The Optimization of a Formula SAE Vehicle's Suspension Kinematics

by

William Thomas Harvey

Submitted to the Department of Mechanical Engineeringin Partial Fulfillment of the Requirements for the Degree of

Bachelor of Science in Mechanical Engineering

at the

Massachusetts Institute of Technology

June 2018

C2018 William Thomas Harvey. All rights reserved.

The author hereby grants to MIT permission to reproduce and todistribute publicly paper and electronic copies of this thesis document

in whole or in part in any medium now known or hereafter created.

Signature redactedSignature of Author: ...................... . . . ...-----.------------.- -

Department of Mechanical Engineering

C ertified by: ..................................... Signature redacted........Amos Winter

Associate Profes eMechanical EngineeringThesis Supervisor

Signature redactedC ertified by: ..................................

MASSACHUSTSINTTTOF TECHNOLOGY

SEP 13 2018

LIBRARIESARCHIVES

.......................Rohit Karnik

Professor of Mechanical EngineeringUndergraduate Officer

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The Optimization of a Formula SAE Vehicle's Suspension Kinematics

by

William Thomas Harvey

Submitted to the Department of Mechanical Engineeringon May 17, 2018 in Partial Fulfillment of the

Requirements for the Degree of

Bachelor of Science in Mechanical Engineering

ABSTRACT

The suspension geometry is the foundation of a performance vehicle's design because it dictatesthe overall packaging constraints and the connection between the chassis and the tires. Thisthesis details the design process used to produce the suspension geometry for MIT Motorsports'2018 Formula SAE car and the justification for each design decision made. A thorough iterationprocess was used to prevent compromises that could significantly detract from specificcomponent performance in order to meet suspension kinematic requirements. Using this process,the kinematic performance of the suspension was maximized by minimizing the roll center'smovement and designing the tire camber change characteristics to achieve 0* of outer-wheelcamber while at the car's maximum lateral acceleration.

Thesis Supervisor: Amos Winter

Tile: Associate Professor of Mechanical Engineering

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Acknowledgements

I would like to thank Becky Steinmeyer, Harriet Chiu, Miranda Kotidis, Mark Harvey, and KatieKrajovic for reviewing the initial iterations of this thesis. A special Nook Nook goes to ElliotOwen for developing MIT Motorsports' design review process for 2017-2018. It reinforced thedesign iteration process during the build cycle for the 2018 car.

Nothing written here can communicate how grateful I am to the Edgerton Center for providing thefacilities and support that makes MIT Motorsports possible. Without Sandi keeping the team inline, we would be bankrupt, and without Pat, we couldn't maintain our machinery, let alone theshop space.

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Table of Contents

Abstract

Acknowledgements

Table of Contents

List of Figures

List of Tables

1. Introduction

1.1 Design Motivation

1.2 Kinematics in a Performance Vehicle

1.3 Scope of Project

2. Background

2.1 Roll Center

2.2 Camber

2.3 Ball Joint Geometry

3. Experimental Design

3.1 Design Requirements

3.2 Design Method

4. Results

5. Conclusions

6. References

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List of Figures

Figure 1: A photograph of two Formula SAE cars competing at the Lincoln competition. 9

Figure 2: A photograph of MIT Motorsports' 2017 car with labels indicating the key componentsin overall suspension design. 11

Figure 3: A chart of MIT Motorsports' 2017-2018 team structure developed to produce the 2018car 13

Figure 4: A diagram of a vehicle's suspension linkage geometry with the instant centers of eachtire labeled "IC" and the resulting roll center labeled "RC." 15

Figure 5: A figure showing a representation of the jacking effect. 16

Figure 6: An illustration of negative camber on a simple axle. If the top of the tires lies furtherfrom the vehicle centerline than the bottom, then the positive camber is positive. 17

Figure 7: A diagram depicting the significant measurements related to ball joint geometry on thewheel upright 18

Figure 8: A flow chart of the feedback loop that guides the suspension point design iteration usedto meet the performance requirements of the suspension system. 22

Figure 9: An image of the suspension point sketch used in Solidworks@ that defined thesuspension geometry within each of the component files that interfaced with the suspension. 24

Figure 10: A screenshot of the outputs from the kinematic analysis software -Wingeo- describedin the Design Method. 25

Figure 11: A plot of the left tire's camber change over the expected roll angles during the car'snormal operation. 27

Figure 12: Images of the front left A-arm on the 2017 (top) and 2018 (bottom) cars. 29

Figure 13: The relationship between the left tire camber and chassis roll in a corner for the 2017,2018, and initial 2018 iteration of the car's geometry. 31

Figure 14: The relationship between the roll center height and wheel's travel over a bump for the2017, 2018, and initial 2018 iteration of the car's geometry. 31

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List of Tables

Table 1: A table detailing a selection of the possible remedies for the positive camber issue. 28

Table 2: A table listing the suspension's kinematic characteristics expected for the finalsuspension geometry at rest, at maximum lateral acceleration (roll), and at maximum wheeltravel (bump) as well as the ball joint geometry measurements in the front and rear of the car. 30

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1. Introduction

Developing a car from concept to completion involves breaking the vehicle down into

various subsystems that require knowledge in both mechanical and electrical engineering. In every

subsystem's design, the suspension geometry is the greatest factor, as it produces the constraints

that dictate how each subsystem can interface within the overall system. The goal of a suspension

system is to connect the vehicle's chassis to its tires in a way that maximizes the grip of the tires

during normal operation. Driving the geometries of the wheel packages, A-arms, steering, frame,

and brakes, the performance of the suspension kinematics depends on the compromises that occur

between the geometry and the subsystems with which it interfaces. Beyond the direct geometric

constraints, the remainder of the vehicle is indirectly affected because the frame and geometry

change in conjunction with each other, which impacts the packaging and structural constraints of

every subsystem in some manner. Moving from a packaging focus to a performance focus, a

kinematic analysis provides data to assess the performance of a suspension geometry. This thesis

details the development of the suspension kinematics of a student-produced car to maximize the

area of contact between the tire and ground (known as the contact patch).

