Optimization of Formula Car Double Wishbone Suspension System

2012

Debraj Roy, Kulkeerty Singh, Harshit Agarwal,

Aman Bansal, Ashutosh Sharma

B.Tech (MAE) V Sem, ASET

FORMULA CAR SUSPENSION SETUP OPTIMIZATION

Amity School of Engineering & Technology Page 1

Abstract

The report intrigues with the variations and optimizations in the suspension

design of formula cars, the fastest automobiles. We elaborate the concepts coined

with a suspension system setup for a formula car. Suspension is what harnesses the

power of the engine, the downforce created by the wings and aerodynamic pack

and the grip of the tyres, and allows them all to be combined effectively and

translated into a fast on-track package[i]

. Suspension systems serve a dual purpose

— contributing to the vehicle's handling and braking for good active safety and

driving pleasure, and keeping vehicle occupants comfortable and reasonably well

isolated from road noise, bumps, and vibrations, etc. These goals are generally at

odds, so the tuning of suspensions involves finding the right compromise[ii]

The suspension of a modern Formula One car forms the critical interface

between the different elements that work together to produce its performance. The

analytical part comprises of study of double wishbone setup used nowadays with

the effect of roll centre on the car‘s performance. The optimization for a perfect

balance between the various criteria affecting the suspension has been scrutinized

from different aspects. A brief view on the different options for the suspension

setup has been presented. A critical point to the controversial ‗active suspension‘

systems


Acknowledgements

I would like to extend my heartiest gratitude to respected Mr. Vijay Shankar

Kumawat, Department Of Mechanical Engineering, Amity School of Engineering

& Technology for his visionary guidance and sizable subvention at each and every

step of the project. It was his precisionist & rationalist remonstrance that obscured

the way for us to work through this project and develop an apical precinct for the

task. It was extremely amiable experience to work under a truly devoted and

ingenious scholastic.

Also, it would be malefic of us if we fail to extend our gratitude to all the

colleagues whom we interacted with the time being. We would immensely like to

appreciate the support of each other for their generous & receptible nature

throughout the work.

The fact that this small journey is approaching its end is sorrowful for us as

we would have liked to gain more from all the aforementioned delightful

personnel. We were also willing to complete a optimisation of the setup from

ourown, but shortage of time and material requisites have hindered our willingness.

It would be grateful of us to lend our hand in nearby future for any other task in the

project and even work on it.


Table of Contents

Abstract……………………………………………………..…………………….1

Acknowledgements……………………………………….……………………....2

Table of Contents…………………………………………..……………………..3

List of Figures….......................................................................................................5

Tables & Graphs……………………………………………….…………………7

Certificate………………………………………….……………….…………...8

1. Introduction…………………………………………………………….9

2. Understanding Basics of Formula Car Suspension…………………...10

Jounce…………………..………………………………………...10

Rebound…………………………………………………………..10

Springs……………………………………………………………11

Sprung Weight…………………………..……………………......11

Unsprung Weight…………………………………………………11

Ride Height……………………………………………………….12

Vehicle Trim Height……………………………………………...13

Setback……………………………………………………………13

Thrust Angle……………………………………………………...13

Caster Angle……………………………………………………...14

Camber Angle…………………………………………………….14

Toe Angle…………………………………………………….…...15

Shock Absorbers, and Travel……………………………….…….16

Wheelbase and Track Width……………………………………...16

Kingpin Inclination & Scrub Radius……………………….…..…16

Damping………………………………………………….……….17

Roll Centre………………………………………………………..19

Anti-Squat………………………………………………………...28

Suspension Travel………………………………………………...28

Anti-Roll Bars…………………………………………………….29


Shock-Mounting Locations………………………………….……30

3. Mobility of Formula Car Suspension Mechanisms..……………..........33

4. Double Wishbone Suspension for Formula Car...……………………..35

Multi-Link Suspension.…………………………………………….39

5. Optimized Suspension Geometries for Formula Car………………....40

Design Overview………………………………………………….47

o Static Weight……………………………………………….47

o Lateral load transfer due to lateral acceleration……………48

o Longitudinal weight transfer due to negative acceleration...49

o Maximum loads achieved………………………………….50

o Maximum Tractive Forces ………………………………...50

o Factor of Safety Development……………………………...51

o A-Arm Force Calculations…………………………………52

o Front Uprights……………………………………………...54

o Rear Uprights………………………………………………56

o Rockers……………………………………………………..57

o Push rods…………………………………………………...58

o Steering Arms………………………………………………62

6. Process Controls (Troubleshooting)…………………………………..63

7. Safety Considerations……………………………………………........65

8. Manufacturing Considerations………………………………………..66

9. Modifications…………………………………………………………66

10. Conclusion…………………………………………………………….67

11. References…………………………………………………………….68

12. Bibliography…………………………………………………………..69


Figures

Figure 1: Jounce and Rebound……………………………………………………10

Figure 2: Spring Rate Comparison……………………………………………....11

Figure 3: Ride Height[iv]

………………………………....……………………….12

Figure 4: Setback & Thrust Angle………………………………………………13

Figure 5: Caster & Camber Angle[v]

…………………………………………….15

Figure 6: Toe Angle[vi]

…………………………………………….…………….16

Figure 7: Kingpin Inclination & Scrub Radius…………………………………17

Figure 8: Suspension of a Typical Car………………………………………….19

Figure 9: Intersection Point of Poles………………...............................................20

Figure 10: Applying Theorem of Kennedy……………………………………..22

Figure 11: Obtaining Roll Centre….……………………………………………22

Figure 12: Inertial Force…………………………………………………………23

Figure 13: Positioning of CG & RC……………………………………………..24

Figure 14: Roll Moment…………………………………………………………24

Figure 15: Change in Roll Centre on Cornering……………………………..…25

Figure 16: Roll Axis: Side View…………………………………………………26

Figure 17: Anti-Roll Bar[vii]

……………………..……………………………….30

Figure 18: Shock Mounting Locations & Wheel Rates….………………………31

Figure 19: Ferrari 663[xiv]

………………………………….……………………..33

Figure 20: Double Wishbone Suspension Multi-Link Solidworks Model[xi,xii]

…...36

Figure 21: Double Wishbone Suspension Rear View[iv]

………………………….38


Figure 22: Double Wishbone Suspension with Pull Rod Arrangement[viii]

..........39

Figure 23: Double Wishbone Suspension Coil Spring Solidworks Model[xiii]

….40

Figure 24: Optimized Roll Centre Location………………………….…………43

Figure 25: Tire Data……………………………………………………………..44

Figure 26: Scrub radius………………………………………………………….45

Figure 27: Plot of Relevant Forces………………………………………………48

Figure 28: Tire Force Schematic …………………………………………….…49

Figure 29: Schematic of tire with axes ………………………………………….51

Figure 30: Force Schematic & Truss Design …………………………….……..53

Figure 31: Front Uprights ………………………………………………………55

Figure 32: Front Uprights CATIA V5 Model Static Load Test ..………………56

Figure 33: Rear Uprights ……………………………………………………….56

Figure 34: Rear Uprights CATIA V5 Model Static Load Test ……………….…57

Figure 35: Rockers ………………………………………………………………58

Figure 36: Rebound Damping[10]

………………………………………………….59

Figure 37: Compression Damping …………………………………………….….60

Figure 38: Pushrods.………………………………………………………………61

Figure 39: Bell Crank FEA Results[11]

………………………………………..…61

Figure 40: Motion Ratio…………………………………………..…………….62

Figure 41: Steering Arms…………………………………………..……………62

Figure 42: Supra SAE AUR Prototype Solidworks Model[ix]

………………..…67


Tables

Table 1: Geometries of Double Wishbone SLA Suspension……………..…...41-42

Table 2: Acceleration Data used for Calculations……………………………..….48

Table 3: Vertical Tire Force Calculation…………………..……………………...49

Table 4: Lateral Acceleration Loads…………………..………………………….49

Table 5: Longitudinal Weight Transfer…………..……………………………….50

Table 6: Maximum Achievable Loads …………………..……………………….50

Table 7: Horizontal Tire Force …………………..……………………………….51

Table 8: Material Properities for a 14 inch pin-pin beam …………………..……54

Graphs

Graph 1: Roll Centre v/s Displacement………………………..………………….21

Graph 2: Camber v/s Wheel Displacement…………………..…………………...45

Graph 3: Toe-In/Out v/s Wheel Displacement……………..…………………......46

Graph 4: Caster Angle v/s Wheel Displacement………………...……………......47

Graph 5: Kingpin Angle v/s Wheel Displacement……………………………......47


CERTIFICATE

This is certified that this project report "A Technical Report On

Optimization Of Formula Car Double Wishbone Suspension

System" is the bona fide work of Debraj Roy, Kulkeerty Singh,

Harshit Agarwal, Ashutosh Sharma, Aman Bansal studying in

B.Tech(MAE) V Semester of Amity School of Engineering &

Technology, Jaipur who carried out the project under my supervision.

Signature of the HOD Signature of Supervisor

(Mr.Mangal Singh Sisodia) (Mr. Vijay S. Kumawat)

Lecturer,Mechanical Engg. Deptt. Lecturer, Mechanical Engg. Deptt.

