design of the suspension system for a fsae race car
TRANSCRIPT
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Design of the Suspension System for a FSAE Race Car
Sergio Valencia Arboleda
201126788
Faculty advisor: Juan Sebastián Nuñez Gamboa
Faculty co-advisor: Andres Gonzalez Mancera
Towards the degree of:
Bachelor in Mechanical Engineering
Universidad de Los Andes
Mechanical Engineering Department
May 2016
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Contents
Chapter 1. Introduction
1.1 Project Background
1.2 Problem definition
Chapter 2. Objectives & Design Methodology
2.1 Objectives
2.2 Design Methodology
Chapter 3. Literature Review
3.1 The suspension of an FSAE and its objective
3.2 FSAE suspension elements
3.3 Full vehicle Parameters
3.4 Vehicle Dynamic Load Transfer
3.5 Tire Relative Angles
3.6 Suspension Behaviours
3.7 Steering Behaviours
3.8 Formula SAE Suspension Requirements
Chapter 4. Preliminary Design decisions
4.1 Benchmark Information
4.2 Rims & Tires
4.3 Vehicle´s Overall Weight Estimation
4.4 Center of Gravity Estimation
4.5 Type of Suspension
4.6 Vehicle´s Basic Dimensional Parameters
4.7 Overall Performance Targets & Design Recommendations
Chapter 5. Modelling the suspension in Autodesk Inventor®
5.1 Chassis Geometry
5.2 Geometric Suspension Design
Chapter 6. Suspension Geometry evaluation using MatLab®
6.1 Previous Geometric analysis
6.2 Objective of the code
6.3 Analysis Methodology
6.4 Front Suspension Static Analysis
6.5 Relationship Between the variables and the parameters
6.6 Front Suspension Results
6.7 Rear Suspension Static Analysis
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6.8 Rear Suspension Results
6.9 Final Considerations
Chapter 7. Suspension modelling & evaluation in Adams/Car®
7.1 Introduction to Adams/Car®
7.2 Modelling the suspension in Adams/Car®
7.3 Suspension Actuation Analysis and Design
7.4 Front Suspension DOE
7.5 Rear Suspension DOE
7.6 Full vehicle Analysis
7.7 Final Configuration of the suspension
7.8 Design Evaluation
Chapter 8. Conclusions and future work
7.1 Conclusions
7.2 Future work
References Appendix A. FSAE Lincoln electric vehicles information Appendix B. Hoosier Tire Information Appendix C. Keiser Rim Information Appendix D. MatLab® Code Appendix E. Front Suspension MatLab® analysis results Appendix F. Rear Suspension MatLab® analysis results Appendix G. Front & Rear suspension: Wheel rate Appendix H. Full Vehicle DOE Results Appendix I. Front Suspension Results: Final Parameters Appendix J. Rear Suspension Results: Final Parameters
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List of Figures:
Figure 1. Chassis Render (taken from: Sarmiento, 2015 pg. 60) Figure 2. Types of Independent suspension configurations Image A. Pull rod Suspension (taken from: Kiszko, 2011 pg. 58) Image B. Push rod Suspension (taken from: Farrington, 2011 pg. 122) Image C. Direct Actuation of the shock absorber (taken from: http://trackthoughts.com/wp-
content/uploads/2010/11/M0401751.jpg)
Figure 3. ADAMS/Car® fsae_2012 Front Suspension Assembly Figure 4. ADAMS/Car® fsae_2012 Rear Suspension Assembly Figure 5. ISO International Vehicle axis system (taken from: http://white-
smoke.wikifoundry.com/page/Heave,+Pitch,+Roll,+Warp+and+Yaw) Figure 6. Roll Center height diagram (Taken from Chang, 2012 pg. 2) Figure 7. Instant Roll Center (Taken from: Jazar, 2014 pg. 527 ). Figure 8. Vehicle Roll Axis (Taken from: http://dreamingin302ci.blogspot.com.co/2013/06/flckle-roll-center.html) Figure 9. Different Toe Angle´s (Taken from: Jazar, 2014 pg. 528) Figure 10. Caster angle geometry (Taken from: http://www.autozone.com/repairguides/Toyota-Celica-Supra-1971-
1985-Repair-Guide/FRONT-SUSPENSION/Front-End-Alignment/_/P-0900c1528007cc57) Figure 11. Camber angle geometry (Taken from: http://www.autozone.com/repairguides/Pontiac-Fiero-1984-1988-
Repair-Guide/Front-Suspension/Front-End-Alignment/_/P-0900c152801dace). Figure 12. Kingpin angle & scrub radius geometry (Taken from: http://www.mgf.ultimatemg.com/ ) Figure 13. Jacking Force estimation (Taken from: Smith, 1978 pg. 39) Figure 14. Tire´s slip angle (Taken from: Milliken & Milliken, 1995 pg. 54) Figure 15. Oversteer & Understeer (Farrington, 2011 pg. 33) Figure 16. Vehicle Fundamental dimensions Figure 17. Rollover stability test (Taken from http://www.bbc.co.uk/news/uk-england-northamptonshire-14184535) Figure 18. FSAE Hoosier tire (Taken from: https://www.hoosiertire.com/Fsaeinfo.htm ). Figure 19. Keiser Kosmo Forged (Taken from: http://keizerwheels.com/ )
Figure 20. Center of gravity location of the actual chassis Figure 21. First layout of the major components Figure 22. Second layout of the major components Figure 23. Third layout of the major components Figure 24. Equal Length & Parallel arms configuration (Taken from: Farrington, 2011 pg. 22) Figure 25. Unequal Length & Parallel arms (Taken from: Farrington, 2011 pg. 22) Figure 26. Unequal Length & Non-Parallel arms (Taken from: Farrington, 2011 pg. 22) Figure 27. Chassis design Figure 28. Chassis with the modifications in the rear section Figure 29. First iteration of the suspension geometry attached to the chassis Figure 30. Chassis possible modifications Figure 31. Roll Center Height and KPI angle estimation using the graphical method Figure 32. Coordinate system & Hardpoints assignation (Wolfe, 2010). Figure 33. Relationship between the Variables & Parameters Figure 34. yl vs Roll Center Height (RCH in inches) Figure 35. Results after iterating the Upper A-arm width (Z coordinate of Hardpoints 1 & 2). Figure 36. ADAMS/Car® fsae_2012 full vehicle assembly Figure 37. First design iteration of the FRONT_UNIANDES assembly Figure 38. First design iteration of the REAR_UNIANDES assembly Figure 39. First design iteration of the FSAE_UNIANDES assembly Figure 40. Equivalent Coordinate system (MatLab & ADAMS/Car). Figure 41. Origin of the coordinate system in ADAMS/Car® Figure 42. Öhlins TTX25 MkII (50 mm). (Taken from: http://www.kaztechnologies.com/fsae/shocks/ohlins-fsae-
shocks/). Figure 43. Suspension actuation mechanism (Front & Rear assemblies)
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Figure 44. HYPERCO FSAE springs (Taken from: http://www.kaztechnologies.com/fsae/springs/) Figure 45. Location of each of the 5 input factors (Front Suspension) Figure 46. Simulation conditions during the Front Suspension DOE Figure 47. Opposite Wheel travel simulation Figure 48. Influence of the factors respect the Roll Center vertical displacement (Front suspension) Figure 49. Influence of the factors respect the Roll Center lateral displacement (Front suspension) Figure 50. Influence of the factors respect the Camber gain (Front suspension) Figure 51. Influence of the factors respect the Toe gain(Front suspension) Figure 52. Location of each of the 6 input factors (Rear Suspension) Figure 53. Simulation conditions during the Rear Suspension DOE Figure 54. Influence of the factors respect the Roll Center vertical displacement Figure 55. Influence of the factors respect the Roll Center Lateral displacement Figure 56. Influence of the factors respect the Camber gain Figure 57. Influence of the factors respect the Toe gain Figure 58. Vehicle trajectory while performing a Step-steer simulation Figure 59. Simulation Conditions: Step-steer Figure 60. Influence of the factors respect the Lateral Acceleration Figure 61. Influence of the factors respect the Chassis Roll Figure 62. Influence of the factors respect the Yaw rate Figure 63. Influence of the factors respect the Vehicle Slip Angle Figure 64. FRONT_UNIANDES final configuration Figure 65. REAR_UNIANDES final configuration Figure 66. FSAE_UNIANDES vehicle vs fsae_2012 vehicle Figure 67. Straight line acceleration conditions Figure 68. Vehicle´s pitch angle vs simulation time (FSAE_UNIANDES vs fsae_2012) Figure 69. Vehicle´s pitch angle vs Longitudinal acceleration (FSAE_UNIANDES vs fsae_2012) Figure 70. Front and Rear normal forces (FSAE_UNIANDES) vs simulation time Figure 71. FSAE_UNIANDES longitudinal acceleration vs simulation time Figure 72. Lane change simulation conditions Figure 73. Chassis roll ange vs lateral acceleration (FSAE_UNIANDES vs fsae_2012 Figure 74. Lateral Acceleration vs simulation time (FSAE_UNIANDEs vs fsae_2012) Figure 75. Constant Radius simulation conditions Figure 76. Vehicle´s Side Slip Angle vs simulation time (FSAE_UNIANDES vs fsae_2012) Figure 77. Tire normal forces vs simulation time (FSAE_UNIANDES) Figure 78. Internal combustión engine vs electric engine: Torque vs rpm (taken from: https://simanaitissays.com/2013/07/20/tranny-talk/) Figure 79. Vehicle side-slip angle (taken from: http://www.racelogic.co.uk/_downloads/vbox/Application_Notes/Slip%20Angle%20Explained.pdf)
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List of Tables:
Table 1. FSAE Lincoln Electric vehicles parameters (2015) Table 2. Hoosier tire specifications Table 3. Weight estimation of the vehicle Table 4. Types of Batteries used in the FSAE electric vehicles (Info taken from: http://batteryuniversity.com/learn/article/types_of_lithium_ion).
Table 5. Center of Gravity estimation for each configuration Table 6. Vehicle´s Dimensional Parameters Table 7. Recommended values for the suspension parameters* Table 1. Front Suspension Input Variables domain Table 2. Front Suspension Parameters domain Table 10. Front Suspension Results (New domain for each Hardpoint) Table 11. Rear Suspension Input Variable Domain Table 12. Desire RCH domain for the rear suspension Table 13. Rear Suspension Results (New domain for each Hardpoint Table 14. Suspension parameters needed for the analysis Table 15. Final values for the front & rear suspension mechanism Table 16. Input factors Front suspension Assembly Table 17. Input factors Rear suspension Assembly Table 18. Input factors Full vehicle suspension Assembly Table 19. Final Parameters for the FRONT_UNIANDES and REAR_UNIANDES suspension assemblies Table 20. FRONT_UNIANDES Hardpoint location Table 21. Meaning of each Hardpoint that represents the front suspension assembly. Table 22. REAR_UNIANDES Hardpoint location
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Chapter 1. Introduction
1.1 Project Background
The Formula SAE is a student competition organized by the Society of Automotive Engineers
(SAE) in which each team, composed by undergraduate and graduate engineering students
has the challenge to design and fabricate a small formula style vehicle in order to compete
among each other. The main objective of this competition is to provide a unique educational
experience to their participants as well as enable them to create and innovate.
The events are held annually on different locations such as Germany, the US, Australia, the
UK, Japan, Italy and Brazil. In general, the competition is divided into two types of events:
The static events, where students present details of the design, cost and manufacturing
processes and the dynamic events, which test the vehicle’s acceleration, braking and
handling under different race car conditions (Kiszko, 2011).
In recent years, the vehicle industry has faced new challenges due to their necessity to
implement high efficiency powertrains, which are design in order to achieve sustainable
energy vehicles that can reduce their global warming impact. With this in mind, the formula
SAE has incorporated new categories to their events such as the FSAE hybrid and the FSAE
electric, looking forward to promote new technologies in these new fields.
The Universidad de Los Andes is willing to participate on a Formula SAE electric competition,
reason why the last semester the mechanical engineering student Camilo Sarmiento
realized the first iteration of the chassis design. During this first design, the geometry of the
chassis was established among other subsystems of the vehicle such as the powertrain, the
transmission and the suspension arms.
Figure 2. Chassis Render (Sarmiento, 2015)
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1.2 Problem Definition:
The suspension system proposed by Camilo Sarmiento in his project has some serious
design issues and lacks of a proper engineering design, reason why this project pretends to
design a suspension system that can overcome the demands imposed not only by the
different dynamic events but also by the requirements stated in the FSAE normative. On
the other hand, the geometry of the chassis proposed by Camilo serves as a starting point
for the design; however, this design is prone to changes according to the suspension
geometrical demands.
9 *The fsae_2012 is a 3D computation vehicle model elaborated by the engineers from the MSC ADAMS/Car® program.
Chapter 2. Objectives & Design Methodology
This chapter describes the objectives settled for this thesis work as well as the methodology
implemented throughout the design process. It is important to recognise that this is the first
time that the team FSAE Uniandes is looking forward to compete in one of these events,
and so the design of the whole vehicle started from scratch.
2.1 Objectives:
The objectives that are listed ahead were established in order to overcome the design issues
that the actual suspension design has. On top of that, their main aim is to achieve a proper
suspension configuration that can obtain good results during the dynamic events.
General Objective:
The main objective of this thesis is to establish a design methodology to achieve a
suspension configuration that can meet the following overall targets:
Allow a proper tire grip under different conditions (cornering, straight line, etc.)
Promote the stability & Manoeuvrability of the vehicle.
Meet all the restrictions imposed by the FSAE rules.
Adjust to the actual chassis design
Specific Objectives:
Analyse information from previous FSAE electric vehicles in order to establish some
preliminary constrains and parameters
Identify the influences of some relevant design parameters on the vehicle´s
performance throughout a series of simulation analysis,
Simulate the suspension design proposed for the Uniandes FSAE vehicle under
different race car conditions (acceleration, cornering, lane change, etc.) and
compare the performance results with the fsae_2012*.
10 *A Hardpoint represents the physical location of a suspension joint (such as a ball joint or a bushing).
2.2 Design Methodology:
The methodology described ahead is a chronological design process. Each of the ten steps
listed ahead were established takin into account the recommendations offered by different
suspension and vehicle literature authors.
1. Analyse the FSAE rules:
The first step in the design of any subsystem from a FSAE is to make sure that the
designer has a thorough understanding of the rules and regulations.
2. Establish preliminary design parameters:
Before modelling the suspension geometry, a series of fundamental parameters that
affect the performance of this subsystem must be established. A useful way to
determine these parameters is by analysing previous FSAE suspension designs as
well as taking into account the recommendations offered by the literature. Some
crucial preliminary parameters are listed ahead (for a more detailed information see
chapter 4).
Center of Gravity
Roll Center domain (Lateral and horizontal displacements)
Camber, caster, KPI, etc.
Spring and dampers
Hardpoints* allocation & Restrictions
Rims & Tires
Fundamental dimensions (Wheelbase, Track, ride height, etc.)
3. Determine the type of suspension that would be implemented:
Nowadays exist a great variety of suspension configurations such as the Double
Wishbones, the MacPherson, the Trailing Arm, etc. During this stage, the designer
must choose a suspension configuration that can match not only the requirements
imposed by the FSAE rulebook, but also the desire vehicle dynamic performance.
4. Incorporate the suspension basic elements into the actual chassis (CAD model)
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Once the designer knows the suspension configuration that will be implemented,
the next step is to incorporate the geometry of the suspension into the actual chassis
design. During this process, the software Autodesk Inventor Professional 2015® will
be used in order to achieve a proper design.
5. Geometric design analysis:
To evaluate the suspension geometry previously designed, a MatLab® code was
implemented. During this stage, the designer obtains crucial information about the
location of the suspension Hardpoints according to the geometric constrains &
parameters (for a more detailed information see chapter 6)
6. ADAMS/Car® suspension modelling:
During this stage, the suspension design must be modelled in ADAMS/Car® so that
the kinematic simulations can be carry out. Additionally, a series of suspension
elements must be designed and evaluated (rocker, spring & damper, push rod).
7. Kinematic suspension analysis:
During the kinematic analysis, the suspension assemblies (Front & Rear) are
simulated and the designer evaluates the influence of some variables based on a
factorial experiment design.
8. Full vehicle Dynamic analysis:
Once again, a factorial experiment design is implemented during the evaluation of
the whole vehicle suspension assembly. The objective is to obtain information
regarding the influence of the suspension variables (such as the roll center height or
the spring´s stiffness) in the vehicle´s performance parameters (Side slip angle, Roll
angle, pitch angle and Lateral acceleration).
9. Suspension Geometry modification:
Based on the results obtain on the previous analysis, the designer now has helpful
information to adjust the actual suspension design looking forward to obtain the
desired performance.