With upwards of fifteen to twenty subsystems comprising a vehicle, car design projects

produce a tremendous opportunity for students to engage their classroom knowledge in a practical

environment. MIT Motorsports, a student-engineering team at the Massachusetts Institute of

Technology, is one such example of the engaging opportunity because the group competes with

an electric-powered formula-style race car annually in the Formula SAE (FSAE) Electric

competition. This collegiate competition challenges student teams to design, build, and compete

with a scale formula vehicle in a multi-day event that evaluates both the dynamic and static

performance of the final vehicle. To prevent stagnation in the competition, a new chassis is

required to compete each year. Therefore, the results detailed in section four only apply to MIT

Motorsports' vehicle for the 2018 Formula SAE Electric competition.

1.1. Design Motivation

FSAE is one category of the design, build, and compete events sanctioned annually by the

Society of Automotive Engineers (SAE) in North America to promote real-life experience in a

collegiate environment. MIT Motorsports specifically competes in the FSAE Electric competition,

which takes place every June and hosts forty teams that spend four days presenting their designs

8

to industry judges, arguing their business cases, and driving on-track to compete with hopes of

proving their car to be the strongest competitor. Developing a new car for the annual competition

in Lincoln, NE gives FSAE team members the opportunity to learn multiple subsystems and

understand how to approach a new design problem within a larger system before graduating and

entering industry. A 175-page book [1] dictates the overall competition rules, but an understanding

of the competition's environment drives the design considerations that affect the final competition

vehicle and motivates the team's priorities during a vehicle build cycle. The cars competing in the

electric category can fit drivers ranging from a 5 th percentile female to a 9 5' percentile male and

are constrained by an 80kW power limit for a roughly 220kg vehicle.

.%ZVAM3MM-. JE 206

Figure 1: A photograph of two Formula SAE cars competing at the Lincoln competition.The vehicles competing at the event are often constrained by team size, budget, andexperience, which leads to significantly different vehicle architectures. [3]

The underlying motivation driving the competition is an idea that these are cars designed

as prototypes for low-cost performance cars that would be appealing to enthusiasts who enjoy

driving autocross courses (a circuit defined by cones in a paved space) on the weekends. Although

this doesn't significantly affect the dynamic events, the motivation greatly affects the judged static

events. Designing a suspension system that is dampened by adjustable shock absorbers is

encouraged; however, a weekend enthusiast may not be as knowledgeable as a design engineer

when it comes to tuning the car, so the addition of weight from cockpit-accessible adjustment

devices would have to be justified over simple shock absorbers that have adjustment mechanisms

built in. Similarly, a carbon fiber seat may appeal to the students designing the car, but if that

additional cost cannot be justified over a cheap, moldable foam seat, then competition points may

be more difficult to acquire.

9

The prior considerations dive into external factors that may affect performance during events

at competition, but the greatest factor that comes into play at competition is the fact that an FSAE

car is a student-built vehicle that is prepared and operated by students attending a university. Many

of these students encounter thorough design reviews for the first time in their careers, but are

constrained by a lack of experience, time, and conceptual knowledge. The performance of

subsystems within the full vehicle cannot be validated until the car is complete, so the most senior

members of the team have three iterations of personal work assisting their final designs. In addition

to this, all team members are constrained by their class schedules and the team's budget

constraints, which significantly decreases the amount of time that can be used to explore alternate

approaches to part design. Great caution is critical when finalizing the design because despite

significant effort, the previously mentioned constraints can induce unexpected issues.

Keeping the event's complexities in mind, the suspension kinematics were designed to

maximize vehicle performance by simplifying the design goals to critical figures that could be

maintained reliably through the manufacturing and operation processes of the car.

1.2. Kinematics in a Performance Vehicle

The suspension of a car consists of elements that connect the wheel assemblies to the vehicle

structure and the components that control movement of the wheels relative to the vehicle. This

movement is constrained to a single path, which equates to five degrees of restraint [10], where

the only motion is the wheel package following the trajectory of the outboard suspension linkage

points. Modern formula-style cars utilize a double wishbone suspension setup to achieve this due

to the low weight and structural simplicity of the linkages. This setup is characterized by two A-

Arms that each connect two points on the frame to a ball joint on the wheel upright and a linkage

to transmit forces from the wheel through a spring-dashpot system then into the chassis. The

linkage can be designed to push (compress) or pull the spring and dashpot when the wheel

encounters by designing the linkage to connect to the bottom or top A-Arm respectively. Although

the kinematics are not affected by the linkage (a pushrod in the case of the cars presented), its

performance dictates the A-arm size, which feeds into the geometric constraints. Figure 2 shows

the front suspension assembly on the team's 2017 vehicle and labels the relevant components to

the kinematics' design process.

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Figure 2: A photograph of MIT Motorsports' 2017 car with labels indicating the key

components in overall suspension design. Although not all components are relevant to thesuspension kinematics, they remain important for packaging.

It is readily apparent that the suspension points (the points in space where the suspension

linkages connect to the wheel or frame components) directly impact packaging, but the beauty in

the suspension points lies in the fact that they go beyond the structure to also dictate the dynamic

ability of the vehicle through the tires and vehicle weight transfer. From a tire standpoint, the

suspension geometry affects the contact patch (the area that both surfaces are in direct contact),

which couples with the tire to dictate how much lateral acceleration the car can achieve in a corner.

On the weight transfer side, the geometry produces a roll center (explained in section 2.1) about

which the vehicle's center of gravity rotates about when cornering on a track. Understanding the

vehicle's mass in relation to the roll center point makes it possible to control the vehicle's weight

transfer through a corner, significantly improving the driver's ability to navigate a course

Achieving the optimal camber change throughout the range of vehicle motion maximizes the

contact patch during operation, but more significantly, it maximizes the efficiency. Camber is the

11

.1

angle between the side plane of the car and the plane parallel with the wheel. As lateral forces

increase in a turn, the vehicle's weight is transferred to the outside, and the tires take the brunt of

it. If tires were mounted perpendicular to the ground, their grip performance would only decrease

with cornering speed because less tire would be in contact with the ground (more would be lifted

into the air by reaction forces) as speed (and therefore force) increased. Using this knowledge,

suspension geometry can utilize camber to improve vehicle cornering.

