FSAE Suspension report

FSAE IIT Delhi Suspension Report

Suspension Report Team Axlr8r, IIT Delhi

ACHIN JAIN ANSHUL SINGHAL SHUBHAM AKSHAT

PREFACE Team AXLR8R

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The primary goal of the suspension in the context of a Formula SAE vehicle is to provide a proper interface between the driver and the car such that a high level of road handling can be realized in a predictable fashion under all expected accelerations. Even when the limit of adhesion is reached, driver control and the ability to manage the vehicle are of paramount importance. Although superficially simple, the selection of parameters to achieve the ideal package of a vehicle control systems is the result of evaluating and weighing numerous competing objectives, many of which require iterative calculations and educated predictions of values that cannot be determined until an entire vehicle is constructed, instrumented and fully tested. This report summarizes the design of the vehicle control systems that have been considered, not only by defining the important parameters alone but also by considering the effects of one parameter on the others. The design considerations have resulted in the construction of the complete suspension system, in resonance with other departments like brakes, steering of IIT DELHI’s Formula SAE car. It should serve as a summary of suspension basics in the context of a complete race car.

It contains all the intricate details of the Suspension starting from the Elementary Study to Final CAD models describing at each and every step, the principles involved. Suspension Geometry Analysis has been done on the SusProg3D Software and CAD modeling on SolidWorks. Efforts have been made to justify every decision at every step. The work is completely genuine and free from Plagiarism. All the references of Study have been mentioned.

The report also accounts for the problems encountered and mistakes committed at some steps in order to ignore those in the future. It also talks about the Future Perspective, what else can be done, but could not be done due to time constraints, resource constraints and other factors.

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CONTENTS INTRODUCTION.................................................................................................... 10 TYPES OF SUSPENSION............................................................................................11 

SOLID BEAM AXLE.......................................................................................... 11



SWING AXLE SUSPENSION...........................................................................12



MACPHERSON.................................................................................................13

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EQUAL LENGTH DOUBLE A-ARM..................................................................14



UNEQUAL LENGTH DOUBLE A-ARM SUSPENSION....................................15

DESIGNING APPROACH........................................................................................ 17 1. PARAMETERS OF STUDY................................................................................... 18 1.1

CAMBER............................................................................................................ 18

1.1.1 Neutral Camber...........................................................................................18 1.1.2 Positive Camber..........................................................................................18 1.1.3 Negative Camber.........................................................................................19 1.1.4 Camber Gain.................................................................................................19 1.1.5 Effects of Negative Camber.......................................................................21 1.1.6 Conclusion.................................................................................................... 21 1.2

CASTER............................................................................................................. 23

1.2.1 Neutral Caster.............................................................................................. 23 1.2.2 Negative Caster........................................................................................... 24 1.2.3 Positive Caster............................................................................................. 24 1.2.4 Effects of positive caster...........................................................................25 1.2.5 Conclusion.................................................................................................... 25 1.3

TOE IN/OUT...................................................................................................... 26

1.3.1 Neutral Toe Angle........................................................................................26 1.3.2 Toe In............................................................................................................. 26 1.3.3 Toe Out.......................................................................................................... 26 1.3.4 Effects of Toe................................................................................................ 27 1.3.5 Conclusion.................................................................................................... 27 1.4

KINGPIN (KPI) ANGLE.....................................................................................28

1.4.1 Purpose of Kpi inclination..........................................................................28 1.4.2 Effects of Kpi inclination............................................................................28 1.4.3 Conclusion.................................................................................................... 29 1.5

Anti Dive and Anti Squat...............................................................................29

1.5.1 Methods to achieve Anti-dive and Anti-squat........................................30

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FSAE IIT Delhi Suspension Report 1.5.2 Effects of Anti Dive and Anti Squat..........................................................32 1.5.3 Conclusion.................................................................................................... 32

2. SELECTION OF WHEEL BASE AND TRACKWIDTH..............................................33 2.1

Salient Features for Larger Rear Track Width............................................33

