Design of a Formula Student

Race car Spring, Damper

and Anti-roll Bar System By Keiran Anthony Stigant

XE337 – Group project

Supervisor: Dr Khizer Saeed

March 2015

Final year report submitted in partial fulfilment of the requirements for the degree of Bachelor of Science (Honours) in Automotive Engineering.

Disclaimer I hereby certify that the attached report is my own work except where otherwise indicated. I

have identified my sources of information; in particular I have put in quotation marks any

passages that have been quoted word-for-word, and identified their origin.

Signed…………………………………………

Date…………………………………………...

Abstract A team of students at the University of Brighton have been given the opportunity to take part

in the design of a race car to compete in the Formula Student race series.

The subject of this report contains the design of the spring, damper and anti-roll systems

including: the chassis kinematics, motion analysis, individual component design and all

supporting material including: possible limitations, rules, regulations and group contribution

within the project.

The principle of a suspension system is explained and then further detail is applied to the

design of the spring, damper and anti-roll system including: possible design solutions,

reasoning behind the chosen designs, calculated data to support the design, stress analysis and

visual representations of the final solutions.

The result of the project is a system that could be manufactured and applied to the vehicle for

use within the competition that conforms to rules, regulations and meets the specified

requirements.

The data, methods and concepts used within the report aren’t just specific to a race car, they

can be used widely within the automotive industry to provide solutions for many scenarios if

used in the correct manner.

Contents

1. Introduction ............................................................................................................................. 1

2. Suspension System .................................................................................................................. 2

2.1. Suspension principle ............................................................................................................. 2

2.2. System Requirements....................................................................................................... 2

2.3. Spring and damper arrangement concepts…….………………….………..…...……4

3. Spring and damper arrangement selection………….……………..……………………….5

3.1. Anti-roll bar………………….…………………………………….………………………6

3.2. Anti-roll bar arrangement concepts ….......................................………………………6

4. Anti-roll bar arrangement selection………….……………………………………………..7

5. Chassis kinematics……………………...…………………………………………………….8

5.1 Roll axis definition……….......……………………………………………………………..8

5.2 Primary roll moments……………………………………………….....………………..9

5.3 Unsprung moments and total roll moment……………………….......………………9

5.4 Resistive moments……………………………….......…………………………..10

5.5 Weight transfer……………………….......…………………………………..12

6. Damper Choice……………………….....…………………………………………………….12

7. Spring Design….........................................................................................................................14

8. Front spring, damper and anti-roll system design…………………………………………15

8.1 Working principle………………………………………………………………………..15

8.2 Final Design overview………………………………………………………………15

8.3 Bump motion ratio……………………………………………………………...16

8.4 Front Pull rod design………………………………………........................17

8.5 Front Rocker design………………………………………………..…19

8.6 Front Anti-roll design………………………………………….…20

9. Rear spring and damper design……………………………………………………….……..22

9.1 Final design overview…………….……………………………………………………..22

9.2 Bump motion ratio…………………………………………………………………23

9.3 Rear push rod design………………………………………………………….24

9.4 Rear Rocker design………………………………………………………..24

10. Conclusion…………………………………………………………………………………....25

11. Recommendations…………………………………………………………………………... 25

References……………………………………………………………….…………………….…26

Appendix A – Decision matrix criteria……………………………………...…………….……27

Appendix B – Roll axis Definition………………………………………………………………29

Appendix C – Equations used…………………………………………………..………………34

Appendix D – Resistive moments……………………………………………………………….36

Appendix E – Spring design…………………………………………………………………….38

Appendix F – Final designs……………………………………………………………………...39

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1 Introduction

The students at the University of Brighton have been given the opportunity to take part in

the design of a race car to compete in the Formula Student competition. Formula Student

began its life in the United States in 1981 by the Society of Automotive Engineers (SAE) and

has been a global success since. The overall goal of Formula student is to provide students

with the opportunity and experience of taking part in all aspects of Engineering including;

management, design, manufacturing, marketing and to increase the ‘people skills’ of the

students by working as part of a large team. The way in which this is conducted is by

enabling the students to design, develop and manufacture a single seated race car. In Europe,

there are four races available, these are hosted in the Germany, Austria, Italy and the United

Kingdom by the Institute of Mechanical Engineers (IMechE), who have hosted the European

division of Formula student since 1998.

Figure 1.1 Shows the Winning Car for 2014 (TU Delft DUT-14)

(Racecar Engineering, 2015)

During the design process of the cars, the teams get a lot of freedom to do as they please but

there are rules that need to be followed to ensure the safety of the occupant and to provide

equal opportunities for each team. The most important rules are as follows:

1. The chassis of the vehicle must be designed in accordance to the strict number of

safety rules and regulations.

2. A four stroke engine must be used with a maximum displacement of 610cc.

3. An inlet restrictor must be fitted with a maximum inner diameter of 20mm.

4. The vehicle must be equipped with a fully operational suspension system

The subject of this report, the design of a spring, Damper and Anti-roll bar system, lies within

rule four above. The suspension system as a whole is being designed by a team of five

students including myself. Close contact is kept between us and the other students involved in

the design of the rest of the vehicle, to not only produce a system that functions as a sub-

category but as a whole vehicle design that can be used competitively within Formula

Student. The following chapter explains the function of a suspension system.

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2 Suspension System

A suspension system compromises of the springs, dampers, linkages, uprights, wheels and

tyres that connect the body of a vehicle to the road surface. How the suspension system is

optimised depends on the vehicle application. For a road car there has to be a compromise

between performance and overall comfort for the users. For a race car the comfort of the

driver is not important and overall performance is what the vehicle must be optimised for.

2.1 Suspension principle

The most important part of a car are the tyres. They transmit all of the drive of the vehicle

through a very small contact area with the road surface. Not only do they transmit the drive,

they also have to handle all braking and steering forces applied by the driver. The purpose of

the suspension system is to keep the tyre contact patch optimal with the road surface to

increase traction. This can be done very effectively in a race car using the correct geometry

and kinematics but often comes at a cost of driver comfort.

2.2 System Requirements

There are two sets of requirements that are required to progress with the design of the spring,

damper and anti-roll system. The first of which are a general set that apply to the whole

vehicle. The second set are specific to the spring, damper and anti-roll system.

The general requirements are as follows:

1. High reliability

2. Low centre of gravity

3. Low weight

4. Aerodynamically efficient

5. Reasonable Costing

6. Must comply with FSAE rules and regulations

The specific requirements for the spring, damper and anti-roll systems are as follows:

1. Adjustability – The system must be as adjustable as possible to suit a wide range of

applications

2. Good accessibility – The whole system must be easily accessible so adjustments and

maintenance can be made with ease.

3. The packaging of the system must not interfere with other vehicle components.

Rules set by the FSAE prescribe: (2015 Formula SAE rules, 2015)

4. Rule 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.

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5. Rule T6.1.2 - All suspension mounting points must be visible at Technical Inspection,

either by direct view or by removing any covers.

6. Rule 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.

2.3 Spring and Damper arrangement concepts

Firstly the type of spring and damper arrangement must be selected for the vehicle. As a

group, an early decision was made that the vehicle would be equipped with a double

wishbone suspension arm design. The reason for this choice was that it offered the best

adjustability (Four adjustable chassis mounting points), strength (Two suspension arms

opposed to one) and geometry (best control over camber during bump and droop) than any

other system. Looking through a selection of previously successful Formula Student cars, it is

apparent that the vast majority of teams also share the same thought process.

