Design of a Formula StudentRace Car Spring-Damper

System.

P.C.M. van den Bos, 0576519

CST2010.024

Master traineeship

Supervisor: Dr.ir. P.C.J.N. Rosielle

Technische Universiteit EindhovenDepartment of Mechanical EngineeringControl Systems Technology Group

Eindhoven, March, 2010

Abstract

University Racing Eindhoven (URE) is a team of 50 students who compete in theFormula Student competition. For the 2009-2010 season, URE started building theirsixth car: the URE06.

The URE06 will be equipped with a newly designed front and rear multi-linkwheel suspension. The rear frame that holds the powertrain, drivetrain and suspen-sion will be shortened to reduce total mass and yaw inertia of the car.

The main subject of this report is the design of a spring-damper system for theURE06. First, the working principle of a suspension system is explained and a listof requirements the spring-damper system has to fulfill is determined. Subsequently,the kinematics of the front and rear spring-damper systems have been set. Thisresulted in a set of coordinates. The individual parts have been constructed next,taking the requirements into account. Components such as the anti-roll bars havebeen analyzed by hand calculations, while other parts have been optimized usingFEM analysis.

Contents

1 Introduction 1

2 The suspension system 2

2.1 Working principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Front spring-damper system 5

3.1 Final design overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Front bump system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2.1 Bump motion ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.2 Dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.3 Main rocker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2.4 Wheel travel sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Front anti-roll system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3.1 Stiffness of the anti-roll bar . . . . . . . . . . . . . . . . . . . . . . 10

3.3.2 Stress in the anti-roll bar . . . . . . . . . . . . . . . . . . . . . . . 11

3.3.3 Spline connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Rear spring-damper system 12

4.1 Final design overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2 Rear bump system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2.1 Pushrod versus pullrod . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2.2 Main rocker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2.3 Wheel travel sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Rear anti-roll system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3.1 Placement of the anti-roll system . . . . . . . . . . . . . . . . . . . 18

4.3.2 Bearing tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.3.3 Stiffness of the anti-roll bar . . . . . . . . . . . . . . . . . . . . . . 21

4.3.4 Stress in the anti-roll bar . . . . . . . . . . . . . . . . . . . . . . . 23

5 Conclusion and recommendations 24

References 25

A Front spring-damper system coordinates 26

B Rear spring-damper system coordinates 27

C Working drawings of the front and rear spring-damper system 28

Paul van den Bos Introduction

1 Introduction

University Racing Eindhoven (URE) is a team of 50 students who compete in the FormulaStudent competition. This competition was initiated in the United States in 1981 by theSociety of Automotive Engineers (SAE). The main goal is providing students with anopportunity to gain experience in design, manufacturing, management, marketing andpeople skills by designing, building and racing a single seater race car. Nowadays, fourEuropean races are available in the United Kingdom, Germany, Italy and Austria.

Figure 1.1: Last year’s car of University Racing Eindhoven: the URE05.

Teams get a lot of freedom to design their own car. The most important rules a Formulastudent car has to comply with state that it has to have:

• a chassis that is designed in accordance with a number of safety regulations.

• a four-stroke engine with a maximum displacement of 610 cc.

• an inlet restriction with a maximum diameter of 20 mm.

• a fully operational suspension system.

For the 2009-2010 season, URE started building their sixth car: the URE06. Besidesthat, it’s predecessor, the URE05 (see figure 1.1), will be converted from petrol driven tofull electric. It will be used to compete in new the Formula Student Electric competition.

The URE06 will be equipped with a newly designed front and rear multi-link wheelsuspension. The rear frame that holds the powertrain, drivetrain and suspension will beshortened to reduce total mass and yaw inertia of the car. A new spring-damper systemhas to be designed to make this possible.

The main subject of this report is the design of a spring-damper system for the URE06.Chapter 2 explains the working principle of a suspension system and lists the requirementsthe spring-damper system has to fulfill. The mechanical design of the spring-dampersystems for the front and rear of the car will be discussed in chapters 3 and 4 respectively.

1

Paul van den Bos Working principle

2 The suspension system

Suspension is the term given to the system of springs, dampers and linkages that connectthe body of a vehicle to it’s wheels. This system serves a dual purpose: optimizing thevehicle’s handling, and keeping the occupants comfortable. In case of a race car, thelatter is off course insignificant. The only goal of a race car is maintaining the maximumachievable acceleration in the appropriate direction.

The working principle of a suspension system will be explained first. After that, a set ofrequirements is formulated.

2.1 Working principle

Tyres are the most important parts of a race car. They have to transmit all drive, brakeand steering forces to the road through a very small contact patch. This makes it veryimportant for a car to keep the tyres in optimal contact with the road at all times. Thatis the task of the suspension system. In case of a race car, the suspension system can bedesigned specifically for that goal, at the cost of driver comfort.

A schematic representation of a suspension system can be seen in figure 2.1. The wheeland brake disc are connected to the upright by bearings. Carbon fibre rods with balljoints on each end connect the upright to the chassis. One of these six rods (the inclinedone) is not mounted to the chassis, but to a rocker. If the wheel moves up with respect tothe vehicle body, the upright pulls on the rod, which in turn causes the rocker to rotateabout it’s pivot point. A spring-damper is connected to the bellcrank on one end, and tothe chassis on the other. So by rotating the rocker, the spring-damper is compressed.

z

y

Figure 2.1: Rear view of a vehicle suspension system.