2.2

Salient Features for Larger Front Track Width...........................................33

2.3

Procedure followed to determine Track Width..........................................33

2.4

Conclusion........................................................................................................ 34

3. TIRE and RIM SELECTION.................................................................................35 3.1

Objective.......................................................................................................... 35

3.2

Parameters...................................................................................................... 35

3.2.1 Aspect Ratio.................................................................................................35 3.2.2 Hydroplaning............................................................................................... 35 3.2.3 Traction......................................................................................................... 36 3.2.4 Tire Tread Width.......................................................................................... 36 3.2.5 Basic Terminology.......................................................................................36 3.2.6 Tire Type....................................................................................................... 37 3.2.7 Spring Rate.................................................................................................. 37 3.3

Load Analysis.................................................................................................. 38

3.4

Considerations for Selection.........................................................................39

3.5

Shortlisted Tires.............................................................................................39

3.5.1 Dry Tires....................................................................................................... 39 3.5.2 Wet Tires...................................................................................................... 40 3.6

Selected Tires.................................................................................................. 40

3.6.1 Dry Tires....................................................................................................... 40 3.6.2 Wet tires....................................................................................................... 41 3.7

RIMS.................................................................................................................. 42

3.7.1 Wheel Offset................................................................................................42 3.7.2 PCD................................................................................................................ 44 3.7.3 Spigot Size................................................................................................... 46 3.7.4 Conclusion.................................................................................................... 46

4. ROLL CENTER & MOVEMENT OPTIMIZATION....................................................47 4.1

Effects of height of Roll Center....................................................................47

5. FINALIZATION OF A ARM POINTS......................................................................49 5.1

Front................................................................................................................. 49

5.1.1 Front A Arm Geometry................................................................................51 5.1.2 Front Roll and Bump Data..........................................................................55 5.2

Rear.................................................................................................................. 59

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FSAE IIT Delhi Suspension Report 5.2.1 Rear A Arm Geometry.................................................................................61 5.2.2 Rear Roll And Bump Data...........................................................................65 5.3

Verification of Susprog Results....................................................................68

6. SHOCK ABSORBERS....................................................................................... 69 6.1

Parameters of Study......................................................................................69

6.2

Bell Crank......................................................................................................... 69

6.3

Push Rod/Pull Rod........................................................................................... 69

6.4

Ride/Suspension Frequency..........................................................................70

6.4.1 Effects at Lower frequencies.....................................................................70 6.4.2 Effects at Higher frequencies....................................................................70 6.4.3 Deciding the Ride Frequency.....................................................................70 6.5

Spring Rate...................................................................................................... 72

6.6

Motion Ratio.................................................................................................... 73

6.7

Wheel Rate...................................................................................................... 73

6.8

Roll Gradient.................................................................................................... 74

6.9

Damping........................................................................................................... 76

6.9.1 What is damping?........................................................................................ 76 6.9.2 Damping ratio..............................................................................................76 6.9.3 Transmissibility............................................................................................ 79 6.10 Shock Absorber...............................................................................................79 6.10.1

Introduction.............................................................................................. 79

6.10.3

Working Principle.....................................................................................82

6.10.4

Adjustments..............................................................................................85

6.10.5

Conclusions............................................................................................... 85

6.10.6

Calculations.............................................................................................. 87

6.10.7

Shortlisted Shock Absorbers..................................................................88

6.10.8

Finalised Shocker.....................................................................................92

7. ANTI ROLL BARS.............................................................................................. 93 7.1

Introduction..................................................................................................... 93

7.1.1 Main Functions.............................................................................................93 7.2

Body Roll.......................................................................................................... 93

7.2.1 Negative Aspects of Body Roll..................................................................94 7.2.2 Ways to Prevent Body Roll.........................................................................94 7.3

Types of Anti Roll Bar.....................................................................................94

7.3.1 U-shaped Anti Roll Bar...............................................................................95 7.3.2 T-shaped Anti Roll Bar................................................................................96 7.4

Principles......................................................................................................... 98

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FSAE IIT Delhi Suspension Report 7.5