Based on the suspension arm choice, research into potential solutions for the spring, damper

and anti-roll bar could be made to find the most appropriate choice to fulfil the requirements

shown in chapter 2.2:

Outboard coil-over

Positioning a coil-over damper unit in-between the wishbones is a solution that a lot of

modern road vehicles use. Attaching the bottom of the damper directly to the lower wishbone

and then supporting the top of it to the chassis via an inclination angle. The advantages of this

solution lie within packaging constraints and simplicity of design. The disadvantages are that

the motion ratio of the unit is not adjustable and in an open wheel scenario found in Formula

Student, the unit is subject to increasing the aerodynamic drag of the vehicle.

Figure 2.1 Outboard Coil-Over Unit (Car Bibles, 2015)

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Push rod suspension

Using a push rod system allows the coil-over unit to be mounted “in-board”, within the main

structural part of the chassis of a vehicle. In the case of a push rod design the coil-over unit is

mounted higher than the upper wishbone and fixed at one end. The force during a bump

situation is then transferred through a linkage in a pushing motion (push rod) to a rocker with

a fixed pivot point to the chassis. The rocker can then supply the force to the other end of the

damper via a linkage and rotating on its axis. This can be seen below:

Figure 2.2 Push rod suspension (Btcc technical, 2015)

There are many advantages of this setup, including a reduction in aerodynamic drag by reducing the

surface area of the components that are subject to a drag force. The ratio of damper movement to

wheel travel can also be adjusted to increase damping performance by changing the rocker design.

The main disadvantage of this setup is by mounting the coilover unit in the upper part of the chassis

will lead to an increase in centre of gravity.

Pull rod Suspension

A pull rod system works in much the same way as the push rod system above. Instead of the coil-over

unit being mounted high up in the chassis, it is mounted in the lower regions below the upper

wishbone. Rather than the force being transferred in a pushing motion, the force is transferred from

the upper wishbone during a bump situation in a pulling motion using the same rocker concept as the

push rod design. This can be seen below:

Figure 2.3 Pull rod suspension (F1 Fanatic, 2015)

The main advantage of using this system opposed to the push rod alternative previously

mentioned, is the reduction in centre of gravity that can be achieved by mounting the

5

components low down in the chassis. A disadvantage of this system is that it can often be

difficult to package within a vehicle as not to interfere with other components.

3 Spring and damper arrangement selection

Based on the requirements, a decision can be made on which of the three systems found in

chapter 2.2 are most suitable for application to both the front and rear of the vehicle. In order

to justify the decision in a quantitative manner a decision matrix is used incorporating the

important aspects of the requirements but also taking into account the designs that have been

previously successful within Formula Student.

The results of the decision matrices can be seen below in Figures 3.1 and 3.2. The weightings

and criteria can be found in Appendix A.

Figure 3.1 Front suspension decision matrix

Figure 3.2 Rear suspension decision matrix

As can be seen from the decision matrices, the most suitable choice for the front suspension on

the race car is a pull rod system. The deciding factors within the decision matrix are the centre

of gravity location of the system and also the packaging within the chassis.

For the rear suspension, a push rod system is most suitable. The deciding factor within the

matrix is the compatibility and packaging with the chassis. Due to the high concentration of

mechanical components at the rear of the chassis it would be nearly impossible to use a pull

rod system effectively. Therefore a compromise in the centre of gravity location of the

components has to be made. This will be a minor limiting factor of the system though due to

the concentration of other heavy components located in a similar position.

3.1 Anti-roll bar

Now that a decision has been made for the arrangement of the spring and damper system,

research can be made into possible concepts for an anti-roll system. Firstly, what is an anti-roll

6

bar? An anti-roll bar is a length of rod that is able to supply an opposing moment from one side

of an axle to the other via a set of linkages. It is used try and reduce the amount in which the

body of the vehicle rolls during cornering by keeping the suspension components as level with

each other as possible. This keeps the tyres of the vehicle as flat to the road surface as possible

increasing the contact area and therefore increasing the level of traction that is able to be

supplied to the road surface.

3.2 Anti-roll bar arrangement concepts

For the chosen spring and damper arrangement there are two possible concepts for how the

Anti-roll bar can be applied to the vehicle. These are as follows:

Wishbone linked anti-roll bar

By anchoring the bar to the chassis and then connecting the ends of the bar to both wishbones

using a swing arm or drop links, will enable the bar to be put under a torsional load if the

wishbones don’t move in a parallell manner to each other. This opposing moment being

supplied by the bar is what reduces the body roll.

Figure 3.3 Wishbone linked anti-roll bar (Car Bibles, 2015)

The advantage of this setup is in its simplicity of design, there are few linkages and it is

relatively simple to package within a vehicle. The big disadvantage with this system is the

weight. The bar has to be long enough to stretch from one wishbone to the other and adding

on linkages and mounting points further increases the weight of the system.

Rocker integrated anti-roll bar

Instead of supplying the opposing moment of the anti-roll bar through links to the wishbones,

a system can be integrated within the rocker assembly of the chosen spring and damper

system to supply the same resistive forces but within a much smaller and lightweight

package.

7

Figure 3.4 Rocker integrated anti-roll bar (ScarbsF1, 2015)

The main advantage of this system is that it can be packaged within a small area due to the

size of the components needed. The whole system will weigh a substantial amount less than

the previously mentioned concept and remains highly tuneable.

4 Anti-roll bar arrangement selection

Out of the two possible systems previously explained, there is a clear advantage in integrating

the anti-roll systems of the race car to the rocker assemblies supplied by the spring and

damper arrangement previously determined.

A typical wishbone linked anti-roll bar can weigh in excess of 4kg and is subject to an

aerodynamic drag force due to the majority of the components being mounted outside the

main structural part of the chassis. Whereas a rocker integrated anti-roll bar is more likely to

weigh under 1kg and because it is mounted within the chassis it isn’t subject to reducing the

aerodynamic performance of the vehicle.

There is one minor disadvantage to the system, the complexity of the design. With the

advantages that can be taken from using the design, this is negligible, as the extra time and

effort in the design and development stage will be worth the final outcome.

Based on this, there is no need to produce any quantitative analysis between the two systems

as the rocker integrated anti-roll system would be the clear favourite based on the advantages

previously mentioned.

5 Chassis Kinematics

To progress with the design of the spring, damper and anti-roll systems, there are key aspects

of the chassis that need to be understood. This chapter will explain the kinematics of the

chassis, specifically, the primary moments that need to be resisted in order to supply the

correct handling properties for the vehicle.

By understanding the way in which forces are transferred during cornering will allow the

spring, damper and anti-roll arrangements to be optimised to counteract the forces and keep

the body roll of the vehicle to a minimum. This will then support the function of the

suspension system previously mentioned in Chapter 2.2.

8

5.1 Roll axis definition

Figure 5.1 Roll axis definition data

The first step is to determine the height of both the front (m) and rear (n) roll centre. This is

done using wireframe drawings of the wishbone designs. These can be seen in Appendix B,

Figure B1 and B2. They define the end points at which the vehicle will roll.

An approximation of the vehicles height of centre of mass (h) needs to be found in order to

determine the point in which the mass of the vehicle will act upon the roll centres. At this

stage in the design of the race car, there is very limited information available on component

weights, so an educated approximation must be made to obtain the data needed. This can be

seen in Appendix B, Figure B3.