The spring-damper system consists of two subsystems: the coil-over damper itself (seefigure 2.2, and the anti-roll system. The coil spring absorbs the energy from a bump bycompressing, and releases it again at an uncontrolled rate. The spring will continue tobounce until all of the energy originally put into it is dissipated. Dampers are used tocontrol this energy dissipation. They slow down and reduce the amplitude of the wheelmotion by converting kinetic energy into heat.

The anti-roll system consists of a torsion bar with a lever on each end. If the movementson each end of the bar are not exactly the same, it will be twisted. This results in areaction force.

2

Paul van den Bos Working principle

The main rocker connects the pull rod to the two subsystems. The geometry of this rockerdetermines the movement of the spring-damper and the anti-roll bar as a result of themovement of the pullrod.

Two operating conditions will be explained to show how the subsystems work to controlthe movements of the suspension.

• Bump situation.If the car drives over a threshold, the left and right wheels will move up an equalamount. This results in the same angular rotation of the left and right main rocker.The spring-dampers are therefore actuated equally. Since left and right levers of theanti-roll bar are rotated to the same angle in the same direction, it will not createa reaction moment.

• Cornering situation.If the car drives through a corner, it’s body will roll to the outside of the bend. Asa result, the outer wheel moves up with respect to the chassis, and the inner wheelwill move down. This means the main rockers are rotated in opposite directions.The load on the outside spring will become higher, while the inside spring will be(partially) unloaded. The anti-roll bar will be twisted, which results in an opposingmoment that tries to keep the vehicle body level.

x

z y

Bump Corner

Spring-damper

Main rocker

Anti-roll bar

Figure 2.2: Working principle of a spring-damper system.

3

Paul van den Bos Requirements

2.2 Requirements

To design the suspension system for the URE06, a set of requirements has to be formu-lated. These can be split up in general requirements that apply to all parts designed forURE, and demands that apply specifically to the suspension system.

The general requirements are:

1. High reliability.

2. Low weight.

3. Low center of gravity.

4. Low yaw inertia.

5. Low production costs. This includes both the prototype and series production of1000 cars/year.

6. Must comply with FSAE rules [1].

The spring-damper system’s specific requirements are:

7. The motion ratio (see equation 1) has to suit the chosen dampers.

8. The anti-roll system has to be adjustable. This can be used to control the over- andundersteer behavior of the car. The system has to be adjustable from 0.5k − 2k.

9. Accessibility has to be such that settings can quickly be adjusted.

10. Friction (hysteresis) has to be kept low.

11. The system should be free of play.

12. Wheel displacement has to be measured with integrated sensors.

13. The required stiffness of the anti-roll bars and bump springs will be determined bythe designers of the new multilink suspension. An advanced vehicle model will beused for this.

14. Minimum wheel travel is prescribed by rule B6.1.1 [1]:B6.1.1 The car must be equipped with a fully operational suspension system with shockabsorbers, front and rear, with usable wheel travel of at least 50.8 mm (2 inches), 25.4mm (1 inch) jounce and 25.4 mm (1 inch) rebound, with driver seated. The judges reservethe right to disqualify cars which do not represent a serious attempt at an operationalsuspension system or which demonstrate handling inappropriate for an autocross circuit.

15. Visibility is prescribed by rule B6.1.2 [1]:B6.1.2 All suspension mounting points must be visible at Technical Inspection, either bydirect view or by removing any covers.

16. Ground clearance is prescribed by rule B6.2 [1]:B6.2 The ground clearance must be sufficient to prevent any portion of the car (other thantires) from touching the ground during track events, and with the driver aboard there mustbe a minimum of 25.4 mm (1 inch) of static ground clearance under the complete car atall times.

4

Paul van den Bos Front bump system

3 Front spring-damper system

The concept of the front spring-damper system of 2008-2009 season’s car, the URE05,was quite nice. It is mounted on the underside of the car, with the anti-roll bar in front,and the dampers behind the main rockers. This order results in a lower yaw inertia thanthe other way around. The low mounting position is not only beneficial for the height ofthe center of gravity, but also uses the otherwise wasted space beneath the drivers’ legs.

Since the monocoque of the URE06 will be roughly the same as that of the URE05, theconcept of the front suspension system can remain. The main points of attention are thenew multilink suspension and ground clearance. On the URE05, if the front suspensionbottoms out (maximum compression) the rotation sensor and damper hit te ground. Thiswill, off course, have to be prevented on the URE06.

3.1 Final design overview

The final design of the front spring-damper system can be seen in figure 3.1. The rightpart of the figure shows the names of the points that are used in a Simulink model. Thecorresponding coordinates can be found in appendix A. The working drawings have beenincorporated in appendix C. The bump system consists of points 1 - 4. The anti-rollsystem includes points 5 - 7.

Figure 3.1: Final design of the front spring-damper system.

The various parts of the design will be explained in this chapter; the bump system first,and the anti-roll system afterwards.

3.2 Front bump system

The bump system includes the pull-rod, main rocker, spring and damper. The pull-rodis attached to the upright and the main rocker. The main rocker has a pivot point onthe monocoque. The coil-over damper is attached to the main rocker on one end, andto the chassis with the other. If the car drives over a bump, the wheel and upright arepushed up, causing the pull-rod to rotate the rocker. The rotation of the rocker resultsin compression of the spring-damper.

