
0.768
2.66 roll
-1.253
0.973
3.33 roll
-1.633
1.146
4.00 roll
-2.050
1.273
4.00 roll
-2.525
1.332
Side view swing axle and instant centre
IC
IC
axle
length height height angle
1.500 bump 4000000.000 0.000 0.000 0.000
1.125 bump 4000000.000 0.000 0.000 0.000
0.750 bump 4000000.000 0.000 0.000 0.000
0.375 bump 4000000.000 0.000 0.000 0.000
Static 4000000.000 0.000 0.000 0.000
0.375 droop 4000000.000 0.000 0.000 0.000
0.750 droop 4000000.000 0.000 0.000 0.000
1.125 droop 4000000.000 0.000 0.000 0.000
1.500 droop 4000000.000 0.000 0.000 0.000
LH
83
brake drive
a-dive% a-lift%
1.500 bump
0.0
0.0
1.125 bump
0.0
0.0
0.750 bump
0.0
0.0
0.375 bump
0.0
0.0
Static
0.0
0.0
0.375 droop
0.0
0.0
0.750 droop
0.0
0.0
1.125 droop
0.0
0.0
1.500 droop
0.0
0.0
SusProg3D 2009_3.s3d Rear Roll and bump
Chassis roll values calculated every 0.66 degrees. Roll left.
Full dynamic roll centre. Roll starts at Static.
Toe variation has NOT been calculated.
LH wheel
0.00 roll
0.66 roll
1.32 roll
1.98 roll
2.64 roll
3.30 roll
3.96 roll
4.00 roll
RH wheel
0.00 roll
0.66 roll
1.32 roll
1.98 roll
2.64 roll
3.30 roll
3.96 roll
4.00 roll
camber caster
kpi wheel
axle
toe
roll centre
angle angle angle scrub tramp
in offset height
fvsax
-1.000 0.000 1.000 0.000 0.000 0.000 0.000 -0.645
44.812
-0.670 -0.034 0.670 -0.001 -0.006 0.000 3.949 -0.623
43.581
-0.290 -0.102 0.290 -0.002 -0.004 0.000 8.898 -0.483
42.577
0.158 -0.215 -0.158 -0.002 0.010 0.000 18.410 -0.138
41.855
0.734 -0.406 -0.734 -0.003 0.043 0.000 91.881 1.770
41.651
1.717 -0.891 -1.717 -0.011 0.149 0.000 -16.360 0.361
43.764
1.783 -0.781 -1.783 -0.015 0.109 0.000 -29.057 -0.345
41.742
1.626 -0.574 -1.626 -0.022 0.046 0.000 -187.407 -6.156
39.249
camber caster
kpi wheel
axle
angle angle angle scrub tramp
-1.000 0.000 1.000 0.000 0.000
-1.339 0.034 1.339 0.000 0.006
-1.631 0.032 1.631 -0.001 0.022
-1.867 -0.013 1.867 -0.002 0.048
-1.995 -0.139 1.995 -0.006 0.095
-1.580 -0.587 1.580 -0.021 0.214
-2.152 -0.412 2.152 -0.020 0.187
-2.822 -0.144 2.822 -0.021 0.134
toe
roll centre
in offset height
fvsax
0.000 0.000 -0.645
44.812
0.000 3.949 -0.623
46.051
0.000 8.898 -0.483
47.514
0.000 18.410 -0.138
49.245
0.000 91.881 1.770
51.436
0.000 -16.360 0.361
54.993
0.000 -29.057 -0.345
55.352
0.000 -187.407 -6.156
55.053
LH wheel
camber caster
kpi wheel
axle
toe
rc roll centre height
angle angle angle scrub tramp
in offset chassis ground
fvsax
1.500 bump
-3.071 -0.193 3.071 -0.116 -0.015 0.000 0.000 -1.234 -2.734
37.590
1.125 bump
-2.519 -0.145 2.519 -0.074 -0.011 0.000 0.000 -1.100 -2.225
39.386
0.750 bump
-1.991 -0.097 1.991 -0.040 -0.008 0.000 0.000 -0.956 -1.706
41.191
0.375 bump
-1.485 -0.048 1.485 -0.016 -0.004 0.000 0.000 -0.804 -1.179
43.001
Static
-1.000 0.000 1.000 0.000 0.000 0.000 0.000 -0.645 -0.645