The next step is to find the longitudinal distances between the front and rear roll centre and

the centre of mass of the vehicle. Again, an approximation needs to be made as to how the

weight is distributed throughout the chassis to locate the longitudinal centre of mass. This can

be seen in Appendix B, Figure B4. The longitudinal distance between the front of the

vehicle and the centre of mass (a) and the longitudinal distance between the rear of the

vehicle and the centre of mass (b) can be seen in Appendix B, Figure B5.

The final steps involve calculating the height of the mean roll centre (RCz mean) and the

value Delta Z. Delta Z is the height of the centre of mass minus the height of the mean roll

centre.

To find the height of the mean roll centre (RCz mean), Equation 1 in appendix C is used.

5.2 Primary roll moments (sprung moments)

Figure 5.2 Primary roll moments

9

The next step is to determine the primary roll moments of the vehicle. Firstly the weight of

the vehicle needs to be found, an approximation of the overall vehicle sprung weight

including the driver can be seen in Appendix B, Figure B4. This weight can then be

represented as a force by multiplying it by gravity (9.81m/s).

A friction coefficient of the tyre to the road surface must be specified as this will determine

the amount of lateral force from the weight of the vehicle will be transferred during

cornering, before the tyre loses traction resulting in a max force. The below quote explains

friction coefficients in detail:

“Jones and Childers report coefficients of friction of about 0.7 for dry roads and 0.4 for wet

roads. The tread design represents an "all weather" compromise. If you were an Indianapolis

race driver, you would use "slick" racing tires with no tread. On dry surfaces you might get as

high as 0.9 as a coefficient of friction, but driving them on wet roads would be dangerous

since the wet road coefficient might be as low as 0.1.” (Jones and Childers, 1994)

During a dry day, the race car will be equipped with slick tyres in order to maximise the

traction, therefore I will base further calculations for the chassis kinematics around a 0.9

coefficient, this will be a “worst case scenario” for the amount of force transferred through

the tyre and suspension components.

Based on the friction coefficient and the weight of the vehicle, a lateral force (mu W) can be

calculated by multiplying the vehicle weight (W) by the Coefficient of friction (mu).

Finally the roll moment of sprung mass (Wx) can be found by multiplying the lateral force

(mu W) by the height of the mean roll centre (RCz mean), found in the previous chapter

(5.1).

5.3 Un-sprung and total roll moments

Figure 5.3 unsprung and total roll moments

Now that the primary roll moments have been found, the un-sprung moments need to be

found. An un-sprung mass needs to be specified for the calculations. “Weight controlled by

the suspension, and usually below the suspension, which forces it into contact with the road

surface or other components, is un-sprung weight.” (Victorylibrary.com, 2015) This includes

such things as the wheels, brakes, wishbones, springs, uprights, dampers and any linkages in-

between the previously mentioned.

Between the group of students including myself designing the suspension system we came to

an agreement for an un-sprung mass target of 15kg per axle. Keeping un-sprung mass to a

10

minimum is crucial for improving vehicle handling. The lower the weight, the lower the work

the springs and dampers have to do to keep the tyre in contact with the road surface.

Using the same approach as the primary roll moments a lateral force (mu W unsprung) can be

computed based on the un-sprung mass (m unsprung) and the coefficient of friction (mu)

determined in Chapter 5.2.

The roll moment of the unsprung mass must be determined individually based on the location

within the vehicle. This is due to the different roll centres front and rear (Chapter 5.1). To

calculate the roll moments the lateral force (mu W unsprung) must be multiplied by the

rolling radius of the tyre ( r ) minus the roll centre height (m or n). The equation can be seen

in Appendix C, Equation 2.

The total roll moment of the vehicle (Wx total), is the sum of the roll moment of the sprung

mass (Wx) and the front and rear variant of the roll moment of unsprung mass (Wx

unsprung).

5.4 Resistive moments

Figure 5.4 Resistive moments

To calculate the resistive moments needed, the moment balance method will be used. (Coren,

2015). Using the information previously found in Chapter 5.1 on the roll axis definitions,

rates are able to be calculated by supplying a spring rate to both the front and rear suspension

setup. The idea of the moment balance method is to try and match the resistive moments to

the total roll moment supplied by the vehicle during cornering. It is also crucial to try and

match the front and rear suspension resistive moments to maintain a 50/50 weight transfer,

this will make the race car balanced during cornering and less prone to understeer and

oversteer behaviour. This will be explained in more detail further in the report.

11

The first step is to take moments about the lower, inner wishbone pivot point (Kp) and the

instantaneous centre (Kw) on both the front and rear suspension. Graphical representations of

the geometry and where the moments are acting can be seen in Appendix D, Figures D1 and

D2.

The push/pull rod setup for the race car will be using a motion ratio of 1/1, this means that for

every 1mm of wheel travel, there will be 1mm of travel for the spring and damper. Therefore,

this eliminates the need to supply an angle of spring inclination and the rate can be taken for

the whole length of the lower wishbone rather than the traditional anchorage point of the

spring. This can be seen by observing dimension l1 in Figure 5.4 and Figure D1/D2 in

appendix D. The motion ratios of the systems will be explained in detail further in the report,

during the design process.

To calculate the rates, Kp and Kw, based on the dimensions shown in Figure 5.4 and Figure

D1/D2 in appendix D, Equations must be used, these can be found in Appendix C,

Equations 3 and 4. To begin with a value must be specified for the spring rate (Ks) for input

into the equation. This can then be changed at a later time to balance the moments. This will

be explained in detail further in this chapter.

The last input value needed for the resistive moment’s calculations is a target roll angle

(theta). The angle at which the body rolls is directly linked to the deflection of the wishbone

arms, therefore a target roll angle can be set so that the correct resistance is provided by the

spring to achieve it. In this case, a target roll angle of three degrees is set. This is so that the

body of the vehicle stays as flat as possible during cornering but is able to roll enough for the

correct camber control to be achieved by the wishbone geometry, this therefore enables the

contact patch of the tyre to be as flat to the road surface as possible at all times, increasing

traction and the overall performance of the vehicle.

Now that the correct dimensions for the rates have been found (excluding the spring rate), the

total resistive moment for both the front and rear suspension can be found (momentf and

momentr). This is achieved by taking the previously found moments (Kw,Kp) by the roll

centre (b) and then multiplying the figure by two, as the springs are acting on both sides of

the vehicle. The final equation is the same for both the front and rear suspension but the input

values are substituted for each. The equation for calculating this can be seen in Appendix C,

Equation 5. The total resistive moment (resmomenttot) for the vehicle is simply the front and

rear resistive moment added together.

Using the moment balance method, the total resistive moment (resmomenttot) must be equal

to the total roll moment (momenttot) previously determined in Chapter 5.3.

To retain a 50/50 weight transfer front and rear during cornering, the resistive moments for

the front and rear suspension must also be matched. Achieving this will ensure the front and

rear tyres are loaded evenly during cornering. If the front tyres lose traction before the rears

this can lead to understeer behaviour, if the rears lose traction before the fronts then oversteer

behaviour is achieved. Keeping the front and rear tyres loaded evenly is crucial.