AMITY SCHOOL OF ENGINEERING & TECHNOLOGY

NH-11C, Kant Kalwar, RIICO Industrial Area,

Jaipur, Rajasthan-302006


Introduction

Suspension is the term given to the system of springs, shock absorbers and

linkages that connects a vehicle to its wheels and allows relative motion between

the two [1] [ii]

. Apart from your car's tyres and seats, the suspension is the prime

mechanism that separates one‘s rears from the road. It also prevents one‘s car from

shaking itself to pieces. No matter how smooth we think the road is, it's a bad, bad

place to propel over a ton of metal at high speed. So we rely upon suspension.

People who have once travelled on underground trains wish that those vehicles

relied on suspension too, but they don't and that's why the ride is so harsh. Actually

it's harsh because underground trains have no lateral suspension to speak of. So as

the rails deviate side-to-side slightly, so does the entire train, and its passengers. In

a car, the rubber in the tyre helps with this little problem, while all the other

suspension parts do the rest[i]

. It is important for the suspension to keep the road

wheel in contact with the road surface as much as possible, because all the forces

acting on the vehicle do so through the contact patches of the tires. Thus the

suspension protects the vehicle itself and any cargo or luggage from damage and

wear. The design of front and rear suspension of a car may be different.

In 1901 Mors of Paris first fitted an automobile with shock absorbers. With

the advantage of a dampened suspension system on his 'Mors Machine', Henri

Fournier won the prestigious Paris-to-Berlin race on the 20th of June 1901.

Fournier's superior time was 11 hours 46 min 10 sec, while the best competitor was

Léonce Girardot in a Panhard with a time of 12 hours 15 min 40 sec.[2]

In 1920, Leyland used torsion bars in a suspension system. In 1922,

independent front suspension was pioneered on the Lancia Lambda and became

more common in mass market cars from 1932. [3]

Unlike road cars, occupant comfort does not enter the equation for formula

cars - spring and damper rates have to be very firm to ensure the impact of hitting

bumps and kerbs and have to be defused as quickly as possible. The spring absorbs

the energy of the impact; the shock absorber releases it on the return stroke, and

prevents an oscillating force from building up. Think in terms of catching a ball

rather than letting it bounce.[i]


Understanding Basics of Formula Car Suspension

Jounce[4]

It is the upward movement or compression of suspension components.

Rebound

It is the downward movement or extension of suspension systems.

Springs

The most common variety of springs are coil springs, these are usually

placed around the damper housing to form a spring-damper unit. A spring is an

elastic device that resists movement in its direction of work. The force it exerts is

proportional to the movement of one of its ends. Or to put this into a mathematical

equation:

Force = Movement * Spring constant

A high value for the spring constant makes for a stiff spring, and a low

value makes for a soft spring.

Jounce Rebound FIG. 1


Sprung Weight

Sprung weight transfer is the weight transferred by only the weight of the

vehicle resting on the springs, not the total vehicle weight. Calculating this requires

knowing the vehicle's sprung weight (total weight less the unsprung weight), the

front and rear roll center heights and the sprung center of gravity height (used to

calculate the roll moment arm length). Calculating the front and rear sprung weight

transfer will also require knowing the roll couple percentage.

The roll axis is the line through the front and rear roll centers that the vehicle

rolls around during cornering. The distance from this axis to the sprung center of

gravity height is the roll moment arm length. The total sprung weight transfer is

equal to the G-force times the sprung weight times the roll moment arm length

divided by the effective track width. The front sprung weight transfer is calculated

by multiplying the roll couple percentage times the total sprung weight transfer.

The rear is the total minus the front transfer.

Body and frame

Engine and transmission

Load or cargo

Fuel tank

Unsprung Weight

FIG. 2 Spring Rate Comparison


Unsprung weight transfer is calculated based on the weight of the vehicle's

components that are not supported by the springs. This includes

Wheels and tires

Wheel bearings and hubs

Axles and steering knuckles

Wheel mounted brake components

These components are then (for calculation purposes) assumed to be

connected to a vehicle with zero sprung weight. They are then put through the

same dynamic loads. The weight transfer for cornering in the front would be equal

to the total unsprung front weight times the G-Force times the front unsprung

center of gravity height divided by the front track width. The same is true for the

rear.

Ride Height

Ride height is the height at which a vehicle‘s sprung components are carried

over the vehicle‘s un-sprung components. It is a suspension measurement taken

from un-sprung to sprung components. Vehicle ride height is not the same as:

Vehicle trim height

Curb riding height

Side-to-side lean

Ride height FIG. 3


Vehicle Trim Height

Side-to-side lean is a term used to describe the difference in the height of the

vehicle body usually measured from a point on the body to the ground on both

sides of the vehicle.

Setback

It is a reference to the difference in side-to-side wheelbase.

Positive Setback :  The RH wheelbase is longer, using the left side as a base.

Negative Setback : The RH wheelbase is shorter, using the left side as a

base.

Thrust Angle

FIG. 4 Setback & Thrust Angle


It is the angle between the vehicle's centerline and the thrust-line of the rear

axle.

Negative thrust angle- rear wheels point left.

Positive thrust angle - rear wheels point right.

Caster Angle

It is the forward or rearward inclination of the steering axis. It acts as a  

directional control angle. It would will pull the vehicle to the least positive side. It

is sometimes misinterpreted as a tire wear angle which isn‘t so.

Camber Angle

Camber describes the angle between the tyre‘s centreline and the vertical

plane. It is also a directional control angle and would pull the vehicle to most

positive side. It is a ‗Tire wear angle‘. If the wheels of the car lean inwards, the

camber angle is said to be negative, if they lean outward, the angle is said to be

positive. It is usually measured at ride height, and angles of -0.5 to -3 are the most

common.[6]

First of all, positive camber is never used, only negative. Negative camber is

necessary because when a car turns into a corner, it experiences chassis roll, which

increases the tires' camber angle. Also, because most rubber tires are quite flexible,

they get a little deformed in the direction of the Centre of the corner. If the car

doesn‘t have any negative camber, only the tires' outer edge and sidewall would

touch the ground, which isn't beneficial for traction. A tyre‘s coefficient of

traction (grip) increases as its contact surface increases, so the ideal situation

would be that the tire would stay perpendicular to the ground at all times, and that

it wouldn‘t deform under heavy side load. Unfortunately, this isn‘t the case; most

of the time one has to find the best compromise. The problem is that if one wants

maximum forward traction, he has to set the camber to 0°, and if he wants

maximum cornering action he has to set it to a few degrees negative, depending on

the softness of the suspension and tire carcass. So one can't have both, but you can

try to make the best possible compromise. The easiest way is to set camber so the

tires wear evenly across their surface, that way one can be sure every part of the


surface is used to the maximum of its potential. Keep in mind that a car with very

soft suspension settings and very little camber change will need more negative

camber than a car with a very stiff suspension and in very bumpy off-road

conditions however, it can be beneficial to use more camber than would be needed

for uniform wear across the surface. The excess camber stabilises the car in large

bumps and reduces the risk of catching a rut and flipping over.

Camber can also be used as an adjustment to attain a desired handling effect,

but we definitely won' t recommend this: a non-optimal camber setting always

yields less traction, which inevitably makes the car slow.

Toe Angle

It is inward or outward variation of tires from a straight ahead position.

Possibilities of toe are in form of ‗Toe In‘ or ‗Toe Out‘. It is not a directional

control angle. It is also a ‗Tire wear angle‘ like camber angle.

FIG. 5 Caster & Camber Angle


Shock absorbers, and travel

Shock absorbers and dampers are important elements of suspension and are

the key element to supporting and balancing the forces that the arm will be

suffering. Functions of Shock Absorbers

Control spring oscillation and rebound

Reduce body sway and lean on turns

Reduce the tendency of a tire to lift off the road

Compression Ratios are expressed in terms of extension/compression

with ratios from 50/50 to 80/20 available. A ratio of 70/30 is common.

Wheelbase and Track Width

The wheelbase is the distance between the centers of the front and rear

wheels.

Track width is usually measured from the center point of the tires. The

track widths may be different, but the smaller track width cannot be less than 75%

of the larger track width. This will provide a stability, but it should not be so wide

that it hinders cornering and maneuverability.

Kingpin Inclination and Scrub Radius

FIG. 6 Toe Angle


The first parameter that had to be determined besides track width was

kingpin inclination. This is the angle between vertical and the axis running through

the upper and lower ball joints. The kingpin inclination affects steering

performance and return ability. This is interrelated with the scrub radius and the

spindle length, which were minimized for this design.

The spindle length is the distance from the kingpin axis to the centerline of

the wheel at the wheel axis.

The scrub radius is the distance from the kingpin axis to the center of the

wheel at the ground. By minimizing the spindle length and scrub radius, the

jacking effect when the wheels are steered is minimized. That results in less

steering effort on the driver‘s part and less sensitivity to braking inputs.

Damping

Damping is needed to absorb the energy associated with suspension travel. Bumps

or lateral or longitudinal acceleration can induce that suspension travel. Without

damping, the magnitude of the suspension movement would never stop increasing,

leading to a very humorous situation. In terms of energy, damping absorbs most of

the energy the car receives as it moves, unlike springs, which store the energy, and

FIG. 7 Kingpin Inclination & Scrub Radius


release it again. Imagine a car with no damping driving on a bumpy road. The

subsequent impacts from the bumps on the tires would make the suspension

bounce very intensely, which is not a good thing. Dampers absorb all the excess

energy, and allow the tires to stay in contact with the ground as much as possible.