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10. Simulate, compare and iterate:
Finally, during this stage the designer must carry out an iterative process looking
forward to obtain the final suspension configuration. According to Allan Staniforth
in his book “Competition Car Suspension”: The design of a suspension system is a
perpetual adjustment of conflicting parameters in search of an allusive all satisfying
condition that ultimately concludes in the best achievable compromise. As there is
no definitive solution to suspension geometry design, sometimes considered more
art than science, guidelines have been devised based on empirical evidence
(Staniforth, 1999).
13 *https://simcompanion.mscsoftware.com/infocenter/index?page=home
Chapter 3. Literature Review
This chapter shows a brief resume of the main components and parameters from a formula
SAE suspension system. Its purpose is to familiarize the reader with the engineering terms
that will be present throughout the entire document.
3.1 The Suspension of a FSAE and its objective:
The main objective of the suspension in any vehicle is to isolate the occupants or cargo
inside from the shocks and vibrations induced by the road. Besides, the suspension design
has a great influence in the final performance of the vehicle as it promotes stability and
control. A good suspension design optimizes the contact between each tire and the road
surface under different conditions.
A formula SAE requires a race car suspension, which means that this mechanism needs to
sacrifice parameters such as the driver´s comfort in order to improve its handling
performance. The characteristics of a race car suspension differs from a salon car in many
aspects; some of this are: low un-sprung weight, low aerodynamic drag and high spring
stiffness.
Figure 2. Types of Independent suspension configurations
In general, the suspension of a Formula SAE is an independent suspension (most of the
times a double wishbone configuration). The springs & dampers are actuated via pull/push
rod (figure 2 – A & B) or in some few cases, with a direct actuation of the spring & damper
(figure 2 – C).
3.2 FSAE suspension elements.
The next two figures correspond to the front & Rear suspension assemblies elaborated by
the engineers of Adams/Car®. This vehicle can be downloaded from the MSC
SimCompanion web page and has a purely educational purpose*. The aim of these two
images is to illustrate all the components present in a Formula SAE suspension
configuration.
A B
C
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Figure 3. ADAMS/Car® fsae_2012 Front Suspension Assembly
Figure 4. ADAMS/Car® fsae_2012 Rear Suspension Assembly
1. Steering Wheel
2. Spring & Damper (also known as shock absorber)
3. Steering column
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4. Anti-Roll Bar (also known as anti-sway bar).
5. Rocker (also known as Bell-crank)
6. Rack & Pinion
7. Tie-Rod
8. Push-Rod
9. Lower suspension arm (also known as lower: wishbone, control arm or A-arm)
10. Upper suspension arm (also known as upper: wishbone, control arm or A-arm)
11. Upright (also known as Kingpin)
12. Drive Shaft
13. Tire
14. Rim
Springs & Dampers:
In general, the main aim of the springs is to keep the chassis at a constant ride height.
Additionally, they are highly responsible of the handling and stability of the vehicle.
Currently, there are four types of springs utilised in cars: the coil, the leaf, the torsion bar
and the air springs. A race cars suspension systems usually uses the coil spring due to its
favourable dynamic response as well as its geometrical & lightweight properties.
Dampers and springs go hand in hand; the springs absorb shocks whereas the dampers
dampen the energy stored in the springs as they absorb these shocks. Without dampers,
the vehicle will continue to oscillate up and down at its natural frequency after travelling
over a disturbance in the road (Farrington, 2011).
Anti-Roll Bar:
The objective of these elements is to reduce the chassis roll while cornering. The mechanism
is incorporated to the suspension geometry in order to supply extra stiffness to the springs.
The idea is to equalise the amount of force shared by the suspension elements on both sides
of the car in order to avoid chassis roll (figure 3 – element 4).
3.3 Full Vehicle parameters:
Vehicle motions:
In order to calculate accelerations and velocities in directions of interest, it is necessary to
define the axis systems to which the accelerations, velocities and the forces/torques can be
referred (Milliken & Milliken, 1995).
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Figure 5. ISO International Vehicle axis system
Roll is the rotation of the vehicle’s sprung mass about the vehicle’s longitudinal axis usually
during cornering. Yaw is the rotation about the vehicle’s vertical axis as a result of the
vehicle’s change of direction and pitch is the rotation about the lateral axis usually a result
of braking or acceleration (Kiszko, 2010).
Sprung & Un-Sprung Weight:
The Sprung weight of a vehicle is the portion of the total car weight that is supported by the
springs. This weight is much larger than the un-sprung weight as it consists of the weight
from the majority of the car components, which include the chassis, driver, engine, gearbox,
batteries, etc.
In contrast to the sprung weight, the un-sprung weight is the fraction of the total weight
that is not supported by the springs. This weight usually consist of the wheels, brakes, drive-
shaft, etc. (Smith, 1978).
Center of Gravity (CG):
The definition of centre of gravity for a car is not different from a simple object such as a
cube. Essentially, it is a three dimensional balance point where if the car was suspended
by, it would be able to balance with no rotational movement. Recognising this concept, it
is clear that the centre of gravity of the car will be located at where mass is most highly
concentrated which for a race car is typically around the engine and associated drive
components. It is also expected that all accelerative forces experienced by a vehicle will act
through its centre of gravity (Farrington, 2011). It is recommended that the centre of gravity
for a vehicle be kept as low as possible to reduce the moment generated as the vehicle
experiences lateral acceleration. (Smith, 1978)
Roll Center (RC):
The SAE defines the suspension roll center as the point at which lateral forces may be
applied without producing rolling of the sprung mass (Chang, 2012). The Roll center height
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is the distance from the instant roll center to the tire contact, measured on the vertical
centreline of the vehicle (figure 6).
Figure 6. Roll Center height diagram (Chang, 2012)
For the case of an independent double A-arm suspension, the instant roll center can be
external or internal (figure 7 – a & b). In addition, the instant roll center may be on, above,
or below the road surface (figure 7).
Figure 7. Instant Roll Center (Jazar, 2014).
Roll Axis:
On the other hand, the roll axis is the instantaneous line about which the body of a vehicle
rolls. Roll axis is found by connecting the roll center of the front and rear suspensions of the
vehicle (figure 8). Usually, the rear roll center is higher than the front, reason why the
vehicle roll axis is not parallel to the ground plane.
Figure 8. Vehicle Roll Axis
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Importance of the Roll Center:
When the car is turning in a curved path, the centripetal force: 𝑓𝑦 =𝑚𝑣2
𝑅 is the effective
lateral force at the mass center that generates a roll torque 𝑀𝑥 about the roll center:
𝑀𝑥 =𝑚𝑣2
𝑅∗ ℎ𝑟
The roll center, hence the roll angle of a car increases proportional to the roll height, and
square to the velocity; therefore, if you double the speed, you will need to have four times
a shorter roll height to maintain the same roll angle (Jazar, 2014).
If the roll center of the car is located below the CG (the most common case), when
the car makes a turn, it will roll outward of the turning path.
On the other hand, if the roll center is above the CG, the car will roll inward in a
turning path (like a boat).
3.4 Vehicle Dynamic Load Transfer:
Lateral load transfer:
Every vehicle tends to roll during cornering. The car roll is dependent on its center of gravity,
the roll axis, the lateral force in cornering and suspension geometry. Lateral weight transfer
of a vehicle is the weight transfer between the left and right side of the center-line. During
cornering, the effect of weight transfer will cause the inner tires to lift while outer tires will
be press down to the road (Svendsen, 2014).
Longitudinal load transfer:
During acceleration and braking the weight of the car tends to shift forward and rearward
respectively. Longitudinal weight transfer of a vehicle is weight transfer between the front
and the rear of the car, where the center of gravity is the center point. The effect is similar
to lateral weight transfer and increased proportional to center of gravity height of the car
(Svendsen, 2014).
Anti-dive & Anti-squat
Dive and squat are fundamentally the same concept except reversed. Dive is where the
front end of the car dips down under braking due to the longitudinal weight transfer from
the back of the car to the front acting on the front springs. Squat is where the back springs
are compressed due to longitudinal weight transfer from the front of the car to the back,
which in effect causes the end of the vehicle to depress towards the ground plane
(Farrington, 2011).
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3.5 Tire relative angles:
“The cornering force that a tire can develop is a function of its angles relative to the road
surface” (Jazar, 2014).
Toe Angle:
The angle that a wheel makes with a line drawn parallel to the length of the car when viewed
from above itself.
Figure 9. Different Toe Angle´s (Jazar, 2014)
Toe settings affect three major performances: Tire wear, straight-line stability and corner
entry handling.
Front toe-in: slower steering response, more straight-line stability, greater wear
at the outboard edges of the tires.
Front toe-zero: medium steering response, minimum power loss, minimum tire
wear.
Front toe-out: quicker steering response, less straight-line stability, greater wear
at the inboard edges of the tires.
Rear toe-in: straight-line stability, traction out of the corner, more steerability,
higher top speed.
In general, toe-in will provide greater straight line stability whereas a controlled amount of
toe-out can improve the car´s turn-in ability to a corner and makes the steering response
faster; reason why most race cars are set to have a few toe-out angle in their front wheels.
Caster Angle:
Caster is the angle to which the steering axis is tilted forward or rearward from vertical as
viewed from the side. It is positive when the kingpin axis (steering axis) meets the ground
ahead of the vertical axis drawn through the wheel center (Farrington, 2011).
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Figure 10. Caster angle geometry
Zero caster provides easy steering into the corner, low steering out of the corner
and a low straight-line stability.
Positive caster provides lazy steering into the corner, easy steering out of the corner,
more straight-line directional stability, high tire-print area during turn and good
steering feel.
When a positive castered wheel rotates about the steering axis, the wheel gains
negative camber. This camber is generally favourable for cornering.
As a result, while greater caster angles improves straight-line stability, they cause an
increase in steering effort.
Mechanical Trail:
The mechanical trail is defined as the distance between the intersection of the steering axis
and the ground measured to the center of the contact patch, viewed perpendicular to the
vertical longitudinal plane. As well as the Scrub Radius, this parameter is important for the
steering effort that the driver has to apply.
Camber:
Camber is the inclination angle the wheel plane makes with respect to the vehicle's vertical
axis. This angle plays a fundamental roll on the road holding of the car due to its ability to
generate lateral forces, reason why the Camber angle also works like steer: When a tire is
cambered it tends to pull the car in the same direction in which the top of the tire is leaning.
Figure 31. Camber angle geometry
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Race car’s have a small wheel travel and a high roll stiffness; for these conditions, it is easier
to control the ideal camber angle in order to have a good tire performance. Generally, these
vehicles are designed with a relatively small negative camber angle statically applied.
Kingpin Angle (KPI) & Scrub radius:
Is the angle between the wheel centreline (perpendicular to the ground) and the steering
(kingpin) axis as viewed form the front. Positive Kingpin is when the kingpin axis angles in
towards the centre of the vehicle whereas negative inclination is the opposite.
Figure 12. Kingpin angle & scrub radius geometry
The Scrub radius is proportional to the kingpin offset at ground, which means that is the
lateral distance between the intersections of the wheel center plane and the steering axis
with the ground plane. The scrub radius relates to the steering feel to a large degree.
A smaller scrub radius promotes easier steering movement as the friction created by the
tire scrubbing across the road surface is reduced. A larger scrub radius means a greater
distance from the point where the weight of the car concentrates on the tire’s contact patch
and the location where the steering or kingpin axis meets the ground plane; which provides
a larger moment arm for the frictional forces to act on making it harder for the driver to
turn the wheels.
Hence, it is mechanically desirable to have a zero Scrub radius offset because it puts much
less stress on the suspension components; however, the KPI angle and the scrub radius
creates the phenomena of the return of the wheels to straight position after a steering
operation. They also tent to maintain this position after an impact with an obstacle that
attempts to alter the trajectory, reason why these parameters are widely implemented in
all the suspension´s designs.
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3.6 Suspension Behaviours:
Bump & Droop:
Bump and droop are positions of an independent suspension under certain scenarios.
Bump occurs when the wheels hit a bump on the track surface, whereas droop occurs when
the wheels drop into a depression in the track surface. Bump and droop movements
associate with the suspension travel terms, rebound and jounce, where jounce describes
the upwards movement of the wheel or movement in bump while rebound describes the
downwards travel of the wheel or droop movement (Farrington, 2011).
Jacking:
Any vehicle possessing independent suspension with its roll centre above the ground plane
will exhibit some extent of jacking and is where the car will appear to lift itself up while
cornering. This effect may be visualised on the following figure and occurs when the
reaction force acting on the tyre acts through the roll centre to balance the centrifugal force
generated as the car is turning. This effect is highly undesired as it raises the centre of
gravity and places the suspension linkage in the droop position which results in poor tyre
camber, in effect, hindering the tyre’s adhesion to the track surface. This phenomenon is
experienced a lot more significantly in vehicles possessing a high roll centre and narrow
track width (Smith, 1978).
Figure 13. Jacking Force estimation (Smith, 1978)
3.7 Steering Behaviours:
Slip Angle, Oversteer & Understeer:
Slip angle is the angle between a rolling wheel's actual direction of travel and the direction
towards which it is pointing. Lateral force increases with increasing slip angle until the tyre’s
maximum co-efficient of friction is breached and the tire breaks loose (Kiszko, 2011).
23
Figure 14. Tire´s slip angle (Milliken & Milliken, 1995)
As a result, the dynamic behaviour of the vehicle is affected:
Oversteer: When the front wheel slip angles are smaller than the rear ones.
Understeer: When the front wheel slip angles are larger than the rear.
Neutral steering: When the slip angles for the front and rear wheels are equal.
Figure 15 Oversteer & Understeer (Farrington, 2011)
Bump Steer:
When the front wheels of a vehicle vary their toe angle as the suspension moves in Bump
or Droop its call bump steer. This phenomenon could cause a poor handling feel and
unwanted driver uncertainty (Staniforth, 1999). However, under some cases, the designer
can used it to improve the vehicle response while taking cornering.
Roll Steer:
Roll Steer is the self-steering action of any automobile in response to lateral acceleration.
This phenomenon consists of slip angle changes due to camber change, toe change and the
inertias of the sprung mass (Staniforth, 1999).
24
This effect will be present in all double wishbone setups although can be limited by reducing
the gross weight of the car, centre of gravity height, eliminating deflection in the suspension
and associated chassis mounting components, and lastly, by adjusting bump steer
(Farrington, 2011).
3.8 Formula SAE Suspension Requirements
Before taking any decision concerning the suspension of the vehicle, an extensive research
of the rules was realized in order to assure the suspension subsystem meet all the
requirements imposed by the FSAE rulebook.
Even though there are a series of different Formula SAE competitions all over the glove such
as the Formula SAE Lincoln, Formula SAE Australia, etc. A common denominator between
all these competitions are the rules imposed to every team.
The rulebook from the FSAE competitions takes into account a great variety of aspects such
as engineering design, project management, finances, etc. However, the constraints
discussed in this chapter are limited to the suspension requirements. After analysing all the
rules that affect the suspension system, a small number of restrictions were found. This
limited amount of constrains allows the designer to have a large degree of flexibility in his
design; the main constraints that affect the suspension are listed ahead and are quoted
directly from the 2015 Formula SAE rulebook:
Figure 16. Vehicle Fundamental dimensions
Two key dimensional restrictions that affect the final geometry of the suspension are the
vehicle Wheelbase and track. According to the FSAE rulebook these two variables should
be:
(T2.3) Wheelbase: of at least 1525 mm (60 in) measured from the centre of ground
contact of the front and rear tires with the wheels pointed straight ahead.
25
(T2.4) Vehicle track: The smaller track of the vehicle (front or rear) must be no less
than 75% of the larger track.
Driver’s Leg Protection (T5.8):
(T5.8.1): To keep the driver’s legs away from moving or sharp components, all moving
suspension and steering components, and other sharp edges inside the cockpit between
the front roll hoop and a vertical plane 100 mm (4 inches) rearward of the pedals, must be
shielded with a shield made of a solid material. Moving components include, but are not
limited to springs, shock absorbers, rocker arms, antiroll/sway bars, steering racks and
steering column CV joints.
(T5.8.2) Covers over suspension and steering components must be removable to allow
inspection of the mounting points.
Suspension (T6.1):
(T6.1.1): The car must be equipped with a fully operational suspension system with shock
absorbers, front and rear, with usable wheel travel of at least 50.8 mm (2 inches), 25.4 mm
(1 inch) jounce and 25.4 mm (1 inch) rebound, with driver seated. The judges reserve the
right to disqualify cars which do not represent a serious attempt at an operational
suspension system or which demonstrate handling inappropriate for an autocross circuit.
(T6.1.2): All suspension mounting points must be visible at Technical Inspection, either by
direct view or by removing any covers.
(T6.2) Ground clearance: must be sufficient to prevent any portion of the car, other than
the tires, from touching the ground during track events. Intentional or excessive ground
contact of any portion of the car other than the tires will forfeit a run or an entire dynamic
event.
Wheels (T6.3)
(T6.3.1): The wheels of the car must be 203.2 mm (8.0 inches) or more in diameter.
