PROJECT MANAGEMENT & DESIGN II
MAE 435
Formula SAE
Authors:
Robert Costen
James Fulcher
Matthew Galles
Christopher McHugh
Xavier Thompson
Ashley Wyatt
Class Supervisors:
Dr. Sebastian Bawab
Mr. Michael Polanco
Project Advisors:
Dr. Sebastian Bawab
Dr. Colin Britcher
Mr. Nathan Luetke
December 3, 2014
CONTENTS
1
ABSTRACT
1
2
INTRODUCTION
2
2.1
2.2
2.3
2.4
2.5
2.6
3
6
6
8
8
11
13
PROPOSED METHODS
13
WHEELS
UPRIGHTS
BRAKES
SUSPENSION
STEERING
13
13
14
14
14
RESULTS
5.1
5.2
6
6
WHEELS
UPRIGHTS
BRAKES
SUSPENSION
STEERING
FRAME
4.1
4.2
4.3
4.4
4.5
5
2
3
3
4
5
6
COMPLETED METHODS
3.1
3.2
3.3
3.4
3.5
3.6
4
WHEELS
UPRIGHTS
BRAKES
SUSPENSION
STEERING
FRAME
14
MATERIAL SELECTION
DESIGN
14
15
DISCUSSION
15
i
LIST OF FIGURES
Figure 1: Disk Braking System & Drum Braking System................................................................... 4
Figure 2: Push-Rod Suspension System ............................................................................................... 6
Figure 3: Front Upright ......................................................................................................................... 7
Figure 4: Rear Upright Design Change ................................................................................................ 7
Figure 5: AHP Criteria Combined Results ........................................................................................... 9
Figure 6: Camber Change with Vertical Load Calculator .................................................................. 10
Figure 7: Camber Angle vs Degrees Vertical Load ............................................................................ 10
Figure 8: Ackerman Angle Geometry................................................................................................. 12
Figure 9: Ackerman Geometry and Chassis ....................................................................................... 12
APPENDICES
Appendix 1: Gantt Chart
Appendix 2: Budgeted Hours and Progression
Appendix 3: Budget
a
b
c
ii
1 Abstract
The Formula Society of Automotive Engineers (FSAE) competition requires students to
design, fabricate, and test an open-wheeled race car. This paper presents completed research and
development, resources, and processes used to complete the design and analysis process of a FSAE
chassis working from an outside to inside approach; wheels to the frame. The 2014-2015 team
focused on stopping safely, which lead to changes in the braking system. The rear axle braking
system was modified to include a rotor and caliper for each wheel. The suspension design is being
revised to improve handling and reduce driver fatigue. The 2014-2015 rear suspension will have a
push rod system rather than a pull rod system. The front suspension geometry is being adjusted to
provide optimal camber gain for vertical tire displacement and steering input. This is to ensure the
largest contact patch is maintained between the tire and the ground. A new steering system will be
designed with proper Ackermann angles to improve cornering. Frame modifications were
implemented to reduce overall size and weight. The main hoop, mid hoop, and frame width were
reduced. A different tire compound will be used to improve heat retention and slip angle. The front
uprights will include proper caster and kingpin inclination angles (KPI) while maintaining a strong
and light weight design.
2 Introduction
In 2014, the ODU FSAE team finished with four hundred and thirteen points placing thirtyseventh of one hundred and nine teams. The 2013-2014 team focused on a complete chassis design
that would allow for a higher power to weight ratio. Suspension redesign will improve vehicle
handling and steering to accommodate the increase in available power.
The 2013-2014 ODU FSAE team integrated a new frame design with the 2012-2013
suspension design. The combination of two designs created a car that placed well in competitions
but did not have competitive handling because of excessive tire movement, bump steer, understeer,
poor cornering and uneven steering caused by poor steering linkage placement. A competitive
suspension design makes the car more predictable to maneuver through high speed turns and
improves the size of the contact patch, allowing for better road holding and load distribution [1-5].
Because a competitive engine design was achieved on the 2013-2014 car, the 2014-2015
team is focusing on the frame design, suspension design, tire selection, upright design, brake
component selection, and correcting the uneven steering by shifting the steering linkage placement.
2.1 Wheels
The wheel assembly consists of the tire, rim, and wheel center, which connects to the wheel
axle. Different tire compounds affect traction of the vehicle and allow for controlled braking and
maneuvering [4]. Different tire compounds have unique values for ground patch, heat retention,
and grip [1, 5]. The 2013-2014 tire compound did not retain heat effectively which, in turn affects
2
handling. Different size and material rims are available for purchase. Common choices for racing
are carbon fiber and aluminum rims in either 13” or 10” sizes.