This also indicates that the damping should always be matched to the spring ratio:

never runs a very stiff spring with very soft damping or a very soft spring with

very stiff damping. Small changes however can give interesting results. Damping

that‘s a bit on the heavy side will make the car more stable; it will slow down both

the vehicle‘s pitch and roll motions, making it feel less twitchy. Damping only

alters the speed at which the rolling and pitching motions occur, it does not alter

their extent. So if one wants his vehicle to roll less, anti-roll bars, or the springs

should be adjusted, but not the dampers.

Something you can adjust with the damping rate is the speed at which the

suspension rebounds: if a car with soft springs but hard dampers is pushed down,

it will rebound very slowly, and a car with stiff springs and light damping will

rebound very quickly. The same situation occurs when exiting corners: in the

corner, the weight is transferred, and the chassis has rolled and/or dived, but when

the steering is straightened out, and the cornering force disappears, the chassis

comes back to its original position. The speed at which this happens is controlled

by the damping rate. So the car with the soft springs and hard damping will tend to

want to continue turning when the steering is straightened. It will also tend to

continue running straight when steering is first applied; it will feel generally

unresponsive, yet very smooth. The car with firm springs and soft damping will be

very responsive: it will follow the driver‘s commands very quickly and

aggressively.

We may not always be able to use the spring and damping rates one like, because

of bumps. Small, high-frequency bumps require soft settings for both damping and

springs. We can‘t use such soft settings for big, harsh bumps, because the car

would bottom out a lot, so we‘ll need to set our car a little stiffer. On very smooth

tracks you can use very stiff settings for both springs and damping. But it‘s not

quite as simple as that: even in the simple dampers used in R/C cars, there is a

difference between high-speed and low-speed damping. They‘re also

independently adjustable.


Roll Centre

Predicting how a car will react when forces are applied at the tires is not

easy. The force can be absorbed, split, converted into a torque... by all sorts of

suspension components. To avoid all of this one can try to find the roll centre of

his car and try to predict the reaction of the car from there. A roll centre is an

imaginary point in space; look at it as the virtual hinge the car hinges around when

its chassis rolls in a corner. It's as if the suspension components force the chassis to

pivot around this point in space.

Let's look at the theory behind it first. The theorem of Kennedy tells us that

if three objects are hinged together, there are at most three poles of movement, and

they are always collinear, i.e. they are always on one line. To understand what a

pole really is, consider the analogy with the poles of the earth: as earth rotates, the

poles stay where they are. In other words, the earth rotates around the imaginary

axis that connects the two poles. Now this is a 3-dimensional analogy, in the case

of the roll centre we only need two dimensions at first. So a pole of an object (or a

group of objects) is like the centre point of a circle it describes.

If we look at the suspension of a typical Formula car, with a lower A-arm

and an upper link, we see a bunch of objects that are all hinged together. These

objects include the chassis, the upper link, the A-arm, and the hub. For now we

consider the hub, the axle and the wheel as one unit. First, let‘s look at the chassis,

the upper link and the hub. They are hinged together, so the theorem of Kennedy

FIG. 8 Suspension of a typical Car


applies. The pole of the upper link and the hub is the ball joint that connects them,

because they both hinge around it. The pole of the upper link and the chassis is also

the ball joint that connects them.

So if we now look at the chassis, the upper link and the hub, we have

already found two of the three poles, so if there is a third one, it should be on the

imaginary line that connects the other two. That line is drawn on the next drawing.

The same applies to the bottom half of the suspension system, the pole of

the lower A-arm and the hub is the outer hinge pin, the pole of the A-arm and the

chassis is the inner hinge pin, so if there is a third pole it should be on the line that

connects the other two. If the car uses ball links instead of hinge pins, the axis

through the centres of the two balls makes up a virtual hinge pin.

If the two lines intersect, the pole of the hub/wheel and the chassis is the

intersection point I. The distance from point I to the centreline of the tire is

sometimes referred to as 'swing axle length‘, it's as if the hub/wheel is attached to

an imaginary swing axle which hinges around point I. Having that long swing axle

would be equivalent to having the double wishbone-type suspension, but the actual

construction would be very impractical. Nevertheless it serves as a good

simplification. The swing axle length, together with the angle, determines the

amount of camber change the wheel will experience during the compression of the

FIG. 9 Intersection Point of Poles


suspension. A long swing axle length will cause very little camber change as the

suspension is compressed, and a very short one will cause a lot. If the upper link

and the A-arm are perfectly parallel to each other, the two lines won't intersect, or,

in other words, the intersection point I is infinitely far removed from the car. This

isn‘t a problem though: just draw the line (in the next drawing) parallel to the two.

The two lines should always intersect on the side of the centre of the car, if they

intersect on the outside, camber change will be bizarre: it will go from negative to

positive back to negative, which is not a good thing for the consistency of the

traction.

The wheel and the ground can also move relative to each other; let's assume

the wheel can pivot around the point where it touches the ground, which is usually

in the middle of the tire carcass. That point is the pole of the tire and the ground.

As it is drawn, a problem might arise when the chassis rolls: the tires might also

roll, and hence the contact point between the earth and the tire might shift,

especially with square-carcass tires that don't flex much.

Now we can apply the theorem of Kennedy again: the ground, the wheel and

the chassis are hinged together, we have already found the pole of the wheel and

the ground, and the pole of the wheel and the chassis. If the pole of the ground and

the chassis exists, it should be somewhere on the line that connects the other two

poles, drawn in the next drawing.

-3

-2

-1

0

1

2

3

0 2 4 6 8

Wh

eel D

isp

lace

me

nt

(in

)

Roll Centre Height(in)

Graph 1 Roll Centre V/s Wheel Displacement


The same procedure can be followed for the other half of the suspension, as

in the picture below. Again a line will be formed on the pole of the ground and

the chassis should be on. The intersection point of the two lines is the pole of the

ground and the chassis. That point, the pole of the chassis and the ground is also

called the roll centre of the chassis. Theoretically, the ground could rotate around

it while the chassis would sit still, but usually it‘s the other way around; the chassis

rotates around it while the ground sits still.

The roll centre is also the only point in space where a force could be applied

to the chassis that wouldn‘t make it roll. The roll centre will move when the

FIG. 10 Applying Theorem of Kennedy

FIG.11 Obtaining Roll Centre


suspension is compressed or lifted, that‘s why it‘s actually an instantaneous roll

centre. It moves because the suspension components don‘t move in perfect circles

relative to each other, most of the paths of motion are more random. Luckily every

path can be described as an infinite series of infinitely small circle segments. So it

doesn‘t really matter the chassis doesn‘t roll in a perfect circular motion, just look

at it as rolling in a circle around a centre point that moves around all the time.

If we want to determine the location of the roll centre of a car, we can either

‗eyeball‘ it by imagining the lines and intersection points, or you can get a really

big sheet of paper and make a scale drawing of the car‘s suspension system.

Now that we know where the roll centre (RC) is located, let‘ s look at how

it influences the handling of the car. Imagine a car, driving in a circle with a

constant radius, at a constant speed. An inertial force is pulling the car away from

the centre point, but because the car is dynamically balanced, there should be a

force equal but opposite, pulling the car towards the centre point. This force is

provided by the adhesion of the tires.

In principle, the inertia force works on all the different masses of the car, in

every point, but by determining the centre of gravity (CG) it‘s possible to replace

all of the inertia forces by one big force working in the CG. It‘s as if the total mass

of the car is packed into one point in space, the CG. If the CG is determined

correctly, both conditions should be perfectly equivalent.

The forces generated by the tires can be combined to one force, working in

the car‘s roll centre.

Viewed from the back of the car, it looks like this:

FIG.12 Inertial Force


Two equal, but opposite forces, not working in the same point generate a

torque equal to the size of the two forces multiplied by the distance between them.

So the bigger that distance, the more efficiently a given pair of forces can generate

a torque onto the chassis. That distance is called the roll moment. Note that it is

always the vertical distance between the CG and the RC, since the forces always

work horizontally.

The torque generated by the two forces will make the chassis roll, around the

roll centre. This rolling motion will continue until the torque generated by the

springs is equally big, only opposite. The dampers determine the speed at which

this happens. Note that the roll torque is constant, well at least in this example

where the turning radius is constant, but the torque supplied by the spring increases

as the suspension is compressed. The difference between the two torque‘s, the

resultant, is what makes the chassis lean. This resultant decreases because the

torque supplied by the spring‘s increases. So the speed at which chassis roll takes

place always decreases and it reaches zero when both torques are equal. So for a

given spring stiffness a big roll moment will make the chassis roll very far in the

FIG.14 Roll Moment

FIG.13 Positioning of CG & RC


corners, and a small roll moment will make the chassis lean over less. This also

explains why a vehicle with a high CG has a tendency to lean very far in a corner,

and possibly tip over. So at any given time, the size of the roll moment is an

indication of the size of the torque that causes the chassis to lean over while

cornering.

Now, a different problem arises; the location of the roll centre changes when

the suspension is compressed or extended, most of the time it moves in the same

direction as the chassis, so if the suspension is compressed, the RC drops.