(T6.3.2): Any wheel mounting system that uses a single retaining nut must incorporate a
device to retain the nut and the wheel in the event that the nut loosens. A second nut (“jam
nut”) does not meet these requirements.
(T6.3.3): Standard wheel lug bolts are considered engineering fasteners and any
modification will be subject to extra scrutiny during technical inspection. Teams using
modified lug bolts or custom designs will be required to provide proof that good engineering
practices have been followed in their design.
26
(T6.3.4): Aluminium wheel nuts may be used, but they must be hard anodized and in
pristine condition.
Tires (T6.4)
(T6.4.1): Vehicles may have two types of tires as follows:
a. Dry Tires – The tires on the vehicle when it is presented for technical inspection are
defined as its “Dry Tires”. The dry tires may be any size or type. They may be slicks or
treaded.
b. Rain Tires – Rain tires may be any size or type of treaded or grooved tire provided:
i. The tread pattern or grooves were molded in by the tire manufacturer, or were
cut by the tire manufacturer or his appointed agent. Any grooves that have been cut must
have documentary proof that it was done in accordance with these rules.
ii. There is a minimum tread depth of 2.4 mms (3/32 inch).
NOTE: Hand cutting, grooving or modification of the tires by the teams is specifically
prohibited.
(T6.4.2): Within each tire set, the tire compound or size, or wheel type or size may not be
changed after static judging has begun. Tire warmers are not allowed. No traction
enhancers may be applied to the tires after the static judging has begun, or at any time on-
site at the competition.
Rollover stability (T6.7)
(T6.7.1): The track and center of gravity of the car must combine to provide adequate
rollover stability.
(T6.7.2): Rollover stability will be evaluated on a tilt table using a pass/fail test. The vehicle
must not roll when tilted at an angle of sixty degrees (60°) to the horizontal in either
direction, corresponding to 1.7 G’s. The tilt test will be conducted with the tallest driver in
the normal driving position.
Figure 17. Rollover stability test
27
Chapter 4. Preliminary Design decisions
As mentioned during the introduction, this is the first time that our university is preparing
to compete on a Formula SAE event. In order to start the design process, some initial
parameters had to be settle. One key starting point was the information available from FSAE
electric vehicles that competed last year.
4.1 Benchmark information
The following table shows a brief resume from table A1 (Appendix A). The information
illustrated on this table was taken from the FSAE Electric vehicles that participated last year
on the Formula Lincoln event. The table 1 provides a useful tool to get a rough estimation
about the dimensions, weights and possible suspension configurations that can be later
implemented in the suspension design.
Resume table:
Weight
Max: 800 lb Colorado State University
Min: 535 lb University of Washington
Avg: 639 lb
Wheelbase
Max: 1720 mm University of Manitoba
Min: 1529 mm University of Pennsylvania
Avg: 1595 mm
FR Track
Max: 1510 University of Manitoba
Min: 1172 Illinois Institute of technology
Avg: 1252 mm
RR Track
Max: 1495 University of Manitoba
Min: 1100 Polytechnique Montréal
Avg: 1222 N/A
Type of
suspension
Double A-Arm: 100 % of the cars have an independent suspension
system
Push Rod: 6 cars
Pull Rod: 3 cars
Pull/Push Rod: 3 cars used them both (front and rear)
Tire
100% of the cars used a Hoosier set of tires
20.5x7.0-13 6 cars used them
18x6-10 5 cars used them
6.0/18.0-10 2 cars used them
20.0x7.5-13 1 car used them
One car used 20.5x7.0-13 (front) and 20.0x7.5-13 (rear)
Table 1. FSAE Lincoln Electric vehicles parameters (2015)
Taking into account the information from these electric vehicles as well as the literature
review recommendations, the following parameters were established:
28
4.2 Rims & Tires
Tires:
Tires are the only component of a vehicle that transfer forces between the road and the
vehicle (Jazar, 2014), reason why they are a fundamental parameter in the final
performance of the vehicle. With the recent boom of the Formula SAE, a few manufactures
have developed special tires that match the necessities of these vehicles.
Hoosier is perhaps the tire´s manufacturer that has shown the greatest interest in this
vehicles and has develop a set of tires focused specially in the needs of the FSAE; no wonder
why the last decade all the defending champion teams had a set of Hoosier tires on their
vehicle’s (see Appendix B).
Figure 18. FSAE Hoosier tire
The tires that were chosen were the Item Number: 43163 from the Hoosier FSAE catalogue
(See figure A1 - Appendix B) which have the following specifications:
Tire (43163) specifications:
Size 20.5 x 7.0-13 C2500
Overall Diameter 21.0" (53,34 cm)
Tread Width 7.0" (17.78 cm)
Section Width 8.0" (20,32 cm)
Recommended width Rim 5.5-8.0" (13,97 – 20,32 cm)
Rim measured 6.0" (15,24 cm)
Compound R25B
Approximated weight 11 lbs (4,98 kg)
Table 2. Hoosier tire specifications
This tire has proven an excellent dynamic performance and satisfies all the constrains
imposed by the FSAE rulebook. In addition, the literature recommends this type of tires due
to their good packaging properties.
29
Rims:
Based on the previously chosen tire´s and taking into account that there is a possibility to
have electric engines on wheel, one possible option that provides a big packing room is the
13-inch rim. However, this rim does have some issues such as a higher weight and a higher
rotational inertia.
After analysing different rim manufactures, the Keiser ® Company offered a set of different
wheels that matched the previously selected Hoosier tires. Keiser® has also develop a
special set of rims for the FSAE vehicles and offered four different 13-inch rims geometries
(see table A2 - appendix C), each one of them with different properties, prices and materials.
Taking into account the backspacing, the flexibility and the weight, the Formula Kosmo
Forged billet rims were chosen as the proper rim that could satisfy the suspension design
requirements.
Figure 19. Keiser Formula Kosmo Forged billet
4.3 Vehicle´s Overall Weight estimation:
The overall weight of the vehicle is a parameter that plays a fundamental role in the
vehicle´s dynamic performance. This parameter has to be properly established in order to
obtain realistic results during the full vehicle simulation. Taking into account that there is
no information about the other vehicle subsystems, the following weight approximations
were established:
Major Components: Weight (kg)
2x Engines (EMRAX 207) 20
Driver (Taking into account accessories such as helmet, shoes, etc.) 75
Set of Batteries 50
Electronic devices (Drivers, on board computers, wires, etc.) 8
Chassis (Weight of the actual frame estimated by Autodesk Inventor) 58
Wheels (taking into account the weight of the tires) 40
Total Weight 251
Table 3. Weight estimation of the vehicle
30
Looking forward to obtain a more accurate data of the weight of the set of batteries, the
following assumptions were studied. The average energy consumption of all the electric
vehicles that participated on the Formula SAE Lincoln event last year was:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐸𝑛𝑒𝑟𝑔𝑦 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛: 𝟔 𝒌𝑾𝒉 ± 𝟏 𝒌𝑾𝒉 (see table A1 – Appendix A)
The total energy that the batteries have to supply is related with its efficiency and it can be
calculated with the following formula:
𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦:𝐸𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛
𝐵𝑎𝑡𝑡𝑒𝑟𝑦 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦
In order to estimate the total weight of the set of batteries, it is necessary to know its
specific energy:
𝑊𝑒𝑖𝑔ℎ𝑡 (𝑘𝑔) =𝑇𝑜𝑡𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 (𝑊ℎ)
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦 (𝑊ℎ𝑘𝑔
)
The batteries called “LiPo" offered a viable energy solution and are the most used batteries
in this type of vehicles. On the table below are some of the most common “LiPo” Batteries
available in the market nowadays:
Battery type: Specific energy (capacity) Approximated weight for an
energy supply of 6 kWh
Lithium Cobalt Oxide: LiCoO2 150–200Wh/kg. Some special
cells provide up to 240Wh/kg.
Max: 40 kg
Min: 25 kg
Avg: 32.5 kg
Lithium Nickel Manganese Cobalt
Oxide: LiNiMnCoO2 150–220Wh/kg
Max:40 kg
Min:27 kg
Avg: 33.5 kg
Lithium Iron Phosphate(LiFePO4) 90–120Wh/kg
Max: 66 kg
Min: 50 kg
Avg: 58 kg
Lithium Manganese Oxide (LiMn2O4) 100–150Wh/kg
Max: 60 kg
Min: 40 kg
Avg: 50 kg
Table 4. Types of Batteries used in the FSAE electric vehicles:
The weight of the set of batteries was calculated to be 50 kg, value that correspond to the
average weight of the Lithium Manganese Oxide batteries (which are the most used
batteries in the FSAE electric vehicles).
4.4 Center of Gravity Estimation:
According to the literature, the center of gravity of most of the FSAE cars is located
underneath the pilot just behind the steering wheel. The location of the center of gravity in
31
the case of a formula SAE electric is highly influenced by the weight and location of the set
of batteries, the engines and the chassis geometry.
The Center of gravity of the vehicle can be easily estimated using the Autodesk Inventor
toolbox. The figure 20 shows the actual location of the center of gravity; since this location
only considers the weight of the chassis, the two engines, the driver seat and a few
suspension elements it is not a reliable value.
Figure 20. Center of gravity location of the actual chassis
In order to obtain a more realistic value of the center of gravity, the weight and location of
the major components of the vehicle (table 4) had to be taken into account. However, these
elements can be located in various parts of the chassis. To overcome this problem, three
typical FSAE electric vehicle layouts were consider.
Vehicle Packaging and layout configurations:
In the first Configuration, the set of batteries is located behind the driver (purple), the two
engines are inside the chassis parallel to the rear wheels (yellow) and the electronic devices
are on top of the batteries (blue):
Figure 21. First layout of the major components
In the second configuration, the set of batteries is located at the sides of the driver, the
electronic devices behind the driver and the engines are inside the frame, parallel to the
rear wheels.
32
Figure 22. Second layout of the major components
In the Third and last configuration, the set of batteries is located in the same position as in
the second configuration; however, the engines change their position and direction and are
located behind the driver (as in the original design proposed by Camilo Sarmiento). Finally,
the electronic devices are located on top of the engines just behind the driver.
Figure 23. Third layout of the major components
The center of gravity was estimated for each configuration using the software Autodesk
Inventor Professional 2015®. On top of that, each configuration has two different ride
heights (low: 2 in above ground, high: 3 in above ground). The results are illustrated in the
following table:
Configuration: X (respect the front of
the chassis)
Y (respect the
bottom of the
chassis)
Y (respect
ground floor)
Z (respect the
centreline of the
vehicle)
First - High 1397.8 mm
211.9 mm 356.7
0
First - Low 230.13 298.7 mm
Second - High 1281.8
201.3 346.1
Second - Low 219.5 288.0
Third - High 1258.1
207.8 249.8
Third - Low 220.8 288.5
Average 1312.6 215,2 304,6
0 standard
deviation
74,8
10,3 40,0
Table 5. Center of Gravity estimation for each configuration
33
For each coordinate of the center of gravity (x, y, z) the average and the standard deviation
was calculated. This new values were later used during the full vehicle simulations. Apart
from that, the value obtain during this process was later compared with the center of gravity
allocation of other FSAE vehicles. The comparison shows a very close error margin, which
means that the center of gravity was correctly estimated.
4.5 Type of suspension:
Perhaps the most important founding decision made during this chapter is the type of
suspension that will be implemented in the FSAE Uniandes vehicle. The suspension system
that was chosen was the double wishbone with push-rod actuators in the front and rear
assemblies. There are several reasons that support this decision; the most relevant are
listed ahead:
It provides a very accurate control of the camber angle during the suspension travel
The double wishbone independent suspension adapts easily to the different
geometries of the chassis.
The push-rod system allows the designer to locate the springs and dampers in order
to produce a proper packaging configuration. This type of system reduces the
interference with other vehicle subsystems such as the direction, powertrain or
even the driver legs.
Implementing a push-rod mechanism reduces the aerodynamic drag forces because
the shock absorbers are placed inside the chassis. Additionally, this configuration
improves the wheel rate control along with the ride height adjustment.
The double wishbone suspension allows the designer to locate and have a more
accurate control of the Roll center.
Its simple geometry provides a low un-sprung weight, high strength and easy
adjustment of various parameters such as camber or toe control.
The double wishbone configuration is probably the most widely used racing
suspension design (Staniforth, 1999).
The double wishbone independent suspension can have different types of configurations
that can be used to alter the vehicle handling properties, some of them are:
Equal Length & Parallel Arms:
When the wheels moves up and down, there is no camber change.
When the vehicle´s sprung mass rolls a certain amount, the camber will change by
the exact same amount with the outside wheel cambering in the positive direction.
This is not desired as the contact patch of the tire becomes reduced, diminishing the
amount of grip available to the vehicle.
34
The roll center is always above ground; under Rebound or jounce, it maintain
positive.
Figure 24. Equal Length & Parallel arms configuration
Unequal Length & parallel arms:
The upper link is typically shorter in order to induce a negative camber angle when
the car hits a bump and either a negative or positive camber when the linkages go
into droop
The location of the roll center will generally be very low
The wheels are forced into camber angles defined by the roll direction of the car,
however this time the positive camber of the outside wheel is reduced and the
negative camber of the inside wheel increased.
Figure 25. Unequal Length & Parallel arms
Unequal Length and Non-parallel arms:
Most commonly used set up
This type of set-up allows better camber control of the wheels
It also allows the designer to locate the roll center easily.
Figure 26. Unequal Length & Non-Parallel arms
35
Once the suspension configuration is established, the suspension design must be
incorporated to the actual chassis geometry and then a series of suspension analysis and
simulations are held in order to evaluate the suspension performance.
4.6 Vehicle Basic Dimensional Parameters:
The wheelbase of a vehicle is defined as the distance between the front wheels and the rear
wheels measured from their center point; while the vehicle´s track is define as the distance
between the left tire and the right tire, measured from their centreline (see figure 16).
These two parameters among with the vehicle´s ride height affect considerably the vehicle
performance, especially during a straight-line acceleration or a cornering manoeuvre. The
table below shows the final values of these dimensions:
Parameter Value
Wheelbase: 1600 mm
Front Track 1300 mm
Rear Track 1200 mm
Ride height Between 2.5 – 3.5 in
Table 6. Vehicle´s Dimensional Parameters
There are several reasons why these values were chosen; the most important are listed
ahead:
According the FSAE rules, the wheelbase must be at least 60 in (1525 mm); however,
due to packaging and performance reasons, the literature recommends at least 1600
mm.
A longer Wheelbase prevent future issues related not only with the subsystems
packaging but also with possible interference among each other.
The wheelbase has a big influence on the axle load distribution. During accelerating or
breaking, a longer wheelbase will generate a lower longitudinal load transfer; on the
other hand, a shorter wheelbase has the advantage of accomplishing a smaller turning
radius for the same steering input. A 1600 mm wheelbase provides a good compromise
between the longitudinal load transfer and the vehicle cornering performance.
The track width has influence on the vehicle´s cornering behaviour and tendency to roll.
A larger track generates a smaller lateral load transfer while cornering and vice versa,
however, a larger track generates difficulties to the driver while trying to avoid
obstacles.
Generally, the front track is larger than the rear track in order to decrease the roll in the
front of the vehicle; this configuration provides the driver a better handling feeling and
control.
36 *The values listed in table 7 were selected based on the recommendations offered by the following references: 1. Formula SAE forums: http://www.fsae.com/forums/forum.php 2. Kiszko, M. REV 2011 Formula SAE Electric – Suspension Design, 2011. University of Western Australia, Australia. 3. Farrington, J. Redesign of an FSAE Race Car´s Steering and Suspension System, 2011. University of Southern Queensland, Australia.
4.7 Overall Performance Targets & Design Recommendations:
In order to accomplish the objective set at the beginning of this paper, the suspension
design should take into account the following recommendations. All the information
mentioned ahead comes from the literature review, information available from previous
FSAE vehicles as well as the Formula SAE forums.
In order to Maximize tire grip under different conditions, the roll Stiffness of the vehicle
must increase. This can be achieved by modifying the spring stiffness, implementing
anti-roll bars, using a wider track or altering the Roll center of the suspension.
Nevertheless, as everything on engineering is a compromise, some other vehicle
performance parameters would be affected; for example, the ride comfort or the tires
wear.
The wheels relative angles such as the toe or the camber have a great influence not only
in the tire´s grip but also in the vehicle stability & manoeuvrability. The following table
resumes the recommended values for each of this parameters:
Parameter: Maximum value: Minimum value:
Kingpin Inclination angle (deg) 6 0
Scrub Radius (mm) 30 12
Mechanical Trail (mm) 30 12
Caster Angle (deg) 10 4
Camber Angle (deg) 3 0
Toe Angle (deg) 3 0
Table 7. Recommended values for the suspension parameters*
Additionally, the following considerations should be taken into account:
Camber under bump/rebound should never go positive. The camber gain for the
front axle should be smaller than in the rear. The reason for having a much larger
camber gain at the rear axle is to have as big as possible contact patch between the
rear tire and the ground during corner exits.