Factors that Determine Stiffness.................................................................99

7.6

Components of U- shaped anti roll bar.......................................................99

7.7

Tubular Anti Roll Bar....................................................................................101

7.8

Some important Parameters to be used in Calculations........................102

7.8.1 Roll Gradient..............................................................................................102 7.8.2 TLLTD........................................................................................................... 102 7.8.3 Points Concerning Ride Frequency.........................................................104 7.9

Calculation Theory of Anti Roll Bars..........................................................106

7.9.1 Formulas for Required ARB Stiffness Required....................................106 7.9.2 Spring Rate Calculations..........................................................................109 7.9.3 Approximations Done (With Reference to RCVD).................................110 7.10 Materials of Anti Roll Bars...........................................................................112 7.11 Reasons For Using Lever type ARB rather than Bent type....................113 7.12 Where to Install............................................................................................113 7.13 Drawbacks of Using Anti Roll Bar...............................................................113 7.14 Conclusions.................................................................................................... 114 7.14.1

Installation.............................................................................................. 114

7.15 Future Prospects...........................................................................................114

8. SHOCKER AND ANTI ROLL BAR RESULTS FROM SusProg3D...........................116 8.1

Front............................................................................................................... 116

8.1.1 Shocker and Anti Roll Bar Geometry......................................................116 8.1.2 Roll Data..................................................................................................... 119 8.2

Rear................................................................................................................ 126

8.2.1 Shocker and Anti Roll Bar Geometry......................................................126 8.2.2 Roll Data..................................................................................................... 129 8.3

Final Calculations......................................................................................... 136

8.3.1 Spring rate.................................................................................................136 8.3.2 Roll gradient of ride springs....................................................................136 8.3.3 Total ARB roll rate needed to increase the roll stiffness to the desired roll gradient.......................................................................................................... 137 8.3.4 Front and Rear Anti-Roll Bar stiffness...................................................138 8.4

Final Damping Curve....................................................................................141

9. FORCE CALCULATIONS.................................................................................142 9.1

Front............................................................................................................... 142

9.2

REAR............................................................................................................... 147

10.

BEARING SELECTION................................................................................ 153

11.

DESIGNING............................................................................................... 158

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FSAE IIT Delhi Suspension Report 11.1 Hub.................................................................................................................. 159 11.1.1

Estimation of Forces..............................................................................159

11.1.2

Choosing the material...........................................................................160

11.1.3

Designing the CAD model on SolidWorks...........................................161

11.1.4 Stress analysis of the CAD model on Simulation Express Analysis Wizard 166 11.1.5

Optimization of the Design by removing excess material..............168

11.2 Upright........................................................................................................... 172 11.2.1


11.2.2


11.2.3



Optimization of the Design by removing excess material...............182

11.3 Bell crank....................................................................................................... 185 11.3.1


11.3.2


11.3.3



Optimization of the Design by removing excess material..............195

11.4 A-Arms............................................................................................................ 198 11.4.1


11.4.2


11.4.3


11.4.4 Stress analysis of the CAD model on Simulation Express Analysis Wizard 203 11.5 Anti Roll Bar................................................................................................... 204 11.5.1


11.5.2


11.5.3



Optimization of the Design by removing excess material...............209

11.6 Miscellaneous................................................................................................213 11.6.1

Pushrod................................................................................................... 213

11.6.2

Tube Adapter.......................................................................................... 214

11.6.3

Brackets..................................................................................................215

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FSAE IIT Delhi Suspension Report 11.6.4

Rod-ends................................................................................................. 219

11.6.5

Bearings..................................................................................................220

11.6.6

Wheel and tire........................................................................................221

11.6.7

Shocker.................................................................................................... 222

11.7 Assemblies..................................................................................................... 223 11.7.1

Front Wheel Assembly..........................................................................223

11.7.2

Rear Wheel Assembly...........................................................................224

11.7.3

Front Pushrod-bell crank-Shocker Assembly.....................................225

11.7.4

Rear bell crank-Shocker Assembly......................................................226