When the car corners, and the chassis leans over, the RC usually moves

away from the chassis‘ centreline.

Most R/C cars allow for the length and position of the upper link to be

changed, and thus change the roll characteristics of the car. The following

generalizations apply in most cases. An upper link that is parallel to the lower A-

arm will make the RC sit very low when the car is at normal ride height, hence the

initial body roll when entering a corner will be big. An upper link that is angled

down will make the RC sit up higher, making the initial roll moment smaller,

which makes that particular end of the car feel very aggressive entering the corner.

A very long upper link will make that the roll moment stays more or less the same

size when the chassis leans over; that end of the chassis will roll very deeply into

the suspension travel. If not a lot of camber is used, this can make the tires slide

FIG.15 Change in RC on cornering


because of excessive positive camber. A short upper link will make that the roll

moment becomes a lot smaller when the chassis leans; the chassis won‘t roll very

far.

Until now, we‘ve ignored the fact that there are two independent suspension

systems in a car; there‘s one in the front and one in the rear. They both have their

own roll centre. Because the ‗chassis‘ parts of both systems are connected by a

rigid structure, the chassis, they will influence each other. Some people tend to

forget this when they‘ re making adjustments to their cars; they start adjusting one

end without even considering what the other end is doing. Needless to say this can

lead to anomalies in the car‘s handling. Having a very flexible chassis can hide

those anomalies somewhat, but it‘s a far cry from a real solution.

Anyway, the front part of the chassis is forced to hinge on the front RC, and

the rear part is forced to hinge on the rear RC. If the chassis is rigid, it will be

forced to hinge on the axis that connects both RC‘s, that axis is called the roll axis.

The position of the roll axis relative to the cars CG tells a lot about the

cornering power of the car; it predicts how the car will react when taking a turn. If

the roll axis is angled down towards the front, the front will roll deeper into its

suspension travel than the rear, giving the car a ‗nose down‘ attitude in the corner.

Because the rear roll moment is small relative to the front, the rear won‘t roll very

far; hence the chassis will stay close to ride height. Note that with a car with very

little negative suspension travel (droop) the chassis will drop more efficiently when

the car leans over. With the nose of the car low and the back up high, a bigger

percentage of the cars weight will be supported by the front tires, more tire

pressure means more grip, so the car will have a lot of grip in the front, making it

FIG.16 Roll Axis: Side View


oversteer. A roll axis that is angled down towards the rear will promote

understeer.

Remember that the position of the roll centres is a dynamic condition, so the

roll axis can actually tilt when the car goes through bumps or takes a corner, so it‘s

possible for a car to understeer when entering the corner, when chassis roll is less

pronounced, and oversteer in the middle of the corner because the front RC has

dropped down a lot. This example illustrates how roll centre characteristics can be

used to tune a car to meet specific handling requests, from either the driver or the

track.

In general, we could say that the angle of the upper link relative to the A-

arm determines where the roll centre is with the chassis in its neutral position, and

that the length of the upper link determines how much the height of the RC

changes as the chassis rolls. A long, parallel link will locate the RC very low, and

it will stay very low as the car corners. Hence, the car (well at least that end of the

car) will roll a lot. An upper link that‘s angled down and very short will locate the

RC very high and it will stay high as the chassis rolls. So the chassis will roll very

little. Alternatively, a short, parallel link will make the car roll a lot at first, but as it

rolls, the tendency will diminish. So it will roll very fast at first, but it will stop

quickly. And a long link that‘s angled down will reduce the car‘s tendency to roll

initially, but as the chassis rolls it won‘t make much of a difference anymore.

In terms of car handling, this means that the end where the link is angled

down the most (highest RC) has the most grip initially, when turning in, or exiting

the corner, and that the end with the lowest RC when the chassis is rolled will have

the most grip in the middle of the corner. So if you need a little more steering in

the middle of the corners, lengthen the front upper link a little. (Be sure to adjust

camber afterwards) If you‘d like more aggressive turn-in, and more low-speed

steering, either set the rear upper link at less of an angle, or increase the front link‘s

angle a little.

Now you might ask yourself: what‘s the best, a high RC or a low one? It all

depends on the rest of the car and the track. One thing is for sure: on a bumpy

track, the RC is better placed a little higher; it will prevent the car from rolling

from side to side a lot as it takes the bumps, and it will also make it possible to use


softer springs which allow the tires to stay in contact with the bumpy soil. On

smooth tracks, one can use a very low RC, combined with tiff springs, to increase

the car‘s responsiveness and jumping ability.

Anti-squat

It describes the angle of the rear hinge-pins relative to the horizontal plane.

Its purpose is to make the car squat less when accelerating. (Squatting is when the

rear of the car drops down when the car accelerates) More anti-squat will give

more ‗driving traction‘: there will be more pressure on the rear tires as you

accelerate, especially the first few meters. At the same time, it will give more on-

power steering, because the car isn‘t squatting much. The disadvantage is that the

car has an increased tendency to become unstable entering corners, especially in

the rear. Reducing the anti-squat angle has the opposite effect: a lot less on power

steering, and more rear traction when the car isn‘t accelerating as much anymore.

The car will also be a lot more stable entering corners. It also affects the car‘s

ability to handle bumps: more anti-squat will cause the car to bounce more when

accelerating through bumps, but it will increase the car‘s ability to absorb the

bumps when coasting. Reducing the anti-squat does the opposite: it improves the

car‘s ability to soak up the bumps under power, but reduces it while coasting.

Suspension Travel

The amount of negative suspension travel (downtravel) a car has can have a

huge effect on its handling; it influences both the mount of roll and the amount of

pitch the chassis will experience.

With a lot of downtravel, as the chassis rolls into a turn, the height of the CG

doesn‘t change very much. With almost no downtravel, as it rolls into a turn, the

chassis is pulled down as it rolls, effectively lowering the CG.

So, if one end of the car has less downtravel than the other, that end will be

forced down more in a turn, which makes for more grip at that end, especially in

the middle part of the turn, where weight transfer is more pronounced. Very little

downtravel at the front will give a lot of steering, especially when entering a corner

at high speed, or very violently. Very little downtravel at the rear will give a lot,

and consistent traction throughout the turn.


But that isn‘t all there is to it: the amount of suspension travel also

influences the car‘s longitudinal balance, i.e. when braking and accelerating. An

end with a lot of downtravel will be able to rise a lot, so chassis pitch will be more

pronounced, which in turn will provide more weight transfer. For example: if the

front end has a lot of downtravel, it will rise a lot during hard acceleration,

transferring a lot of weight onto the rear axle. So the car will have very little on-

power steering, but a lot of rear traction. A lot of downtravel at both ends,

combined with soft springs, can lead to excessive weight transfer: on-power

understeer, and off-power oversteer. The cure is simple: either reduce downtravel,

or use stiffer springs.

There are also some disadvantages of having very little suspension travel:

the bump handling and the car‘s jumping ability may suffer, it will bottom out very

easily.

Anti-roll Bars

Anti-roll bars are like ‗sideways springs‘, they only work laterally. Here‘s

how they work: if one side of the suspension is compressed, one end of the bar is

lifted. The other end will also go up, pulling the other side of the suspension up

also, basically giving more resistance to chassis roll. How far and how strongly the

other side will be pulled up depends on the stiffness and the thickness of the bar

used: a thin bar will flex a lot, so it won‘t pull the other side up very far, letting the

chassis roll deeply into its suspension travel. Note that the bar only works when

one side of the suspension is extended further than the other, like when the car is

cornering. When both sides are equally far compressed; like, when the car is

braking, the bar has no effect. So anti-roll bars only affect the lateral balance of the

car, not the longitudinal balance.

Unfortunately, anti-roll bars aren‘t the only things affecting the car‘ s

roll stiffness; they work in conjunction with the springs and dampers. Suppose

we add an anti-roll bar at the rear of the car without changing any of the other

settings. When the car enters a turn, the chassis starts to roll.

Normally, the suspension on the outside of the turn would compress, and the

one on the inside would extend, making for a lot more pressure on the outside

tire. With the anti-roll bar however, the suspension on the inside will be


compressed, so the chassis will roll less, and the rear of the car will sit lower than

normal. So the rear has more weight on it, and it‘s distributed more evenly over the

two tires. This makes for a little more and more consistent traction. Remember that

this is in the beginning of the turn; the situation is different in the middle of the

turn. Normally, without the anti-roll bar, the chassis would stop rolling when the

roll torque is fully absorbed by the outside spring. But with the anti-roll bar, some

of that torque is absorbed by the anti-roll bar, and used to compress the inside

suspension. So the outside suspension won‘t be compressed as much as it

normally would, making the rear of the chassis sit up higher than normal, so less

weight is on the rear of the car, and more at on the front. It‘s as if suddenly the

rear has become stiffer, making for more steering and a little less rear traction.

Rear traction is more consistent however, because the weight is distributed

more evenly over the rear tires, unless the track is really bumpy, that is; anti-roll

bars can really mess up a car‘s rough track handling, so they‘re rarely used on

bumpy tracks. Adding an anti-roll bar at the front of the car has a similar, but

opposite effect: it decreases steering, but makes it much smoother and more

consistent.