Steering linkages also interact with the suspension kinematics because vertical and angular

movement of the car relative to the wheels can induce a phenomenon called bump steer. Resulting

from negligence when designing steering linkages, bump steer is the tendency of the wheel of a

car to steer as it moves upwards. Although steering geometry will not be discussed here, the

kinematics of the suspension remain critical to steering control because neglecting small factors

can lead to lower levels of cornering grip, improper tire wear, and straight-line instability, which

do not appeal to judges nor the teams.

1.3 Scope of Project

MIT Motorsports begins its vehicle build cycle in July to be ready for competition the

following June and achieves this timeline by dividing the mechanical and electrical systems into

subsystems with lead engineers to review progress at various system complexities. Every

subsystem from frame to software is affected by suspension through parameters such as the

stiffness required to handle the weight transfer to the packaging space available in the frame to

secure the low voltage system. Figure 3 outlines the division of labor to produce the 2018 car and

provides an idea of the subsystems that are affected in one way or another by the kinematic

requirements of the car.

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Frame

Wheel Packages

Brakes

Steering

Suspension

A-armsChief Engineer ARB/Rocker

Pedal Box

Captain Powertrain Members

Battery

Enclosure/Harness

Aero

E d Low Voltage

Software

Research and Development Team

Business Team

-~ Publicity Team

Figure 3: A chart of MIT Motorsports' 2017-2018 team structure developed to producethe 2018 car. The first 6 subsystems in the 3"' column from the left are directly affected bythe suspension kinematics, while the rest are indirectly affected by the resulting geometriesthat occur to maximize suspension performance.

The team's suspension kinematic goals for the 2018 car were to maximize the contact patch

on all four corners of the vehicle and to minimize the front and rear roll centers' movement from

their designed locations. With this in mind, the geometry considerations of the steering system will

not be discussed beyond bump steer. Similarly, the kinematic calculations of the anti-roll bar

(ARB) and rockers, which manage the cornering forces' effect on the vehicle's weight transfer

will not be detailed below. These factors do play into the physical components of the suspension

and its transient states during operation, but the geometry discussed below will only focus on what

relates to the suspension kinematic goals.

2. Background

Comprehensive suspension design takes into account the suspension kinematics, the control

of the vehicle's weight transfer during dynamic events, and the structures associated with joining

the sprung mass of the vehicle (everything that has a spring-dashpot system between the

component and movement relative to the ground) to its unsprung mass (the wheel and tire assembly

and the suspension connections). The suspension kinematics act independently of the structural

integrity of the system and is only affected by the weight transfer in that the transfer dictates the

maximum lateral acceleration and therefore, the maximum roll of the chassis (found through

13

calculated weight transfer rates) relative to the ground. As a result of this, the suspension

kinematics use the maximum roll value, but do not require a full understanding of the transient

dynamics of a vehicle traversing a course. With this in mind, the provided background will focus

on the metrics used in a kinematic analysis that determine the success of a particular suspension

geometry.

2.1. Roll Center

The roll center of a car dictates the magnitude of the moments that arise during cornering,

affecting both the transient and steady state values of the car. Although the transient values of the

suspension -such as the chassis roll rate and the shock absorber damping - do not pertain directly

to the kinematic analysis, the roll center's position and movement make a significant impact in

calculating the requirements of the transient system. More important to the kinematics side, a roll

center below ground will cause significant vertical motion in the chassis relative to the wheels

during cornering, decreasing the efficiency of the aerodynamic package and destabilizing the car.

Understanding the roll center concept requires a quick overview of rotating linkages. The

center of rotation is the fixed point around which a body moves angularly. Going further, when

two linkages are moving in a kinematic system, the intersection of their two centerlines form an

instant center. Put another way, the instant center is the point at which two linkages intersect if

their lengths were to be extended to infinity. This can be seen for both sides of the vehicle

diagrammed in Figure 4 at the points labeled "IC," and provides valuable information by indicating

how a vehicle's tires' camber will change if mapped. In addition to this, it provides the information

necessary to determine the car's roll center as well.

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-ICIC . - -

.RCH -- --- ~~RC---

Figure 4: A diagram of a vehicle's suspension linkage geometry with the instant centers

of each tire labeled "IC" and the resulting roll center labeled "RC." The instant center on

the left of this page is that of the right wheel and the instant center on the right is a result

of the left wheel's suspension geometry [10].

Using the instant center related to each side of the car, the roll center of the vehicle can be

determined. As seen in Figure 4, the roll center is the intersection of the two lines that connect the

instant centers to their respective contact patch center. Varying the geometry of the suspension

linkages directly affects the magnitude of the roll center movement, making it more difficult to

model the transient behavior of the vehicle. Modeling the behavior during cornering focuses on

the lateral forces that arise on the sprung mass at the center of gravity, which induces a rolling

moment around the roll center. Therefore, as the roll center gets higher off the ground, the moment

decreases and the sprung mass is affected less by lateral forces. This consideration does not hold

direct significance in the kinematic design but remains critical to ensure that the suspension

geometry is not wasted by a car that can neither enter nor exit a corner.

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.....-.-4 Fy at COG

* *z

ZR

Fy at tire

Figure 5: A figure showing a representation of the jacking effect. As lateral force (Fy)increases on the tire, a moment about the vehicle corner's instant center forms. The jackingeffect is the transmission of this moment into the tire, which pushes the tire into the groundand results in the sprung mass rising relative to the tire [10].