The suspension geometry should be designed based on one critical parameter: the
Roll Center. It is desirable to keep this parameter low respect to the ground
37
(between 1 and 4 inches) and also it should be designed to have a predictable
(horizontal & lateral) movement of the roll axle.
The roll center from the rear suspension must be higher than in the front suspension
in order to promote the stability and control of the vehicle while cornering
Low kingpin inclination angle´s are desirable for the front suspension in order to
subtract positive camber gain due to caster on the outside wheel.
For the rear suspension is recommended zero caster and zero kingpin angle´s since
these parameters should be incorporated only in a steering wheel rather than in a
power-train wheel.
It is desirable to have a small scrub radius in order to reduce the effort to turn the
wheel and also to minimize the tire wear
The caster angle has positive effects during cornering, but too much caster
generates undesirable lateral weight transfer, which can lead to an oversteering
effect.
38
Chapter 5. Modelling the suspension in Autodesk Inventor®
Taking into account all the information established previously in the chapter 4, the next step
in the design of the suspension system is to model the geometry of the suspension and
adapt this configuration to the actual chassis design. With this in mind, this chapter shows
the basic design decisions made during this process in order to achieve the first iteration of
the suspension configuration. It is important to clarify that during this design process, the
software Autodesk Inventor Professional 2015® was used to model the geometry of the
suspension elements.
5.1 Chassis geometry
The chassis elaborated by Camilo Sarmiento (figure 27) provides a practical starting point
for the suspension design. According to Camilo´s document, his frame not only meets all
the Formula SAE requirements but also has a proper structural design.
Figure 27. Chassis design
This chassis provides some geometrical elements in order to attach the Hardpoints of the
suspension elements. However, this does not mean that the design of the suspension has
to be restricted to the actual geometry of the chassis; therefore, it is important to clarify
that this geometry can be modify at any moment in order to accomplish the desire
suspension configuration without compromising the structural basis or violating the FSAE
rules.
To simplify the design of the suspension elements, such as the kingpin, the suspension arms
and the push rod elements, the chassis was reduced to its 3D sketch design (figure 27-B).
Additionally, some chassis elements (engine and transmission supports) were removed and
the rear geometry of the chassis was modified. All the chassis modifications can be seen in
the figure 28. According to the literature review, it is desirable to have the Hardpoints of
A B
39
the suspension arms that go attached to the frame parallel to the center plane of the vehicle
(viewed from the top) in order to reduce bump-steer.
Figure 28. Chassis with the modifications in the rear section
Taking into account the previous recommendation, the rear geometry of the chassis was
modified so that the structural elements are parallel among each other (figure 28 – red box).
Now, once these basic modifications were held to the chassis, the designer can proceed to
elaborate the suspension elements and attach them to the frame geometry.
5.2 Geometric Suspension Design
Regarding the parameters established in chapter four and some design recommendations
mentioned in chapter two, the following suspension elements were incorporated to the
chassis geometry: Upper A-arm, Lower A-Arm, Kingpin, Wheels, Push rod, Tie rod, Rocker
and springs. The reader can appreciate the first iteration of the suspension design on the
image below.
Figure 29. First iteration of the suspension geometry attached to the chassis
40
The figure 29 shows that the Hardpoints of the suspension elements are attached to the
chassis bars. However, as it was mentioned before, all these chassis elements can be easily
modified to adjust the suspension requirements. A brief example of the type of
modifications that can be realized to the chassis geometry are illustrated ahead:
Figure 30. Chassis possible modifications
If the designer wants to change the height of the upper suspension A-arm that goes
attached to the horizontal bar (highlighted in the figure 30), the chassis configuration can
adapt without any problem to the requirements of the designer. In this specific case, this
horizontal bar moves up or down in order to accomplish the desire height.
Consequently, the other suspension elements such as the pull rod, or the tie rod were
located taking into account previous Formula SAE vehicle configurations as well as some
recommendations mentioned in FSAE forums and vehicular literature.
Once the first iteration of the suspension geometry has been establish, the next step is to
analyse this configuration in order to refine its design. The following two chapter’s describe
the suspension analysis and simulations that were performed.
41
Chapter 6. Suspension Geometry Evaluation using MatLab®
This chapter shows the geometric suspension analysis that was realized to the suspension
assemblies (Front and Rear) in order to calculate some critical suspension parameters. For
this analysis a code was implemented in MatLab®. This code is based on a previous thesis
work elaborated by the Mechanical Engineering student Sage Wolfe (Ohio State University).
His work consists on a MatLab® based program call SLASIM, which attempts to provide a
powerful yet user-friendly utility for the novice suspension designer (Wolfe, 2010).
6.1 Previous Geometric Analysis
The traditional way to analyse the geometry and kinematics of a suspension design is using
the graphical method. This method consist in drawing the geometry of the suspension
elements and then using basic desktop items (such as a ruler or a protractor), the designer
can estimate some suspension parameters such as the roll center height (RCH in figure 31),
or the kingpin inclination angle (𝜃 in figure 31).
Figure 31. Roll Center Height and KPI angle estimation using the graphical method
The graphical method has some advantages such as its simplicity and low-cost, but on the
other hand, it suffers of being only in two dimensions. Also, if done on paper (as opposed
to line drawings in CAD), the accuracy may be questionable. In general terms, the graphical
method discourages iterative improvements due to its labour intensity (Wolfe, 2010).
This method was initially implemented during the suspension geometric analysis (figure 31).
However, due to its clear disadvantages, it was necessary to implement a more
sophisticated and reliable method that could satisfy the designer requests as well as provide
useful information for future interventions in the suspension design.
6.2 Objective of the Code
The objective of this MatLab® code is to find the most suitable allocation for a specific
number of Hardpoints in order to achieve a suspension configuration that could match all
42
the desire performance parameters. To obtain this information, the code uses an iterative
process based on a Low discrepancy Sequence. The function implemented in MatLab® is
called SobolSet, which is a quasi-random sequence that fill the space in a highly uniform
manner.
6.3 Analysis methodology
To accomplish the objectives of this analysis, a series of chronological steps were realized;
this process as well as the main elements of the code are explain in detail ahead:
1. The first step of the analysis is to identify the desire input variables. These variables
correspond to possible suspension Hardpoints allocation and are specified based on
some packaging constrains.
2. The second step is to define the output performance parameters. For each of the
parameters a minimum and a maximum values have to be established based on the
performance targets previously specified (chapter 2).
3. Once the input variables and the output parameters are defined, the next step is to
introduce this information into the MatLab® code in order to be analysed.
4. The code assigns to each input variable a quasi-random value within the specified limits.
This set of values conforms a suspension configuration, to which the code calculates all
the output parameters.
5. Next, the code analyses one by one all the suspension configurations that were created
in order to evaluate if each configuration satisfies or not the performance parameters
pre-set.
6. If a configuration satisfies all the performance parameters, it is saved as a satisfactory
configuration.
7. Finally, the array of satisfactory configurations provide useful information regard the
ideal allocation of each input variable.
Typically, for each suspension assembly the code realizes about 5 million iterations, i.e. 5-
million suspension configurations. This iteration process takes in average 3 days to find all
the satisfactory configurations. The MatLab® code can be appreciated in the Appendix D.
6.4 Front Suspension Analysis
Following the methodology previously established, the first step during the front
suspension analysis is establishing the initial input variable constrains. The next table shows
all the variables that were taken into account as well as their upper and lower limits.
43
Variable Meaning Minimum value
(in)
Maximum value
(in)
yu
Height of the upper A-arm Hardpoints that go
attached to the chassis (“y” coordinate of the
Hardpoints 1 & 2).
8.5 11
yl
Height of the lower A-arm Hardpoints that go
attached to the chassis (“y” coordinate of the
Hardpoints 4 & 5).
2.5 3.5
xu
Distance from the centreline of the vehicle to
the Hardpoints of the upper A-arm that go
attached to the chassis (“x” coordinate of the
Hardpoints 1 & 2).
11.5 12.5
xl
Distance from the centreline of the vehicle to
the Hardpoints of the lower A-arm that go
attached to the chassis (“x” coordinate of the
Hardpoints 4 & 5).
11.5 12.5
x_uobj
Distance from the centreline of the vehicle to
the Hardpoint of the upper A-arm that goes
attached to the kingpin (“x” coordinate of the
Hardpoint 3).
19.5 22.5
y_uobj
Height of the upper A-arm Hardpoint that goes
attached to the kingpin (“y” coordinate of the
Hardpoint 3)
12.5 15.5
z_uobj
Distance from the center of the tire (plane xy) to
the Hardpoint of the upper A-arm that goes
attached to the kingpin (“z” coordinate of the
Hardpoint 3).
-2 2
x_lobj
Distance from the centreline of the vehicle to
the Hardpoint of the lower A-arm that goes
attached to the kingpin (“x” coordinate of the
Hardpoint 6).
19.5 22.5
y_lobj
Height of the lower A-arm Hardpoint that goes
attached to the kingpin (“y” coordinate of the
Hardpoint 6)
5.5 8.5
z_lobj
Distance from the center of the tire (plane xy) to
the Hardpoint of the lower A-arm that goes
attached to the kingpin (“z” coordinate of the
Hardpoint 6).
-2 2
Table 8. Front Suspension Input Variables domain
The minimum and maximum values of each input variable were selected based on the
packaging constraints, geometric limitations and the some initial parameters such as the
vehicle´s track, or rim diameter (established in chapter 4). For example, the lower limit of
the variable “yu” which in this case is 2.5 inches corresponds to the minimum ride height
44
desire (table 6) , which makes a lot of sense since the Hardpoints of the lower A-arm must
be attached to the lower elements of the chassis.
To understand each of the ten input variables the next figure illustrates a typical double A-
arm suspension within the coordinate system that was used during this suspension analysis.
It is important to mention that during this whole chapter, the sign convention differs from
the ISO standard (figure 5) besides all the variables and parameters dimensions are in
inches. The reason of this because the code written by Sage Wolfe uses this convention.
Figure 32. Coordinate system & Hardpoints assignation (Wolfe, 2010).
The origin (0, 0, 0) of the coordinate system is located at half-track (longitudinal center
plane of the vehicle) on the ground plane (the tire contact patch is zero in the Y coordinate)
and the zero in the Z coordinate corresponds to the wheel center. X is positive towards the
left of the vehicle, Y is positive upwards, and Z is positive towards the front of the vehicle.
Now that the input variables are totally defined, the next step is to establish the output
parameters and their ideal domain. As it was mention previously, the information collected
from the literature review in chapter two was implemented during this geometric analysis.
Parameter Lower Limit Upper Limit
Caster (deg) 4 8
Trail (2) 0.5 2
KPI (deg) 0 4
Scrub (in) 0.5 1.5
RCH (in) -0.5 2.5
Table 9. Front Suspension Parameters domain
45
6.5 Relationship Between the variables and the parameters
Each output parameter depends on a series of input variables (Hardpoint location). The
following diagrams illustrate this dependency:
Figure 33. Relationship between the Variables & Parameters
All this relationships are important because if the designer wants to modify any of these
parameters, he now knows which Hardpoints he has to alter and also he will know which
other parameters would be affected during the modification.
6.6 Front Suspension Results
The following table resumes the results after analysing 5 million possible combinations of
the suspension geometry.
Variable Lower Limit (in - mm) Upper Limit (in-mm)
yu 8 in / 203 mm 10 in / 254 mm
yl 4 in / 102 mm 5 in / 127 mm
xu No clear pattern
xl No clear pattern
x_uobj 23.5 in / 597 mm 24.5 in / 622 mm
y_uobj 14 in / 356 mm 15.5 in / 394 mm
z_uobj -0.5 in / 12.7 mm 0 in / 0 mm
x_lobj 24 in / 610 mm 25 in / 635 mm
y_lobj 5.5 in / 140 mm 6.5 in / 165 mm
z_lobj 0 in / 0 mm 1 in / 25 mm
Table 10. Front Suspension Results (New domain for each Hardpoint)
46
For each input variable a new domain was established based on the satisfactory
configurations obtain during the analysis. As an example, the results from variable “yl” will
be explained:
Figure 34. yl vs Roll Center Height (RCH in inches)
The figure 34 shows on the X-axis the initial domain of the variable “yl” (which can be seen
in table 8). On the Y-axis is the Roll Center Height parameter with is upper and lower limits
(established in the table 9). Each dot in the graph represents a satisfactory configuration,
which means that any of those 686 points not only satisfy the Roll Center Parameter
request, but also satisfies all the other parameters restrictions listed in the table 9.
With this in mind, and analysing the figure 34 with more detail, it is clear that the best
location of the lower A-arm Hardpoints that go attached to the chassis is between 4 and 5
inches above the ground (Red box in figure 34). The reason why this is true is that in this
new domain, the designer can situate the Roll Center Height within the recommended
values. This same exercise was realized to the other 9 variables in order to find their new
ideal location domain. All the graphs can be seen with more detail in the appendix E.
6.7 Rear Suspension Analysis
The same procedure was realized to the rear suspension in order to achieve the initial
dimensional constrains (input variables). However, in this case the number of input
variables as well as the objective parameters change. The main reason of changing these
variables is that operational conditions of a rear suspension differ from a front suspension
assembly; basically because of the lack of steering needed.
2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
3.5
4
yl (in)
RC
H (i
n)
47
Variable Meaning Minimum
Value (in)
Maximum
Value (in)
yu Height of the upper A-arm Hardpoints that go attached to the
chassis (“y” coordinate of the Hardpoints 1 & 2). 9 12
yl Height of the lower A-arm Hardpoints that go attached to the
chassis (“y” coordinate of the Hardpoints 4 & 5). 3.5 5
xu
Distance from the centreline of the vehicle to the Hardpoints
of the upper A-arm that go attached to the chassis (“x”
coordinate of the Hardpoints 1 & 2).
10 12
xl
Distance from the centreline of the vehicle to the Hardpoints
of the lower A-arm that go attached to the chassis (“x”
coordinate of the Hardpoints 4 & 5).
10 12
x_ul_obj
Distance from the centreline of the vehicle to the Hardpoints
of the lower and upper A-arm that go attached to the kingpin
(“x” coordinate of the Hardpoints 3 & 6).
19.5 23.5
y_lobj Height of the lower A-arm Hardpoint that goes attached to the
kingpin (“y” coordinate of the Hardpoint 6) 5.5 8.5
y_uobj Height of the upper A-arm Hardpoint that goes attached to
the kingpin (“y” coordinate of the Hardpoint 3) 12.5 15.5
Table 11 Rear Suspension Input Variable Domain
The output performance parameters such as the Caster angle, kingpin inclination,
mechanical trail or scrub radius are not desire for the rear suspension design and so where
chosen to be static cero. Taking this into account, the only performance target during the
rear suspension analysis will be the Roll Center Height (RCH).
Parameter Dimensional constrain
RCH [1 , 5] in
Table 12. Desire RCH domain for the rear suspension
6.8 Rear Suspension Results
Once again, the same considerations made during the front suspension analysis were taken
into account during this analysis. The following table resumes the results after analysing 1
million possible combinations of the rear suspension geometry.
Variable (in) Lower Limit (in - mm) Upper Limit (in-mm)
yu 9 in / 229 mm 10 in / 254 mm
yl 4.5 in / 114 mm 5 in / 127 mm
xu No clear pattern
xl No clear pattern
x_ul_obj No clear pattern
y_uobj 14 in / 356 mm 15.5 in / 394 mm
y_lobj 5.5 in / 140 mm 6.5 in / 165 mm
Table 13. Rear Suspension Results (New domain for each Hardpoint)
48
The graphs that support his results can be seen on the appendix F. This time, three of the
seven input variables show no clear correlation between them and the performance
parameter, which means they can be located within their initial dimensional domain and
the results would not be affected in a considerable way.
6.9 Final Considerations
The reader may ask why there are so few input variables, if for each Hardpoint shown in the
figure 32, there must be three coordinate variables (X, Y and Z). One reason is because some
coordinates of some Hardpoints does not alter any of the output parameters. For example,
the Z coordinate of the Hardpoints 1 and 2 or the Hardpoints 4 and 5, which represent the
width of the suspension A-arms does not affect any of the five performance parameters
evaluated during this analysis. The following figure corroborates this assumption:
Figure 35. Results after iterating the Upper A-arm width (Z coordinate of Hardpoints 1 & 2).
The figure 35 shows that after modifying the width of the upper suspension arm, from 0 in
to 5 inches, the five output parameters show no modification, which means that neither
the Z coordinates of the upper or lower A-arms should be taken into account during this
analysis.