5

Paul van den Bos Front bump system

3.2.1 Bump motion ratio

The coil-over dampers need to be compressed and extended in a certain velocity rangeto work properly. The velocity of the damper is of course dependent on the (vertical)velocity of the wheel, and the suspension system. The ratio between damper travel andwheel travel is called the motion ratio.

MRbump =xdamper

xwheel[−] (1)

Due to the kinematics of the suspension system, the relation between wheel travel anddamper travel is highly non-linear. To analyse the kinematics of the system, a Simulinkmodel is used. This model allows the user to simulate steering, wheel bump and bodyroll. The wheels are moved 30 mm up and down during a wheel bump simulation. Theresulting motion ratio lies well within a 0.5± 1% margin as can be seen in figure 3.2.

−30 −20 −10 0 10 20 300.48

0.485

0.49

0.495

0.5

0.505

0.51

0.515

0.52Motion ratio vs wheel travel

Vertical wheel travel [mm]

Mot

ion

ratio

bum

p [−

]

MRbump

0.5 ± 1%

Figure 3.2: Motion ratio versus vertical wheel travel of the front bump system.

3.2.2 Dampers

Because of good experiences, low weight and compact design, KONI 2612 series coil-overdampers are chosen. These shock-absorbers can be mounted in any desired orientation,because they are pressurized with nitrogen gas to avoid cavitation. To achieve the rightdamper velocities, a motion ratio of MR = 0.5 is needed. FSAE rules [1] require aminimum wheel stroke of ±25.4 mm. The minimum stroke of the 2612 series dampers is29 mm [2]. The front and rear coil springs will be the same 61 N/mm Merwede springsas those on the URE05.

The driver will be seated further back in the car in comparison to last year. In combinationwith the new multilink suspension, this yields a far larger distance between the dampermountings on the monocoque and the rocker than is needed for the shortest length ofdamper. This space could of course be bridged with a large mounting bracket attachedto the monocoque. But if the length of the damper is increased by choosing a longer topeye (see figure 3.3), the rocker can be adapted to eliminate a stress concentration andincrease the stiffness.

6

Paul van den Bos Front bump system

28.50 mm

x

y

x

z

Figure 3.3: Koni 2612 damper with the shortest top eye (top) and a longer top eye (bottom).The one with the shortest top eye will be used in the rear suspension system of thecar, the longer one in the front.

3.2.3 Main rocker

The main rocker will be a sandwich of two laser-cut aluminium sheets. This gives aconstruction that is stiff for in-plane forces, but is a lot weaker for out-of-plane forcesthat try to bend it. To assure that the rocker is loaded the optimal way, al forces willhave to act in the same plane, called the work plane. This can be achieved by placing thecentre line of the connection rod (pull rod), damper and anti-roll bar connection rod inthe same plane, in neutral position of the wheels.

To construct the work plane, a reference plane is created through the pull rod and anarbitrary point (the origin). The work plane is also created through the pull rod, but at anangle to the reference plane. By varying the angle, the orientation of the spring-dampersystem can be altered. The angle is set such that the dampers lie in a horizontal planeto minimize packaging volume, height of the centre of gravity and the risk of hitting theground if the suspension bottoms out.

Unlike the URE05, the connection points on the main rocker are all connected via straightlines, as can be seen in figure 3.4. This way, there is no stress concentration and reductionin stiffness like there is in the kink of the URE05 rocker. Furthermore, flaps are added tothe sides of the rocker. These flaps are bend and welded together to create a semi closedbox with a higher out-of-plane stiffness than a pure sandwich construction.

Kink

Flaps

3

4

5

1

2

1

2

3

4

5

1: rotation sensor mount2: damper3: pull-rod4: rotation axis5: anti-roll bar connection rod

Figure 3.4: Main front rocker of the URE05 (left) and URE06 (right). The kink in the URE05rocker causes a stress concentration and stiffness reduction. The flaps on theURE06 rocker are welded together to create a semi closed box.

7

Paul van den Bos Front bump system

Figure 3.5 shows an exploded view of the front main rocker assembly. The rocker rotationaxle and insert will be glued and bolted to the carbon fibre monocoque. The axle runsthrough the monocoque wall to ensure that the forces are transferred to both layers of thecarbon fibre sandwich and increase the bending stiffness of the axle. The two plates ofthe main rocker will be laser-cut out of a 3 mm thick aluminium sheet. They are held inplace on the bearing holder by two C-clips. The bearing holder contains two deep-groovebearings directly under the rocker plates. A spacer between the inner rings of the bearingsprevents an axial load due to tightening of the nut. FSAE rules state that C-clips maynot be used as positive locking mechanisms in the bump suspension system [1]. Thewasher between the nut and the bearing is therefore enlarged to act as a positive lockingmechanism. The rotation sensor is fixed to the rocker rotation axle with a grub screw,and to the main rocker by a bracket and a bolt that runs through two spacers. A sectionview of the main rocker can be seen in figure 3.6.

In

sert ro

tatio

naxle

Ro

cker ro

tatio

naxle

C-c

lip

Bearin

g

Bearin

gh

old

er

Bearin

gsp

acer

Bearin

g

C-c

lip

Wash

er

Nut

Senso

r bra

cket

Ro

tatio

nsenso

r

Main

rocker

Ro

cker s

pacer

Bra

cket s

pacer

Figure 3.5: Exploded view of the front main rocker assembly.