Although movement of the sprung mass about the roll center holds only a small significance

with respect to the suspension's kinematics, movement of the unsprung mass requires a greater

focus on the roll center. The unsprung mass of each wheel package and tire rotates about the

corner's instant center. Thus, as the lateral force on the tire increases, the moment on the center of

gravity about the instant center increases (as seen in Figure 5). As shown above, the resulting

moment pushes the tire into the ground with an instant center above the ground plane, lifting the

sprung mass up slightly. However, if the instant center is below the ground plane, the wheels will

be lifted up relative to the sprung mass, lowering the chassis and potentially causing ground

clearance issues that cannot be mitigated without compromising steady state longitudinal driving.

With aerodynamic balance and a higher normal force on the tire at stake, a roll center above ground

is standard.

2.2. Camber

Without camber, a car could not maximize its tires' performance when that performance is

most needed: the middle of a turn. Camber is the angle that the tire centerline makes with the

ground and is used to maximize tire performance while cornering by sacrificing straight-line tire

performance. This is done by inducing a negative camber on all four tires while the car is at a

static resting position, as can be seen in Figure 6. As the car enters a corner though, the vehicle

weight is pushed outward, and the outside tire gains positive camber. Tire performance is

maximized in a corner when the tire achieves 0* at peak lateral acceleration because the area of

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contact (contact patch) between the tire and the road surface is maximized. Achieving the peak

contact patch maximizes the rubber that can be used to produce grip, which in turn maximizes

the speed that a car can maintain through lateral movement.

Front 9iew

Centerfine of wheel

Perpendicular tothe road surface

Figure 6: An illustration of negative camber on a simple axle. If the top of the tires lies

further from the vehicle centerline than the bottom, then the positive camber is positive [2].

If the tires do go beyond the 0' line, the positive camber would discourage the driver from

achieving the limit of the car's capabilities because it would induce more wear on the tires for a

smaller increase in cornering speed, degrading performance over time. To prevent this from

occurring, unequal A-arm lengths are used to change the rate at which camber changes as the

chassis rolls over due to the cornering force present as a result of the vehicle's weight. The rate

at which the camber changes is dependent on the length between the upright and the instant

center of the connecting arms. Therefore, when designing the suspension geometry, a longer

lower A-arm length can be used to slow down the rate of camber change through a vehicle's

range of motion, while a shorter upper A-arm length can speed up the rate because the shorter

length increases the angle change of the wheel package when the same magnitude of

displacement occurs. To account for this relationship, standard practice dictates that the length of

the upper A-arm is 50-80% of the lower A-arm length when designing a Formula SAE car.

Taking this into consideration during a kinematic analysis, the camber can then be adjusted

through a further iteration to ensure that unnecessary tire wear doesn't occur.

2.3. Bali Joint Geometry

Whereas the front plane A-arm geometry dictates the camber and roll center characteristics,

the ball joint geometry is closely involved in the relationship between camber and steering. Not

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-A

only do the inside and outside tires travel different distances in a corner, they also experience

camber change at different rates. To design a system that achieves camber and tire heat as close to

optimally as possible, the kingpin angle, scrub radius, caster angle, and mechanical trail require

attention, as they can be adjusted to take advantage of the upright's characteristics.

Kingpin inclination

Wh6IOftet - UPperlJoin1(High)

SPMnO Lengip (4)

Location Upper Ball Joint (Low)

(Front Steer)

Figure 7: A diagram depicting the significant measurements related to ball joint geometryon the wheel upright [8].

In a design that features no kingpin angle nor caster angle, the camber will remain constant

throughout a steering motion because the ball joints form a line perpendicular to the ground plane.

While a lack of camber change may not detract from vehicle performance, it leaves room to

improve the car's handling characteristics, which improves driver response and in turn, the car's

success in a competitive environment. Caster angle is the angle between the steering axis (line

formed by the two ball joints) and the wheel centerline extending perpendicular from the contact

patch. Its presence decreases the inside tire's negative camber and increases the outside tire's

negative camber while steering, allowing both tires to operate closer to their optimal positions.

Complementing the caster angle, a kingpin angle can be added by moving the upper ball joint

towards the chassis or the lower ball joint away from the chassis, which induces positive camber

on the outside wheel when steering. Inducing positive camber may sound like a poor choice, but

the effect of the kingpin angle means that the inside wheel's camber can be design to be less

negative during steering inputs via caster without worrying about the outside wheel gaining too

much negative camber. With a proper balance of kingpin and caster angles, the difference between

front and rear tire wear that normally occurs becomes less significant.

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The scrub radius and the caster trail, which can be seen in Figure 6, result from the

kingpin and caster angles, but play their own role in improving the steering response by dictating

the amount of force required to turn the wheel about its steering axis. Both parameters can be

tuned by the height of the ball joints relative to the ground, and while they both affect steering

response, their manifestations differ. The scrub radius produces a moment that must be overcome

to steer the wheels, which dictates how quickly the tires build up heat as well as how much effort

a driver must input to maintain control throughout operation of the car. Similar to the

complementary relationship of the angles, the caster trail complements the scrub radius by

inducing a self-righting effect in the tires where they return to the forward path provided no other

input.

All four parameters are developed in formula SAE applications from empirical evidence

where suspensions are built to focus on the camber and roll center parameters rather than the ball

joint parameters. Eventually the performance maximization leads to the ball joint parameters

being compromised in the production of a car that has undesirable steering effort. Although it

can be mitigated slightly by steering linkage geometry, these trials have led to a conservative

range of values that allow a balance of the steering effects without pushing the limit of what a

driver can handle.

3. Methods

The suspension point design process consists of collecting expected constraints from the

subsystems that are directly affected by the design, producing an initial set of analyzed points, and

then iterating until the subsystem designers are happy with their packaging and the suspension

kinematics' metrics are met. This iterative process enables the inboard points (points closer to the

driver) and outboard points (points within the wheel assembly) to move with more freedom

because they can move at the expense of each other without compromising the kinematics. A

perfect suspension design method has yet to be created for vehicles because of the dynamic and

packaging constraints unique to each vehicle. Because of this, establishing hard requirements that

cannot budge and soft requirements that can be stretched are key to success in the geometry

development process.