FIG.17 Anti-Roll bar


Shock mounting locations

Most R/C vehicles have several possible mounting points for the shock

absorbers, both at the upper mount (area 1) and at the A-arm (area 3). By mounting

the shocks in a different position, spring action can be altered. The question is:

how will this affect the handling, or the ‗feel‘ of the car? To understand this, first

you need to know about wheel rates.

A wheel rate is an equivalent spring rate at the wheel; it‘s the spring rate of

a spring that would give the same stiffness as the current one, if it was to be

attached right at the centreline of the wheel. After all, that‘s where the traction

forces act: at the wheel.

A wheel rate is defined as (motion ratio)² * spring rate * sin(spring angle),

and motion ratio is the distance between the lower shock mounting position and the

inner hinge pin divided by the distance between the inner hinge pin and the tyre‘s

centreline. The spring angle is the angle between the shock and the lower A-arm.

Wheel rate = spring rate * (D1/D2)² * sin a

FIG.18 Shock Mounting Locations & Wheel Rates


This formula tells us two things:

1. The more the shocks are inclined, the softer the wheel rate.

2. The closer the bottoms of the shocks are mounted to the middle of the

chassis, the softer the spring rate.

Note that if we change the lower shock mounting location, we change both the

shock angle and the motion ratio, but it's usually the change in motion ratio that

has the biggest effect. This also shows in the formula: the motion ratio is squared,

and the spring angle isn‘t. The amount of suspension travel also changes, which

can also affect the car's handling.

The shock angle isn't constant either: it gets bigger as the suspension is

compressed. This effect is more pronounced as the shocks are more laid down, so

the more inclined the shocks are, the more progressive the wheel rate will be. So

think of the top mounting positions as a means of fine-tuning spring and damper

rates, and changing the progressiveness.

Keep in mind this isn't perfectly correct: if the centreline of the tire doesn't

intersect with the outer hinge pin, a considerable part of the forces acting on the

tire are transmitted to the chassis along the upper link. Nevertheless, it's a very

good approximation.

Since the shocks' angle changes their progressiveness, it also influences the

shaft speed: if the shock is laid down (progressive), shaft speed will increase as the

shock is compressed, if it is close to vertical (linear), shaft speed won't vary a lot

with suspension travel. Obviously, this affects high-speed damping too; it affects

when the transition from low-speed to high-speed damping occurs. It will occur

earlier when the shock is closer to vertical, because when it is inclined, it takes

some time (and some positive suspension travel) for the shaft to ' speed up', and

reach the same shaft speed. So inclining the shocks more has more or less the same

effect as using a piston with slightly bigger holes, and mounting it more upright

has the same effect as using a piston with slightly smaller holes.

We find that changing the lower mounting location of the shocks comes in

handy sometimes when we want to change the amount of negative suspension

travel, but we don't feel like altering the length of the shock, or when we need the

springs to be just a little stiffer or softer. Changing the top mounting location is a


very subtle adjustment, we like to change it after all of the other, more important

adjustments have been made, and the car is handling more or less the way we want

it to. It's especially helpful to alter the 'feel' of the steering entering corners. Now

we don't know if this applies when the springs' action is very progressive, but the

more the shocks are stood up (less inclined), the more direct their action will be

entering the corner. For instance: if the front shocks are close to vertical, and the

rears are somewhat laid down, the car will have a lot of turn-in steering; it will be

very responsive. If the rears are close to vertical, and the fronts are more laid

down, the car won't have a lot of turn-in, but it will have more steering in the

middle of the turn; it will 'square' . In some cases, the rear might actually begin to

slide. It works much in the same way as having stiff springs or heavy damping: if

you have stiff springs, or heavy damping up front, the initial reaction when you

enter a turn will be very strong. In the middle part of the corner the car

will probably understeer, but it's the initial reaction that gives the car a 'responsive'

character.

Even roll centre works this way: a very high roll centre in the front will make

the car turn in very aggressively, but understeer in the middle of the corner. It's

nice if one likes an aggressive car one can ' throw' into the corners, but we doubt

it‘s the fastest way round the track. Conversely, if the rear roll centre is set very

high, the car will turn in very gently, and possibly oversteer after that.

Mobility of Formula Suspension Mechanisms

Suspension systems are in general three-dimensional mechanisms and as

such are difficult to analyze fully without the aid of computer packages. Their

analysis is complicated by the inclusion of many compliant bushes which

effectively result in links having variable lengths.

FIG.19

5

Ferrari 663


Notwithstanding these complications it is possible to gain an appreciation of

the capabilities and limitations of various mechanisms used in suspension design

by neglecting bush compliances and concentrating on the basic motion of

suspension mechanisms.

A fundamental requirement of a suspension mechanism is the need to guide

the motion of each wheel along a (unique) vertical path relative to the vehicle body

without significant change in camber. This requirement has been addressed by

employing various single degree of freedom (SDOF) mechanisms which have

straight line motion throughout the deflection of the suspension. Despite the

apparent complexity of some suspension systems, a basic understanding of their

kinematics can be derived from a two-dimensional analysis, i.e. by considering the

motion in a vertical transverse plane through wheel centre. Fundamental to this

analysis is an understanding of how the number of degrees of freedom (mobilityin

mechanisms parlance) of a mechanism are related to the number of links and the

types of kinematic constraint imposed on them. In general the aim is for a SDOF or

a mobility of one. Mechanisms which have a mobility of zero are structures, i.e.

not designed for motion, while those having two degrees of freedom require two

prescribed inputs to position them uniquely. This is not desirable for suspensions.

Most of the kinematic connections between the members of a suspension

mechanism can be reduced down to the kinematic pairs. Each has an associated

number of degrees of freedom and can be classified as lower pairs (connections

having a SDOF) or higher pairs (more than one DOF). It has been shown that the

mobility M, of a plane mechanism forming a closed kinematic chain, is related to

the number of links n, the number of lower pairs jl and the number of higher pairs

jh. According to the Kutzbach criterion:

M= 3(n –1) – jh-2jl

For spatial (three dimensional) mechanisms there is an equivalent equation.

The use of equation can be illustrated with reference to the double wishbone and

MacPherson strut suspensions. Both suspensions can be seen to represent a single

closed kinematic chain. In the case of the double wishbone suspension, there are

four links, AB, BC, CD and DA forming a four-bar chain , i.e. n= 4. Each of the

four joints are of the revolute type (lower pairs) and hence jl = 4. There are no


higher pairs and therefore jh = 0. Substituting into above equation gives M = 3 ×(4

–1) –0 ×(2 ×4) = 1, i.e. a SDOF mechanism.

In the kinematically equivalent mechanism for the MacPherson strut

thetelescopic damper is replaced with an extension of the wheel attachment to pass

through a trunnion (a 2DOF joint) at C. The mechanism thus has three links AB,

BC and CA, i.e. n= 3. There are two lower pairs (one at A and one at B) and one

upper pair (at C). This gives jl = 2 and jh = 1. Hence M= 3 ×(3 –1) –1 –(2 ×2) = 1,

i.e. a SDOF mechanism.

While mobility analysis is useful for checking for the appropriate number of

degrees of freedom, it does not help in developing the geometry of a mechanism to

provide the desired motion.For suspension mechanisms this process is called

position synthesis and requires the use of specialized graphical and analytical

techniques, aided by computer software. This departure from the well established

suspension types is only required when it is necessary to produce enhanced

suspension characteristics, e.g. to produce changes in camber and toe under certain

operating conditions to improve handling.

Double Wishbone Suspension for Formula Car

The autocross course is constructed of several components that are typically

found in formula racing: straight-aways, slaloms, constant radius turns, hairpin

turns, chicanes, multiple turns, and varying radius turns.

The suspension of a Formula One car has all of the same components as the

suspension of a road car. Those components include springs, dampers, arms and

anti-sway bars. To keep things simple here, we'll say that almost all Formula One

cars feature double wishbone suspensions. Before any race, a team will tweak

suspension settings to ensure that the car can brake and corner safely, yet still

deliver responsiveness of handling.

Following the ban on computer-controlled 'active' suspension in the 1990s, all

of the Formula car's suspension functions must be carried out without electronic

intervention. The cars feature 'multi-link' suspension front and rear, broadly

equivalent to the double wishbone layout of some road cars, with unequal length

suspension arms top and bottom to allow the best possible control of the camber


angle the wheel takes during cornering. As centrifugal force causes the body to

roll, the longer effective radius of the lower suspension arms means that the bottom

of the tyre (viewed from ahead) slants out further than the top, vital for maximising

the grip yielded by the tyre.

A double wishbone (or upper and lower A-arm) suspension is an

independent suspension design using two (occasionally parallel) wishbone-shaped

arms to locate the wheel. Each wishbone or arm has two mounting points to the

chassis and one joint at the knuckle. The shock absorber and coil spring mount to

the wishbones to control vertical movement. Double wishbone designs allow the

engineer to carefully control the motion of the wheel throughout suspension travel,

controlling such parameters as camber angle, caster angle, toe pattern, roll center

height, scrub radius, scuff and more.

The double-wishbone suspension can also be referred to as "double A-arms,"

though the arms themselves can be A-shaped, L-shaped, or even a single bar

linkage. The upper arm is usually shorter to induce negative camber as the

suspension jounces (rises), and often this arrangement is titled an "SLA" or "short

long arms" suspension. When the vehicle is in a turn, body roll results in positive

FIG.20 Double Wishbone Suspension Coil Spring Solidworks Model


camber gain on the lightly loaded inside wheel, while the heavily loaded outer

wheel gains negative camber.