Another simplification made during this analysis was the X and Y location of the Hardpoints
that belong to the suspension A-arms; more specifically the front (1) and rear (2) Hardpoints
of the upper control arm, and the front (4) and rear (5) Hardpoints of the lower control arm
(see figure 32). Each pair of Hardpoints from each suspension arm is represented with the
same X and Y coordinates in order to reduce the amount of variables, i.e. the Y coordinate
of both front (4) and rear (5) Hardpoints of the upper A-arm is represented with the variable
“yu” which means “Y-Upper”. On top of that, according the literature review, the
suspension A-arms should keep an isosceles or equilateral shape, reason why this both Y
and X coordinates of each A-arm should be the same.
Finally, the Hardpoints 9 & 10 that correspond to the geometry of the tie-rod were not
taken into account during this analysis because they belong to the steering subsystem. The
design and analysis of this other vehicle subsystem is responsibility of other thesis work.
49
Chapter 7. Suspension modelling & evaluation in Adams/Car®
This chapter is perhaps the most important of the whole document since it explains how
the suspension assemblies (front, rear and full vehicle) were evaluated kinematically and
dynamically in order to accomplish a suspension design that could meet all the initial
objectives.
The suspension geometry of both front and rear assemblies has suffered some important
changes since their first design realized during the chapter 5. However, the changes
proposed during the suspension MatLab® analysis (chapter 6) only satisfy a few parameters
and the analysis realized only considers a static suspension.
The first thing that would be done during this chapter is modelling the suspension geometry
proposed during the chapters five and six into ADAMS/Car®. Then, the suspension actuation
elements (push-rod, spring/damper & rocker) will be analysed. Both, modelling and
analysis, leads to refinements and modifications of these actuation elements.
Once this elements are properly design, a series of experimental design analysis would be
implemented into the simulations in order to quantify the relevance of some critical
suspension variables. Finally, the suspension geometry will suffer some modifications in
order to obtain a design that could match the objectives.
7.1 Introduction to ADAMS/Car®
ADAMS/Car® is the world´s most widely used multibody dynamics software, which allows
engineers to quickly build and simulate functional virtual prototypes of complete vehicles
and vehicle subsystems. Working with ADAMS/Car® allows automotive engineering teams
to evaluate their vehicles or subsystems under various conditions such as different road
surfaces, typical race-car manoeuvres or tests that are normally run in a lab, however saving
them experimental costs & time.
Modelling a suspension system or a full vehicle assembly from zero requires an advance
knowledge of the program, reason why the engineers from the MSC software developed a
special Formula SAE database, which includes a fairly well defined preliminary suspension
setup from a typical Formula SAE vehicle. The database includes three main assemblies
which are: the front suspension assembly (figure 3), the rear suspension assembly (figure
4) and the full vehicle assembly (figure 36).
Each of these assemblies is build up from a series of vehicle subsystems, for example the
front suspension assembly is composed by three main subsystems: the steering, the anti-
roll bar and the suspension geometry.
50
Figure 36. ADAMS/Car® fsae_2012 full vehicle assembly
7.2 Modelling the Suspension in ADAMS/Car®
Since the first suspension design (chapter five), the suspension geometry has suffered some
changes due to the new Hardpoint restrictions obtained during the MatLab® analysis. These
modifications might look as a movement of a few inches from each Hardpoint, however
they represent significant improvement in the suspension performance.
Now, the geometry from the fsae_2012 suspension assemblies has to be adapted to the
design proposed during this work. These new assemblies in ADAMS/Car® will represent the
suspension design that would be later adapted to the chassis geometry proposed by Camilo
Sarmiento.
Front Suspension Assembly:
The figure 37 represents the transition from the suspension CAD designed obtain after the
MatLab® analysis (A) and the new front suspension model in ADAMS/car® (B). Therefore
there is a need for a new tag, the front suspension assembly proposed during this thesis
work will be known as: FRONT_UNIANDES, in order to differentiate it from the fsae_2012
assemblies elaborated by ADAMS/Car® engineers.
Figure 37. First design iteration of the FRONT_UNIANDES assembly
A B
51
Rear Suspension Assembly:
Once again the same procedure was realized to the rear suspension assembly. This new
ADAMS/Car® suspension assembly will be known as REAR_UNIANDES. The following figure
illustrate this assembly along with the previous CAD design.
Figure 38. First design iteration of the REAR_UNIANDES assembly
Full Vehicle Assembly:
Finally, the full vehicle assembly has significant importance because without it, the vehicle
performance objectives cannot be quantify and evaluated. This assembly not only
represents the front and rear suspension configurations, but also takes into account the
parameters established during the founding decisions in chapter four. Some of these
decisions were: Wheelbase, vehicle weight, vehicle center of gravity and ride-height among
others. The following figure illustrates this assembly, which since now on is going to be
called: FSAE_UNIANDES.
Figure 39. First design iteration of the FSAE_UNIANDES assembly
On top of that, it is important to clarify all the subsystems that belong to the
FSAE_UNIANDES vehicle assembly:
Front Suspension (FRONT_UNIANDES)
52
Steering
Rear Suspension (REAR_UNIANDES)
Chassis
Front tire
Rear tire
Powertrain
Breaks
Before performing any simulation, a few considerations must be clarify. The first one is the
tire model that would be used during the simulations. ADAMS/Car® provides a tire database
which contains a great variety of tire models. Among these models, perhaps the most
accurate, realistic and effective model is the PAC_2002, which is based on the Pacejka magic
formula. Considering this, the PAC_2002 model was implemented to the suspension design
and was later modify in order to match the tire parameters from the Hoosier datasheet (tire
diameter, width and vertical stiffness).
The Chassis subsystem is represented as a spherical element where all the mass and inertial
properties of the whole vehicle are concentrated; furthermore, the location of this sphere
represents the center of gravity of the vehicle. This subsystem was modified in order to
match the vehicle´s weight established in the table 3 and the center of gravity location
established in table 5.
On the other hand, some subsystems were not modify from the original fsae_2012 full
vehicle assembly such as the breaks, powertrain and steering. The design and analysis of
these subsystems is responsibility of other students and their respective thesis works.
Finally, the origin and orientation of the coordinate system from the MatLab® analysis
differs from the ADAMS/Car® system. The positive Y values in MatLab® are now the Z values
in ADAMS/Car®, the positive X values of MatLab® are now the negative Y values in
ADAMS/Car® and finally the Z values of MatLab® are now the negative X values in
ADAMS/Car®.
Figure 40. Equivalent Coordinate system (MatLab & ADAMS/Car).
53
The ADAMS/Car origin is also located in a different place (see figure below):
Figure 41. Origin of the coordinate system in ADAMS/Car®
7.3 Suspension Actuation Analysis and Design:
On this section, the selection and placement of the Shock absorbers as well as the design of
their associated actuation mechanism (push-rod & rocker) will be determine. Until now,
these elements hadn´t suffer any modification since their first design intervention in
chapter five. Nevertheless, without a proper design of this mechanism the whole geometry
of the suspension previously established wouldn´t work properly.
The first step during this design is establishing some preliminary parameters that will be
used throughout the whole section. Then, a series of simulations are performed to the front
and rear suspension assemblies in order to estimate some parameters that will later be
necessary to calculate the suspension ride frequencies. This is an iterative process because
if the obtain ride frequencies are above or below the target values, the whole configuration
must be modify.
Initial Parameters:
The parameters listed in the table 14 are necessary to estimate the vehicle´s ride
frequencies; the values were taken from the information available in the previous chapters.
Parameter Value
Sprung Mass (kg) 200
Un-Sprung Mass (kg) 50
Tire radial stiffness (Newton/millimetre) 200
Front & Rear wheel load (%) 45:55
Table 14 Suspension parameters needed for the analysis
54
The reader may notice that the tire radial stiffness corresponds to an average stiffness value
from the figure A2 (appendix B). The radial stiffness is highly influenced by the air pressure
inside, so in order to calculate the ride frequencies and then later simulate the vehicle´s
behaviour this unique value (200 N/mm) will be implemented in the tire model (PAC_2002).
Motion ratios:
The motion ratio is the ratio between how much the spring is compressed compared to how
much the wheel is actually moved. This parameter can be interpreted as the mechanical
advantage associated to the suspension mechanism.
𝑀𝑜𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑖𝑜𝑛 (𝑀𝑅) =𝑆𝑝𝑟𝑖𝑛𝑔 𝑚𝑜𝑣𝑒𝑚𝑒𝑛𝑡
𝑊ℎ𝑒𝑒𝑙 𝑑𝑖𝑠𝑝𝑎𝑐𝑒𝑚𝑒𝑛𝑡
For an FSAE car is recommend a motion ratio of 1.0 or near. This means that to meet the
FSAE requirement of 50.8 mm (2 inches) of wheel travel, you will want to specify a damper
with at least 63.5mm (2.5 inches) of travel. At a 1.0 motion ratio, this will allow for 50.8mm
(2 inches) of wheel travel and 12.7mm (0.5 inches) of jounce bumper travel (Kasprzak,
2014).
Wheel Rate:
On the other hand, the wheel rate is the actual rate of a spring acting at the tire contact
patch. Another way of interpreting this parameter is as the vertical stiffness of the
suspension relative to the body, measured at the wheel center. This value is measured in
lbs./in. (N/mm), and can be determined by using the formula below which relates the
mechanism motion ratio and the spring rate in order to obtain the actual wheel rate:
𝑊ℎ𝑒𝑒𝑙 𝑅𝑎𝑡𝑒 (𝑘𝑤) = 𝑆𝑝𝑟𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 (𝑘𝑠) ∗ (𝑀𝑅)2
Ride frequencies:
The undamped frequency at which the sprung mass will resonate or bounce is often called
the ride frequency. This is the same as the sprung natural frequency. Since the front and
rear will resonate or bounce at different frequencies, we typically reference a front and rear
ride frequency. The reason the front and rear have different ride frequencies is to reduce
the pitch of the vehicle over bumps. The rear ride frequency is typically higher than the
front, so that after encountering a bump, the rear will “catch up” with the front, and the
front and rear will move in phase (Kasprzak, 2014).
𝝎𝒏(𝒔) =𝟏
𝟐𝝅√
(𝒌𝒘 ∗ 𝒌𝒕)/(𝒌𝒘 + 𝒌𝒕)
𝒎𝒔
Where:
55
𝜔𝑛(𝑠) = 𝑆𝑝𝑟𝑢𝑛𝑔 𝑚𝑎𝑠𝑠 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝑘𝑤 = 𝑊ℎ𝑒𝑒𝑙 𝑟𝑎𝑡𝑒
𝑘𝑡 = 𝑡𝑖𝑟𝑒 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠
𝑚𝑠 = 𝑆𝑝𝑟𝑢𝑛𝑔 𝑀𝑎𝑠𝑠
𝝎𝒏(𝒖𝒔) =𝟏
𝟐𝝅√
𝒌𝒘 + 𝒌𝒕
𝒎𝒖𝒔
Where:
𝜔𝑛(𝑢𝑠) = 𝑈𝑛𝑠𝑝𝑟𝑢𝑛𝑔 𝑚𝑎𝑠𝑠 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝑚𝑢𝑠 = 𝑈𝑛𝑠𝑝𝑟𝑢𝑛𝑔 𝑀𝑎𝑠𝑠
According to Jim Kasprzak, the ride frequencies from a Formula SAE vehicle should stay
between 2.5 and 3.5 Hz with the rear suspension frequencies 0.2 to 0.4 Hz higher that the
front. Besides, the Un-sprung Natural frequencies should stay between 15 to 19 Hz.
Shock Absorbers selection & location:
The shock absorber selected for the suspension configuration were the FSAE Öhlins TTX25
MkII. These shocks are specially design to supply the suspension demands imposed by a
Formula SAE vehicle. The overall length (from center to center of spherical bearings, fully
extended) is 200 mm, which fits perfectly to the suspension geometry established.
Additionally, the maximum stroke is equal to 57 mm, which means it can resist the two
inches displacement specified by the FSAE rulebook.
Figure 42 Öhlins TTX25 MkII (50 mm).
Based on the geometric constrains imposed by the other subsystems, the front suspension
shock absorbers were located above the drivers legs and the rear suspension shock
absorbers were located above the set of batteries; both actuated Push-Rod. The figure 43
shows that the push rods, rockers and shock absorbers of both front and rear suspensions
are situated in the same plane (perpendicular to the ground floor), in order to promote
56
simplicity of the mechanism. On top of that, this configuration improves the smoothness
and quality of the suspension actuation by reducing friction and ensuring all pivots and
bearings only experience forces normal to their rotating axes (Farrington, 2011).
Figure 43. Suspension actuation mechanism (Front & Rear assemblies)
Springs:
The FSAE TTX25 MkII shocks uses spring over dampers, which provide great flexibility to the
designer in order to choose the best spring that better suits to the suspension demands.
The HYPERCO FSAE springs offered by Öhlins are specially design for the TTX25 MkII shocks,
they are manufactured using high-tensile Chrome-Silicon wire for maximum reliability and
durability. Furthermore, they offer eight different spring stiffness’s, however during this
project only two of these springs will be analysed (300 & 350 lb/in).
Figure 44. HYPERCO FSAE springs
57
Design & Final Performance Parameters:
The front and rear suspension assemblies were once again analysed independently in order
to find a suspension mechanism that could match the natural frequencies previously
mention. With this in mind, a series of simulations were realized in order to estimate some
critical variables:
The design variables & parameters that were taken into account during this analysis were:
Wheel Travel
Wheel rate, spring rate and tire vertical stiffness
Sprung & Un-sprung Natural Frequency
Rocker & Push rod dimensions & locations
Sprung & Un-sprung vehicle masses.
A single wheel travel simulation was realized in order to find the wheel rate of each
suspension mechanism. Then, the sprung & un-sprung natural frequencies were calculated
using the information from table 14 as well as the stiffness data from the previously selected
springs. The whole process is iterative since the geometrical configuration and dimensions
of the rocker and push rod elements were modify several times until the design frequencies
were satisfy. The following table illustrates the results from the final suspension mechanism
design; the wheel rate graphics along with the simulation conditions can be seen in the
appendix G.
Parameter
Front Suspension Assembly Rear Suspension Assembly
Spring rate: 300
lb/in
Spring rate: 350
lb/in
Spring rate: 300
lb/in
Spring rate: 350
lb/in
Average Wheel
rate (N/mm) 25 30 40 50
Sprung Natural
Frequency (Hz) 3.53 3.83 3.91 4,29
Un-sprung Natural
Frequency (Hz) 16,82 17,11 17.43 17,79
Table 15. Final values for the front & rear suspension mechanism
7.4 Front Suspension DOE
The front suspension assembly requires a more detail analysis of its geometry in order to
match the kinematic suspension requirements. However, before modifying the
configuration obtain during the MatLab® analysis, a DOE (Design of Experiment) was
implemented to the kinematic simulations in order to obtain more information regards the
influence of some critical suspension Hardpoints (input variables) respect the desire
performance parameters.
58
The software that analysed the performance parameters obtain during the simulations was
Design Expert 10®; which is a statistical package specifically dedicated to performing design
of experiments. Within the great variety of options offered by this programme, Design–
Expert provides a two level factorial design analysis, which was the one implemented to the
kinematic simulations. The statistical significance of the factors (or also known as input
variables) was established with an analysis of variance (ANOVA). Moreover, graphical tools
help identify the impact of each factor on the desired outcomes.
Two level factorial design:
On this type of experiment, each factor (input variable) has two levels (low & high) which
were assign based on the results obtain during the previous MatLab® analysis (tables 10 &
13). The amount of experiments (or in this case simulations) that must be carry out depends
directly on the number of factors selected. For the front suspension assembly five critical
factors were chosen, which means that 32 simulations were realized:
𝑇𝑤𝑜 𝑙𝑒𝑣𝑒𝑙 𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑎𝑙 𝑑𝑒𝑠𝑖𝑔𝑛: 2𝑘 → 25 = 32 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑠
For each of those 32 simulations a different suspension configuration is evaluated. These
configurations come as a result of a combinatory of each of the possible levels of all the
input factors. Finally, it is important to mention that because this design of experiment was
implemented to a series of simulations, it does not require any type of replicates.
Input variables (factors):
The folling table ilustrates the five imput variables (factors) with their respective levels. As
it was mentioned before, the MatLab® coordinate system differs from the ADAMS/Car®
system. The table shows that for each MatLab® variable, there is an equivalent variable and
level values for the ADAMS/Car analysis.
Factor Matlab
Variable Low (mm) High (mm)
Equivalent variable in
ADAMS Low (mm) High (mm)
A x_uobj 596.9 622.3 loc_Y (uca_outer) -596.9 mm -622.3 mm
B y_uobj 355.6 393.7 loc_Z (uca_outer) 266.7 mm 304.8 mm
C yu 203.2 254 loc_Z (uca front /
uca_rear) 114.3 mm 165.1 mm
D y_lobj 139.7 165.1 loc_Z (lca_outer) 50.8 mm 76.2 mm
E z_lobj 0 25.4 loc_X (lca_outer) -521.0 mm -537.4 mm
Table 16. Input factors Front suspension Assembly
The figure 45 ilustrates more clearly the location of each input variable:
59
Figure 45. Location of each of the 5 input factors (Front Suspension)
Simulation Parameters & conditions:
Now that the input variables were established, the next step of the analysis is to specify the
type of simulation that will be implemented as well as the output performance parameters
that are going to be evaluated.