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3.1 Design Requirements

Four hard requirements and five soft requirements constrained the design to achieve a rules

compliant, kinematically successful vehicle. The hard requirements were in place to ensure that

the design allowed for full wheel travel relative to the chassis while also avoiding unnecessary tire

wear and instability. Meanwhile, the soft requirements focused on maximizing tire efficiency

while cornering and improving the predictability of the vehicle's weight transfer and steering

response for the driver.

The need to achieve rules compliance resulted in the hard requirements that the suspension

linkages do not contact other components of the car if the wheels travel through their full range of

vertical motion, as well as if the wheels are turned to achieve the minimum turn in the competition.

To substantiate this with numbers, there could be no contact if the wheels travel vertically 25.4mm

in either direction nor with the steering input required to make a turn with an outside diameter of

9.Om [1]. Although they fell under suspension rules, these were critical considerations for the A-

Arms, uprights, brakes, frame, and steering subsystems. While many iterations were necessary,

they were critical for each subsystem and therefore did not require the amount of compromises

that went into achieving the soft requirements.

Beyond rules compliance, the most important hard requirement was that no tire camber

becomes positive during normal usage of the car. As discussed in section 2.1, positive camber

indicates that the suspension was not designed for the actual cornering ability of the vehicle or that

a component has broken during vehicle operation. Positive camber puts the load on a corner into

a more concentrated area, causing quicker and more excessive tire wear while the car is at its peak

cornering speed. Static camber adjustments from the designed value can minimize manufacturing

issues, but a hard limit was placed on the designed camber change to prevent it from going beyond

0' at maximum lateral acceleration.

The final hard requirement was that no bump steer existed in the rear and that front bump steer

was minimized to where wheel travel in a positive vertical direction produced the same steering

angle as that of wheel travel in a negative vertical direction. This ensured that the car was as stable

as it could be during operation, minimizing the driver effort to maximize performance in the

dynamic competition events.

Whereas the hard requirements ensured that the vehicle cannot become hazardous during

operation, the soft requirements focused on maximizing the suspension's performance to achieve

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the goals of maximizing the contact patch on all four corners of the vehicle and minimizing the

front and rear roll centers' movement from their designed locations. Leading the soft requirements

was that the camber change curve achieves 0' camber for the outside tire at maximum lateral

acceleration (or maximum cornering speed). Camber changes less through the designed range of

vertical travel than through the range of chassis roll, so the lateral acceleration (which induces roll)

serves as the best means of maximizing tire performance without exceeding the positive camber

hard requirement.

In line with the previous requirement, the other soft requirement related to the camber was

that the front and rear camber values should be within 10% of each other at full vertical travel as

well as at maximum lateral acceleration. Static camber could have been adjusted if the maximum

camber values differed significantly, but uneven tire wear would have resulted due to more

concentrated loading on the tires with greater static camber. With uneven tire wear, the

replacement rate of front and rear would vary, but more importantly, the car could not be tuned to

handle well for an entire endurance run due to the changing front/rear grip balance over the course

of normal operation. Therefore, while it was a soft requirement, the camber trends of the front and

rear remained significant in the list of considerations while completing the design.

As long as a vehicle's roll center is above ground and doesn't move many meters during

operation, the vehicle performance will not suffer significantly. However, the soft requirement for

the roll center positions dictated that the front roll center should have a static height between

6.4mm and 12.7mm while the static rear roll center should be between 25.4mm and 38.1mm. This

ensured that the front end of the car possesses a greater moment about the roll center relative to

the rear when cornering, which prevents the car from losing stability due to an unpredictable rear

while also giving the front end a faster response to turning motions given the same spring rates.

Minimizing the roll center's movement also was a soft requirement because it further aids the

vehicle stability while also making the system easier to model for vehicle simulations.

The final soft requirement, which entailed that kingpin angle and caster angle were between

10 and 40with a scrub radius and mechanical trail near 12.7mm, was implemented to ensure that

the tire camber during cornering did not destabilize the car when the steering wheel was turned.

These ranges and aims result from generally recommended rules of thumb and empirical data from

previous cars produced by MIT Motorsports. The restoring effect usually associated with caster

and a general degree of feeling within the steering of the team's 2017 and 2016 cars, which had

21

values on both edges of the angle range, indicate that the requirements were sufficient to produce

a satisfactory result. With this in mind, the design focused more on the higher value requirements

that more significantly affected performance while monitoring these figures at the same time.

3.2 Design Method

Before any designing started, a few basic parameters required establishment. The vehicle's

wheelbase (distance between the centers of the front and rear wheels) was minimized at 1.524m -

a minimum value dictated by the rules - to make it as easy to navigate the tight cone courses

present at competition. Likewise, a track width of 1.219m (distance from the center of the right

tire to the center of the left tire) and wheel size (457mm radius tire on a 254mm rim) was decided

before design began, dictating boundaries for packaging the upcoming suspension points. Upon

establishing the initial design parameters and adding them to the requirements above, the starting

suspension points were chosen. Using the 2017 vehicle's parameters, necessary changes were

made and implemented to update the system to become rules and constraints-compliant before

entering the designs of every subsystem involved. This section details the step-by-step process that

ensured the success of the team's 2018 car once the starting points were determined.

Feedback & Update M - Rol

Requests from -ete - n .CamberHardware Teams Req-irem-n-

Figure 8: A flow chart of the feedback loop that guides the suspension point designiteration used to meet the performance requirements of the suspension system. The greenbox is where the entire process starts and the location that each subsequent iteration starts.The blue boxes represent the steps required to produce a new iteration. The red box iswhere the design iteration finishes for team review, and the yellow box represents theperiod of analysis from the interfacing subsystems between iterations.