FUTURE SCOPE.................................................................................................. 227 ACTIVE Suspension.................................................................................................227 Pure Active Suspensions.....................................................................................228 Semi-active Suspension......................................................................................229 Anti Roll Bar............................................................................................................. 231

REFERENCES...................................................................................................... 232

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ACKNOWLEDGEMENT We are very grateful to our Faculty Advisors Prof. Naresh Bhatnagar and Prof. Rahul Ribeiro for helping us through the Project. Our Sincere thanks to our Student advisors Ankit Dhall and Mudit Goel to keep us motivated throughout the year and for supporting us at each and every step. We are also thankful to the entire Team AXLR8R. At the end of the day, it has been possible only because of Team’s cooperation and management. We would also like to thank people from SusProg3D and SolidWorks, who provided us with Prestigious License to work on the software.

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INTRODUCTION Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's road holding /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. 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. The suspension also 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. The study of the forces at work on a moving car is called vehicle dynamics, and these concepts define why a suspension is necessary in the first place. The dynamics of a moving car is considered from two perspectives: 

Ride - a car's ability to smooth out a bumpy road



Handling - a car's ability to safely accelerate, brake and corner

These two characteristics can be further described in three important principles - road isolation, road holding and cornering. The table below describes these principles and attempts need to solve the challenges. Road Isolation: The vehicle's ability to absorb or isolate road shock from the passenger compartment. Goal: Allow the vehicle body to ride undisturbed while traveling over rough roads. Road Holding: The degree to which a car maintains contact with the road surface in various types of directional changes and in a straight line (Example: The weight of a car will shift from the rear tires to the front tires during braking. Because the nose of the car dips toward the road, this type of motion is known as "dive." The opposite effect -- "squat" -- occurs during acceleration, which shifts the weight of the car from the front tires to the back.) Goal: Keep the tires in contact with the ground, because it is the friction between the tires and the road that affects a vehicle's ability to steer, brake and accelerate.

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Cornering: The ability of a vehicle to travel a curved path. Goal: Minimize body roll, which occurs as centrifugal force pushes outward on a car's center of gravity while cornering, raising one side of the vehicle and lowering the opposite side.

TYPES OF SUSPENSION 

SOLID BEAM AXLE In the beam of the front connected to solid axle. For semi or heavy of the front connect by a

axle setup both wheels are each other by a example: in a duty truck both wheels are solid axle.

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FIGURE: TYPICAL BEAM AXLE DESIGN, SHOWING THE WHEELS CONNECTED BY THE AXLE AND THE WHOLE ASSEMBLY CONNECTED TO THE CHASSIS BY THE SPRINGS AND SHOCKS



SWING

AXLE SUSPENSION pivot about a somewhere centre of the the wheels to down through respective arcs. was eventually rear

The axles location near the car and allow travel up and their This system adapted for suspensions.

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FIGURE 1: SWING AXLE SUSPENSION AT DIFFERENT POSITIONS. THE HUGE DEGREE OF POSITIVE CAMBER WHEN THE AXLES JACK UP (TOP) THIS IS WHAT CAUSES THE DISTINCT LOSS IN CORNERING POWER.



MACPHERSON This strut based system, where the spring/shock directly connects the steering knuckle to the chassis and acts as a link in the suspension, offers a simple and compact suspension package. This is perfect for small front wheel drive cars where space is tight and even allows room for the drive shaft to pass through the knuckle. Today most small cars will use this type of suspension because it is cheap, has good ride qualities, and has the compact dimensions necessary for front wheel drive cars.

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FIGURE: TYPICAL MACPHERSON ASSEMBLY LOOKS LIKE THIS. THE STRUT ACTS AS THE UPPER SUSPENSION LINK.