The Opposite travel simulation provides the opportunity of analysing both vertical and
horizontal displacement of the suspension roll center, reason why this simulation was
chosen as the appropriated for this type of analysis. On top of that, this simulation also gave
us information regards the toe gain as well as the camber gain. The following figure
illustrates the simulation conditions that were taken into account for all the 32 simulations.
Figure 46. Simulation conditions during the Front Suspension DOE
The four performance parameters that were evaluated are:
Roll Center Vertical displacement
Roll Center Lateral displacement
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Camber gain
Toe gain
All four parameters were evaluated respect the suspension wheel travel. The figure below
shows the front suspension while performing the opposite wheel travel simulation:
Figure 47. Opposite Wheel travel simulation
DOE results:
The following four figures show the influence from the intput variables respect each
performance parameter. For instace, if the designer whats a suspension configuration that
reduces the camber gain, the best way to obtain this results is by modifying the location of
the factor C, since this factor has the highest percentage of participation (relevance) for that
specific performace parameter.
Figure 48. Influence of the factors respect the Roll Center vertical displacement (Front Suspension)
0
10
20
30
40
50
60
A-y_uca_outer B-z_uca_outer C-z_uca_F&R D-z_lca_outer E-x_lca_outer Combined effects
%
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Figure 49. Influence of the factors respect the Roll Center lateral displacement (Front Suspension)
Figure 50. Influence of the factors respect the Camber gain (Front Suspension)
Figure 51. Influence of the factors respect the Toe gain (Front Suspension)
0
10
20
30
40
50
60
70
80
90
100
A-y_uca_outer B-z_uca_outer C-z_uca_F&R D-z_lca_outer E-x_lca_outer Combined effects
%
0
10
20
30
40
50
60
70
80
90
A-y_uca_outer B-z_uca_outer C-z_uca_F&R D-z_lca_outer E-x_lca_outer Combined effects
%
0
10
20
30
40
50
60
A-y_uca_outer B-z_uca_outer C-z_uca_F&R D-z_lca_outer E-x_lca_outer Combined effects
%
62
Now with this information, the designer has some useful information in order to obtain the
best compromise between all the performance parameters that could match the desire
suspension needs. The results obtain from this analysis show that the variable A
(y_uca_outer) does not have any significant relevance in any of the four performance
parameters. However, if we take a look to the input variable C (z_uca_F&R), we can clearly
see that this factor has a positive impact in two of the performance parameters: Roll Center
vertical displacement and camber gain. Finally, the figure 49 shows that none of the factors
show a significant individual impact on the Roll center horizontal displacement, which
means that this performance parameter should be modify using a combination of this
factors or it also can be modify by changing other Hardpoints in the suspension setup.
7.5 Rear Suspension DOE
Once again the same procedure was realized to the rear suspension assembly. However,
this time the amount of input factors changed. The DOE implemented for this analysis is
known as 2𝑘−𝑝 factorial design, which reduces the amount of simulations while providing
the opportunity to analyse more factors. The input variables and their respective levels are
listed in the table below.
Factor Matlab
Variable Low (mm) High (mm)
Equivalent variable in
ADAMS Low (mm) High (mm)
A yl 114,5 127 loc_Z (lca front /
lca_rear) 25,4 38,1
B xl 254 304,8 loc_Y (lca front /
lca_rear) 254 304,8
C y_lobj 139.7 165.1 loc_Z (lca_outer) 50,8 76,2
D y_uobj 355.6 393.7 loc_Z (uca_outer) 266,7 304,8
E x_uobj 508 533.4 loc_Y (uca_outer) 508 533,4
F z_uobj 0.0 12.7 loc_X (uca_outer) 1087,3 1100
Table 17. Input factors Rear suspension Assembly
Figure 52. Location of each of the 6 input factors (Rear Suspension)
63
This time, six factors where taken into account during the analysis, but once again only 32
simulations were realized.
2𝑘−𝑝 → 26−1 = 32 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑠
This important reduction in the amount of simulations is reflected in the accuracy of the
results. On top of that, it also excludes from the analysis some factor combinations and their
respective percentage of contribution to each performance parameter. However, this
combinations where not taken into account during the results, which causes this reduced-
factorial design to fit perfectly to the requirements of this analysis.
Simulation Parameters & conditions:
Due to the benefits offered by the opposite wheel travel simulation, it was again
implemented during the rear suspension DOE. The simulations conditions are shown in the
figure below:
Figure 53. Simulation conditions during the Rear Suspension DOE
Furthermore, the same four performance parameters were also used to evaluate the
influence that has each of the six factors on them.
DOE Results:
The following 4 figures show the influence of each intput variable respect each performance
parameter. These plots come from the ANOVA results obtain with the Design Expert 10®
programe.
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Figure 54. Influence of the factors respect the Roll Center vertical displacement (Rear Suspension)
Figure 55. Influence of the factors respect the Roll Center Lateral displacement (Rear Suspension)
Figure 56. Influence of the factors respect the Camber gain (Rear Suspension)
0
5
10
15
20
25
30
35
40
A-z_lca_F&R B-y_lca_F&R C-z_lca_outer D-z_uca_outer E-y_uca_outer F-x_uca_outer Combinedeffects
%
0
10
20
30
40
50
60
70
80
90
100
A-z_lca_F&R B-y_lca_F&R C-z_lca_outer D-z_uca_outer E-y_uca_outer F-x_uca_outer Combinedeffects
%
0
5
10
15
20
25
30
35
40
45
50
A-z_lca_F&R B-y_lca_F&R C-z_lca_outer D-z_uca_outer E-y_uca_outer F-x_uca_outer Combinedeffects
%
65
Figure 57. Influence of the factors respect the Toe gain (Rear Suspension)
In the results from the rear suspension DOE, the total sum of the combined effects play a
crucial role in two of the performance parameters (Roll center lateral displacement and toe
gain). This is interesting because on the previous analysis (front suspension DOE), the roll
center lateral displacement also show a similar behaviour towards the input factors,
although some of these factors differ in each analysis. As a final observation, it is important
to emphasize the fundamental role of the input factors that represent the location of a
Hardpoint towards the Z coordinate. This factors (B, C & D in the Front suspension DOE; A,
C, & D in the Rear suspension DOE), have a significant relevance in almost all the
performance parameters which means that the designer must pay special attention to their
location.
7.6 Full Vehicle Analysis
The last DOE was applied to a full vehicle assembly simulation. This time, the factors that
were analysed correspond to some specific suspension parameters (such as the roll center
height) of both front and rear assemblies.
These suspension factors were evaluated respect some vehicle performance parameters
under a typical race car condition. The following table illustrates the input factors within
their respective lower and higher values.
Input factor Low High
RCH Front Suspension (mm) 3 70
RCH Rear Suspension (mm) 75 160
Spring Stiffness Front&Rear (N/mm) 50 60
Front Suspension Caster (deg) 0 7.5
Front Suspension KPI (deg) 0 7.5
Table 18. Input factors Full vehicle suspension Assembly
0
5
10
15
20
25
30
35
40
45
A-z_lca_F&R B-y_lca_F&R C-z_lca_outer D-z_uca_outer E-y_uca_outer F-x_uca_outer Combinedeffects
%
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Simulation Conditions:
The simulation that was implemented during this analysis is called a Step-steer. This
simulation recreates a manoeuvre where the vehicle takes a curve at high speed. The
trajectory that the vehicle travels (viewed from above) is represented in the next figure.
Figure 58. Vehicle trajectory while performing a Step-steer simulation
The reason why this full vehicle simulation was chosen, is because this type of manoeuvre
gives crucial information about the vehicle stability as well as the dynamic performance
while cornering. The simulation conditions that were taken into account during this analysis
are illustrated in the next figure:
Figure 59. Simulation Conditions: Step-steer
DOE Results:
The results obtain from the ANOVA analysis are resumed in the following figures.
Alternatively, if the reader wants a more detailed information, the appendix H illustrates
the results obtain for each of the 16 simulations as well as the suspension configurations
that were implemented in those simulations.
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Figure 60. Influence of the factors respect the Lateral Acceleration
Figure 61. Influence of the factors respect the Chassis Roll
Figure 62. Influence of the factors respect the Yaw rate
0
5
10
15
20
25
30
35
40
45
RCH Front (mm) RCH Rear (mm) Spring StiffnessFront&Rear
(N/mm)
Front Caster (deg) Front KPI (deg) Combinations
%
0
10
20
30
40
50
60
70
80
90
100
RCH Front (mm) RCH Rear (mm) Spring StiffnessFront&Rear
(N/mm)
Front Caster(deg)
Front KPI (deg) Combinations
%
0
5
10
15
20
25
30
35
40
45
RCH Front (mm) RCH Rear (mm) Spring StiffnessFront&Rear
(N/mm)
Front Caster (deg) Front KPI (deg) Combinations
%
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Figure 63. Influence of the factors respect the Vehicle Slip Angle
The previous four graphs demonstrate the importance of the first three factors (RCH front,
RCH rear and Spring Stiffness) in the final dynamic performance of the vehicle. On the
contrary, the last two factors (Caster and KPI), doesn’t play a key role in any of the four
performance parameters that were evaluated during this analysis.
As a final annotation before closing this chapter section, it is important to mention the type
of information that was introduced to the Design Expert® programme during this last DOE.
Unlike the previous two analysis, the results obtain during the full vehicle simulations are
much more complex to analyse due to their dynamic nature. The values that were analysed
correspond to the maximum values reported from each dynamic performance parameter
(see figures in Appendix I). The two main reasons that validate this decision are:
The two level factorial design analysis require a unique value for each of the
performance parameters that are going to be evaluated.
The maximum value is the most accurate response that represents the dynamic
behaviour the vehicle experiments during the manoeuvre.
7.7 Final Configuration of the Suspension system
The aim of the previous suspension analysis and their respective DOE´s was to obtain more
information about the relevance of some critical suspension Hardpoints. Now the designer
can realize changes on the suspension geometry knowing the influence that those
modifications have on the final performance of the suspension.
Based on this methodology, a series of geometrical modifications were carry out to both
front and rear assemblies until the performance of the suspension matched the objectives
initially formulated. This was clearly an iterative process due to the nature of the results
0
10
20
30
40
50
60
RCH Front (mm) RCH Rear (mm) Spring StiffnessFront&Rear
(N/mm)
Front Caster (deg) Front KPI (deg) Combinations
%
69
and simulations performed, the final suspension configurations obtain from this process are
described ahead:
Font & Rear Suspension final Configuration:
The front suspension geometry has a higher degree of difficulty due to its interaction with
the steering subsystem. As it was mention before, the performance parameters must be
different from the rear assembly in order to obtain a proper dynamic response. The final
values from the front and rear suspension assemblies are listed in the next table.
Parameter: Front Suspension Rear Suspension
Suspension Type
Independent Double Wish-bone (A-arms).
Push rod actuated with springs & dampers
horizontally orientated
Static Roll Center Height (mm): 95 160
Roll Center Lateral Gain (mm/deg of roll) 137 73
Roll Center vertical Gain (mm/mm) 1.88 2.4
Toe Gain (deg/mm) 0.061°/ mm -0.08°/ mm
Camber Gain (deg/mm) -0.08 -0.12
Static Caster (deg) 4.25 0
Static KPI (deg) 5 0
Tires Hoosier 20.5x7-13 R25B
Rims Keiser Formula Kosmo Forged billet 13”
Maximum suspension Design travel 60 mm in jounce / 60 mm in bounce
Average Wheel Rate (N/mm) 30 50
Sprung Natural Frequency (Hz) 3.83 4.29
Un-Sprung Natural Frequency (Hz) 17.11 17.79
Springs HYPERCO FSAE Springs (60 N/mm)
Dampers Öhlins TTX25 MkII
Static camber 0° for both assemblies
Static toe 0° for both assemblies
Anti-drive / Anti-squat N/A
Table 19. Final Parameters for the FRONT_UNIANDES and REAR_UNIANDES suspension assemblies
The table 19 represents a preliminary spec sheet from the suspension configuration
proposed during this thesis work, however, this values may change during the future
suspension design interventions. The following two figures illustrate the geometry and
design details from each suspension assembly:
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Front Suspension
Figure 64. FRONT_UNIANDES final configuration
A. The steering subsystem geometry and parameters where not modify from the
Fsae_2012 assembly. The figure shows that the rack & pinion is located behind the
wheel centers.
B. The PAC_2002 property file that was used to model the tire & rim geometry does not
represent entirely the Hoosier tires selected. However, due to the lack of information
available from this tires, the PAC_2002 was the most appropriated and realistic model
in order to simulate the vehicle under different race car conditions.
C. The dimensions & parameters of the springs and dampers correspond to the
information given by the Ohlins datasheet, though a more detailed analysis of these
elements is recommended.
The coordinates from each Hardpoint that compose the front suspension can be seen in the
following figure:
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Table 20. FRONT_UNIANDES Hardpoint location
ADAMS/Car® uses abbreviations for each Hardpoint in order to simplify their names. The
following table explains with more detail the meaning of each Hardpoint:
Location ADAMS/Car® Meaning
1 hpl_BC_axis
Imaginary Hardpoint that defines the axis about which the rocker
rotates; can be any other point on this axis.
2 hpl_BC_center Hardpoint from the rocker that goes mount to chassis
3 hpl_damper_inboard
Hardpoint from the shock absorber that goes attached to the
chassis
4 hpl_damper_outboard
Hardpoint from the shock absorber that goes attached to the
rocker
5 hpl_lca_front
Front Hardpoint form the Lower Control Arm that goes attached
to the chassis
6 hpl_lca_outer
Outer Hardpoint from the Lower Control Arm that goes attached
to the Kingpin
7 hpl_lca_rear
Rear Hardpoint from the Lower Control Arm that goes attached
to the chassis
8 hpl_prod_inboard Hardpoint from the push rod that goes attached to the rocker
9 hpl_prod_outboard Hardpoint from the push rod that goes attached to the kingpin
N/A hpl_ride_heigh Imaginary Hardpoint that represents the chassis ride height
10 hpl_tierod_inner
Hardpoint from the tie rod that goes attached to the rack and
pinion
11 hpl_tierod_outer Hardpoint from the tie rod that goes attached to the kingpin
12 hpl_uca_front
Front Hardpoint form the Upper Control Arm that goes attached
to the chassis
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13 hpl_uca_outer
Outer Hardpoint from the Upper Control Arm that goes attached
to the Kingpin
14 hpl_uca_rear
Rear Hardpoint from the Upper Control Arm that goes attached
to the chassis
15 hpl_wheel_center
Hardpoint that represents the center plane of the wheel where
the bolt goes attached to the kingpin
N/A hps_camber_adj_orient
Imaginary Hardpoint that is used to modify the static camber
orientation of the wheel.
Table 21. Meaning of each Hardpoint that represents the front suspension assembly.
Some of these Hardpoints doesn´t represent a physical element of the suspension.
However, they do have a geometrical meaning. The only problem that was found during the
suspension analysis was that the static configuration of the toe and camber angles, (that is
related with the Hardpoint hps_camber_adj_orient) can´t be modify and so these both
parameters were left always zero degrees static.
Rear Suspension
Figure 65. REAR_UNIANDES final configuration
A. The drive shaft as well as the engine mechanical properties from the fsae_2012 model
were not altered. On the contrary, this powertrain does not correspond to a typical FSAE
electric vehicle because the fsae_2012 assembly is modelled with a combustion engine,
reason why a future intervention in this subsystem must be done.
B. The table 19 shows that the rear assembly has a zero static toe. However, this assembly
does have a special type of tie-rods (white elements in figure 65) which are used to
modify this parameter.
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C. The rear assembly also has the shock absorbers horizontally orientated, although their
height respect the ground is considerably much lower than in the front suspension. The
height of Hardpoints from the rockers that go attached to the frame is strongly related
with the dimensions of the battery set.
The coordinates from each Hardpoint that compose the rear suspension can be seen in the
following figure:
Table 22. REAR_UNIANDES Hardpoint location
The only difference between the front and the rear suspension geometry is that in the rear
geometry there is an additional Hardpoint that represents the location of the power drive
shaft.
Full vehicle Dynamic performance:
The main aim of this work was to design a suspension system that could match the
performance parameters initially established.
Allow a proper tire grip under different conditions (cornering, straight line, etc.)
Promote stability & Manoeuvrability of the vehicle.
In order to evaluate this objectives, three full vehicle simulations were realized to the final
suspension design. Apart from this, the dynamic performance of the suspension elaborated
74
during this project was compared with the fsae_2012 full vehicle assembly. The simulation
conditions together with results of both vehicles are shown ahead.