22

As seen in Figure 8, realizing the constraints of each subsystem interfacing with the

suspension was the first step in maximizing performance once the initial points were determined.

Although the hard and soft requirements set constraints that affect the performance of the

suspension system, further consideration was required throughout the iterative process with

regards to the frame, steering, A-arms, wheel packages, and brakes systems because their

constraints varied over the course of the design process.

During the design of the 2018 car, structural constraints changed most often, resulting in a

changing list of constraints. However, in general, each system dictates their own set of standard

constraints that always play into the suspension geometry. The packaging of the powertrain in the

rear of the vehicle dictates the height of the inboard points to a degree because additional mass in

the frame would be required via an extra tube if the points were to significantly differ from the

locations of the frame tubes used to structurally support the motor and differential. Additionally,

the steering system cannot contact the A-arms nor the frame, which constrains the designer's

ability to eliminate bump steer entirely. Meanwhile, the wheel uprights require the ball joints be

spaced far enough apart to allow for the hub assembly to fit, while the wheel constrains the

maximum separation between joints. Because the points are not connected via infinitely thin

components, the thickness of the A-arms and its components must also be accounted for, which

requires iteration because their thickness is directly dependent on the geometry. Many of these

constraints only affect one or two of the points in a single direction, but altogether, they define a

finite number of possibilities that can be explored to maximize performance.

Once all of the constraints are defined for an iteration, the balancing act of changing points

within the constraints begins. The frame geometry for example may significantly change if a new

course of action is taken to meet its stiffness requirement. Some iterations simply require the points

be moved into the new range to see an improvement. When an old constraint is replaced by a new

one, it does not always result in a performance loss. Comparing performance figures of the points

in the initial configuration versus the updated configuration sets the tone for the level of

compromise that will be required in the iteration.

23

Car Centerline

Figure 9: An image of the suspension point sketch used in Solidworks@ that defined thesuspension geometry within each of the component files that interfaced with thesuspension. Each iteration of geometry was entered in this sketch, which then assistedclearance and structure checks during the iterative process.

With the new constraints in mind, the performance maximization within the roll center and

camber requirements can begin. The points are first analyzed in their newly constrained

configuration via Wingeo, a software that performs the kinematic calculations throughout the

range of wheel travel, chassis roll, and steering input. This produces the roll center position and

camber angles of the tires, which can then be compared to the unconstrained initial baseline values

as well as the requirements in section 3.1 to determine the ensuing steps. If the figures show an

improvement, the point should be moved to the greatest possible magnitude in the direction of the

initial adjustment to maximize the performance increase resulting from the new constraints.

Similarly, if the figures deteriorate with the new constraints, the next step is to minimize the

coordinate change from the previous iteration. In the situation that the coordinate change remains

significant in deteriorating the suspension performance, other points become the focus. Therefore,

if the upper ball joint must move positions and significantly reduces the camber change through

wheel travel, the lower ball joint and upper frame (inboard) points become the new focus.

Maximizing all of the parameters becomes a balancing act where one fix for camber prohibitively

affects the roll center movement, so a cost-benefit analysis often occurs in this step of an iteration.

24

Front Wheel

1J

Rear Wheel

F T Fgrmal SAE c:rf et imcnem anc aecUnalysintssftratqrsmy bOcetsane77 aeacmaette ofChbeid . is t1 aise

Cambe RCamber-I .957. 1.W-6.117

6t*OrOS Steere

Scrub Scrub

Cagter Kingpin inspin Candr-3.46 -1.412 -3.252 -3.468-0.721 1.63S 1.637 -4:794

Ins.Cee. Nell Can iea.Cen.71.64? -4 .653 SS.6"

4.6"5 1 .263 3.162

Figure 10: A screenshot of the outputs from the kinematic analysis software-Wingeo- described in the Design Method section. After inputting the suspensiongeometry, the software can calculate the critical kinematic parameters when the wheelheight varies, the chassis rolls, and the tires are steered.

Once the camber and roll center values produce an acceptable balance, the upright

geometry becomes the primary focus to make sure that the ball joint geometry improves the

steering-camber relationship rather than hindering it. Ideally the kingpin, caster, scrub radius, and

mechanical trail are within their design ranges after the previous step. If the ball joint geometry

can be mitigated by moving the inboard points without significantly affecting the camber and roll

center, that is the preferred option. When that mitigation strategy is not an option, the angles should

be maximized to 4* or minimized to 10* to minimize the effect on the suspension performance.

Likewise, the scrub and mechanical trail should be set to an edge case of the 12.7mm to 50.8mm

range. Although these metrics play a role in the driver's feeling in the car, their exact value can be

overcome by driver training and conditioning, lowering their relevance.

Upon confirmation of the upright geometry, each of the points affecting the A-arms and

frame are locked in for the iteration. Completing the iteration requires adjustment of the tie and

toe rod linkages to minimize bump steer throughout the vertical travel of the wheel. In the rear,

the task is simply to make sure that when looking at the car from the front, the two toe rod points

are in the same plane as the lower A-arm. In the front, due to the connection with the steering rack,

the tie rod must be tuned to minimize the steering angle at the top and bottom of the wheel's range

of travel. Placing the outboard point of the tie rod further from the ground plane than the lower

25

ball joint on the upright lowers the bump steer because it's axis of rotation becomes more similar

to the instant center of the A-Arms. However, only so much can be done due to packaging

constraints within the wheel and on the upright.

With suspension points resolved, the iteration can be released to the team for component

updates and clearance checks. As the design phase of the project progresses, the changes by the

hardware teams after suspension point updates become increasingly smaller, changing from

structural constraints to clearance constraints with the wheel and other components. Once each

subsystem design has been updated to use the points and a clearance check has been completed,

feedback is collected to determine if a further iteration is required. Even if an iteration is not

required, further work may be beneficial if an old constraint is lifted by the updated design. This

feeds back to the start of the process, with the last iteration providing the new starting points to

repeat the cycle. Only with sufficient clearances and design requirements achieved does the cycle

stop with a completed set of suspension points.