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EQUAL LENGTH DOUBLE A-ARM

This is commonly referred to as a “double wishbone” suspension as the A shaped control arms resemble a wishbone. In this design the suspension is supported by a triangulated A-arm at the top and bottom of the knuckle. The earliest designs of the A-arm suspension included equal length upper and lower arms mounted parallel to the ground. In this design wishbones – or A arms – are used top and bottom to support an upright

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to which the wheel is attached. The broad lower base of the arms connects to the frame while the ball-joints are mounted on the apex of the arms. When the arms are of equal length and mounted parallel to each other and to the road, the swing-arm is infinitely long and the roll centre is at ground level.



UNEQUAL LENGTH DOUBLE A-ARM SUSPENSION

This design is currently used by most of the universities. By using an upper control arm that is shorter than the lower one, as the wheel travels up it tips in, gaining negative camber. This is because the upper arm swings through a shorter arc than the lower and pulls in the top of the tire as the wheel travels upwards. The advantage in this negative camber gain is that as the chassis rolls against the wheels, the increasing negative camber on the outside wheel helps keep the wheel upright against the road surface and allows the tire to generate the maximum possible cornering force. By adjusting the length of the arms and their respective angles to the ground, there are infinite possibilities in the design of a vehicles roll centre height and swing arm length. This flexibility gives suspension designers unlimited options on how to best setup the suspension. The advantages of an equal length wishbone system are retained but in addition, camber gain can be created during bump – and so camber of the outer (loaded) tyre during cornering. Furthermore, by changing the angles

and lengths of the arms, it is possible to change the amount of camber gain during deflection, and also alter the roll centre position and swingarm length.

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The Suspension analysis includes: 

Weight distribution and its effect on the above



Tire/wheel properties (Tread, rubber compounds, wheel materials)



The relationships between tire and road



The center of gravity and roll center relationship



Unsprung weight.



Suspension geometry and handling



Anti-roll bar principles



Damper/shock absorber principles



Suspension components, their use and placement for optimum performance

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DESIGNING APPROACH We followed the following procedure for the designing of the Suspension: 1. Study of Basic Parameters. 2. Selection of Wheel Base and Track Width. 3. Selection of Tires. 4. Roll Center Location and Movement Optimization. 5. Finalization of A Arm Mounting Points on SusProg3D. 6. Study and Selection of Shock Absorbers. 7. Study of Anti Roll Bars. 8. Finalization of Shocker and Anti Roll Bar Mounting Points on SusProg3D. 9. Forces Calculation 10. Designing of All Suspension Parts on SolidWorks 2010.

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1. PARAMETERS OF STUDY The definition of all the Parameters, their effects on other Parameters, advantages, disadvantages and the Optimum Range has been discussed. All these Parameters must be decided before progressing to Optimization of Results on SusProg3D.

1.1 CAMBER It is the angle between the vertical axis of the wheel and the vertical axis of the vehicle when viewed from the front or rear. If the tire is to be perfectly positioned on the ground, and the wear on the tread is to be symmetrical, the wheel should have a zero camber (perfectly perpendicular to the ground tilting in corners or on bumps minimizes the area of the wheel in contact with the road so this is not desired. This tilting of the wheel is called camber. In an ideal situation the camber angle of the wheel is always zero degrees. In reality the camber angle changes with the up and down movement of the suspension. Also body roll affects the camber angle. Often cars have a light Positive camber angle under no load conditions to make up for the compression of the suspension and rubber bushes. When normally loaded the camber angle becomes zero. Camber is adjusted by tilting the steering axis from the vertical which is usually done by adjusting the ball joint locations. Because the amount of tire on the ground is affected by camber angle, camber should be easily adjustable so that the suspension can be tuned for maximum cornering.

1.1.1

Neutral Camber

The image on the left shows a tire that is set to a position that is referred to as neutral camber. This means that the top and bottom of the wheels and tires are parallel to each other which is measured as 90 degrees to the track surface. This is the base line measurement from which the other two positions are measured from.

1.1.2

Positive Camber

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The image on the left shows a tire that is in a cambered position that is referred to as positive. This means that the tops of the wheels and tires are leaning outwards from the centre of the car.

1.1.3

Negative Camber

Shown left is a wheel/tire where the camber angle is set negatively. This means that the top of the wheel is leaning toward the centre of the car.