Using excel, all of the previously determined equations and data can be entered to create a

working spreadsheet. By carefully changing the spring rates (Ks) front and rear, using the

‘Goal seek’ function as an aid, the total resistive moment (resmomenttot) can reach

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equilibrium with the total roll moment (momenttot) while ensuring the front and rear resistive

moments (momentf and momentr) are also closely matched.

5.5 Weight transfer

Figure 5.5 Weight transfer

To support the theory of matching the front and rear resistive moments of the vehicle, the

weight transfer for both the front and rear of the vehicle can be calculated using data

previously obtained, specifying the track of the vehicle and Equation 6 in Appendix C. The

total weight transfer is simply the front and rear added together.

As can be seen in Figure 5.5 by matching the resistive moments as closely as possible front

and rear, the weight transfer is very close to being a 50/50 split.. This should lead to the race

car having very good handling characteristics as the front and rear tyres will be subject to the

same forces.

6 Damper Choice

In order to progress with the spring design, a coil over damper needs to be selected so that the

spring is designed in accordance with the spring seat and damper length. The damper chosen

for application to the Brighton University race car is the KONI 2612 series damper. There are

two variants of the damper that will be used, the first incorporates the standard top eye from

the factory for use on the rear system. The second incorporates an extended top eye for use on

the front suspension, where extra length and clearance is needed to eliminate obstruction of

both the chassis and the rocker design. The two designs can be seen below.

Figure 6: KONI 2612 Damper standard top eye (right) extended top eye (left)

Why the KONI 2612? “They are specifically designed for competition purposes and offer full

adjustability while fitted on the car. Their precision adjustment mechanisms allow maximum

13

control over the damping forces generated, especially in the low speed damping range.”

(Koni.de, 2015).

The KONI 2612 series damper has been used extensively within formula student with many

of the successful teams incorporating them into their designs. Some of the main advantages

are as follows:

Gas filled monotube design – “Mono tube dampers use a single outer tube. The oil

and nitrogen gas inside are separated by a free piston. Mono tube dampers use much

higher gas pressure than twin tube dampers to better stabilise the oil inside under

extreme usage. The advantages of the mono tube design are larger internal parts,

which mean greater damping force, increased oil capacity, improved heat dissipation,

and the ability to function when inverted” (MeisterR High Performance Suspension &

Coilovers, 2015)

High level of adjustability – The dampers are adjustable in both ‘bump’ and ‘rebound’ states,

this allows fine tuning of handling characteristics by being able to control the generated

damping force in both states.

Lightweight design – The main body, adjustment discs and eyes are all made from cast

aluminium this ensures overall weight is kept to a minimum at just over a kilogram per

damper.

Stroke – The chosen damper has a total stoke of 59mm (29.5mm bump and 29.5mm rebound)

which is the ideal size for the application to this vehicle and conforms to the FSAE rule

T6.1.1 previously mentioned in Chapter 2.2.

The dimensions of the height adjustable spring seat will give the required measurements for the spring

design and can be seen below:

Figure 6.1 height adjustable spring seat dimensions

The large dimension shown above is the outer diamteter of the spring seat, this gives the maximum

value for the coil diameter of the spring. The smaller dimension shows the distance between the inner

section of adjuster and the outer diameter, this specifies the maximum gauge width of the spring wire.

The minimum pressure (Pmin) at which the damper needs to be filled with the nitrogen gas is

calculated using Equation 7 in appendix C, the figure for the area of the piston (Apiston)

minus the area of the of the rod (Arod) is supplied by KONI in the technical manual for the

2612 damper (KONI.com) as 0.869x10-3 m2. The maximum bump force is the lateral force

(mu W) previously calculated in Chapter 5.2. The minimum pressure needed, is calculated to

be 2.77N/m2.

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7 Spring design

Figure 7 Spring geometry

Now that the spring stiffness (Ks) has been found for both the front and rear suspension

(Chapter 5.4) and the maximum coil and wire gauge diamter has been found (Chapter 6),

the rest of the spring can be designed by rearranging the general spring stiffness equation

below, to make the number of active windings (N) the subject.

𝐾𝑠 =𝑑4×𝐺

8×𝑁×𝐷3 - General spring stiffness equation

𝑁 =𝑑4×𝐺

8×𝐷3×𝐾𝑠 – Rearranged to make the number of active windings (N) the subject

The diameters of the coil and gauge of the wire seen above in Figure 7 are slightly smaller

than the spring seat size and maximum wire diameter specified in Figure 6.1 in Chapter 6.

This is so there is room for the spring to fit in the seat without force but tight enough so that it

cannot move enough to cause concern.

The number of active windings is equal to the total windings minus the number of windings

that don’t contribute to the load bearing properties of the spring. In this case, the number of

active windings is equal to the total, as each winding will be used to support the load.

The total height of the spring top to bottom remains the same front and rear as the there is

plenty of room to accommodate the 29mm compression needed without the coils binding, this

conforms to rule T6.1.1 set by the FSAE previously mentioned in Chapter 2.2.

The chosen material for the spring is AISI 304 steel. The reason for this choice is the

relatively low shear modulus in comparison to other steels. This is needed to reduce the

spring windings to an amount that can fit the damper with enough room for compression

without binding together.

Renders of the complete spring and damper assemblies can be seen below and drawings of

the springs can be seen in Appendix E, Figures E1 and E2.

Figure 7.1 Render of the front spring and damper (right) and

the rear spring and damper (left)

15

8 Front spring, damper and anti-roll system design

The front system is divided into two sub-systems. The first system is the ‘bump’ system that

includes a pull rod design incorporating a rod, rocker and the coil-over spring/damper unit.

The second system is the anti-roll system that uses the motion of the rocker to apply a

torsional force through a bar via a set of linkages and levers, supplying an opposing moment

to the opposite wheel during a roll situation to keep the vehicle as flat as possible during

cornering.

8.1 Working principle

During a ‘bump’ scenario when both wheels are deflected in the same manner, for example,

on a straight piece of track with a hump, the push rods act on the rocker attached to the

chassis equally. This results in both coil-over damper units being compressed equally. With a

mirrored movement of the rockers on both sides of the vehicle, the anti-roll bar levers are

moved in the same direction also, resulting in no torsional moment being applied to the anti-

roll bar itself. A working diagram of this principle can be seen in Appendix F, Figure F1.

During a ‘roll’ scenario when weight is transferred to a side of the vehicle, for example,

during cornering, the body of the vehicle rolls towards the outside of the bend, the outer

wheel will move into a ‘bump’ state in respect to the chassis, the inner wheel on the other

hand moves into a droop state and is partially unloaded. With both rockers being rotated in

the opposite direction this results in the levers attached to the anti-roll bar acting in the

opposite direction, this applies a torsional, opposing moment that tries to keep the body of the

vehicle level during cornering. A working diagram of this principle can be seen in Appendix

F, Figure F2.

8.2 Final design overview

Figure 8.1 Front spring, damper and anti-roll system final design

16

Figure 8.2 Front spring, damper ant anti-roll parts list

The two sub systems will be explained individually starting with the front bump system

labelled 1-6 in Figures 8.1 and 8.2. The anti-roll system will be explained after, labelled 7-9

in Figures 8.1 and 8.2

8.3 Bump motion ratio

Pull rod motion ratio

Figure 8.3 Motion ratio of the pull rods to wheel movement

When designing a pull rod system such as the one shown in Figure 8.1, the motion ratio of

the rod movement to wheel movement needs to be found. The movement is not equal due to

the angle at which the rod is mounted (theta) and also the distance at which it is mounted (A)

from the total moving distance (B) in-between the chassis and the upright mount. A working

drawing of the dimensions listed in Figure 8.3 can be found in Appendix F, Figure F1. The

equation used to find the ratio can be found in Appendix C, Equation 8.