3.2.4 Wheel travel sensor

Data logging is a very helpful tool to reach a good setup for a race car and to train thedrivers. One of the signals that are logged is wheel and damper travel. This will be pro-vided by a Penny & Giles SRH280 contactless rotary sensor with a D style shaft [3]. Thissensor has been specially developed for the extreme conditions encountered in motorsport,such as vibration, dirt and moisture.

In order to make sure that the sensor does not get damaged when the front suspension isin maximum compression, the rocker rotation axle, where the sensor’s shaft is mountedto, is shortened. In combination with the orientation of the rocker plane, this ensures

8

Paul van den Bos Front anti-roll system

that the sensor is no longer the lowest part of the car. The sensor mounting bracketthat connects the sensor to the rocker is stiffened by making it a triangle instead of aT-shape. An extra spacer is added in between the rocker sandwich which greatly increasesthe bending stiffness of the sensor mounting. These adjustments allow for more accuratemeasurements, because signal noise due to flexing of the sensor mount is reduced.

Rotation sensor

Grub screw hole

Sensor bracket

Bracket spacers

Rocker rotation axis

Figure 3.6: Front rocker top and section view showing the wheel travel sensor mounting.

3.3 Front anti-roll system

If a car drives through a corner, it’s body will roll towards the outside of the bend. Thisis not only uncomfortable for the occupants, it is far from ideal with respect to vehicledynamics. One could choose to use stiffer bump springs, but that would result in a harshride and a loss of traction over bumps. To decouple bump and roll stiffness, an anti-rollsystem is used which adds roll stiffness without altering the bump stiffness.

This system consists of a solid torsion bar with splines on each end. Splined busheswith levers welded to them are slid over the splines. These anti-roll rockers are axiallysecured by C-clips. Needle bearings hold the anti-roll bar (ARB) radially in place in themonocoque. Teflon spacers prevent the anti-roll rockers from touching the bearing holderand monocoque and axially lock the ARB. The anti-roll rockers are connected to the mainrockers via carbon fiber rods with aluminium inserts glued to them, the same conceptthat is used for the connection rods of the multilink wheel suspension. Figure 3.7 showsan exploded view of the front anti-roll assembly.

9

Paul van den Bos Front anti-roll system

Anti-roll bar

Inner ring

Needle bearing

Bearing holder

Teflon spacer

Rocker plate

Spline bush

Rocker plate

Carbon rod

Insert

C-clip

Washer

Bolt

Ball joint

Insert

Nut

Washer

Conespacer part1

Ball joint

Conespacer part 2x

y

z

Figure 3.7: Exploded view of the front anti-roll assembly.

3.3.1 Stiffness of the anti-roll bar

Vehicle dynamics simulations with an advanced Simulink model show that the stiff-ness of the front anti-roll bar has to be such that the vehicle feels a roll-stiffness ofkvehicle,front = 118.000 Nm/rad. The stiffness of the ARB depends on the roll motionratio, which is defined as the ratio between the chassis roll angle and anti-roll bar twist.

MRroll =ARB twist θ

body roll angle φ[−] (2)

The Simulink model mentioned in section 3.2.1 can be used to determine the roll motionratio of the system. If the default setting (fifth hole from full stiff) of the anti-roll rockersis used, the roll motion ratio is MRroll = 10.7. This results in a required anti-roll barstiffness of:

kARB =kveh,fr

MR2roll

≈ 1000 Nm/rad (3)

Using the equations for torsion of a solid shaft [4], the required diameter of the ARB canbe calculated, see equations 4 and 5.

kARB =G · IL

I =π

32d4

G =E

2(1 + ν)

kARB =

E · π · d4

64(1 + ν)L⇒ d = 4

√64(1 + ν)L · kARB

Eπ(4)

Where G is the shear modulus, E is the modulus of elasticity and ν is the contractioncoefficient of the material. The torsion length is L, d is the diameter of the torsion-bar.The ARB will be made of 34CrNiMo6+QT.

10

Paul van den Bos Front anti-roll system

This results in:

d = 4

√64(1 + ν)L · kARB

Eπν = 0.3 [−]L = 0.238 [m]

kARB = 1000 [Nm/rad]E = 200 · 109 [Pa]

d = 13.4 mm (5)

3.3.2 Stress in the anti-roll bar

The Von Mises yield criterion [5] states that

τmax =σy√

3(6)

Since σy,34CrNiMo6+QT = 1000 MPa [6], τmax,34CrNiMo6 = 575 MPa.The maximum shear stress in a shaft is given by:

τ =T · d2I

I =π

32d4

T = 190 [Nm]d = 13.4 [mm]

τ =

16Tπd3

= 400 MPa (7)

Therefore the safety factor of the front anti-roll bar is SF = 1.4.

3.3.3 Spline connection

The anti-roll rockers transfer torque to the ARB via splines. Because the diameter andlength of the splines of the front and rear sway bar are the same, but the applied torqueis much higher in the front, it is sufficient to check only the front spline connection.

The maximum shear stress in the spline connection will be at it’s inner diameter. Thiscan be calculated using equation 8, where r is de inner radius, L is the length of the splineand T is the applied torque.