1.1.4

Camber Gain

The camber gain is very important to take into consideration, because it plays an affect on your front geometry. CAMBER GAIN ILLUSTRATION

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

To maximize the grip of a race car tire, the wheel must be at a certain angle – camber angle. However, this angle varies as the wheel and suspension move up and down in response to bumps and cornering forces.



As no two corners are the same, and the forces generated are never the same, a single camber angle would only work occasionally. So, we need a system of variable camber, the result: camber gain suspension.



The reason the camber gain is important, is because the static camber will change if the camber gain changes. Understanding the relationship between camber gain and static camber is important. The wheel goes thru the travel and the camber changes as that happens. Keeping the whole tire patch on the surface of the racetrack for the whole camber gain is what will make the car turn the best.

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How camber gain is obtained 1. Camber gain is usually obtained by having different length upper and lower control arms. Different length control arms will cause the ball joints to move through different arcs relative to the chassis. 2. The angle of the control arms relative to each other also influences the amount of camber gain. 3. Caster angle (positive) is also used to increase the camber gain for the tight corners.

1.1.5

Effects of Negative Camber



More grip and stability while cornering: While cornering the body of the car will start rolling, inducing positive caster. Negative caster will compensate this effect. If the tire had zero camber, the inside edge of the contact patch would begin to lift off of the ground in cornering, thereby reducing the area of the contact patch. In case of negative camber, this effect is reduced, thereby maximizing the contact patch area. However, this is only true for the outside tire during the turn; the inside tire would benefit most from positive camber.



Straight Line Stability: Negative camber creates force on the wheels called “Camber Thrust”. Going straight, Left and Right will in balance and car goes straight. For maximum straight-line acceleration, the greatest traction will be attained when the camber angle is zero and the tread is flat on the road.



Better cornering: While cornering inner wheel will be lifted from a little to sometimes completely. Then the camber thrust will cause the car to take a sharper turn.

1.1.6

Conclusion

On the Basis of Study and Literature, Camber generally will be around -0.5 to -5.5 degrees (negative). As seen in the Graph below, Coefficient of Friction is maximum at Camber Angle of -1 degree and hence, the maximum grip. Hence, Camber Angle is chosen as -1 degree.

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1.2 CASTER Caster refers to the angle made between the centres of the lower pivot point of the axle block to the centre of the upper pivot point of a model car axle block when looking from the side of the car. Caster, like Camber, has three possible states, neutral, negative and positive. Caster can be measured in degrees.

1.2.1

N e u tr al

Caster Neutral caster has the upper and lower pivot points aligned vertically. The forces that bear down on the car and the wheel have only a single vertical point of contact which is at the mercy of any external forces that may act upon it. Any car set with neutral caster will be an unstable one.

1.2.2

Negative

Caster Team AXLR8R


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Negative caster is sometimes referred to as leading caster. Negative caster, which is sometimes referred to as leading caster, has the upper pivot points positioned in front of the lower pivot points. Because of the horizontal offset between these two pivots the forces that bear down on the car are transmitted with a forward bias. Depending on the driving configuration of the car, this either adds stability or makes it un-drivable. It is better for Front Wheel Drive.

1.2.3

Positive

Caster

Positive caster is sometimes referred to as trailing caster. Positive caster, which is sometimes referred to as trailing caster, has the upper pivot points positioned in behind of the lower pivot points. Because of the horizontal offset between these two pivots the forces that bear down on the car are transmitted with a rearward bias. Depending on the driving configuration of the car, this either adds stability or makes it un-drivable. It is better for Rear Wheel Drive.

1.2.4

Effects of positive caster Team AXLR8R


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Straight Line Stability: The greater the angle of caster, the stronger the centering force, which effectively means heavier steering and the car will be reluctant to turn into a corner. Conversely, if the car were to be given negative caster, with the lower end of the axis further back than the top, there would be no directional stability at all.



Self Centering of Steering: The bigger the angle the stronger the self centering action. If the angle is negative the steering is very light and very nervous.