The reason for the rod being angled in the position seen, is so that it is perpendicular to the

lower chassis tube, this is crucial, as in order to retain the correct ratios amongst the system

they must be designed on a single axis plane so not to add additional angles that will affect

the overall ratio, this therefore means that the pull rod must be angled towards the centre of

the lower chassis tube, as such that the rocker can be mounted with ease from both sides of

the tube.

17

The next step is to acquire the rocker dimensions needed to amplify the 0.41/1 ratio supplied

by the push rods back to a 1/1 ratio. This is needed to support the previous kinematics

calculations and also supply the correct damper movement and velocities for optimum

performance.

Rocker and final motion ratio

Figure 8.4 Motion ratio of the rockers and final motion ratio

Now that the motion ratio of the pull rods has been found, the rocker co-ordinates need to be

designed in such a way that the final motion ratio is 1/1. This is not the only concern, as the

rocker needs to be designed in such a way that the arm connected to the coil-over unit (A) is

situated high enough to clear the lower wishbone when mounted. With a wishbone deflection

of 3 degrees (target roll angle) in either bump or droop and an arm length of 0.14m (A), there

is enough clearance plus a safety margin of an extra 1 degree. By tweaking the distance (B)

and angle (Theta) of the pull rod connection arm on the rocker and using the goal seek

function in excel, the final motion ratio, which is the motion ratio of the pull rods multiplied

by the rocker motion ratio, can be found and altered to meet the 1/1 (Front 1) ratio needed.

The dimensions can then be checked against the chassis to see if they are suitable and if there

is enough clearance for movement. The dimensions found in Figure 8.4 meet these

requirements and there is enough room for the rocker to rotate with the 0.012 linear rod

movement. A working drawing can be found in Appendix F, Figure F4. The equation used

to calculate the motion ratio of the rockers is the same used to find the motion ratio of the

pull rods substituting the relevant dimensions above.

As an addition to the chosen 1/1 ratio design, there are also rocker dimensions above (Front 2

and Front 3) that are also safe to use on the chassis but supply a lower and higher variant

motion ratio. These could be used for reducing or increasing the amount that the spring and

damper are compressed in comparison to wheel travel. A scenario where this would be useful

is if the spring geometry changes to a point where a smaller compression is needed to stop the

coils binding, this may happen in the event of the springs changing for a softer variant with

more coils on a severely wet day, where a low friction coefficient is apparent. The rockers

can be designed and manufactured separately and swapped in and out by the 4 mounting

points used on them in a short amount of time.

18

8.4 Front pull rod design

Figure 8.5 Exploded view of the front pull rods

Each front pull rod consists of five components. Two rose joints, two end pieces and a carbon

fibre tube. The distinct feature of the design is its simplicity and lightweight construction.

Each pull rod weighs just 0.17kg. A brief description of the components and material choice

is as follows:

Rose joints

This is the component that allows a free moving connection via a ball joint between the rest

of the pull rod and the mounting points on the rocker and wishbone. Each rose joint is made

of three sub components, the housing, a Teflon liner and the ball itself. The Teflon liner

between the ball and the housing allows for a free moving but secure connection. The

housing also features a male connection rod that is threaded, so that it can be screwed into the

end piece. The material used in manufacture of the component is plain carbon steel, being the

direct link to the mounts via a bolt, it is essential that the component is strong enough to

withstand extensive use and movement, plain carbon steel has a much higher yield strength

than an aluminium alloy and is used extensively in tool making due to its hardness and good

wear properties. The dimensions for the rose joints can be found in Appendix F, Figure F5.

End pieces

This component is the part that allows the rose joint and carbon fibre tube to be connected. It

features a female thread in one end that allows the rose joint to be screwed in to and a male

joint matching the inside diameter of the carbon fibre tube. The male part of the end piece is

mated to the inside of the carbon fibre tube using a strong, permanent adhesive. This reduces

the need for other anchoring components, saving weight and cost. This method is used widely

in motorsport and has been proven reliable. The end piece features a flared end that butts up

against the rod for a secure and accurate connection. The material chosen for the end piece is

1060 alloy aluminium. Its lightweight construction keeps the overall weight down while

providing enough tensile strength to withstand the tension applied during use. The

dimensions for the end pieces can be found in Appendix F, Figure F6.

19

Carbon fibre tubes

Being the main structure, and largest component in the assembly, it is essential that the

material chosen for the rod is both strong and lightweight. The carbon fibre tube has a

Young’s modulus of 90Gpa, if compared to plain carbon steel that has a Young’s modulus of

210GPa this seems relatively low, with the forces being applied through the tube, this is more

than acceptable. Stress analysis of the tubes will be explained further in the report when the

rear design is explained, this is because the rear tubes are under compression due to the push

rod configuration so are susceptible to higher stress, the same diameter tube will be used front

and rear so it is only necessary to stress test the rear rods. The main advantage of the carbon

fibre tubes is the weight, the tube itself only weighs 0.05kg, if a plain carbon steel tube of the

same dimensions was used it would weigh 0.21kg, this reduction in unsprung weight will

increase handling performance and increase the power to weight ratio of the race car. The

dimensions of the Front carbon fibre tubes can be found in Appendix F, Figure F7. The pull

rod assembly can be seen in Figure F8.

8.5 Front rocker design

Figure 8.6 Exploded view of the front rocker design

The rocker design for the front system consists of two halves, one half is a standard rocker

design incorporating the dimensions previously obtained in Chapter 8.3, the second half is

the same but also includes a lever design for the anti-roll system. The lever has a second

motion ratio that will be explained further in the report alongside the reasoning behind its

dimensions.

The reason for the rocker being designed in two halves is for manufacturing purposes, each

piece can be milled separately using a CNC milling machine and then welded together using

the supplied attachment tabs incorporated into the design. It would not be possible to machine

the component in one piece due to the hollowed centre.

The material used for the rocker is a 1060 alloy aluminium, as all forces are applied in a

single plane it means that the thickness can be kept to a minimum as the force will be applied

through the length of the part and there will be minimal out of plane forces acting upon the

rocker. The total weight of the complete rocker is just 0.27kg. The rocker dimensions can be

seen in Appendix F, Figure F9.

20

8.6 Anti-roll system design

Figure 8.7 Anti-roll bar properties

The anti-roll system consists of four main components. The rocker, the anti-roll bar rods, the

levers and the anti-roll bar itself. The anti-roll bar is supported between the chassis tubes on

the vehicle using bearings and bearing holders, this allows for free torsional movement of the

bar and good support. The system functions using the rotational movement of the rocker

lever, which is then transferred into a linear motion using the anti-roll bar rods and then back

into a rotational movement via the anti-roll levers to apply a torsional moment to the anti-roll

bar itself.

To be able to calculate the anti-roll bar diameter, the angle of twist (ARB twist) at maximum

wheel travel needs to be found. This depends entirely on the motion ratio of the rocker lever.