4. Results

Starting with the suspension geometry from the team's 2017 car (MY17), the 2018 car was

developed under new constraints dictated by the interfacing subsystems. The high-level design of

the car remained roughly the same as MYl7 with a 1.524m wheelbase, a 1.219m track width, and

254mm wheels surrounded by 457mm tires. This was intended so that it would allow more time

for testing and validation before competition by minimizing the design time. In action, the design

phase required a nearly equal amount of time because of packaging constraints unique to the 2018

design.

The initial suspension geometry required small deviations in both the ball joints and frame

points before an initial suspension geometry could be produced. Different ball joint positions were

necessary to accommodate a new upright design that required more space. Rear frame points

became closer together and closer to the ground because the battery packaging for 2018 minimized

the width of the frame, and therefore allowed more design freedom for the suspension geometry.

Upon completing the initial geometry, its camber and roll center were examined over the planned

operating range of movement, yielding a baseline answer that the suspension performance would

indeed be similar to MY 17 on the 2018 car.

26

-Initial Front Geometry0- MY17 Front Geometry -

Initial Rear GeometryMY17 Rear Geometry

-0.5-

o -1 -~F

-2-

-1.5 -1 -0.5 0 0.5 1 1.5Chassis Roll Angle ()

Figure 11: A plot of the left tire's camber change over the expected roll angles during the

car's normal operation. The Initial geometry resulted from necessary tweaks to the MY 17

geometry to achieve initial packaging and rules compliance for the 2018 car.

Comparing the initial 2018 geometry to that of MY17 indicated similar performance because

both of their roll center heights remained relatively static throughout wheel movement via bump

and roll actions. Figure 11 illustrates that although the camber curves did vary between the initial

points and previous year's points, they still followed a similar trend with an acceptable level of

deviation. With the kinematics analyzed and design requirements met, the ensuing time was spent

preparing for packaging constraint issues that would arise due to the redesigned structures of the

2018 car.

This new constraint came in the form of a frame packaging issue where the frame designer

was attempting to make the frame rules compliant by raising the bar that the suspension mounts to

vertically. This led to a significant issue in terms of suspension geometry because the outside wheel

camber in a roll situation became positive, which broke a kinematic hard requirement. Without an

easy fix to remedy the camber issue appearing, a design study was performed where each point

affecting the geometry was moved vertically and laterally in both directions to develop an

understanding of where a solution might reveal itself. A few of the trials from this study are listed

in Table 1, where the results of interest were predominantly in the Right Camber column.

27

Right Roll Center Roll CenterIteration Camber Delta Lateral Delta Height Delta

MY17 -0.099 N/A -0.396 N/A 0.284 N/A

Base 0.382 0 -0.767 0 0.315 0Upper Inboardpoint Down .5" 0.179 -0.203 -0.137 0.63 1.009 0.694

Upper BJ up .5" 0.2 -0.182 -0.543 0.224 0.945 0.63Lower InboardPoint Up .5" 0.263 -0.119 -0.13 0.637 1.518 1.203Upper InboardPoint Outward .5" 0.372 -0.01 2.023 2.79 0.328 0.013Lower Inboard -Point inward .5" 0.38 -0.002 2.535 3.302 0.313 0.002

Table 1: A table detailing a selection of the possible remedies for the positive camber issue. The baseiteration represents the geometry that contained the problem and the results that came from it. The red

rows were not suitable changes due to undesirable changes in the roll center's height.

The study revealed two helpful insights for completing the suspension design because it

illustrated how each type of movement by the point could affect the kinematic properties of the

suspension and more importantly, revealed that a new solution would be required to satisfy both

the frame and suspension kinematics' design requirements. Each of the variations that yielded

significant improvement with regards to the camber displayed significant increases in the roll

center height that could not be mitigated by other geometric adjustments. Removing those for the

purpose of achieving a design compromise, the lower two changes in the table were the best

options for moving forward. However, their improvement over the base camber was negligible at

best.

28

Figure 12: Images of the front left A-arm on the 2017 (top) and 2018 (bottom) cars. The

circled area highlights each A-arm's rearward inboard suspension point. The arrow indicates the

mitigation of the frame vs. suspension point issue by manufacturing a tab that could attach to thelower side of the frame tube triangulation.

Having exhausted the possible solutions from the suspension kinematics' standpoint, the

frame was changed to remedy the camber issue by placing the suspension points along the

predominantly vertical structural tubes that connect the lower and upper steel tubes that produce

the driver cell. This was a critical point in achieving the final optimization because it allowed the

frame to vary through different configurations without constraining the suspension geometry.

After 86 iterations ranging from small A-arm dimension changes to changing the range over which

an upper inboard suspension point could be placed, a final iteration was confirmed as suitable for

manufacturing. The performance figures for the design are shown in Table 2, but in addition to

maximizing the car's performance through those values, bump steer was eliminated in the rear and

minimized to 0.090 for both upward and downward wheel travel in the front.

29

Front Rear

Static 1.5* Roll 1" Bump Static 1.50 Roll 1" Bump

Roll Center 0.377 in .374 in 1.47 in 1.376 in 1.383 in 2.399 inHeight

Roll Center 0 in 3.222 in 0 in 0 in 0.003 in 0 inLateral Position

Inside Camber -1.0000 -2.0540 -0.32* -1.0000 -1.957* -0.168*

Outside -1.0000 -.0120 -0.32* -1.0000 -0.1170 -0.1680Camber

KPI/Scrub 4.168' 0.856 in KPI/Scrub -2.37' 1.636 in

Caster/ 3.33' 0.5 in Caster/ -3.457 0.782 inCaster Trail Caster Trail

Table 2: A table listing the suspension's kinematic characteristics expected for the final suspensiongeometry at rest, at maximum lateral acceleration (roll), and at maximum wheel travel (bump) as well as

the ball joint geometry measurements in the front and rear of the car. Imperial units were used forsuspension analysis due both to the competition's rules originating in Imperial and the Wingeo software

only outputting distance in inches. For reference, lin=2.54cm.