Cornering: With a low caster angle, centering force will be weak and car will be more willing to go around the corners but counter effect is that it will be less willing to straighten up afterwards.



Effect on Camber: Caster also causes change of camber when the steering is turned, which results in more negative camber on the outside front wheel and more positive camber on the inside front wheel. Caster angle affects the camber gain of the car. The tilted steering axis has important effect on suspension geometry. Since the wheel rotates about a tilted axis, the wheel gains camber as it is turned. This effect is best visualized by imagining the unrealistically extreme case where the steering axis would be horizontal-as the steering wheel is turned, the road wheel would simply change camber rather than direction. This effect causes the outside wheel in a turn to gain negative camber, while the inside wheel gains positive camber.  Therefore the aim with caster is to get a balance between straightline stability and getting the car to turn easily, without too much effort from the driver. This is achieved by having different amounts of caster on each wheel. The inside wheel will have a low caster angle, though still positive. This gives the light steering into the corner. A higher amount of caster on the outside wheel will give the car the straight-line characteristics that are required.

1.2.5

Conclusion

Since we have rear wheel driven system, positive caster is beneficial. Its value will generally lie between +2 to +5.5 degrees (positive). Only applies to Front/Steering wheels. We have chosen Caster Angle of 3 degrees.

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1.3 TOE IN/OUT The term toe angle refers to the longitudinal angle of the wheels on your car, i.e. how parallel they are to each other and the car. 1.3.1 Neutral Toe Angle Front wheels are parallel to both each other and to the direction of travel of the car.

1.3.2 Toe In Toe in occurs when the front of the wheels point towards the car.

1.3.3 Toe Out Toe Out occurs when the wheels point outwards from the car. It can be specified in mm, inches or degrees.

1.3.4

Effects of Toe Team AXLR8R


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Cornering: As the vehicle goes around a turn, the inside tire must travel in a smaller radius circle than the outside. If the two wheels were parallel, one of the two would not be running in a natural arc when cornering and would be scrubbing sideways as before. When going around a corner with toe-out the inner wheel will be turned in slightly further than the outer, and both wheels will go round the corner properly.



Steering Response: Steering response will be improved with toe-out. Toe-out encourages turn-in since the inside tire turns at a greater angle than the outside. Hence, the car is sensitive to the slightest steering input. Toe-out will make the car wander on the straight-aways requiring corrective steering. The car will always be turning unless the steering is perfectly centered. With toe-in, the inside tire fights the outside since the inside is trying to trace a larger radius arc than the outside. As a result, toe-in discourages turn-in and makes the car less sensitive to steering input.



Straight Line Stability: Straight line stability will be improved with toe-in because rear wheel drive cars have tendency to over steer and toe-in will induce under steer, thus compensating the previous effect.



Tire Wear: The best tire wear is achieved with completely parallel tires – 0 degrees of toe. However, this is not the best for straight line stability or cornering ability!  Excessive toe-in will cause the tire to scrub on the outboards.  Too much toe-out will cause the inboard edges to wear out.

1.3.5 Conclusion Only applies to Front/Steering wheels.  Toe-out is preferred. We preferred toe-out sacrificing the straight line stability for good cornering and its value is chosen to be 5mm.

1.4 KINGPIN (KPI) ANGLE Team AXLR8R

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The angle is described by a line drawn down through the top and bottom ball-joint (swivel pin) centers and vertical viewed from the front. Extended to ground level, the distance from here to the wheel/tire centre-line at ground level is the ‘King Pin Offset’ or ‘Scrub Radius’. Ideally the lines should intersect at ground level. This will give both lightness of steering ‘feel’ and virtually no kick back through the steering wheel when hitting bumps – known as ‘centre-point steering’. A negative Scrub Radius is when the Kingpin Angle hits the road on the outside of the centre line of the tyre contact point.

1.4.1     

To ensure the returning of the wheels after a bend (self centering of the steering). Together with the camber it provides centre point steering (scrub radius zero or negative). Reduces steering effort. Aids directional control. Helps to distribute vehicle weight evenly across the tire.