Using the same theory and calculations previously used in Chapter 8.4, with the exception of

angle theta as there is no angle to be accounted for, this can be done with ease based on the

dimensions of the lever. The dimensions of the lever were found by examining the best way

in which to package the system so that the lever is orientated around the chassis tube and long

enough to have enough room for movement without obstruction. These can be seen in

Appendix F, Figure F10. The motion ratio of the rocker lever can be seen below in Figure

8.8.

Figure 8.8 Motion ratio of the rocker lever

By observing the results it can be seen that with 0.029m of wheel travel there will be 0.034m

of linear travel transmitted to the roll bar rods. By observing the dimensions of the anti-roll

bar levers this linear movement can be used to calculate how much twist will be applied to

21

the anti-roll bar (ARBtwist) by rotating the bar around the diameter of the arc made by the

levers, this is shown below in Figure 8.9:

Figure 8.9 Angle of twist observation

The roll stiffness of front of the vehicle (momentf) was previously determined in Chapter

5.4. A motion ratio of the target roll angle (theta) previosuly set in Chapter 5.4 and the anti-

roll bar twist angle (ARB twist) can then be calculated using Equation 9 in Appendix C.

Using the previously found values, the required roll stiffness of the anti-roll bar (karb) can

then be found using Equation 10 in Appendix C.

The diameter of the bar needed can be calculated based on the material choice, length of the

bar and the previously calculated values. The material used for the bar is plain carbon steel

which has a modulus of elasticity (E) of 2x1012 pa and a contraction coefficient (v) of 0.3.

The length of the bar (L) is dictated by the packaging and measures 0.326m. The diameter of

the bar (d) can now be calculated using Equation 11 in Appendix C. The diameter of the bar

(d) is calculated to be 0.0146m. The anti-roll bar is connected to the anti-roll levers by a

splined connection.

A completed model of the system can be seen below in Figure 8.10, dimesnions of the Anti-

roll bar, levers and rods can be seen in Figures 11,12 and 13 in Appendix F. The rose joints

and end pieces remain the same as the pull rod design.

Figure 8.10 Anti-roll system

22

9 Rear spring and damper system design

Unlike the front system the rear system incorporates a ‘bump’ only system. The reason for

the rear system not containing an anti-roll solution is due to it not being needed. When

forces are applied to the vehicle during a cornering scenario they tend to be under breaking

conditions where an extra roll stiffness is needed to counteract the extra force of weight

being distributed towards the front of the vehicle. During this same scenario the rear

suspension becomes partially unloaded eliminating the need for extra stiffness to be

applied. By not incorporating an anti-roll system to the rear of the vehicle also has other

advantages such as; weight reduction, more room for vital drivetrain components to be

accessed and an increase in reliability with less moving parts susceptible to failure.

9.1 Design overview

Figure 9.1 Rear design render

Figure 9.2 Rear spring and damper system parts list The rear system uses a push rod design opposed to the pull rod design used on the front of the

vehicle, the working principle remains the same except the rocker is actuated in a pushing

motion rather than a pulling motion.

23

9.2 Bump motion ratio

Pull rod motion ratio

Figure 9.2 Motion ratio dimensions of the push rods

Just like the front system, the motion ratio of the push rods needs to be found in relation to

wheel travel. Instead of the ratio being taken from the top wishbone like the front system, it is

taken from the lower wishbone as this is where the pushing movement is supplied from and

the rod is attached to. A working drawing of the dimensions listed in Figure 9.2 can be seen

in Appendix F, Figure F14. Much the same as the front system the angle of the push rods is

dictated by packaging constraints and the rocker mounting location.

The next step is to acquire the pivot dimensions for the rocker to regain the 1/1 ratio lost with

the push rod dimensions.

Rocker and final motion ratio

Figure 9.3 Motion ratio dimensions of the rocker

Much the same as the front system the rear rocker had to be designed to regain the 1/1 ratio

needed for the kinematics calculations. The rocker chassis pivot and damper connection had

to also be situated above each other so that the damper orientation is correct for mounting the

to the central rear chassis bar. This led to an acute angle (Theta) and long rocker arms (A, B)

being needed to package the system correctly. Using the same process as the front system, the

rear rocker dimensions are tweaked in excel using the goal seek function as an aid until a 1/1

ratio is achieved. The dimensions were continuously checked against the chassis making sure

that with a maximum rod movement of 0.022m the rocker and rod remained operational and

no contact is made with the rest of the chassis components. A working drawing of the

dimensions listed in Figure 9.3 can be seen in Appendix F, Figure F15.

24

9.3 Rear push rod design

The rear push rods are designed in the same way as the front rods using the same end pieces

and rose joints. Due to the rod being under compression it is essential that the carbon tubes

are strong enough to handle the bump force acting on them during use. This force was

previously calculated as the lateral force (Flateral) of the vehicle during cornering. As the

rods are under compression they are subject to failing more than the front rods which are

under tension. For this reason it is only essential to test the rear tubes.

Euler buckling theory can be used to test the strength of the tubes. Figure 9.4 below shows

the essential input data (shaded) and the calculated data (unshaded) using this theory. All

equations used can be found in Appendix C, Equations 12-17. Working drawings of the rear

tubes and push rod assembly can be seen in Appendix F, Figure F16.

Figure 9.4 Euler buckling theory

As can be seen by the data shown in Figure 9.4 above the carbon tubes have a safety factor

of over 35 and are more than up to the task of the handling the required forces while

remaining extremely lightweight at just 0.05Kg each.

9.4 Rear Rocker design

The rear rocker uses the same two piece design as

the front rocker and for the same reasons, the

material choice is also the same 1060 alloy and

brings the total weight to just 0.18Kg. The reason

for the cut-out centre section of the rocker is to

accommodate the damper, without the removed

material, the damper would foul against the rocker

during rotation. With the amount of material

removed, there is enough room for the damper

during the maximum 29mm travel in either bump

or droop while providing enough structural support

to cope with the in-plane forces applied. Working

drawings of the rear rocker can be seen in

Appendix F Figure F17 Figure 9.5 Rear rocker design

25

10 Conclusion

The subject of this report is the design of the spring, damper and anti-roll systems for the

University of Brighton race car to compete in the Formula student competition. The

requirements of the systems have been explained in Chapter 2. The kinematics of the vehicle

have been thoroughly explained in Chapter 5 and the design has been undertaken

successfully based on these in the subsequent chapters.

The overall goal of Formula student is to provide students with the opportunity and

experience of taking part in all aspects of Engineering including; management, design,

manufacturing, marketing and to increase the ‘people skills’ of the students by working as

part of a large team.

During the whole process there has been good communication and planning between

everyone involved in the design. For example, without the wishbone geometry supplied by

Ricky Clayton (Wishbone design) and the rolling radius of the tyre (Oliver Mowbray), the

kinematics of the system could not be determined and subsequently the rest of the spring,

damper and anti-roll system design. A fast initial decision also had to be made by the group,

which led to the double wishbone layout of the design, this then enabled the group to focus

research and potential concepts that could be discussed and finalised. Mass sharing of

information led to a final rendered model of the final suspension design including the

wishbones (Ricky Clayton), the uprights (Mark Ragless), the wheels, brakes and tyres (Oliver

Mowbray) and the spring, damper and anti-roll systems (Myself). This can be seen in

Appendix F, Figure F17.

Overall the project has been very successful and as a group have achieved a lot of the goals

that formula student was created for.