44.812
0.375 droop
-0.534 0.048 0.534 0.007 0.004 0.000 0.000 -0.478 -0.103
46.616
0.750 droop
-0.086 0.097 0.086 0.004 0.008 0.000 0.000 -0.305 0.445
48.411
1.125 droop
0.347 0.146 -0.347 -0.008 0.011 0.000 0.000 -0.125 1.000
50.189
1.500 droop
0.764 0.195 -0.764 -0.029 0.015 0.000 0.000 0.061 1.561
51.946
Equivalent suspension travel due to chassis roll
RH
LH
0.00 roll
0.000
0.000
0.66 roll
-0.259
0.259
1.32 roll
-0.563
0.473
1.98 roll
-0.921
0.628
2.64 roll
-1.372
0.673
3.30 roll
-2.117
0.220
3.96 roll
-2.184
0.654
4.00 roll
-2.115
1.194
Side view swing axle and instant centre
84
IC
IC
axle
length height height angle
1.500 bump
463.794 16.424 2.231 2.028
1.125 bump
458.447 16.228 2.230 2.027
0.750 bump
453.849 16.052 2.228 2.026
0.375 bump
449.904 15.894 2.226 2.023
Static
446.531 15.752 2.222 2.020
0.375 droop
443.661 15.624 2.219 2.017
0.750 droop
441.240 15.509 2.214 2.013
1.125 droop
439.219 15.404 2.209 2.009
1.500 droop
437.561 15.309 2.204 2.004
LH
brake drive
a-lift% a-squat%
1.500 bump
2.6
6.5
1.125 bump
2.5
6.3
0.750 bump
2.5
6.2
0.375 bump
2.4
6.1
Static
2.4
6.0
0.375 droop
2.3
5.9
0.750 droop
2.3
5.8
1.125 droop
2.3
5.7
1.500 droop
2.2
5.6
-----Inline Attachment Follows----Front Suspension
Bump steer
1.500 bump
1.125 bump
0.750 bump
0.375 bump
Static
0.375 droop
0.750 droop
1.125 droop
1.500 droop
absolute
in
0.002
0.001
0.000
0.000
0.000
0.000
0.000
-0.001
-0.001
toe in
toe in
toe out
toe out
Steering Toe out Wheel toe angle Rack Camber (actual) Camber (change)
Caster (actual) Caster
(change)
Jacking effect Steering Ratio:1
Caster trail
KPI Offset
turn angle in turn
LH
RH travel
LH
RH
LH
RH
LH
RH
LH
RH
LH
RH
LH
RH
LH
RH
LH
RH
24.000 LH 11.475 -35.475 -24.000 0.956 4.149 -3.637 4.649 -3.137 6.893 7.155 -1.107 -0.845
0.172 -0.129 3.288 7.468 0.349 0.359 2.236 2.234
20.000 LH 6.390 -26.390 -20.000 0.790 3.036 -3.143 3.536 -2.643 7.440 7.383 -0.560 -0.617
0.133 -0.108 4.338 7.405 0.444 0.403 2.233 2.233
16.000 LH 3.561 -19.561 -16.000 0.625 2.150 -2.634 2.650 -2.134 7.734 7.577 -0.266 -0.423
0.101 -0.087 5.080 7.300 0.494 0.440 2.232 2.232
12.000 LH 1.813 -13.813 -12.000 0.463 1.382 -2.113 1.882 -1.613 7.902 7.736 -0.098 -0.264
0.072 -0.065 5.647 7.153 0.521 0.472 2.231 2.232
8.000 LH 0.747 -8.747 -8.000 0.304 0.695 -1.582 1.195 -1.082 7.988 7.859 -0.012 -0.141
0.046 -0.043 6.093 6.963 0.533 0.497 2.230 2.231
4.000 LH 0.176 -4.176 -4.000 0.150 0.070 -1.044 0.570 -0.544 8.016 7.948 0.016 -0.052
0.022 -0.022 6.445 6.729 0.535 0.516 2.230 2.230
Straight 0.000 0.000 0.000 0.000 -0.500 -0.500 0.000 0.000 8.000 8.000 0.000 0.000
0.000 0.000 6.584 6.584 0.529 0.529 2.230 2.230
4.000 RH 0.176 4.000 4.176 0.150 -1.044 0.070 -0.544 0.570 7.948 8.016 -0.052 0.016 0.022 0.022 6.729 6.445 0.516 0.535 2.230 2.230