τ =F

AA = 2 π r L

F =T

r

τ =T

2 π r2 L

r = 5 · 10−3 [m]L = 22 · 10−3 [m]T = 190 [Nm]

τ = 55 MPa (8)

The spline bushings will be made of steel-37, which has a yield strength of 225 MPa [6],so the maximum allowable shear stress is:

τmax,st37 =σyield√

3= 130 MPa (9)

This gives a safety factor for the spline connection of SF = 2.4

11

Paul van den Bos Final design overview

4 Rear spring-damper system

Unlike the front, the rear of the URE06 will be completely different than that of theURE05. The main motivations to change the rear are yaw inertia and the total vehiclemass. To achieve this, the rear bulkhead will be placed between the engine and thedifferential instead of behind the differential. Therefore, the rear suspension system ofthe URE05, which was mounted on the bulkhead, can not be used for the URE06.

4.1 Final design overview

The final design of the rear spring-damper system can be seen in figure 4.1. The right partshows the names of the points that are used in the Simulink model. The correspondingcoordinates can be found in appendix B. The working drawings have been incorporatedin appendix C. The bump system consists of points 1 - 4. The anti-roll system includespoints 5 - 7.

Figure 4.1: Final design of the rear spring-damper system.

The various parts of the design will be explained in this chapter; the bump system first,and the anti-roll system afterwards.

12

Paul van den Bos Rear bump system

4.2 Rear bump system

4.2.1 Pushrod versus pullrod

One of the most important choices to be made when deciding on a suspension conceptis between pushrod and pullrod configuration. A schematic bump suspension system isvisible in figure 4.2. It shows a rear view of a left wheel and it’s upright, a vehicle bodyand the suspension in between.

As can be seen in figure 4.2(a), a pullrod is mounted on or near the upper wishbone andruns down to a bellcrank near the bottom of the chassis. The orientation of this rocker canbe adjusted to mount the damper vertical as in the figure, or horizontally in x-directionas used for the front suspension system. Other orientations are off course possible, butthese are the two most common ones. The main advantage of a horizontally mounteddamper is height of the centre of gravity. Secondly, a pullrod is in tension, so it can belighter than an equivalent pushrod that might fail due to buckling.

z

y

F3

F2

F2

F F

F3

a b

Figure 4.2: Rear view of two different suspension configurations: pullrod (a) and pushrod (b).

The alternative is a pushrod system, which can be seen in figure 4.2(b). With this concept,a pushrod is mounted near or on the lower A-arm and runs up to a rocker near the top ofthe rear frame. The damper can be mounted vertically as in the figure, or in a differentorientation.

Mounting the pull- or pushrod on the upper or lower A-arm will introduce a bendingmoment on it. The wheel suspension on the URE06 will be full multilink on both frontand rear. It will be constructed of carbon fiber rods with glued aluminium inserts thathold the rod ends. These rods are very strong and stiff in compression and tension, butcan not endure bending. The connection rod will therefore be mounted directly on theupright.

During cornering, the outside upper A-arm is in tension, while the lower one is in com-pression. This compressive force is 1.8 times higher than the lateral tyre force, becauseof the leverage between the road surface and the upper and lower wishbone. To makematters worse, the lower connection rods of the multilink system are longer than theupper ones to achieve the desired camber gain, which makes them even more prone tofail. Therefore, the toe link is placed on the same level as the lower connection rods toreduce the load per rod. This load per rod can be reduced even further by choosing apushrod configuration.

When a car drives over a bump, the upper connection rods will be loaded with a com-pressive force, and the lower ones with a tensile force. In case of a pullrod system, the

13

Paul van den Bos Rear bump system

upper connection rods gain an extra compressive load due to the pullrod. In case of apushrod configuration, the lower connection rods gain an extra tensile load.

These two cases can off course also be combined: a car hits a bump while cornering.Then, the upper connection rods, which are under tension from the lateral tyre forces,are (partially) unloaded, or even change to a push rod. The compressive cornering forceon the lower ones will also be reduced or switched to tensile.

If the orientation of a pushrod is chosen such that the centre line (force line) goes throughthe tyre contact patch in both x and y (as in figure 4.3), no moments are created thattry to change camber and caster angles.

z

x

z

y

Figure 4.3: Left and rear view of a wheel and its suspension showing that the force line runsthrough the tyre contact patch.

Combining all of the above, the pushrod configuration with the centre line of the con-nection rod through the tyre contact patch is chosen (see figure 4.3). This results in asuspension system that makes use of the toe link that is mounted level with the lowerA-arm and thus creates better loading conditions for the connection rods.

4.2.2 Main rocker

The pushrod is connected to the main rocker. The coil-over damper is mounted to thisbellcrank on one end, and to the rear frame on the other. The rocker rotates in a bearingholder which is mounted on top of the bulkhead. The rocker is made up of two laser-cutaluminium sheets with a thickness of 3 mm, just like the front main rocker. Parts thathave been used on the front will also be used on the rear as much as possible, for costs,ease of manufacturing, assembly and maintenance and to reduce the amount of spareparts that have to be produced and brought along to test days and events.

The work plane of the rear main rocker is created through the pullrod connection pointon the upright, and the centre line of the vertical bulkhead tube.