Figure 66. FSAE_UNIANDES vehicle vs fsae_2012 vehicle
Straight-line acceleration
The full vehicle acceleration evaluates the dynamic response of the suspension under a
straight line event. During this simulation, the key performance parameters are the vehicle
pitch displacement, the normal forces on the front and rear tires and the longitudinal
acceleration of the vehicle.
Figure 67. Straight line acceleration conditions
75
Figure 68. Vehicle´s pitch angle vs simulation time (FSAE_UNIANDES vs fsae_2012)
Figure 69. Vehicle´s pitch angle vs longitudinal acceleration (FSAE_UNIANDES vs fsae_2012)
Figure 70. Front and Rear normal forces (FSAE_UNIANDES) vs simulation time
76
Figure 71. FSAE_UNIANDES longitudinal acceleration vs simulation time
Lane-change steering manoeuvre:
During this simulation the vehicle emulates overtaking another vehicle, which is a typical
situation that an FSAE driver has to affront during a race or dynamic event. During this
simulation, the performance parameters that were evaluated are: Chassis roll and
maximum lateral acceleration accomplished. The simulation conditions as well as the
results from both vehicles can be seen on the next figures.
Figure 72. Lane change simulation conditions
77
Figure 73. Chassis roll angle vs lateral acceleration (FSAE_UNIANDES vs fsae_2012)
Figure 74. Lateral Acceleration vs simulation time (FSAE_UNIANDEs vs fsae_2012)
Constant Radius acceleration:
The last simulation realized is perhaps the most important because it recreates the skidpad
dynamic event where the suspension mechanism is forced to the limit. The simulation
consist on accelerating the vehicle under a constant radius cornering. The performance
parameters taken into account were: vehicle´s side slip angle and tire´s normal forces. The
simulation conditions and the results can be seen on the following figures:
78
Figure 75. Constant Radius simulation conditions
Figure 76. Vehicle´s Side Slip Angle vs simulation time (FSAE_UNIANDES vs fsae_2012)
Figure 77. Tire normal forces vs simulation time (FSAE_UNIANDES)
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Simulation Results:
The results achieved by the FSAE_UNIANDES vehicle during the first full vehicle simulations
(straight-line acceleration) show that the vehicle´s longitudinal performance is much more
stable than the fsae_2012 vehicle, which clearly presents some irregular behaviour after
the laps of three seconds. This statement is demonstrated on the figure 68, where the
FSAE_UNIANDES pitch angle is considerably smaller and more stable during the whole
simulation than the fsae_2012 vehicle. Additionally, on the figure 69 the slope obtain from
the FSAE_UNIANDES corroborates that for the entire domain of longitudinal accelerations,
the pitch angle is smaller, which means a more uniform load distribution between the front
and the rear axle.
During the lane-change simulation, the roll angle obtain by the FSAE_UNIANDES is smaller
than the fsae_2012 vehicle. This can be clearly seen on the figure 73, where the slope from
the FSAE_UNIANDES (red) is less steep than the slope from the fsae_2012 (blue).
Furthermore, the FSAE_UNIANDES achieved a higher lateral acceleration during the
manoeuvre (figure 74), which means that it can take the curves at higher speeds without
losing control.
The last simulation performed provides information regard the vehicle manoeuvrability
under a constant radius acceleration. The figure 76 clearly shows a more stable behaviour
of the FSAE_UNIANDES vehicle because the vehicle´s slip angle stabilizes in a constant value
after a brief period. On the other hand, the fsae_2012 had a different behaviour towards
this performance parameter because instead of stabilizing in a unique value, the slip angles
starts to increase instead.
This unexpected growth of the fsae_2012 slip angle can be related with a bad vehicle control
and can eventually turn into an under-steering behaviour, which is definitely not desire
when performing a constant radius manoeuvre.
To sum up all the previous information, the results obtained by the FSAE_UNIANDES show
a better vehicle performance under the three different situations that where evaluated.
Moreover, on the next segment of this chapter a more profound analysis of the whole
suspension design is realized.
7.8 Design Evaluation
The evaluation process utilised involves assessing the design in regards to fulfilment of the
design targets listed back in chapter 2. This evaluation not only takes into account the
results obtain during the dynamic performance of the FSAE_UNIANDES vs the fsae_2012
vehicle but also recapitulates all the analysis realized to the suspension configuration
80
throughout the whole design process. The two main objectives that the suspension
configuration must fulfil in order to obtain a successful design are explained ahead:
Allow the vehicle a proper tire grip under different conditions:
Evaluating the tire grip is very important in a suspension design because one of the main
aims of any suspension is to maximise this parameter. The tire grip depends on a series of
factors such as the tire mechanical properties, the tire relative angles and the forces
develop between the tire and the ground surface.
In order to evaluate this objective two main parameters were taken into account: The
camber gain and the normal forces acting on each tire under different testing conditions.
As it was mention before, the grip available from the tires is strongly related with the
camber placed on the wheels. The ideal tire behaviour under a cornering situation is
generally accomplish with a negative camber gain. This is true because the camber angle
produces some additional lateral force that enables the vehicle to take a corner with a
higher speed. However, the values of the camber angle must be within the limits pre-
established by the manufacturer.
The kinematic results obtain from the front & rear suspension assemblies show that for
both assemblies, the camber gain is always negative (Appendix I: figure A19 and Appendix
J: figure A22). On top of that, the operating range does not exceed the 3° of camber, which
is the maximum value that the tires can support before losing tire grip. As a final observation
of this parameter, the front suspension camber gain is slightly smaller than the rear; the
reason: the rear suspension does not have a steering mechanism, which means that a larger
camber provides the additional lateral force needed during a corner.
On the other hand, the normal force that acts on each tire is also a good performance
parameter to evaluate the tire grip. The vertical tire loads influence the tire´s ability to
produce lateral and longitudinal forces. As a rule of thumb, less normal forces produce less
tire grip. With this in mind, the two simulations that evaluate this parameter were the
straight-line acceleration and the constant radius acceleration.
During a straight-line acceleration, the load will be less at the front axle, which means that
the front tires will have less tire grip. A good suspension design is able to maximize the front
normal forces under this type of condition. The results from simulations show that the
FSAE_UNIANDES pitch angle is much more stable and smaller than the fsae_2012, which
means that the longitudinal weight transfer is more equally distributed throughout the
front and rear tires. This uniform load distribution is directly related with the normal forces
acting on each tire, which means that the tire grip from the front tires does not suffer some
mayor changes.
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The figure 70 corroborates the previous statement and shows how the normal forces acting
on the rear tires increase as the vehicle accelerates while the normal force in the front tires
decreases. During the first four seconds, the normal forces from the front and rear tires do
not show an important growth. However, when the simulations reaches the four seconds,
these two forces rapidly increase, showing some instable behaviour in the longitudinal load
transfer.
This undesired behaviour is related with the engine properties, which correspond to a
typical 4-stroke gasoline engine. As the reader may know, the torque vs angular velocity
curve from a petrol engine differs radically from an electric engine curve (figure 78). An
electric engine has instant torque at 0 rpm while the internal combustion engine achieve its
maximum torque at high rpm.
Figure 78. Internal combustion engine vs electric engine (Torque vs rpm)
When the simulation reaches 4 seconds, the vehicle suffers an important longitudinal
acceleration pick (figure 71), which is related with the engine power and torque curves. This
acceleration pick directly affects the normal forces on the front and rear axles, reason why
in the figure 70 there is an important increase in the rear tires normal forces and a decrease
in the front tires. It is worth mentioning that if it had been used a powertrain that
represented the properties from an electric engine during the simulations, this undesired
behaviour wouldn´t had occurred.
To close up this objective, it is important to mention the results obtain in the figure 77. In
this case, the normal forces at the outer tires (right front and right rear) gradually increase
while the inner tires (left front and left rear) are gradually decreasing. However, on both
cases the forces stabilizes in a constant value, which grants a good tire grip under a skip-
pad dynamic event.
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Promote stability & Manoeuvrability of the vehicle.
This objective represents a vehicle dynamic characteristic that is hard to measure due to its
nature. However, if we take into account the recommendations offered by the literature as
well as the performance parameters that can describe this vehicle phenomenon it is
possible to explain the reasons why this objective is accomplished by the suspension design
proposed during this work.
The Toe angle is one of the suspension parameters that can be related with the vehicle´s
manoeuvrability and handle; especially while taking a corner. According to the literature
recommendations, in order to obtain a quicker steering response and improve the vehicle´s
turn-in ability to corner, the front suspension should have a positive toe gain; which means
increasing the toe out angle under jounce (Smith, 1978). On the other hand, for the rear
suspension a negative toe gain is recommended in order to achieve a better traction out of
the corner as well as improving the vehicle´s steerablibily under high speed (Jazar, 2014).
With this in mind, the front and rear suspension assemblies were design to meet this toe
gain conditions, the table 19 shows the final values achieved by these assemblies. The
results demonstrate that the front suspension has a positive toe gain while the rear
suspension has ha negative toe gain. Additionally, the toe gain for the front suspension is
smaller than the rear toe gain. This condition is important because a large toe gain in the
front would generate unwanted driver uncertainly and a poor handling feel (Staniforth,
1999). As a final observation of this parameter, the figures A19 and A22 from the appendix
I and J respectively show that the maximum toe angle that the front suspension achieved
under full jounce or rebound was 1.6° while the rear suspension achieved a slightly higher
value of 2.0°.
The relevance of these values is that both of them are within the limits recommended by
the literature, which estates that in order to obtain a good dynamic response not only while
cornering but also during a straight-line acceleration a good compromise in the maximum
toe value is between 1.5° and 2.5° degrees of toe.
The other performance parameter that can evaluate this objective is the vehicle´s slip angle,
also known as sideslip angle or body slip angle. This parameter evaluates the difference
between the direction the vehicle is travelling and the direction that the body of the vehicle
is pointing.
83
Figure 79. Vehicle side slip angle
When the slip angle stabilizes in a unique value while performing a cornering manoeuvre,
the vehicle has a good dynamic response and handle. However, if this parameter starts to
increase, the vehicle could eventually lose control due to its understeering behaviour. On
the previous section the results obtain from this performance parameter where discussed,
and the figure 76 shows a better response from the FSAE_UNIANDES vehicle.
In general, the results obtain for both of the performance parameters that were analysed
in order to evaluate the manoeuvrability and stability of the vehicle under a cornering
situation demonstrate a good performance, so it can be concluded that the objective was
met successfully.
84
Chapter 8. Conclusions and future work
The whole design process of the suspension mechanism for the FSAE Uniandes vehicle
started barely from scratch and ended with a full vehicle suspension configuration. The
methodology proposed was successfully implemented during suspension design and the
results obtain from this final configuration does satisfy the objectives initially established;
however, the design process also left a series of learnings that could be useful during future
interventions. These new findings are listed ahead:
The MatLab® analysis showed that the dimensions of the kingpin has a critical
impact in the final dynamic performance of the vehicle. The designer must pay
special attention to the height of the upper and lower ball joints of the A-arms
because these Hardpoints have a major influence in the roll center height. On top of
that, they are also very sensible towards the kingpin inclination and the caster angle.
The MatLab® analysis revealed that the dimensions of some suspension elements
have no influence in any of the performance parameters that were studied; one such
example is the width of both upper and lower A-arms. Nevertheless, this analysis
does not take into account the structural integrity of these elements, in which the
width of the A-arms does has a relevant impact.
The modifications that were held during the chapter five demonstrated that the
frame geometry has some great advantages such as a flexible design. With this in
mind, the designer can easily modify the chassis design in order to satisfy the
different requirements imposed not only by the suspension mechanism but also by
others vehicle subsystems.
A 1600 mm wheelbase along with a 1300 mm front track and a 1200 mm rear track
provides the vehicle a good compromise between the longitudinal & lateral load
transfer and the cornering performance.
The DOE´s applied to the suspension assemblies revealed the influence that some
critical Hardpoints have towards the performance parameters. During this analysis
was corroborated that the suspension roll center must be the basis and major goal
throughout the entire suspension design due to its critical relevance in the final
dynamic performance of the vehicle.
The final design of the suspension mechanism combined with the selected spring
stiffness provide the vehicle a good roll over stability as well as an acceptable tire
85
grip. The 60 N/mm HYPERCO FSAE springs demonstrated a good compromise
between the ride frequencies and the final performance of the vehicle, reason why
the anti-roll bars were not implemented in neither of the suspensions assemblies.
Lastly, it was also found that parameters such as the kingpin inclination and the
caster angle have a secondary relevance in the vehicle performance, reason why
they should be the last parameters to take into account during the design process.
The suspension design proposed during this thesis has demonstrated a good handling and
performance of the vehicle throughout the various simulations that were realized, in fact
the results obtain during these simulations validate the initial objectives. Furthermore, it is
important to mention that all the simulation scenarios recreate in an accurate and realistic
approach the typical Formula SAE vehicle conditions; this is true because before realizing
any of the simulations a detail amount of variables such as the g-forces, turning radius and
vehicle properties (mass, center of gravity, tires, rims, basic dimensions, etc.) were consider.
Concerning the suspension properties obtain by final suspension design, the values that
were achieved for each of the performance parameters are within the design goals
recommended by the literature review, which in a certain way grants a proper dynamic
behaviour of the suspension subsystem.
Finally, the suspension design does meet all the restrictions imposed by the FSAE rules and
it also adjust to the chassis design elaborated by Camilo Sarmiento, which were two of the
main objectives of this thesis work.
Future Work:
The design of the suspension subsystem still has some major challenges to overcome, within
which we can highlight the following:
Incorporate the suspension geometry and elements with the remaining vehicle
subsystems. This process could generate a series of challenges related with
geometrical interferences that might cause some modifications in the suspension
design. However, the whole design team must find a compromise between the
requirements of each subsystem in order to obtain the best possible performance
of the whole vehicle.
Prior to its manufacture, the suspension design must be properly modelled in
Autodesk Inventor® in order to facilitate the future assemble process. This 3D model
must show a detail design of all the elements that are required in suspension
configuration (bolts, ball-joints, welding’s, etc.).
86
Besides, a structural analysis should be realized in order verify its integrity to
withstand static and dynamic loads associated with its operation. A structural
evaluation using a finite element program is recommended in order to analyse some
critical suspension elements such as the rocker or the push rod.
During this thesis, a number of suspension elements were selected such as the tires,
the shock absorbers, the rims, the springs, etc. However, the cost factor was never
taken into account, reason why a more detailed analysis of this important target
must be realized.
To sum up, the methodology used during the entire design process provides to the future
designers a solid basis that could be very helpful for the next design iterations. The design
recommendations provided by the various experts in their respective articles and books, as
well as the results obtain throughout this thesis work demonstrated that the final design of
the suspension subsystem does met the objectives initially pre-established.
87
REFERENCES:
Formula SAE, 2015 Formula SAE Rules, 2015. SAE International, USA.
Milliken, W. F & Milliken, D. L. Race Car Vehicle Dynamics, 1995. SAE International, Warrendale.
Kiszko, M. REV 2011 Formula SAE Electric – Suspension Design, 2011. University of Western
Australia, Australia.
Sarmiento, C. Diseño de Chasís, tren de potencia y soportes para ruedas de un vehículo de
Fórmula SAE, 2015. Universidad de los Andes, Colombia.
Staniforth, A. Competition Car Suspension, 1991.Haynes Publishing, Newbury Park.
Farrington, J. Redesign of an FSAE Race Car´s Steering and Suspension System, 2011. University
of Southern Queensland, Australia.
Smith, C. Tune to win, 1978. Aero Publishers, USA.
Chang, Y. Kinematic Analysis of Roll Motion for a Strut/SLA Suspension System, 2012. International
Journal of Mechanical, Aerospace, Mechatronic and Manufacturing Engineering Vol: 6, No:5, Taiwan.
Jazar, R. Vehicle Dynamics (2nd Edition), 2014. Springer, New York.
Svendsen, 2014. Dynamic analysis of damping system in FS car using ADAMS Multidynamics
Simulations, 2014. University of Stavanger, Norway.
Wolfe, S. SLASIM: A Suspension Analysis Program, 2010. Ohio State University, USA.
Kasprzak, J. Understanding your Dampers, 2014. Kaztechnologies, USA. Taken from:
www.kaztechnologies.com
Gaffney, E. Salinas, A. Introduction to Formula SAE Suspension and frame Design, 1996. University
of Missouri, USA.
Sun, L. Deng, Z. Zhang, Q. Design and Strength Analysis of FSAE Suspension, 2014. The Open
Mechanical Engineering Journal, China.
Allen, R. Design and Optimization of a Formula SAE Racecar Chassis and Suspension, 2009.
Massachusetts Institute of Technology, USA.
Theander, A. Design of a Suspension for a Formula Student Race Car, 2004. Royal Institute of
Technology, Stockholm.
Mueller, R. Full Vehicle Dynamics model of a Formula SAE Racecar Using ADAMS/CAR, 2005.