Between the outboard end of the arms is a knuckle with a spindle (the kingpin),

hub, or upright which carries the wheel bearing and wheel. To resist fore-aft loads

such as acceleration and braking, the arms require two bushings or ball joints at the

body.

At the knuckle end, single ball joints are typically used, in which case the

steering loads have to be taken via a steering arm, and the wishbones look A- or L-

shaped. An L-shaped arm is generally preferred on passenger vehicles because it

allows a better compromise of handling and comfort to be tuned in. The bushing

inline with the wheel can be kept relatively stiff to effectively handle cornering

loads while the off-line joint can be softer to allow the wheel to recess under fore-

aft impact loads. For a rear suspension, a pair of joints can be used at both ends of

the arm, making them more H-shaped in plan view. Alternatively, a fixed-length

driveshaft can perform the function of a wishbone as long as the shape of the other

wishbone provides control of the upright. In elevation view, the suspension is a 4-

bar link, and it is easy to work out the camber gain and other parameters for a

given set of bushing or ball-joint locations. The various bushings or ball joints do

not have to be on horizontal axes, parallel to the vehicle centre line. If they are set

at an angle, then antidive and antisquat geometry can be dialed in.

In many formula cars, the springs and dampers are relocated inside the

bodywork. The suspension uses a bellcrank to transfer the forces at the knuckle

end of the suspension to the internal spring and damper. This is then known as a

"push rod" if bump travel "pushes" on the rod (and subsequently the rod must be

joined to the bottom of the upright and angled upward). As the wheel rises, the

push rod compresses the internal spring via a pivot or pivoting system. The

opposite arrangement, a "pull rod," will pull on the rod during bump travel, and the

rod must be attached to the top of the upright, angled downward.


Locating the spring and damper inboard increases the total mass of the

suspension, but reduces the unsprung mass, and also allows the designer to make

the suspension more aerodynamic.

Modern Formula car suspension is minutely adjustable. Initial set-up for a track

will be made according to weather conditions (wet weather settings are far softer)

and experience from previous years, which will determine basic spring and damper

settings. These rates can then be altered according to driver preference and tyre

performance, as can the suspension geometry under specific circumstances. Set-up

depends on the aerodynamic requirements of the track, weather conditions and

driver preference for understeer or oversteer - this being nothing more complicated

than whether the front or back of the car loses grip first at the limits of adhesion.

FIG.21 Double Wishbone Suspension Rear View


Multi-Link Suspension

This is the latest incarnation of the double wishbone system. The basic principle of

it is the same, but instead of solid upper and lower wishbones, each 'arm' of the

wishbone is a separate item. These are joined at the top and bottom of the spindle

thus forming the wishbone shape. The super-weird thing about this is that as the

spindle turns for steering, it alters the geometry of the suspension by torquing all

four suspension arms. They have complex pivot systems designed to allow this to

happen.

FIG.22 Double Wishbone Suspension With Pull Rod Arrangement


Car manufacturers claim that this system gives even better road-holding

properties, because all the various joints make the suspension almost infinitely

adjustable. There are a lot of variations on this theme appearing at the moment,

with huge differences in the numbers and complexities of joints, numbers of arms,

positioning of the parts etc. but they are all fundamentally the same. Note that in

this system the spring is separate from the shock absorber.

Optimised Suspension Geometries for Formula Car

Choosing which system best suits our project involves a number of factors,

from which we select an SLA (short-long arm) set-up. The first factor was in our

application where, in this type of autocross race, the SLA design is very popular

FIG.23 Double Wishbone Suspension Multi-link

Solidworks Model


and suits the track conditions well. The rack and pinion steering system since it

was the most common for an SLA setup and it kept us within budget.

There are seven different geometric configurations possible for a front SLA

suspension system. In order to narrow down our choices, we tested wheel

displacement verses both camber and roll center. We decided that these two

characteristics were the most important factors since they are essential in the

handling of the car. After reviewing our results, we were able to narrow our

system down to three possibilities. In the following table, all seven SLA

geometries are illustrated. The geometric setup shown third is the suspension

system that is generally usied.[5]

Suspension Set-Up Wheel

Displacement

Camber Roll Center

None

Negative

Positive

Always Negative

Always Positive

Always Positive

Positive

Majority of the

Displacements


Always Negative

Negative

Majority of the

Displacements

One of the most difficult parts of designing a suspension system is

compromising. There is no optimum suspension for all conditions; therefore, for

every improvement there is a sacrifice. The key is to decide what is most

important for your particular application. In our case, we had to account for a race

on a smooth track that contains many tight turns but can be subject to a variety of

weather conditions.

To fulfill our goal of maintaining the largest accelerations possible, we

examined the many components of a suspension design (the definitions of these

terms are conveniently defined during the discussion). The first heavily debated

design component examined was the roll axis, a line that connects the front and

rear roll centers, around which the car body rotates when lateral forces are applied.

The roll center is defined as the effective center that the body will appear to rotate

about. For roll centers with small radii, one could image a box suspended by two

short strings at two corners suspended as something of a pendulum. The longer the

string, the larger the pendulum, and the more minute the angular displacements the

box will achieve. As shown below, the body roll Theta 1 is greater than Theta 2

with a longer roll center located below ground level.

TABLE 1 Geometries of Double Wishbone SLA Suspension


A small amount of negative camber is desirable in a turn, as determined

through a tire manufacturer‘s data.

However, the geometry must be such that the camber is zero for straight

driving. If camber exists even when the car is not turning, the tire patch area is

reduced and maximum possible traction is not attained. This also leads to uneven

tire wear results. The desirable aspect of camber is that it can be used to increase

tire patch area when the vehicle experiences body roll. To achieve this effect,

camber must be positive when wheel displacement is negative (wheel droop), and

negative when wheel displacement is positive (jounce).

Below is a graph for a formula car suspension system. It achieves slightly

more than a degree of camber per inch of displacement. Comparing this slope to

the tire data in, the results support that an increase in lateral force can be achieved.

Fig 24 Optimised Roll Centre Location


Fig 25 Tire Data


Many complications are added to the suspension geometry where the

steering control arms and rack are located. One of the biggest effects it can cause

is ―toe-in/out‖, commonly known as ―bump steer‖. ―Toe-in‖ is when the front of

the tires angle in towards each other, and ―toe-out‖ is when they angle away from

each other. It is undesirable to have the tires independently steer the vehicle when

the vehicle hits bump. This characteristic complicates tuning the vehicle by adding

responses that are unpredictable to the driver. Both kinds of toe are a result of the

position of the steering linkages. Since we are using an existing steering rack, its

position has several constraints. To steer the vehicle, the control arms must be a

distance from the axis about which the tire turns specifically the king pin

inclination (KPI) to induce a moment, thus turning the car. As the figure below

demonstrates, the kingpin inclination affects scrub radius, which is pre-determined

by re-using the vertical uprights.

-3

-2

-1

0

1

2

3

-4 -2 0 2 4

Wh

ee

l Dis

pla

cem

en

t (i

n)

Camber (degrees)

Graph 2 Camber v/s Wheel Displacement

Fig 26 Scrub radius


Bump steer is a very difficult characteristic to accommodate. In a majority

of geometries tested, the amount of bump steer cannot be zero for all wheel

displacements. Therefore, we designed our suspension system with a minimal

amount of Toe-In/Toe-Out by placing the rack where the pivots for inner and outer

tie rod match the control arm pivot axis. In standard formula car designs, there has

been as much as 3.5 degrees of toe-out over a 2-inch wheel displacement. Our

results were a considerable improvement since our design has less than a 0.4-

degree angle over 4-inch wheel displacement. This amount will not noticeably

affect the handling of the vehicle.

Another aspect that must be considered is the caster angle. The combination

of the caster angle and kingpin inclination greatly affects the handling of the car.

Both are very important since they influence the steering forces during lateral

acceleration and the self-centering effect of the steering. As with Toe, it is

desirable to minimize both the caster angle and the kingpin angle for all wheel

displacements. The combination of the two has a large effect on the rate of camber

change during wheel displacement.

The final design uses pneumatic trail to provide steering center effect at

higher speeds. Pneumatic trail differs from the mechanical trail defined by the KPI

and caster angle by specific tire characteristics. Pneumatic trail is a result of the tire

patch area shape. The patch area roughly forms a triangle, thus providing a wedge

effect with the ground and provides a horizontal centering force. Both types of

trails act as weather vanes to the steering wheel but have varying effects at over a

given range of speed. Mechanical trail is dominant at low speeds while pneumatic

-3

-2

-1

0

1

2

3

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2

Wh

eel D

isp

lace

me

nt

(in

)

Toe-In/Out (degrees)

Graph 3 Toe-In/Out v/s Wheel Displacement


trail at high speeds. Skid warning is also maintained by minimizing mechanical

trail, and since the effect of pneumatic trail is non-linear with vehicle speed, the

driver will be able to sense when there is a significant decrease in pneumatic trail.

This provides an important source of driver feedback at higher speeds, and the

vehicle will exhibit under steer and feel ―loose‖.