Figure 4.4 shows an exploded view of the rear main rocker assembly. The rocker rotationaxle clamps the inner rings of the deep groove ball bearings, two thin spacers, the mainrocker sandwich plates and a bush in between them.

The axle itself has a large outer diameter, with a hole drilled along it’s axis. This givesan axle with a much higher bending stiffness than a solid one with the same mass. Thehole is also used to mount the shaft of the wheel travel sensor with a grub screw. Thisgrub screw hole is drilled in one of the two flat faces of the axle head, which are used tohold the axle with a standard 15 mm open-ended wrench during tightening of the nylocknut. The same sensor is used as the one on the front.

14

Paul van den Bos Rear bump system

Nylo

ck

nut

Beari

ng

Beari

ng

sp

acer

Ro

cker

sp

acer

Beari

ng

ho

lder

Beari

ng

sp

acer

Main

rocker

Beari

ng

Ro

cker

rota

tio

naxle

Bra

cket

sp

acer

Sen

so

r b

racket

Ro

tati

on

sen

so

r

Figure 4.4: Exploded view of the rear main rocker assembly.

The bearings are placed far apart in the bearing holder instead of in the same plane asthe rocker plates, to ensure bending stiffness when the rocker is loaded out-of-plane. Thisalso results in a lower (and thus stiffer and lighter) bearing holder, since the height of thematerial around the bearings can be less.

The bearing holder will be mounted on the rear frame by a M12 allen bolt. The bearingholder can be rotated about it’s vertical axis for proper alignment with the connection rod.After the bolt has been tightened, the rotation is blocked by friction. If the orientationof the bearing holder would be fixed by, for example, a ridge, the orientation of thevertical bulkhead tube after welding would be critical to avoid unnecessary out-of-planeforces on the rocker. The bottom of the bearing holder is hollowed out to ensure thatthe pressure that is provided by the bolt is applied to the greatest diameter for optimalbending stiffness. A small hole is drilled through the bearing holder for safety wiring ofthe allen bolt.

15

Paul van den Bos Rear bump system

−30 −20 −10 0 10 20 300.48

0.485

0.49

0.495

0.5

0.505

0.51

0.515

0.52Motion ratio vs wheel travel

Vertical wheel travel [mm]

Mot

ion

ratio

bum

p [−

]

MRbump

0.5 ± 1%

Figure 4.5: Motion ratio versus wheel travel of the rear bump system.

The Simulink model that is mentioned in section 3.2.1 is also used to determine the motionratio of the rear bump system. The rear dampers require a motion ratio of 0.5 for optimalperformance, just like the ones in the front of the car. Figure 4.5 shows that it lies wellwithin a 0.5 ± 1% margin.

Dynamic simulations of the wheel suspension system with an advanced Simulink vehicledynamics model show that the maximum force in the pushrod is Fpushrod = 3600 N .Solving the momentum rule about the rocker rotation axis, and force equilibrium in twodirections gives the forces which the bearing holder has to exercise on the rocker (seefigure 4.6). To do a finite element method (FEM) analysis of the bearing holder, themaximum of the forces is taken (2700 N), and applied as a bearing load in both y andz direction, on both the bearings. This gives a very high safety factor on the load case.Figure 4.7 shows that the maximum stress is 150 MPa. Parts with stresses below 50 MPaare colored black.

F =3600 Npushrod

F = 5200 Ndamper

F = 2000 Ny

F = 2700 Nz

Figure 4.6: Forces acting on the rear mainrocker.

Figure 4.7: FEM analysis of the rear bearingholder.

4.2.3 Wheel travel sensor

Travel of the rear wheels will be measured with the same Penny & Giles SRH280 contact-less rotary sensor as the ones used on the front of the car. Unlike the front suspension

16

Paul van den Bos Rear bump system

system, the shaft of the sensor of the rear main rocker will be connected to the movingpart of the rocker, while the sensor housing remains stationary with respect to the bearinghousing (see figure 4.8).

Rotation sensor

Rocker rotation axis

Grub screw hole

Sensor bracket

Bracket spacer

Figure 4.8: Rear and section view of the rear main rocker assembly.

17

Paul van den Bos Rear anti-roll system

4.3 Rear anti-roll system

The rear anti-roll system will make use of a solid torsion bar with levers on each end, justlike the front of the car. The vehicle roll stiffness has to be adjustable from 1/2· kroll,vehicle

to 2 · kroll,vehicle, to be able to adjust the under- and oversteer behavior of the car overa wide enough range. The anti-roll system will therefore have to be adjustable from√

1/2 · kroll,vehicle to√

2 · kroll,vehicle, to account for the roll motion ratio. Severalconcepts have been examined, which will be briefly discussed next.

4.3.1 Placement of the anti-roll system

At first glance, when looking at figure 4.9, it seems as there are several possibilities to placethe rear anti-roll system. If the ARB would run through the engine mounting (number 1in the figure), with the levers pointing backwards, the connection rod for the ARB wouldcollide with the wheel suspension connection rods. Pointing the levers forward wouldeither result in very large out-of-plane forces on the main rocker, or the work plane of themain rocker would have to be under an extreme angle.

Figure 4.9: Left view of the engine, rear frame, differential assembly and bump suspensionsystem. The numbers 1-7 indicate possible anti-roll bar locations.