The final geometry sufficiently achieved the design requirements; however, a few values

require discussion to properly validate their existence. Comparing the front and rear roll centers at

1.5* of roll, indicates a consistent system from the perspective of the roll center height; however,

the front roll center travels significantly more over the course of a rolling motion. While this wasn't

an ideal value, it was required to achieve the camber curves desired, so because the roll center

height was relatively stable, the compromise was made to allow the lateral movement. Similarly,

the kingpin angle and scrub radius pushed the edge of the soft requirements by exceeding the

desired ranges. This also was compromised for the camber change relationship because the effect

of changing the ball joint geometry to improve KPI induced a positive outside camber, which is

significantly less desirable than a slightly larger angle and radius.

30

Initial Front Geometry0- MY17 Front Geometry -

MY18 Front GeometryInitial Rear GeometryMY17 Rear Geometry

-0.5 - MY18 Rear Geometry -

EC. -1-

-2

-1.5 --

-1.5 -1 -0.5 0 0.5 1 1.5Chassis Roll Angle (')

Figure 13: The relationship between the left tire camber and chassis roll in a corner for the2017, 2018, and initial 2018 iteration of the car's geometry.

2.5

2-

1.5

0.5

0- Initial Front GeometryMY17 Front GeometryMY18 Front Geometry

-0.5 -- Initial Rear Geometry -MY17 Rear GeometryMY18 Rear Geometry

-1--1 -0.8 -0.6 -04 -0.2 0 0.2 0.4 0.6 0.8 1

Bump Travel (in)

Figure 14: The relationship between the roll center height and wheel's travel over a bumpfor the 2017, 2018, and initial 2018 iteration of the car's geometry.

Although the necessary compromises prevent every performance figure from becoming

optimal in every system, the camber and roll center height movement indicated that the suspension

will perform well in a dynamic environment. The 2017 car accumulated weekly testing data from

June, 2017 to September, 2017 and its handling ability was empirically found to be agreeable by

the team's drivers whose experience varies from semi-professional auto racing to previous testing

events accumulated while being a part of MIT Motorsports. Therefore, the similarities in the

camber curves between the MY18 and MY17 kinematics (shown in Figure 13) indicated that the

31

2018 geometry could take full advantage of its tires' capabilities. Likewise, the roll center height

change in the final geometry was determined to vary less than MY 17's, which not only made the

car more predictable to drive from a driver's standpoint, but also easier to model for further

calculations in designing the remainder of the car.

5. Conclusions

Despite the packaging challenges that develop while looking to achieve kinematic goals, the

resulting gains in tire performance and system predictability prove the significance of the design

process. By ensuring that the final figures were within the requirements' ranges, the design allowed

MIT Motorsports' 2018 car the greatest chance of extracting the greatest possible performance

from its tires in a competition, testing, or general performance driving environment.

The build cycle timeline for the 2018 car places the vehicle in the debugging stage at the time

of writing, so physical validation of the suspension geometry's performance has not been

completed and will not be possible until unreserved performance driving occurs. The simulated

numbers indicate similar characteristics to the 2017 car with improved camber change

relationships. Manufacturing methods (including jigging and welders) did not change between the

build cycles and the previous car placed second at the Formula SAE Electric competition in 2017,

so it can be gathered that the 2018 design successfully met its goals.

To take this work further in the future, improved validation methods beyond tire wear and

camber inspection via photographs would be the primary focus. Although tire wear and lap times

are reliable indicators of a vehicle's overall performance, they come up short when validating

whether a particular ball joint configuration made a significant impact on the driver's interfacing

with the car. Similarly, a second route to explore is validating the camber angle through the roll of

the car in a turn, which would provide more information than patterns on the tire that can change

over the course of an event.

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6. References[1]

2016, "2017-18 Formula SAE Rules." [Online]. Available:https://www.fsaeonline.com/content/2017-18%20FSAE%2ORules%209.2.16a.pdf. [Accessed:03-May-2018].

[2]Santa Fe Garage, "A Discussion on the Handling Effects of Camber." [Online]. Available:http://www.santafegarage.com/precision-alignments/camber-explained/. [Accessed: 06-May-2018].

[3]John Burchardt, 2017, A Photo from the Formula SAE Lincoln Competition.

[4]Adams, H., 1992, Chassis Engineering, Penguin Group, New York.

[5]Samant Saurabh Y., Santosh Kumar, Kaushal Kamal Jain, Sudhanshu Kumar Behera, DhirajGandhi, Sivapuram Raghavendra, and Karuna Kalita, 2016, "Design of Suspension System forFormula Student Race Car," Elsevier Ltd.

[6]Smith, C., 1996, Drive to Win: The Essential Guide to Race Driving, Carroll Smith ConsultingIncorporated, Rolling Hills Estates, CA.

[7]Smith, C. 1984, Engineer to Win: The Essential Guide to Racing Car Materials Technology,Carroll Smith Consulting Incorporated, Rolling Hills Estates, CA.

[8]User: hifiandmtb, 2013, "LotusTalk Forum." [Online]. Available:http://www.lotustalk.com/forums/2322089-post12.html. [Accessed: 07-May-2018].

[9]Smith, C., 1975, Prepare to Win: The Nuts and Bolts Guide to Professional Race CarPreparation, Aero Publishers, Inc.

[10]Milliken, W., and Milliken, D., 1995, Race Car Vehicle Dynamics, Society of AutomotiveEngineers.

[11]Smith, C., 1978, Tune to Win: The Art and Science of Race Car Development and Tuning,Carroll Smith Consulting Incorporated, Rolling Hills Estates, CA.

[12]ICT Workshop Solutions, "Wheel Alignment - Part 2" [Online]. Available:http://www.ictworkshopsolutions.com/2011/06/wheel-alignment-3/. [Accessed: 07-May-2018].

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