2.2 Uprights
The upright assembly serves as the connection between the tires and the suspension, and
consists of the upright, hub, wheel bearings, steering attachment, and braking components [4, 5].
Packaging restraints, suspension geometry, braking mounts, and steering location are designed into
the uprights, while maintaining a lightweight, strong design.
2.3 Brakes
There are three methods to reduce a vehicle’s velocity: aerodynamic drag, a braking
system, and drivetrain drag. Aerodynamic drag is not a critical braking factor at low velocity. The
braking system is the most important component in safely reducing vehicle velocity when the
magnitude of the drivetrain drag is less than the braking system output [6].
Disc and drum brakes are the two most common braking mechanisms used, while disc
brakes are used exclusively in racing applications due to superior design parameters, including
thermal dissipation, ease of adjustment, and simple mechanism design. A brake functions by
converting the rotational kinetic energy of the wheel to heat by creating friction between the brake
disc and the pads. The coefficient of friction between the disc and pad, the frictional force due to
the actuator, and the actuator performance affect the performance of the braking system [7]. As a
result, heat dissipation of the brake is of utmost importance in increasing braking efficiency [8].
3
Figure 1: Disk Braking System & Drum Braking System
The force of friction between the tire and the road is a limiting factor in braking force.
Aerodynamic ground effects can be used to create high downward forces, increasing frictional
force between the tire and road. This allows for increased braking without creating a wheel lock
condition [9]. In order to achieve maximum deceleration, the front and rear brakes must operate at
their respective traction limits [9]. The traction limit is dependent on the friction coefficient
between the tire and road, and the dynamic weight of the front and rear wheels [8, 9]. The 20132014 car had a braking distribution that was overly biased towards the front.
2.4 Suspension
When designing an FSAE car, the suspension is a top consideration. All loads and
accelerations must be transferred to the ground via the suspension. The car cannot properly
perform if the widest section of tire is not grounded, the chief responsibility of suspension [11].
The camber angle is measured between the centerline of the tire and a line drawn perpendicular to
the ground. It changes under different loadings and while maneuvering. Proper camber gain
4
throughout suspension travel and steering input ensures the tire will remain in contact with the
ground. Changing suspension geometry can move roll centers, causing tire hop or extreme roll
[12]. Weight transfer must also be considered. If the roll axis is routed through the center of
gravity, no roll will occur. However, rapid weight transfer will cause a loss of tire traction [13].
Therefore, camber and roll center changes must be analyzed when designing the suspension.
2.5 Steering
The 2013-2014 FSAE car utilized a rack-and-pinion steering system. Over-steer and understeer were observed during harsh cornering. When the car was turned to the left side, the steering
felt loose. Turning the wheel to the right proved to be stiff. Adequate adjustment to the steering
system did not occur and caused a high steering ratio [14]. The misalignment and inaccurate
placement of the steering system resulted in the front wheels following a different circular route
than anticipated. The steering system requires the innermost wheel to navigate a much smaller
radius than the outer wheel and therefore conducts a tighter turn [15]. The steering linkages
geometry, based on Ackerman steering geometry, requires more turning of the inside wheel than
that of the outside wheel [16].
There are two common types of steering gears: rack-and-pinion and recirculating-ball.
Each end of the rack-and-pinion steering rack is enclosed in a metal tube with a tie rod connected
[17]. The spindle and the steering arm are attached by the ends of the tie rod. The pinion gear,
connected to the steering shaft, is manipulated by the tie rod. When rotated, the pinion gear spins.
5
Figure 2: Push-Rod Suspension System
2.6 Frame
The frame of a race car protects the driver and components of the car. In the FSAE
competition there are rules regulating the frame for safety reasons while still meeting requirements
found in real industry.
3 Completed Methods
3.1 Wheels
Carbon fiber rims were considered to reduce the overall weight of the car. The weight ratio
per rim of carbon fiber to aluminum wheels is 1.73 lbs. to 7.1 lbs. However, the increased cost is
outside of the 2014-2015 budget.
3.2 Uprights
The uprights were redesigned to reduce weight, maintain reliability, and maintain proper
suspension geometry. This design incorporates improved caster angle, roll centers, and king pin
6
inclination angle. The rear upright design has also been completed and allows for rear brake caliper
mounts while reducing the size and weight of the assembly. The uprights will be constructed from
high strength, low weight 6061-T6 aluminum. Finite element analyses performed using Solidworks
confirmed the upright could safely withstand the required applied loads.