Number 2 on the figure points at the lower horizontal tube of the rear bulkhead. Ifthe torsion bar would run through this tube, no extra brackets or supports would benecessary. The tube itself could be used as a bearing holder, resulting in a very lightanti-roll system. Pointing the levers to the rear of the car would give the same problems

18

Paul van den Bos Rear anti-roll system

as concept number 1. Pointing them to the front would be possible, but it would behard to make it such that is has the correct adjusting range, because the levers would bevery short. Furthermore, the levers would not be above the ground clearance plane atthe extremity of their stroke. The ground clearance plane lies 30 mm above the ground,which is the underside of the tubes of the rear frame.

To enable mounting of the ARB at position 3, the lower tube of the toe-link subframewould have to be reinforced to be able to sustain the vertical (bending) load.

Concept number 4 does a better job in that respect, because the ARB could be placedcloser to the corner of the triangle. It would however be impossible to adjust the rollstiffness by means of a varying length lever, because it would have to be very long to getthe required adjustability range. The connection rod would collide with the A-arms inthe stiffest settings, and have a large angle with respect to the work plane of the mainrocker in the softest settings.

The fifth possibility would also result in large bending forces on the inclined tube. Eventhough it is a much stiffer tube because of it’s greater diameter, it would still not be adecent concept because the tube gets loaded on it’s weakest point: in the middle betweenthe connection points. It would also result in a high centre of gravity of the anti-rollsystem.

The differential and sprocket (grey disc) assembly can be moved back and forth to adjustchain slack. In the figure, it is set at it’s most rearward position. Placing the ARB atposition 6 would mean that either the chain or the sprocket runs through it if they aremoved forward.

Number 7 does not have any of the afore-mentioned disadvantages. The radius of the cut-away in the differential mount is just large enough to run the torsion bar through. Theoffset to the bulkhead is needed to mount bearing supports. The levers will be pointingto the front of the car. The ARB can be placed far enough forward to make sure thereare no collisions with the lower multilink connection rod in the stiffest setting. The leverscan be kept short to prevent a very big angle with respect to the plane of the main rockerin the softest setting, while still providing a large enough range of stiffness settings.

19

Paul van den Bos Rear anti-roll system

4.3.2 Bearing tubes

The rear bulkhead is not a rectangle; the lower horizontal tube is shorter than the topone. There are two conceivable options to mount the sway bar to the bulkhead: mountingthe bearings on the bulkhead and making the torsion bar slightly longer than the widthof the bulkhead, to minimize the bending moment about the x-axis on it (figure 4.10(r)).Option number two is to use a longer torsion bar, and creating some sort of supportthat makes it possible to mount the bearings right next to the levers of the torsion bar(figure 4.10(l)). This support will bear the bending load, so the anti-roll bar is only usedfor torsion.

In neutral position of the wheels, the angle between the ARB-connection rod and thexz-plane is about 22◦in case of the short ARB. That is, the force vector of the connectionrod has a lateral component (y-direction) of 0.37 ·Frod, resulting in a big axial load, and alarge moment about the vertical axis through the end of the torsion bar. The levers, thetorsion bar and/or the torsion bar mounting could be constructed in such a way that theyare stiff enough to withstand this moment, but they would still be loaded in a directionthat is not necessary to begin with. A force parallel to the centre line of the sway bardoes not contribute to the torsion of that bar along the same line.

Figure 4.10: Rear view of the bulkhead and two options for the torsion bar: short (right), withthe connection rod under a large angle, or long (left), with the connection rodunder a small angle but with a larger bending length of the anti-roll bar.

By placing the end of the sway bar more outward, and with it the anti-roll connection rodmore upright, the lateral component of the force can be greatly diminished. Decreasingthe angle between the the pullrod and a vertical plane to 8◦will reduce the lateral load to0.14 ·Frod. The greater extension to the sides would increase the bending moment aboutthe longitudinal axis if the bearings were still mounted directly to the bulkhead. Bendingreduces the roll stiffness of the vehicle.

20

Paul van den Bos Rear anti-roll system

Placing the bearings as close to the levers as possible reduces bending of the torsion bar.The bearings will be mounted inside a tube of large diameter for optimal bending stiffness.The bearing-tubes are connected to the rear frame by two plates; one at the standing tubeof the bulkhead, and one that also holds the differential supports (see figure 4.11). Theouter diameter of the tubes is not constant, but is larger from the differential support to5 mm left of the outer support plate, following the momentum line. From there on out,the outer diameter is decreased from 36 mm to 32 mm by means of a taper and an edgeblend to prevent the notch effect. This smaller diameter is needed to avoid collisions withthe multi-link connection rod, as can be seen in figure 4.12. Together with the leverageof the connection rod, this provides enough clearance. The decrease in inner diameter isplaced to the right of the outer support plate. This local increase in wall-thickness of thetube at the outer support plate reduces stress concentrations.

Figure 4.11: Rear bulkhead (blue), suspension system (grey) with bearing tubes (red) and it’smounting plates (green).

The bearing tubes have been checked with a finite element method analysis. This includedthe bearing tubes and the support plates. Translation of the plates was fixed along thewelding lines. The dynamic vehicle simulations show that the maximum torque in theanti-roll bar is about 100 Nm. The length of the lever is 37 mm, which gives a verticalforce of 2700 N at the end of the tube. The result can be seen in figure 4.13.