Texas A&M University, USA.
Montgomery, D. Design and Analysis of Experiments (Eighth edition), 2013. Wiley, USA:
88
Appendix A. FSAE Lincoln electric vehicles information
2015 Lincoln FSAE Electric - Teams:
University: FR/RR track (mm) Suspension Tire Wheelbase (mm) Weight (lb) EMCAC
McGill University 1193.8/1193.8
Double unequal length A-Arm. Push rod actuated spring
and damper.
18x6-10 LC0 Hoosier
1574.8 570 Lithium cobalt
oxide / 6.66kWh
University of California - Davis
1295.4/1295.4
Upper A-Arm, Lower Multilink (F), Twin
Trailing Link, Inverted A-Arm (R)
20.5x7.0-13 Hoosier R25B
1676 675 NCM-cathode Li-
Ion/7.5 kWh.
University of Manitoba
1510/1495
Short-long A-arm. Sprung mass
actuation with custom rockers and
uprights
20.5x7-13 (front) and 20.0x7.5-13 (rear) R25B
Hoosier
1720 711.9 Li[NiCoMn]O2 /
144 Ah
University of Washington
1270/1193.8 Double Unequal
Length A-Arm. Pull Rod Actuated
6.0/18.0-10 LC0
Hoosier 1536.7 535
Lithium-Ion Polymer / 6.109kWh
Massachusetts Institute of technology
1219.2
Double unequal length A-Arm.
Pushrod actuated spring and damper
20.5x7.0-13 Hoosier R25B
1601.0 660 LiFePO4/ 5.5
kWh
University of Michigan - Dearborn
1206.5/1193.8
Double unequal length A-Arm. Pull
rod actuated horizontally oriented
spring
18x6-10 LC0 Hoosier
1550 653 LiMn2O4, 5.1kWh
Missouri University of Science and tech
1250/1190 Short Long A-Arm Pull-rod Actuated
18x6-10 LC0 Hoosier
1630 570 Li-NMC / 5.32
kWh
University of Kansas – Lawrence (2nd place)
1219.2/1168.4 Double A-Arms
Pushrod 20.5x7.0-13
Hoosier R25B 1600 625 7.0 kWHr
Carleton University 1270/1245 Double A-Arm,
pushrod actuated spring
20.5x7.0-13 Hoosier R25B
1550 661 LiFePO4 / 5.5kWh
Colorado State University
1194/1168
Double Unequal Length Carbon Fiber
A Arms, Front Pullrod Rear Pushrod
20.5x7.0-13 Hoosier R25B
1625 800 Lithium Cobalt
Oxide / 7.5 kWh
Polytechnic University of Puerto Rico
1321/1270
Dual Unequal Length A-arm, Actuation by
Push/Pull Rod by Rocker to Coilover
20.0x7.5-13 Hoosier R25B
1626 750 LiFePO4 / 5.2kWh
Illinois Institute of technology
1172/1168 Direct Suspension 18x6-10 LC0
Hoosier 1536 550 LiPo 5.6kWh
University of Pennsylvania (1st
place) 1195/1155
SLA, pushrod actuation, U-bar anti-
roll
20.5x7.0-13 Hoosier R25B
1529 546 LiCoO2 / 5.3
kWh
Purdue University – W Lafayette
1270 Double Wishbone, Pushrod System
6.0/18.0-10 LC0
Hoosier 1575 661 7.5 kWH
Polytechnique Montréal (3rd place)
1200/1100 Double a-arms/push-rod with adjustable
anti-roll bars
18x6-10 LC0 Hoosier
1600 615 NCM vs graphite
/ 5.3 kWh
Table A1. Information of each electric vehicle that participated last year in the FSAE Lincoln.
89
Appendix B. Hoosier Tire Information
Figure A1. Hoosier FSAE tire´s catalogue
Pressure inside: Actual load Static spring Rate (lbs/in) Static spring Rate (N/mm)
14 psi
200 lbs = 889 N 961,06 168,37
300 lbs=1334 N 1083,62 189,85
400 lbs = 1779 N 1104,34 193,48
16 psi
200 lbs = 889 N 1053,66 184,60
300 lbs=1334 N 1222,01 214,09
400 lbs = 1779 N 1260,39 220,82
18 psi
200 lbs = 889 N 1130,16 198,00
300 lbs=1334 N 1364,19 239,00
400 lbs = 1779 N 1419,30 248,66
Figure A2. Vertical stiffness of the 20.5 x 7.0-13 tire under different inflation pressures.
0
200
400
600
800
1000
1200
1400
1600
150 200 250 300 350 400 450
Stat
ic s
pri
ng
Rat
e (
lbs/
in)
Actual Load (lbs)
14 psi
16 psi
18 psi
90
Appendix C. Keiser Rim Information
Wheel Design: Description: Price:
Formula Kosmo forged
billet *Also offered in Magnesium for a lower weight but
a much higher cost.
Is the most utilized wheel in competition history. Its attributes in design flexibility, strength and low moment of inertia have been the top choice of teams for years. The Kosmo is capable of extreme offset requests while being versatile to accept any brake package. It can adapt to center-lock drive pin designs as well as any four-bolt pattern. The magnesium is an excellent choice for teams looking for the lightest of wheels with a difficult packaging problem.
Without Sponsorship: $350 - $375 With Sponsorship: $250 – 275
Formula CL-1 Wheel.
This wheel was created to support almost every centerlock design known to the racing industry. It gives teams the ability to custom design its hub package around a high quality wheel center at an affordable price. The core of the CL-1 strength lies in its cold forged center and extensive precision CNC machining. The CL-1 series wheel is capable of extreme offset requests while remaining versatile to accept any brake package
Without Sponsorship: $350 - $375 With Sponsorship: $250 – 275
Formula A1 forged billet
Is our oldest and most successful model of all time. Providing a light wheel platform at a very inexpensive price has landed the A1 series in victory lane many times over the past 25 years. Keizer’s in house forging technology has provided you with the most economical version of a true race wheel. The A1 series simple design is offered in a wide variety of offset and width options and will support a infinite number of lugs patterns. [3 bolt, 4 bolt and 6 bolt] Low cost, high performance and simplified design make it a viable option for any team on the way to the top!
Without Sponsorship: $315 - $346 With Sponsorship: $375 – 399
Formula 4L forged billet
The 4L begins as a forged billet and is refined through some intense CNC machining. Its flexibility to meet a multitude of SAE needs was our main focal point. This wheel will support any 4-bolt pattern and gives teams the ability to custom design its hub package around a quality piece at an affordable price. The 4L series wheel is capable of extreme offset with no need for spacers!
Without Sponsorship: $250 - $275 With Sponsorship: $250 - $275
Table A2. Keiser Rim´s properties and prices
*The four wheels offer the same O.D of 13” with a wide variety of Backspacing depending on the selected wheel width. For more detail
information about each wheel, please check the specs sheets.
91
Appendix D. MatLab® Code:
tic
close all
clear all
clc
L = 1000000 ; %lenght of numbers to analyze
X = sobolset(7,'skip',10);
N = net(X,L);
E = zeros(1,1);
R = zeros(1,9);
%Input variables:
yu = (N(:,1))*3+9;
yl = (N(:,2))*1.5+3.5;
xu = (N(:,3))*2+10;
xl = (N(:,4))*2+10;
x_ul_obj = (N(:,5))*4+19.5;
y_lobj = (N(:,6))*3+5.5;
y_uobj = (N(:,7))*3+12.5;
for i=1:L;
%REAR SUSPENSION:
upper_fibj = [xu(i) yu(i) 8.179];
upper_ribj = [xu(i) yu(i) -5.6];
upper_obj = [x_ul_obj(i) y_uobj(i) 0];
lower_fibj = [xl(i) yl(i) 8.179];
lower_ribj = [xl(i) yl(i) -5.6];
lower_obj = [x_ul_obj(i) y_lobj(i) 0];
%Half Rear track = 600 mm (23.622 in)
wheel_center = [23.622 10.5 0];
contact_patch = [23.622 0 0];
camber_x = wheel_center(1) - contact_patch(1);
camber_y = wheel_center(2) - 0;
camber = atand(camber_x/camber_y);
caster_y = upper_obj(2) - lower_obj(2);
caster_z = lower_obj(3) - upper_obj(3);
caster = atand(caster_z/caster_y);
m_caster = -caster_y/caster_z;
b_caster = upper_obj(2) - m_caster*upper_obj(3);
trail = -b_caster/m_caster;
kp_x = upper_obj(1) - lower_obj(1);
kp_y = upper_obj(2) - lower_obj(2);
KPI = atand((-1*kp_x)/kp_y);
92
m_kp = kp_y/kp_x;
b_kp = upper_obj(2) - m_kp*upper_obj(1);
scrub = contact_patch(1) - (-b_kp/m_kp);
upper_normal = cross((upper_fibj - upper_ribj),(upper_obj - upper_ribj));
lower_normal = cross((lower_fibj - lower_ribj),(lower_obj - lower_ribj));
instant_axis_normal = cross(upper_normal, lower_normal);
dot_upper = -dot(upper_normal,upper_fibj);
dot_lower = -dot(lower_normal,lower_fibj);
fv_ic = [0;0;0];
fv_ic(1) = (dot_lower*upper_normal(2) -
dot_upper*lower_normal(2))/instant_axis_normal(3);
fv_ic(2) = (dot_upper*lower_normal(1) -
dot_lower*upper_normal(1))/instant_axis_normal(3);
fv_ic(3) = 0;
t = (contact_patch(1) - fv_ic(1))/instant_axis_normal(1);
sv_ic(1) = contact_patch(1);
sv_ic(2) = fv_ic(2) + t*instant_axis_normal(2);
sv_ic(3) = fv_ic(3) + t*instant_axis_normal(3);
m_rch = (fv_ic(2) - contact_patch(2))/(fv_ic(1) - contact_patch(1));
RCH = -m_rch*contact_patch(1);camber_x = wheel_center(1) - contact_patch(1);
if RCH >= 2 && RCH <= 5;
RCH_ok = 1;
else
RCH_ok = 0;
end
E(i,1)= yu(i);
E(i,2)= yl(i);
E(i,3)= xu(i);
E(i,4)= xl(i);
E(i,5)= x_ul_obj(i);
E(i,6)= y_lobj(i);
E(i,7)= y_uobj(i);
E(i,8)=RCH;
E(i,9)=RCH_ok;
end
k=1;
for j=1:L
if E(j,9) > 0;
R(k,:)= E(j,:);
k=k+1;
end
end
t=toc
93
Appendix E. Front Suspension MatLab® analysis results:
Figure A3. yu vs RCH (Left graph) – yl vs RCH (Right graph)
Figure A4. xu vs RCH (Left graph) – xl vs RCH (Right graph)
Figure A5. x_uobj vs KPI (top left graph) – x_uobj vs Scrub (top right graph) – x_uobj vs RCH (bottom).
23 23.5 24 24.5 25 25.50
1
2
3
4
xuobj (in)
KP
I (d
eg°)
23 23.5 24 24.5 25 25.50.5
1
1.5
xuobj (in)
scru
b (
in)
23 23.5 24 24.5 25 25.50
1
2
3
4
xuobj (in)
RC
H (
in)
94
Figure A6. x_lobj vs KPI (top left graph) – x_lobj vs Scrub (top right graph) – x_lobj vs RCH (bottom).
Figure A7. z_uobj vs Caster (left graph) – z_lobj vs Caster (right graph)
Figure A8. y_uobj vs caster (Top left), y_uobj vs scrub (top right), y_uobj vs KPI (Bottom left), y_uobj vs RCH (Bottom right)
23.6 23.8 24 24.2 24.4 24.6 24.8 25 25.2 25.40
1
2
3
4
xlobj (in)
KP
I (d
eg°)
23.6 23.8 24 24.2 24.4 24.6 24.8 25 25.2 25.40.5
1
1.5
xlobj (in)
scru
b (
in)
23.6 23.8 24 24.2 24.4 24.6 24.8 25 25.2 25.40
1
2
3
4
xlobj (in)
RC
H (
in)
12.5 13 13.5 14 14.5 15 15.54
5
6
7
8
yuobj (in)
Caste
r (d
eg°)
12.5 13 13.5 14 14.5 15 15.50.5
1
1.5
yuobj (in)
scru
b (
in)
12.5 13 13.5 14 14.5 15 15.50
1
2
3
4
yuobj (in)
KP
I (d
eg°)
12.5 13 13.5 14 14.5 15 15.50
1
2
3
4
yuobj (in)
RC
H (
in)
95
Figure A9. y_lobj vs caster (Top left), y_lobj vs scrub (top right), y_lobj vs KPI (Bottom left), y_lobj vs RCH (Bottom right)
5.5 6 6.5 7 7.5 8 8.54
5
6
7
8
ylobj (in)
Caste
r (d
eg°)
5.5 6 6.5 7 7.5 8 8.50.5
1
1.5
ylobj (in)
scru
b (
in)
5.5 6 6.5 7 7.5 8 8.50
1
2
3
4
ylobj (in)
KP
I (d
eg°)
5.5 6 6.5 7 7.5 8 8.50
1
2
3
4
ylobj (in)
RC
H (
in)
96
Appendix F. Rear Suspension MatLab® analysis results:
Figure A10. yu vs RCH (top left), yl vs RCH (top right), y_uobj vs RCH (bottom left), y_lobj vs RCH (bottom right).
Figure A11. xu vs RCH (left), xl vs RCH (center), x_ul_uobj vs RCH (right).
97
Appendix G. Front & Rear suspension : Wheel rate
Figure A12. Front suspension Wheel rate (blue line 60 N/mm; red line 50 N/mm)
Figure A13. Rear suspension Wheel rate (blue line 60 N/mm; red line 50 N/mm)
98
Appendix H. Full Vehicle DOE Results:
RUN#_FULL A B C D E
RUN_1_FULL 70 75 45 7,5 7,5
RUN_2_FULL 3 160 45 0 0
RUN_3_FULL 3 75 60 0 0
RUN_4_FULL 3 75 45 0 7,5
RUN_5_FULL 3 160 45 7,5 7,5
RUN_6_FULL 70 160 60 7,5 7,5
RUN_7_FULL 70 160 45 0 7,5
RUN_8_FULL 70 75 60 0 7,5
RUN_9_FULL 70 75 60 7,5 0
RUN_10_FULL 70 160 45 7,5 0
RUN_11_FULL 70 160 60 0 0
RUN_12_FULL 3 75 45 7,5 0
RUN_13_FULL 70 75 45 0 0
RUN_14_FULL 3 160 60 0 7,5
RUN_15_FULL 3 160 60 7,5 0
RUN_16_FULL 3 75 60 7,5 7,5 Table A3. Full vehicle DOE configurations
Results
Max Lateral Accel (g) Max Chassis roll (deg) Max Chassis Yaw (deg) Max Slip Angle (deg)
1,1527 1,2063 42,4299 3,6038
1,1536 1,2869 42,5914 3,3655
1,1497 0,989 42,5774 3,3985
1,1538 1,3294 44,1812 4,136
1,1554 1,2409 42,3288 3,173
1,1152 0,8451 39,2687 2,2408
1,1352 1,148 40,8072 2,6957
1,1381 0,9024 41,0564 2,9528
1,1428 0,901 40,8147 2,9926
1,1389 1,1421 40,6449 2,6935
1,1227 0,8677 39,7622 2,3453
1,1596 1,3056 44,0049 4,1074
1,1482 1,231 42,5709 3,6618
1,1431 0,9532 41,4525 2,7692
1,1465 0,9358 41,1257 2,7677
1,1567 0,9363 42,229 3,4097 Table A4. Full vehicle DOE Results for each configuration
99
Figure A14. Chassis lateral acceleration vs simulation time (Left: run 1 to 8; right run 9 to 16).
Figure A15. Chassis roll angle vs simulation time (Left: run 1 to 8; right run 9 to 16).
Figure A16. Chassis slip angle vs simulation time (Left: run 1 to 8; right run 9 to 16).
Figure A17. Chassis Yaw rate vs simulation time (Left: run 1 to 8; right run 9 to 16).
100
Appendix I. Front Suspension Results: Final Parameters
Figure A18. Roll Center vertical Displacement vs Wheel travel (left) – Roll center Lateral displacement vs Wheel travel (right)
Figure A19. Camber gain vs Wheel travel (left) – Toe gain vs Wheel travel (right)
Figure A20. Kingpin inclination angle vs wheel travel (left) – Caster angle vs wheel travel (right)
101
Appendix J. Rear Suspension Results: Final Parameters
Figure A21. Roll Center vertical Displacement vs Wheel travel (left) – Roll center Lateral displacement vs Wheel travel (right)
Figure A22. Camber gain vs Wheel travel (left) – Toe gain vs Wheel travel (right)
Figure A23. Kingpin inclination angle vs wheel travel (left) – Caster angle vs wheel travel (right)