8.000 RH 0.747 8.000 8.747 0.304 -1.582 0.695 -1.082 1.195 7.859 7.988 -0.141 -0.012 0.043 0.046 6.963 6.093 0.497 0.533 2.231 2.230
12.000 RH 1.813 12.000 13.813 0.463 -2.113 1.382 -1.613 1.882 7.736 7.902 -0.264 -0.098 0.065 0.072 7.153 5.647 0.472 0.521 2.232 2.231
16.000 RH 3.561 16.000 19.561 0.625 -2.634 2.150 -2.134 2.650 7.577 7.734 -0.423 -0.266 0.087 0.101 7.300 5.080 0.440 0.494 2.232 2.232
85
20.000 RH 6.390 20.000 26.390 0.790 -3.143 3.036 -2.643
0.108 0.133 7.405 4.338 0.403 0.444 2.233 2.233
24.000 RH 11.475 24.000 35.475 0.956 -3.637 4.149 -3.137
0.129 0.172 7.468 3.288 0.359 0.349 2.234 2.236
3.536
7.383
7.440
-0.617
-0.560
-
4.649
7.155
6.893
-0.845
-1.107
-
Datum reference dimensions
Chassis lateral datum
(X): Chassis centreline
Chassis vertical datum (Y):
Chassis longitudinal datum (Z):
Chassis pivot points (from chassis X, Y, Z datum)
- tie rod (steering rack)
- X 7.873
- Y 4.303
- Z -2.484
Upright pivot points (from upright X, Y, Z datum)
- tie rod (steering arm)
- X 3.600
- Y -3.500
- Z -3.000
Upright pivot points (from chassis X, Y, Z datum)
- tie rod (steering arm)
- X 20.615
- Y 6.337
- Z -2.484
LH
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Rear Suspension
SusProg3D 2009_3.s3d Rear Steering
Toe control link - chassis (fixed chassis & upright pivots)
Vehicle lateral datum
(X): Vehicle centreline
Vehicle vertical datum (Y): Ground
Vehicle longitudinal datum (Z):
Pivot points (from vehicle X, Y, Z datum)
LH
- toe control link chassis pivot
- X 10.000
- Y 11.000
- Z -68.500
- toe control link upright pivot
- X 19.743
- Y 14.704
- Z -65.500
Toe control link length
10.846
Wheel toe reference length
Bump steer
1.500 bump
1.125 bump
0.750 bump
0.375 bump
Static
0.375 droop
0.750 droop
1.125 droop
1.500 droop
absolute
in
-0.021
-0.015
-0.009
-0.004
0.000
0.004
0.007
0.009
0.011
13.000
toe out
toe out
toe out
toe out
toe in
toe in
toe in
toe in
Datum reference dimensions
Chassis lateral datum
(X): Chassis centreline
Chassis vertical datum (Y):
86
Chassis longitudinal datum (Z):
Chassis pivot points (from chassis X, Y, Z datum)
- toe control link
- X 10.000
- Y 11.000
- Z -68.500
Upright pivot points (from upright X, Y, Z datum)
- toe control link
- X 2.500
- Y 4.500
- Z -2.500
Upright pivot points (from chassis X, Y, Z datum)
- toe control link
- X 19.743
- Y 14.704
- Z -65.500
LH
87
A-5:
References:
1. Milliken, William F. and Douglas L. Milliken. Race Car Vehicle Dynamics.
Society of Automotive Engineers, Inc: Pennsylvania, 1995.
2. Rice, Richard C., ed. SAE Fatigue Design Handbook . Society of
Automotive Engineers, Inc: Pennsylvania, 1997.
3. Bastow, Donald, Geoffrey Howard, and John P. Whitehead, Car
Suspension and Handling. Society of Automotive Engineers, Inc:
Pennsylvania, 1993.
88