Figure 3: Front Upright
Figure 4: Rear Upright Design Change
7
3.3 Brakes
The 2014-2015 car will move to a 2+2 caliper braking configuration. This will center the
braking distribution bias. However, in order to achieve the proper braking distribution, a smaller
rotor will be used in the rear to decrease the braking moment. This will still maintain a small
desired bias towards the front.
Required Deceleration:
a
v 22.352m / s

 11.176m / s 2
t
3s
(1.1)
Required Braking Force:
F  ma  (346.568kg )(11.176 m/ s 2 )  3873.24 N
(1.2)
Front Braking Force (60%):
FF 
0.60
3873.24 N  1161.97 N
2
(1.3)
FR 
0.40
3873.24 N  774.64 N
2
(1.4)
Rear Braking Force (40%):
3.4 Suspension
Two calculators have been created using Microsoft Excel. The first allows for dimensions
of suspension components to be entered and provides camber change when vertical displacement is
introduced. The second calculator will provide camber change for different steering inputs, caster
8
angle and KPI. These calculators ensure the proper control arm length, caster angle, king pin
inclination, and roll center requirements are met.
A level two analytic hierarchy process (AHP) was performed to reduce additional resources
efforts in suspension design. Criteria, based on team member’s feedback and observations of the
2013-14 performance, were selected for evaluation. Each member completed a pair wise
comparison ranking the criterions priority resulting in a six by six matrix for each member. This is
shown in Figure 5. Each individual's matrices were combined using linear algebra into a single
combined six by six matrix and eigenvectors were calculated. The criterions ranging was then
utilized in creating additional AHP matrices to evaluate advantages and disadvantages of a pushrod and a pull-rod suspension system. Based on the results of the AHP, a push-rod suspension
system was chosen for the design evaluation process.
Figure 5: AHP Criteria Combined Results
9
Figure 6: Camber Change with Vertical Load Calculator
180
160
140
120
100
Droop/unloading
Jacking/Loading
80
60
40
20
0
-20
-15
-10
-5
0
5
10
Figure 7: Camber Angle vs Degrees Vertical Load
10
Figure 8: Mock up of front suspension, ensuring proper roll centers and articulation angles
Table 1: Caster, KPI, and steering input vs camber calculator
Input
Caster
Kpi
Tire radius
Sb
Sa
Steering δ
output
camber
10
4
10
1
1
19
3.493021
3.5 Steering
With improved steering, the possibility of over-steer and under-steer will be eliminated. To
eliminate the inconsistencies that can accompany steering, calculations will be performed to ensure
the vehicle will not have a high steering ratio [13]. The accurate placement of the steering system
will result in the front wheels following the correct circular route. The steering system requires the
innermost wheel to navigate a much smaller radius than the outer wheel and therefore conducts a
11
tighter turn [14]. The steering linkages geometry, based on Ackerman steering geometry, requires
more turning of the inside wheel than that of the outside wheel [15].
Utilizing the following formulas (1.5 & 1.6)
tan 𝛿𝑖 =
tan 𝛿𝑜 =
𝑙
𝑅1 −
(1.5)
𝑤𝑓
2
𝑙
𝑅1 +
(1.6)
𝑤𝑓
2
It can be determined with an R1 = 84”, l = 66” and wf = 50” the outer angle of the wheel;𝛿𝑜 ,
would be 22° and the inner angle of the wheel,𝛿𝑖 , would be 30°.
Figure 10: Ackerman Geometry and Chassis
Figure 9: Ackerman Angle Geometry
12
A steering ratio of 12:1 is ideal for our racing car. This will keep the steering ratio as low as
possible, thus, producing a quicker steering response. In addition, this new steering design will
equalize the ratio in both directions. Our rack-and-pinion steering system has been redesigned for
the 2014-2015 ODU FSAE race car. An improved steering system will help with the overall
performance and suspension of the vehicle. This will be accomplished by adjusting the rack-andpinion steering system once installed.
3.6 Frame
The frame size was reduced to lower weight and cost while maintaining safety
requirements. The main hoop, that protects the driver’s head, was brought down 3” while still
allowing for the 95th percentile male to fit in the car with a safety clearance over the driver’s
helmet. The driver’s compartment was narrowed 1.5” on both sides for a total change of 3”. The
mid hoop was lowered by 1” while maintaining the straight plane from the hoop to the top of the
main hoop without intersecting with the steering wheel or any part of the driver.
4 Proposed Methods
4.1 Wheels
Purchase and perform final assembly
4.2 Uprights
Final machining required and fine tuning of caster angle, king pin inclination, and camber
angle during vehicle performance may be necessary.
13
4.3 Brakes
Perform final assembly of brake package and machine brake caliper mount. Additionally,
fine tune adjustments for braking distribution will be performed.