Design Overview

Static weight

The load transfer calculations use the following parameters to model the forces

generated. The static forces are calculated using a driver weight of 80 Kg, vehicle

weight of 240Kg estimated from existing vehicles, front-to-rear weight distribution

-3

-2

-1

0

1

2

3

-0.04 -0.02 0 0.02 0.04 0.06

Wh

eel D

isp

lace

men

t (i

n)

Caster Angle (degrees)

-3

-2

-1

0

1

2

3

-4 -2 0 2 4

Wh

eel D

isp

lace

men

t (i

n)

Kingpin Angle (degrees)

Graph 4 Caster Angle v/s Wheel Displacement

Graph 5 Kingpin Angle v/s Wheel Displacement


50/50, and left-to-right weight distribution 50/50. The height of the CG is

estimated from the average of the moment of inertias of major components.

Height of CG =11” Wheel Base (WB) = 65”

Weight Driver (WD) = 80 kg Front Track – 50”

Weight Vehicle (WV) = 240 kg Rear Track – 51.6”

Total Vehicle Weight (TVW) = WD +

WV = 320

Front Static Roll Center = 4

Front Bias = 0.5 Rear Static Roll Center = 6

Rear Bias = 0.5 Positive Acceleration = 1.5

Left Bias = 0.5 Negative Acceleration = 1.5

Right Bias - 0.5 Lateral Acceleration = 1.5

Lateral load transfer due to lateral acceleration

Table 2 Acceleration Data used for Calculations

Fig 27 Plot of Relevant Forces


The lateral forces generated act through the center of gravity and are summed as

a torque, or moment, to determine the vertical force on a tire. The moments are

summed about the roll center axis when roll centers are determined at a static

height. The two moments are summed to find Ftire and then split front to rear by

multiplying by the bias ratio. The lateral acceleration has been set to a high value

of 1.5 times the force of gravity, 1.5 g‘s. This number is used as a safety factor

since the car will not encounter more than 1.2 g‘s of force.

Front Rear

L1 = Lcg – Lrc,f = 6 L3 = Lcg – Lrc,r = 4 L5 = 11

L2 = front track/2 = 25 L4 = rear track/2 = 25.8 L6 = WB*front bias = 32.5

F1 = a1*(Fz,sfl + Fz,sfr) =521.25 F2 = a1*(Fz,srl + Fz,srr) = 521.25 L7 = WB*rear bias = 32.5

Ft = (F1*L1 + F2*L3)/(L2 + L4) = 102.6082677

Fz, Lateral Acceleration Loads, steady state

Front, 1 tire = 51.30413

Rear, 1 tire = 51.30413

Longitudinal weight transfer due to negative acceleration

Table 3 Vertical Tire Force Calculation

Table 4 Lateral Acceleration Loads

Fig 28 Tire Force Schematic


The rear-to-front weight transfer due to braking is a sum of moments about the

y-axis and is defined by the intersection of the x-coordinate of the CG projected on

the ground.

Fz, Longitudinal weight transfer, negative acceleration, steady state

Front = 264.6346 Front Left = 132.3173 Front Right = 132.3173

Rear = -264.635 Rear Left = -132.317 Rear Right = -132.317

Maximum loads achieved

The maximum vertical loads that could be reached correspond to the combined

forces of negative and lateral accelerations with the static weight of the vehicle.

Fz, Maximum achievable loads; lateral + negative accelerations

static + lateral + negative

Front Left = 357.3714 Front Right = 357.3714

Rear Left = 92.73683 Rear Right = 92.73683

Maximum Tractive Forces

The traction generated by a tire (Fx,y) is a function of vertical force exerted on

a tire and the coefficient of friction () between the tire and ground. The

coefficient of friction is a function of many variables including velocity,

temperature, and tire wear. Wet, dry, and/or sandy surface conditions also serve as

variables. The coefficient is estimated to be high at 1.5 so that the x and y

components of the forces developed are high, since these forces will be used when

determining component materials and dimensions as an added margin of safety.

Table 5 Longitudinal Weight Transfer

Table 6 Maximum Achievable Loads


Horizontal tire force, Fx,y (lbs)

Fy: Cornering = u*(static + lateral acceleration loads)



Fx,y: Cornering & braking=u*(static + lateral + negative acceleration loads)



Fx: Braking = u*(static + negative acceleration loads)



Factor of Safety Development

To determine the factor of safety we will assume worst-case scenarios for the

loading of each component. Specifically the vehicle is under hard braking and hits

a pothole or cone. This example exhibits a realistic case for a high performance

Fig 29 Schematic of tire with axes

Table 7 Horizontal Tire Force


vehicle and parking lot track condition. The following is part of the analysis of the

design of a front pushrod element.

The following forces are developed in the push-rod member during full

spring compression and max damping setting on the Fox Racing shock:

F=n*(k*x + c*velocity)

Where, k is the spring constant, x is displacement, c is the damping coefficient, and

n is the rocker ratio. The damping force is obtained through the manufacturer‘s

supply of damper dyno charts and the spring rate is 39.55 N/m with maximum x

displacement of two inches. To use a worst case scenario we will assume the

vehicle bottoms out, that is max displacement of two inches is achieved, the

damping is set at max 12 clicks closed, and the rocker ratio is three.

NF 3.1464)4092*55.39(3

The pushrod is under buckling in a pin-pin configuration, thus using Bernoulli-

Euler technique:

2L

EIPcrit

(1)

Using this method with an aluminum ¾‖ diameter pushrod member 14‖ long will

result in a factor of safety of four. For this worst-case scenario prediction, we are

able to find a factor of safety by dividing the maximum load/static load to

essentially get a factor of safety for each member. Where the factor of safety was

less than three, the member was re-designed until this criterion was met.

A-Arm Force Calculations

In order to compute the thickness necessary for each arm, the maximum forces

had to be computed. After the forces were found, we used the largest one to

calculate the diameter needed. A factor of safety of three was used. The

relationship between the force in the arm and its area is as follows:

I

Mc

A

P

(2)


The area can then be used to compute the needed diameter. The forces were found

using standard static analysis equations. The four defining equations are as

follows:

0xF (3)

0yF (4)

0zF (5)

0oM (6)

They state that the sum of the forces in x, y, and z directions must be zero.

The last equation states that the sum of the moments about any point in the system

must be equal to zero. The figure below shows the forces involved and their

relationship to each other.

According to the force equations, we determined that the maximum force in

any arm of the A-arms was 4009N. Our computations were completed using just a

basic A-Arm with no truss braces. Therefore, when we discuss the maximum force

in any of the arms, we mean the two major arms of the A-Arm. The truss design

Fig 30 Force Schematic & Truss Design


was incorporated to cut down on the moments acting on the arm. Since that force

was the maximum attained for any member, we used it for all calculations. This

insured that all members would be able to handle the maximum possible force

encountered. Using the maximum forces, the diameter needed for the A-arms was

then calculated. The A-arms were treated as a pin-pin beam, since they are

connected with ball joints on each end. Ball joints do not act against moments,

similar to the behavior of a pin.

The Bernoulli-Euler buckling criterion is given in Eq.1, where I is the

moment of inertia. For a round member:

4

2

1rI

(7)

Using equation 2, we determined the thickness needed for each type of

material that we had considered. Also shown is the weight of an arm of the needed

diameter. The results are shown in the figure below for the 14-inch arm. The

results are based on a maximum force of 4009N and a factor of safety of 3.

Therefore, the force calculated for a pin-pin beam is less than 12.027 kN of force.

Material Modulus of Elasticity Diameter Weight

Aluminum 172.34 GPa 1.62 cm 2.02N

AZ91 146.14 GPa 1.82 cm 1.66N

Steel 308.167 GPa 1.242 cm 3.32N

Front Uprights

One of the critical factors we used to determine the best material was the

strength to weight ratio of each material. We computed this by dividing the

amount of force in the member by the weight required to hold that load. This

determined that AZ91 alloy magnesium is the best of the three materials. In the

end, other factors weighed into the decision of what material to use and AZ91 was

not selected for the steering arms or the push rods. Further detail on this topic is

Table 8 Material Properities for a 14 inch pin-pin beam


discussed in the steering arm and push rod sections. AZ91 was selected for the

front and rear uprights as well as the A-Arms.

The front uprights are usually made of AZ91 magnesium to cut down on the

weight of the vehicle. We modified the design heavily to incorporate a more

adjustable steering arm. The uprights are the centerpieces of the suspension

system; they transfer the forces from the tire to the A-arms. Their geometry is very

important to the handling characteristics of the car.

Magnesium was used for the uprights since they are a part that is cast to the

specific form that is needed. Casting was an excellent option since the uprights are

not a simple shape that can be easily machined. They also can be cast very close to

the exact shape needed. This leads to minimal machining which saves both cost

and time.

Fig 31 Front Uprights


Rear Uprights

Fig 33 Rear Uprights

Fig 32 Front Uprights CATIA V5 Model Static Load Test


The rear upright must only travel within the range that the drive shafts of

rear differential can handle. The suspension characteristics of the rear end were

modified, but this was done in other ways. If the mounting points on the body are

different a different geometrical configuration is obtained. We did this to

customize the handling characteristics, as we wanted them. Magnesium was used

for the same reasons discussed in the front upright section.

