1
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
2
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
3
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
4 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/).
5
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:
6 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
7
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.
8
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.
11
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.
12 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.
14
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
15
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).
16
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
17
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.
18
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 =𝑚𝑣
2
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).
19
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).
20
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.
21
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.
22
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.
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
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
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.
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
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.
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.