4.4 Suspension
Control arm dimensions have been set but still need to be modeled and tested in Solidworks
and fabricated.
4.5 Steering
Final assembly and adjustments of steering components are required.
5 Results
5.1 Material Selection
The material selected for the frame is chromoly steel, purchased from AED Motorsport
Products. The selected tubing will allow for relatively easy fabrication and is readily available. It
was determined that metal inert gas (MIG) welding with flux-cored wire provides an adequate
weld joint but tungsten inert gas (TIG) welding provides a more aesthetically pleasing and higher
strength weld joint. Also, when fabricating the joints, it was determined that a bench grinder
provides a cleaner joint the one cut with an angle grinder, but a coping tool provides the best
fitment. The braking components have been selected. A Wilwood Dual Master Cylinder will be
used with Wilwood GP200 calipers. Streamlined rotors have been selected for the front wheels.
14
5.2 Design
A push rod suspension design was selected. With the push-rod suspension, the bending
moment can be removed from the lower control arm in the previous 2013-2014 design. SolidWorks
was utilized to develop the upright and frame designs. It was determined this software can provide
the proper stress analysis and accurate dimensions required for this project.
6 Discussion
The purpose of our project is to design and construct a Formula SAE car that will
outperform the 2013-2014 teams car by twenty points. This will be accomplished by adjusting the
steering, decreasing the frame size and improving the suspension.
The results mostly came from online research and discussions with the 2013-2014 team
members. It has been determined that steering and suspension were primary issues with the 20132014 vehicle. Research focused on the areas that would improve the current designs. It was
determined that a change to steering creates a better angle between the steering column and the
rack and pinion connection point, which in turn creates smoother turns requiring less effort to
maneuver. The upright was redesigned in SolidWorks. The rack-and-pinion steering system on the
current vehicle is a good system; however it needs to be adjusted to improve the handling of the
car.
A rear brake rotor needs to be designed, fabricated, and tested to insure proper stopping
distance and heat dissipation rates are maintained or improved from previous performance.
15
Additional resources are required to modifying the current brake calipers and pads to work with the
rear rotor.
The future work to be performed is FEA and construction of the Formula SAE car. A final
upright design needs to be machined. A rear rotor needs to be designed and fabricated.
16
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
J. Axerio-Cilies and G. Iaccarino, "An Aerodynamic Investigation of an Isolated Rotating Formula
1 Wheel Assembly," Journal of Fluids Engineering, vol. 134, pp. 121101-121101, 2012.
E. F. Gaffney Iii and A. R. Salinas, "Introduction to formula SAE&reg suspension and frame
design," in 48th Earthmoving Industry Conference and Exposition, April 9, 1997 - April 10, 1997,
Peoria, IL, United states, 1997.
E. Uzunsoy and O. A. Olatunbosun, "A study of the effect of rear suspension auxiliary roll damping
on vehicle-handling dynamics," vol. 219, pp. 21-30, 01/ 2005.
D. Robertson and G. J. Delagrammatikas, "The suspension system of the 2009 cooper union fsae
vehicle: A comprehensive design review," SAE International Journal of Passenger Cars Mechanical Systems, vol. 3, pp. 366-380, 2010.
N. D. Smith, "Understanding parameters influencing tire modeling," Colorado State University,
Formula SAE Platform, 2004.
T. D. Gillespie, Fundamentals of Vehicle Dynamics: Society of Automotive Engineers, 1992.
S. M. Savaresi and M. Tanelli, Active Braking Control Systems Design for Vehicles: SpringerVerlag, 2010.
R. Stone and J. K. Ball, Automotive Engineering Fundamentals: SAE International, 2004.
M. Guiggiani, The Science of Vehicle Dynamics: Handling, Braking, and Ride of Road and Race
Cars: Springer Netherlands, 2014.
V. D. Ingenieure and U. S. N. T. I. Service, VDI 2230: Systematic Calculation of High Duty Bolted
Joints: U.S. Department of Commerce, National Technical Information Service, 2009.
B. A. Jawad and J. Baumann, "Design of Formula SAE Suspension," 2002.
A. Mihailidis, Z. Samaras, I. Nerantzis, G. Fontaras, and G. Karaoglanidis, "The design of a
Formula Student race car: a case study," Proceedings of the Institution of Mechanical Engineers,
Part D: Journal of Automobile Engineering, vol. 223, pp. 805-818, 2009.
D. E. Woods and B. A. Jawad, "Numerical design of racecar suspension parameters," SAE
Technical Paper1999.