11 Recommendations

Although the project went well there are also parts that can be re-visited and improved upon

to further increase the validity of the design. These include:

1. Further stress analysis can be undertaken on specific components to ensure they are

suitable for the operating conditions previously determined, especially the anti-roll

bar design that is subject to large torque.

2. Wet weather kinematics could be investigated in more detail using the moment

balance method spreadsheet within the report. This would lead to separate spring

designs depending on the weather conditions.

3. A more sophisticated Kinematics analysis could be made using computer software

such as Simulink. This would allow for even more precise data that could be used for

fine tuning the system and identifying potential problems.

4. Aerodynamic properties of the system could be investigated and by working in

conjunction with the aero team, a housing design could be made that improves the

aerodynamic efficiency of the vehicle.

26

References

2015 Formula SAE rules. (2015). 1st ed. [ebook] FSAE, p.57. Available at:

http://students.sae.org/cds/formulaseries/rules/2015-16_fsae_rules.pdf [Accessed 31 Mar.

2015].

Btcc technical, (2015). Push rod suspension. [image] Available at:

https://btcctechnical.wordpress.com/ [Accessed 31 Mar. 2015].

Car Bibles, (2015). Anti-roll bar. [image] Available at:

http://www.carbibles.com/suspension_bible_pg4.html#antiroll [Accessed 1 Apr. 2015].

Car Bibles, (2015). Double Wishbone. [image] Available at:

http://www.carbibles.com/suspension_bible.html [Accessed 31 Mar. 2015].

Coren, D. (2015). Chassis Kinematics. 1st ed. [ebook] p.38. Available at:

https://studentcentral.brighton.ac.uk/bbcswebdav/pid-2331131-dt-content-rid-

4497627_1/courses/ME341_SEM1_2014/Session%204%20Chassis%20Kinematics%20SC.p

df [Accessed 7 Apr. 2015].

F1 Fanatic, (2015). Pull rod suspension. [image] Available at:

http://www.f1fanatic.co.uk/2012/03/28/ferraris-front-pullrod-suspension/ [Accessed 31 Mar.

2015].

Jones, E. and Childers, R. (1994). Contemporary college physics. Reading, Mass. [u.a.]:

Addison-Wesley.

Koni.de, (2015). KONI: 2612 series. [online] Available at:

http://www.koni.de/pkw/racing/2612-series/ [Accessed 8 Apr. 2015].

MeisterR High Performance Suspension & Coilovers, (2015). Suspension Basics - MeisterR

High Performance Suspension & Coilovers. [online] Available at:

http://www.meisterr.co.uk/technical/suspension-basics/ [Accessed 8 Apr. 2015].

Racecar Engineering, (2015). TU Delft DUT-14. [image] Available at: http://www.racecar-

engineering.com/cars/delft-4/ [Accessed 31 Mar. 2015].

ScarbsF1, (2015). Rocker Ant-roll solution. [image] Available at:

http://scarbsf1.com/blog1/2011/10/26/front-anti-roll-bar-solutions/ [Accessed 1 Apr. 2015].

Victorylibrary.com, (2015). Sprung Vs. Unsprung Chassis Weight: Definition and Examples.

[online] Available at: http://victorylibrary.com/mopar/sprung-c.htm [Accessed 7 Apr. 2015].

27

Appendix A – Decision matrix Criteria

Decision matrix criteria and weightings

Weight (per axle)

The weight of vehicle components is crucial. By reducing overall vehicle weight will increase

performance based on power to weight ratio as well as handling capabilities. For suspension

components, weight can vary between 5Kg per axle, based on a very simple design, to over

20kg per axle for a complicated design. Therefore I have chosen the three weightings below

to suit this.

1. >15Kg

2. <15Kg

3. <10Kg

For the overall criteria weighting I have chosen 3, this is because weight plays a big part in a

formula student vehicle.

Centre of gravity

The centre of gravity of a vehicle is important to retain good handling. By reducing the centre

of gravity allows for less weight to be transferred into a roll moment when cornering, braking

or accelerating. For suspension components the effect on the centre of gravity depends on

where they are mounted on a vehicle, if they are mounted ‘high’ in the vehicle then this will

increase the height of the centre of gravity and if they are mounted ‘low’ it will reduce the

height of the centre of gravity. Therefore I have chosen the three weightings below to suit

this.

1. High

2. Middle

3. Low

For the overall criteria weighting I have chosen a 2, this is because the centre of gravity plays

a big part in where the weight is distributed around the vehicle and can have a serious effect

on handling capabilities.

Chassis compatibility (Packaging)

The chassis we have supplied has existing mounting points for suspension components. This

is a proven design that has already undergone extensive testing to find good solutions.

Redesigning the suspension system will require adjustment to the chassis in order to fit

components. This is an important criteria as the chassis is complete and modifying it may

compromise other areas of the design. Therefore I have chosen the three weightings below to

suit?

1. Extensive adjustment needed

2. Minor adjustment needed

3. No adjustment needed

28

For the overall criteria weighting I have chosen a 1, this is because the chassis can be

adjusted to suit any of the suspension systems. Although compatibility is important, this

criteria is mainly based on time and ease of fitting.

Adjustability

Being able to adjust the system is crucial. The handling characteristics can be fine-tuned to a

higher tolerance with more adjustability, leading to an overall better performance of the

vehicle. Some systems offer more adjustability than others. Therefore I have chosen the three

weightings below to suit this.

1. Low

2. Medium

3. Extensive

For the overall criteria weighting I have chosen a 3, this is because adjustability is very

important for fine tuning the vehicle to a given scenario and can be the difference between

the vehicle performing well or not.

Exposed surface area (Aerodynamics)

Size of the components can have an impact on such things as aerodynamics, by reducing the

size of the components will reduce the surface area in which the air passes over them. Size

can also have an effect on how the parts are fitted to the vehicle and chassis compatibility.

Although vague, the weightings I have selected below give a rough idea on this.

1. Large

2. Medium

3. Small

For the overall criteria weighting I have chosen 1, this is because weight will have an almost

direct impact on size. For such things as aerodynamics the impact will be small overall.

Previously successful design within formula student

When deciding on a system, looking at previously successful designs within formula student

is very helpful. Research has already been made by other teams into the designs and there are

reasons as to why they have been chosen. The weightings I have selected below will reflect

this.

1. No previous use

2. Have been used to some success

3. Widely used and successful

For the overall criteria weighting I have chosen a 2, this is because previously successful designs

should not be overlooked and should influence the decision to some extent

29

Appendix B – Roll axis definition

Front roll centre height

Figure B1

The above drawing shows the height of the front roll centre. Based on the location of the instantaneous centre, the vehicle centreline and the

contact patch of the tyre. As both sides of the vehicle are symmetrical there is only the need to reference one side. All dimensions are given in

metres and are supplied by Ricky Clayton (wishbone design)

30

Rear roll centre height

Figure B2

The above drawing shows the height of the Rear roll centre. Based on the location of the instantaneous centre, the vehicle centreline and the

contact patch of the tyre. As both sides of the vehicle are symmetrical there is only the need to reference one side. All dimensions are given in

metres and are supplied by Ricky Clayton (wishbone design)

31

Height of centre of mass

Figure B3

To find an approximate value for the height of centre of mass, we can presume that the distribution of mass in the y axis will be central to the

main body of the chassis. Therefore taking the simple measurements seen above in Figure B3, the height of the centre of mass can be found as

0.338 metres. All measurements are given in metres.