4.3.3 Stiffness of the anti-roll bar

The vehicle dynamics simulations mentioned in section 3.3.1 that have been used todetermine the required front and rear vehicle roll stiffness show that the rear vehicle roll-stiffness due to the anti-roll bar will have to be kvehicle,rear = 66.500 Nm/rad. In thedefault setting (fifth hole from full stiff) of the anti-roll rockers, the roll motion ratio isMRroll = 12.1. This results in a required anti-roll bar stiffness of:

kARB =kveh,rear

MR2roll

≈ 450 Nm/rad (10)

Using the equations for torsion of a solid shaft again (see equation 4), the required diam-

21

Paul van den Bos Rear anti-roll system

Bearing tube

Needle bearing

Splines

Torsion bar

Teflon spacer

Bearing tube

Torsion bar

Outer support plate

Inner support plate

36.0

0

32.0

0

28.0

0

32.0

089.00

155.00

z

y

Figure 4.12: Several views of the left part of the rear anti-roll assembly.

Figure 4.13: FEM analysis results of the bearing tubes.

22

Paul van den Bos Rear anti-roll system

eter of the ARB can be calculated, see equation 11. The rear anti-roll bar will also bemade out of 34CrNiMo6+QT, just like the front ARB. This results in:

d = 4

√64(1 + ν)L · kARB

Eπν = 0.3 [−]L = 0.419 [m]

kARB = 450 [Nm/rad]E = 200 · 109 [Pa]

d = 12.6 mm (11)

4.3.4 Stress in the anti-roll bar

As shown in section 3.3.2, the maximum allowable shear stress for 34CrNiMo6+QT isτmax,34CrNiMo6 = 575 MPa.The maximum shear stress in the rear anti-roll bar is given by:

τ =T · d2I

I =π

32d4

T = 95 [Nm]d = 12.6 [mm]

τ =

16Tπd3

= 240 MPa (12)

So the safety factor of the rear anti-roll bar is SF = 2.4.

23

Paul van den Bos Conclusion and recommendations

5 Conclusion and recommendations

The subject of this report is the design of a spring-damper system for the next car thatwill be used by University Racing Eindhoven to race in the Formula Student competition:the URE06.

The requirements have been determined in chapter 2. Subsequently, the kinematics of thefront and rear spring-damper systems have been set. This resulted in a set of coordinates.The individual parts have been constructed next, taking the requirements into account.Components such as the anti-roll bars have been analyzed by hand calculations, whileother parts have been optimized using FEM analysis.

Several recommendations can be made:

• The forces in the multilink connection rods that resulted from dynamic simulationscould be verified with the use of strain gauges. This might show weak spots of thesystem, or the opposite: too high safety factors which mean mass could be saved.

• The suspension system contains a lot of different spacers. Reducing the number ofspacers could save costs and production time.

• Advantages and disadvantages of blade-style anti-roll levers could be investigated.

24

Paul van den Bos REFERENCES

References

[1] http://www.formulastudent.com/universities/Rules.htm

[2] http://www.koni.com/fileadmin/user_upload/business_units/racing/downloads/Technical_Manual_2612_v1.2.1.pdf

[3] http://www.pennyandgiles.com/script_cms/force_file_download.php?fileID=267

[4] P.C.J.N. Rosielle, E.A.G. Reker, (March 2004) Constructieprincipes 1 Lecture notes4007 Technische Universiteit Eindhoven.

[5] R. von Mises, (1913). Mechanik der Festen Korper im plastisch deformablen Zustand.Gottin. Nachr. Math. Phys., vol. 1, pp. 582592.

[6] http://www.mcb.nl/files/File/pdf/MCB_Boek_CD_1.2.pdf

25

Paul van den Bos Front spring-damper system coordinates

A Front spring-damper system coordinates

Figure A.1: Final design of the front spring-damper system.

The coordinates corresponding to the names in figure A.1 are given below. The formatis: name = [x y z], with all values in meters. The given coordinates are for the front leftwheel.

d.front.sb.p1 = [1.4018 0.0588 0.0740]d.front.sb.p2 = [1.6397 0.0641 0.0740]d.front.sb.p3 = [1.6000 0.1290 0.1100]d.front.sb.p4 = [1.6385 0.1176 0.1033]d.front.sb.p5 = [1.6469 0.1475 0.1195]d.front.sb.p6 = [1.8069 0.1462 0.1169]d.front.sb.p7 = [1.8062 0.1462 0.1489]

26

Paul van den Bos Rear spring-damper system coordinates

B Rear spring-damper system coordinates

Figure B.1: Final design of the rear spring-damper system.

The coordinates corresponding to the names in figure B.1 are given below. The formatis: name = [x y z], with all values in meters. The given coordinates are for the rear leftwheel.

d.rear.sb.p1 = [0.2126 0.0263 0.3843 ]d.rear.sb.p2 = [0.1736 0.2321 0.3866 ]d.rear.sb.p3 = [0.1582 0.3072 0.3829 ]d.rear.sb.p4 = [0.1566 0.2296 0.3198 ]d.rear.sb.p5 = [0.1436 0.2752 0.3038 ]d.rear.sb.p6 = [0.1088 0.2410 0.0777 ]d.rear.sb.p7 = [0.0765 0.2410 0.0958 ]

27

Paul van den Bos Working drawings of the front and rear spring-damper system

C Working drawings of the front and rear spring-dampersystem

28