G. C. MARINESCU, N. DUMITRU, and V. OŢĂT, "ANALYSIS OF THE TORQUE APPLIED
TO THE STEERING WHEEL IN STATIC CONDITIONS," Annals of the Faculty of Engineering
Hunedoara-International Journal of Engineering, vol. 11, 2013.
S. Jianmin and Y. Qingmei, "Decreasing Vibration of Vehicle Using Combined Suspension
System," in Robotics, Automation and Mechatronics, 2008 IEEE Conference on, 2008, pp. 358-361.
M. Thoresson, T. R. Botha, and P. S. Els, "The relationship between vehicle yaw acceleration
response and steering velocity for steering control," International Journal of Vehicle Design, vol.
64, pp. 195-213, 2014.
A. M. Odhams and D. J. Cole, "Identification of the steering control behaviour of five test subjects
following a randomly curving path in a driving simulator," International Journal of Vehicle
Autonomous Systems, vol. 12, pp. 44-64, 2014.
17
Appendicies
Appendix A: Gantt Chart
Appendix B: Budgeted Hours and Progression
1000
900
800
700
600
Cumulative Expected Hours
500
Cumulative Actual Hours
400
300
200
100
0
0
5
10
15
20
25
Appendix C: Budget
Budget
Resources
Design
Research
Drawings
Materials Fabrication Assembly
Costs
Costs
Costs
$1,500
$1,500
b
Testing
Frame
tubing
Weld rod/wire
Suspension
fasteners
dampers
heeve spring
A-arms
Uprights
rims
tires
Brakes
calipers
Steering
Rack and pinion
Column
Wheel
Quick dis-connect
Fasteners
Assembly
Final Product
Competition Fees
Entry fee/gas
$1,500
Sub Totals
$14,500
$2,000
$960
$100
$750
$150
$250
$150
$40
$200
$300
$400
$100
$150
$1,000
$400
$625
$1,000
$3,775
$2,000
$100
$50
$150
$100
$50
$6,250
$500
Total Costs
$20,275
c
Appendix D: Parts to Order
Funds
Cost
Each
Qty
Cost
$
$15,000
Ordered? Part
Description
Material used to custom fabricate the 2 front uprights.
-
$14,917
$82.72
1
$82.72
Yes
$14,787
$130.58
1
$130.58
Yes
$14,772
$14.81
1
$14.81
Yes
$14,022
$750.00
2
$1,500.00
Yes
$13,694
$327.95
1
$327.95
Yes
$13,622
$71.95
1
$71.95
Yes
$13,598
$23.95
1
$23.95
Yes
Steering
Steering
$13,499
$98.93
4
$395.72
Yes
Brakes
Wilwood GP200 Caliper
$13,439
$59.93
Yes
Brakes
Suspension
Suspension
Suspension
Suspension
Suspension
Suspension
Steering
Wilwood Composite Metallic Brake Pads
SPM & SPB Series Male Rod Ends - RIGHT HAND
SPM & SPB Series Male Rod Ends - LEFT HAND
SPM & SPB Series Male Rod Ends - RIGHT HAND
SPM & SPB Series Male Rod Ends - LEFT HAND
SPM & SPB Series Male Rod Ends - RIGHT HAND
SPM & SPB Series Male Rod Ends - LEFT HAND
AFCO 30309 U-Joint, 5/8 Inch-36 Spline
Rear
Suspension
PS-78PB-DA Shock, Double Adjustable Compression and Rebound Valve code: 2
4
$239.72
$13,439
10
$0.00
No
$13,439
10
$0.00
No
$13,439
10
$0.00
No
$13,439
10
$0.00
No
$13,439
10
$0.00
No
$13,439
10
$0.00
No
$13,374
$64.99
1
$64.99
No
$12,624
$750.00
2
$1,500.00
No
Total: $12,624
$ 4,352.39
Front
Uprights
Rear
Uprights
Rear A-Arm
Ends
Shocks
Steering
Material used to custom fabricate the 2 rear uprights.
Material used to custom fabricate the 4~8 A-Arm Ends
PS-78PB-DA Shock, Double Adjustable Compression and Rebound Valve code: 2
STILETTO FAST RACK N PINION, 6.4:1 Ratio, Horizontal Bolt Centerline, 3/8 in.
Rod Ends
STILETTO BOOTS (2) WITH WIRES (4), FITS SMALL RACK & PINION
STILETTO SPLINED COUPLER 5/8-36 SPLINE, 5/8" BORE, Fits Stiletto & SPE Racks,
as well as the Funny Car Box. Measures 5/8 in. Inside Diameter on one end, 5/8
in. x 36 female spline on other end.