Rockers

The rocker design is a prototype at a design level rather than a final model.

The final model is based on the dynamic vehicle testing to optimize the wheel to

shock travel ratio that can be changed from 1.3:3 to 3:1.8 in .5 increments. The

design permits the use of a single two-inch travel spring and damper unit to

perform in a spring rate range of 16.95N/m to 65.87N/m while retaining the

required two inches of wheel travel.

This variable system is a design common to some teams and combines

manufacturing time savings with material cost savings by using only one rocker to

do the same work as six individually cast rockers.

Fig 34 Rear Uprights CATIA V5 Model Static Load Test


Push rods

The pushrods are the member that transmits the vertical force of the tire to

the spring/damper unit. As a result this member is subject to buckling loads in a

pin-pin configuration.

If weight was the only factor we considered then we would have used AZ91

for the push rods. We ended up using aluminum push rods for a number of reasons.

A major reason is the availability of materials. Aluminum is readily available, but

magnesium would have to be cast to a specific length. The availability factor also

leads us to aluminum since we want components that can easily be repaired or

replaced at the race. Repairs are very difficult with magnesium since it is not a

weldable metal. Aluminum allowed us more versatility since we could make new

arms quickly. We wanted to be able to change the rod lengths if needed to adjust

the system. Aluminum is much less expensive than magnesium.

Fig 35 Rockers


The push rod design is based on keeping the system highly adjustable. The

push rod is a rod with a left-handed thread on one side and a right-handed thread

on the other. With this setup twisting one way enlarges the length of the rod and

twisting the other decreases the length. A nut is tightened on each end to prevent it

from adjusting while racing due to vibrations. The steering arms are designed with

this same setup.

Fig 36 Rebound Damping


Fig 37 Compression Damping


Fig 38 Pushrods

Fig 39 Bell Crank FEA Results


Steering Arms

Fig 41 Steering Arms

Fig 40 Motion Ratio


Like the pushrods, the steering arms are loaded to buckle in the pin-pin

configuration as well. The force developed in this configuration is tabulated in the

A-Arm force calculations section. The diameter on the rod is calculated using

modulus of aluminum and required length of 12‖.

Process Controls (Troubleshooting)

Process controls are the events that can be attributed to some malfunction or

undesirable handling effect. For example, if the nose of the vehicle dives during

braking, the cause of this problem could be attributed, but not limited to, low front

damping, too soft spring rate, or high center of gravity. The process sheet is

divided into front and rear suspension, steering components, and possible solutions

to the problems listed. The method behind the sheet is to limit total time wasted

during competition trying to tune the car to the current track conditions, or

analyzing a problem.

Stiff Movement

Probable Cause: High spring rate

Possible Solution: Reduce spring pre-load, adjust rocker ratio, and

replace spring with different spring rates

High Friction

Possible Solution: Re-grease rocker and damper bushings, inspect

links for stiff rod-ends, verify misalignment angle to be less than 11,

re-torque rocker bolts to 27.1163 Nm and verify rocker clearance for

.050‖ clearance

High Compression Damping

Readjust damping with 12 click knob one or two clicks lighter

Nose Dive

Probable Cause: Light front spring rate


Possible Solution: Adjust pre-load, replace springs with higher rate,

adjust rocker ratio

Light Front Damping

Possible Solution: Adjust damping compression with incremental

knob

High Center of Gravity

Possible Solution: None; may be more prominent with excessively

large drivers

Front Brakes Over-Biased

Possible Solution: Adjust bias proportioning valve

Rear Steer

Probable Cause: Differential torque bias

Possible Solution: The Torsen differential bias can be adjusted with

different shims, otherwise a common behavior with torque-sensing

differentials

Probable Cause: Improper rear alignment

Possible Solution: Calibrate using caster/camber and toe-in/out device

Vehicle Pulls to One Side

Probable Cause: Torque bias in differential, see rear steer

Over/Under steer

Probable Cause: Ackerman angle

Possible Solution: Increase the Ackerman steering angle if the vehicle

under-steers, decrease for over-steer

Excessive Steering Force


Probable Cause: Binding rack

Possible Solution: Re-grease rack and inspect for component wear

Probable Cause: Rod-end misalignment

Possible Solution: Verify that misalignment angle does not exceed 11

Steering Arm to Short

Possible Solution: Recalculate equivalent Ackerman angle and

manufacture new are with greater length

Improper Rack Ratio

Possible Solution: Re-cut new rack and pinion or replace rack with

lower ratio

Safety Considerations

The suspension system of a vehicle is critical to the safety of the occupant or

occupants of that vehicle. In our case this is a very important issue since our

vehicle is very small and is capable of large accelerations and decelerations. The

vehicle safety issues are minimized by various rules. The rules have many

requirements and restrictions to make the vehicle as safe as possible.

One critical aspect of this project is the factor of safety used. The

appropriate factor of safety can be determined by three different methods. The

most detailed method would be to conduct a full detailed study of the situation

using modeling and equations. Another method is too used ―Back of the envelope

calculations‖, which are best done with worst case scenario numbers used. The

final method is to use standard practice values. This is common since it only

requires a little research and the values found usually have been tested to confirm

their validity. We used this method combined with ―Back of the envelope


calculations‖ to verify the validity. The standard factor of safety for the formula

suspensions systems is three.

Manufacturing considerations

The use of magnesium for some of the suspension components is also a

safety consideration due to its low ignition temperature. The safety issue is more

with machining rather than the actual use on the car. A good analogy of this is the

danger of throwing a match on sawdust compared with throwing a match on a log.

There is just not enough heat to ignite the solid body and this is the case with the

magnesium also. The solution to machining magnesium safely is quite simply to

work at low feed rates, low tool rpm‘s, and use sharp tools. In addition to these

steps one should monitor the temperature of the part during machining. If the part

is getting too hot to touch for more than a moment then a break should be taken to

give the part time to cool. If a fire were to break out water must not be used to

extinguish this, in fact water will usually make it worst. A powder that is specially

formulated to extinguish magnesium fires must be thrown on it.

Modifications

We had made a few major modifications of the design in our system. The

modifications were for various reasons, which include safety, aesthetics,

interference issues, and ease of manufacture. The design of the front uprights was

modified in order to increase the turning ability of the car. Material was removed

from the top of the upright where the oversteer stops and steering mounts were

going to be. The stops were placed directly on the rack. The steering mounts are

located on the side of the upright so they don‘t interfere with the turning of the tire.

The height of the steering rack was modified to allow for more room for the

driver. At the original location, the driver would have difficulty getting his feet

into the vehicle. We added two inches changing the clearance from 7 to 9 inches.

Luckily this change only modified the suspension dynamics minimally. In fact,

none of the changes are large enough to be noticeable to the performance of the

car.


Conclusion

This project was a combination of many smaller design projects involving

interdisciplinary teamwork. The finished projects were incorporated into the

racecar built by the Supra SAE Chapter at Amity School of Engineering &

Technology. The overall goal of the project was to create and intergrate

components into a highly competitive vehicle. The suspension portion of the

project was designed specifically as a mechanical engineering senior design

project.

The goal of the suspension team was to incorporate a system that is both

reliable and adjustable. In the design, both driving conditions and different drivers

were accounted for in creating a versatile car. The suspension had to maintain the

maximum accelerations in the lateral, positive, and negative during the Supra SAE

challenge. The major restriction was the use of many advanced parts due to budget

constraints.

The overall goals of our project were met by producing a working vehicle

design. As a result of the design process, we have learned a great deal about

different engineering disciplines. All of the mechanical systems are interrelated,

especially the suspension system. We think Amity University Rajasthan will be

well represented at this year‘s SAE student design competition.

Fig 42 Supra SAE AUR Prototype Solidworks Model


References

1. Reza N. Jazar (2008). Vehicle Dynamics: Theory and Applications. Spring.

p. 455. Retrieved 2012-06-24.

2. "The Washington Times, Sunday 30 June 1901".

Chroniclingamerica.loc.gov. Retrieved 2012-08-16.

3. Jain, K.K.; R.B. Asthana. Automobile Engineering. London: Tata McGraw-

Hill. pp. 293–294. ISBN 0-07-044529-X.

4. Jones, D. Suspension Systems. Brookhaven College, AUMT 1316, 2011:p.

1-7

5. Bilmanis,A.; Hotaling R.; Mangual J. Suspension, Steering, & Engine

Control System Design Final Report. Senior Design Project 2000-2001

6. Hughes,C.; Understanding Suspension.©eSoft

7. Smith,J.H. An Introduction to Modern Vehicle Design p292-347.©Reed

Educational and Professional Publishing Ltd 2002

8. Bosch, Robert. Automotive Handbook. Bosch; Stuttgart, Germany. 4th

ED,

1996.

9. Milliken, William and Douglas. Race Car Vehicle Dynamics. Society of

Automotive Engineers; Warrendale, PA, 1995.

10. Staniforth, Allan. Altair SuspensionGen User’s Manual. Altair Computing

Inc.; Troy, MI. Version 1.13, 1998.

11. Jawad, A.B; Baumann, J.; Design of Formula SAE Suspension. Lawrence

Technological University, SAE Technical Paper. 2002-01-3310


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Documents

Optimization of Formula Car Double Wishbone Suspension System