32

Vehicle Weight distribution and Centre of gravity

Figure B4

The above diagram and table show the distribution of weight within the vehicle and the length fraction of the centre of gravity. All component

weights are approximated based on researched averages.

Weight distribution and Centre of gravity

no Item Mass (kg) Mass (N) x (m)

1 Driver and seat 65 637.65 1.45

2 Engine 50 490.5 1.78

3 Chassis 50 490.5 1.35

4 Fuel tank 15 147.15 1.88

5 Front hub assemblies (including wheels) 15 147.15 0.88

6 Rear hub assemblies (including wheels) 15 147.15 2.36

7 Steering components 15 147.15 0.82

8 Differential 10 98.1 2.19

9 Driveshafts (pair) 10 98.1 2.27

10 Gearbox 8 78.48 1.78

11 Body panels and aero 7 68.67 1.35

12 Exhaust components 5 49.05 2

13 Front suspension 4 39.24 0.88

14 Rear suspension 4 39.24 2.27

Total 273 2678.13

Longitudinal length of the centre of gravity(m) 1.58

Overall length(m) 2.59

Length fraction of centre of gravity 0.61

33

Longitudinal distance between centre of mass and vehicle length

Figure B5

The above drawing, Figure B5, shows the longitudinal distances between the centre of mass and the front and rear of the race car, this will be

used to determine how the weight is distributed around the vehicle kinematically.

34

Appendix C – Equations used Equation 1 – Height of mean roll centre

𝑅𝐶𝑧,𝑚𝑒𝑎𝑛 =(𝑏×𝑚)+(𝑎×𝑛)

𝑎+𝑏

Equation 2 – Roll moment of unsprung mass

𝑊𝑥𝑢𝑛𝑠𝑝𝑟𝑢𝑛𝑔 = 𝜇𝑊𝑢𝑛𝑠𝑝𝑟𝑢𝑛𝑔 × (𝑟 − 𝑚 𝑜𝑟 𝑛)

Equation 3 – Moment about the lower, inner wishbone pivot (Kp)

𝐾𝑝 =𝐾𝑠×𝑙2

𝑎2

Equation 4 – Moment about the instantaneous centre (Kw)

𝐾𝑤 = 𝐾𝑠 × (𝑙2×𝑑2

𝑎2×𝑐2)

Equation 5 – Front/Rear suspension resistive moment

𝑚𝑜𝑚𝑒𝑛𝑡𝑓𝑟𝑜𝑛𝑡/𝑟𝑒𝑎𝑟 = 2 × (𝑙2×𝑑2×𝑏2

𝑎2×𝑐2 ) × 𝐾𝑠 × 𝜃

Equation 6 – Weight transfer, inside to outside of the wheel (front/rear)

1

𝑡× (𝑊 ×

𝑏

𝑎+𝑏× 𝑅𝐶𝑦 + 𝑊𝑢𝑛𝑠𝑝𝑟𝑢𝑛𝑔 × 𝑚 + 𝑚𝑜𝑚𝑒𝑛𝑡𝑓)

Equation 7 – Minimum gas pressure of the damper

𝑃𝑚𝑖𝑛 =𝐹𝑚𝑎𝑥𝑖𝑛

𝐴𝑝𝑖𝑠𝑡𝑜𝑛−𝐴𝑟𝑜𝑑× 1.1 (𝑠𝑎𝑓𝑒𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟)

Equation 8 – Motion Ratio’s

𝑀𝑜𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝐴

𝐵× sin 𝜃

Equation 9 – Roll motion ratio

𝑀𝑅𝑟𝑜𝑙𝑙 =𝐴𝑅𝐵 𝑡𝑤𝑖𝑠𝑡 𝜃

𝑇𝑎𝑟𝑔𝑒𝑡 𝑟𝑜𝑙𝑙 𝜃

Equation 10 – Required roll stiffness

𝑘𝑎𝑟𝑏 = 𝑚𝑜𝑚𝑒𝑛𝑡𝑓

𝑀𝑅𝑟𝑜𝑙𝑙2

Equation 11 – Anti-roll bar diameter

𝑘𝑎𝑟𝑏 =𝐺×𝐼

𝐿

𝐼 =𝜋

32× 𝑑4 𝑘𝑎𝑟𝑏 =

𝐸×𝜋×𝑑4

64×(1+𝑣)×𝐿 = 𝑑 = √

64×(1+𝑣)×𝐿×𝑘𝑎𝑟𝑏

𝐸×𝜋

4

𝐺 =𝐸

2×(1+𝑣)

35

Equation 12 - Euler second moment of area

𝐼, 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟ℎ𝑜𝑙𝑙𝑜𝑤 = 𝜋×(𝐷4−𝑑4)

64

Equation 13 – Cross sectional area of a hollow tube

𝐴 = (0.25 × 𝜋 × 𝐷2) − (0.25 × 𝜋 × 𝑑2)

Equation 14 – Euler radius of gyration

𝑘 = √𝐼

𝐴

Equation 15 – Euler buckling stress

𝜎 =𝜋2×𝐸

(𝐿

𝑘)2

Equation 16 – Euler maximum allowed force

𝐹𝑎𝑙𝑙𝑜𝑤𝑒𝑑 = 𝜎 × 𝐴

Equation 17 – Safety Factor

𝑆. 𝐹 =𝐹𝑎𝑙𝑙𝑜𝑤𝑒𝑑

𝐹𝑙𝑎𝑡𝑒𝑟𝑎𝑙

36

Appendix D – Resistive Moments

Front resistive rates

Figure D1

The diagram above shows the related dimensions to where the rates are taken for the resistive moments on the front suspension, the rates are also

highlighted by the red arrows and labelled accordingly. All measurements are taken in meters (m).

Kw

Kp, Ks

37

Rear resistive rates

Figure D2

The diagram above shows the related dimensions to where the rates are taken for the resistive moments on the rear suspension, the rates are also

highlighted by the red arrows and labelled accordingly. All measurements are taken in meters (m).

Kw Kp, Ks

38

Appendix E – Spring design

Front spring geometry

Figure E1 Shows

the geometry of the front spring incorporating a 0.0068m wire gauge, a 0.0614m coil

diameter and 7 active windings over a 0.12m height.

Rear spring geometry

Figure E2 Shows the

geometry of the rear spring incorporating a 0.0068m wire gauge, a 0.0614m coil diameter and

6 active windings over a 0.12m height.

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Appendix F – Final designs Figure F1

40

Figure F2

41

Front pull rod motion ratio

Figure F3 Front pull rod motion ratio dimensions

Front rocker motion ratio

Figure F4 Front rocker motion ratio dimensions

42

Figure F5 Rose joint dimensions

Figure F6 End piece dimensions

Figure F7 Front carbon tube dimensions

43

Figure F8 Complete pull rod assembly

Figure F9 Rocker assembly dimensions

Figure F10 Rocker lever motion ratio

44

Figure F11 Anti-roll bar dimensions

Figure F12 Anti-roll levers dimensions

Figure F13 Anti-roll carbon tube and rod assembly dimensions

45

Figure F14 Push rod motion ratio dimensions

Figure F15 Rear rocker motion ratio dimensions

Figure F16 rear push rod tube and assembly dimensions

46

Figure F16 Rear rocker dimensions

47

Figure F17 Final rendered group design