1.4.2 



Purpose of Kpi inclination

Effects of Kpi inclination

Increasing the inclination angle will decrease the self centering steering effect The steer momentum is the product of kingpin offset and the wheel force. The wheel forces will try to pull the center of contact patch of the front wheels forward, thus the wheel will rotate about the point of the kingpin axle projected to the ground. Effect on Roll and Stability Increasing KPI also increases the lateral forces on the cars increase thus making it more receptive to roll and instability.  What happens is that when wheel comes in contact with the bump it tend to turn toward the bump .That is if the left hand front wheel on contacting a bump wants to turn sharply left .This caused by the leverage factor of the relative position of the wheel and its turning axis .The closer the kpi axis to the center of the tyre tread contact patch, the lesser the adverse effect.  Another problem is that when the wheels of the car having a lot of offset, are turned left or right from the straight ahead position, the chassis is raised on one side and lowered on the other. That is, on a

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vehicle turning left, the left hand front wheel tend to lift that side of the car and the right hand front wheel tend to lower its side of the car. The more the offset, the more pronounced the raising and lowering effect of the chassis.

1.4.3 Conclusion Kpi offset is chosen to be 14mm.

1.5

Anti Dive and Anti Squat

A Dive is the action of the front of the vehicle to point downward during braking.

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Anti-dive is a suspension parameter that affects the amount of front suspension deflection when the brakes are applied. It is the forces of inertia and mechanical resistance that the brakes create thru the front suspension. When a car is decelerating due to braking there is a load transfer off the rear wheels and onto the front wheels proportional to the center of gravity height, the deceleration rate and inversely proportional to the wheelbase. If there is no anti-dive present, the vehicle suspension will deflect purely as a function of the wheel rate. This means only the spring rate is controlling this motion. As anti-dive is added, a portion of the load transfer is resisted by the suspension arms. The spring and the suspension arms are sharing the load in some proportion. If a point is reached called 100-percent anti-dive, all of the load transfer is resisted by the suspension arms and none is carried through the springs. When this happens there is no suspension deflection due to braking and no visible brake dive. There is still load transfer onto the wheels, but the chassis does not pitch nose down.

Anti-squat is a suspension parameter that affects the amount of rear suspension deflection when the vehicle is accelerated. The function of anti-squat, like its name, is to reduce the amount of weight transfer to the rear wheels under acceleration. When the vehicle is accelerating there is load transfer from the front to the rear wheels. When Anti-squat is added a portion of load is resisted by suspension arms. With your anti-squat set to zero degrees your rear suspension swings straight up and down. When you increase the degree of anti-squat the plane that your rear suspension swings on also increases. Now, instead of swinging straight up and down, your rear suspension swings up and back.

1.5.1Methods to achieve Anti-dive and Anti-squat Convergent Axes method: This method uses brake torque reactions through the suspension links, which are convergent inclined towards the c.g. location in side elevation to reduce or cancel the driving tendency.

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32

The line extended from the contact patch through the wishbone axes

convergent point would intersect a perpendicular dropped from the cg to the track surface at a point. Ratio of the distance of this point from the ground and the height of cg will give % anti-dive. If the point of convergence of extended wishbone pivot axes intersects a line drawn from the tire contact patch to the c.g. of the sprung mass, then the torque reaction will cancel out the driving moment and we will have 100% anti-dive.

100% Antidive and 100% Anti-squat

30% Anti-squat

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Inclined Parallel Axes method: Wishbones pivot axes are maintained parallel to each other and are inclined both downward towards the front. What happens here is that, under braking, the inertia of spring mass of the sprung mass tries to rotate the sprung mass about the front wheels. The inclined pivot axes from the inclined plane which forces the wishbones into the droop position which effectively lifts the front of vehicle. In this case to achieve 100% anti-dive, the wishbone pivot axes must be parallel to line drawn between the tire contact patch and the c.g.

100% Anti-dive and Anti-squat

1.5.2 ects of Anti Dive and Anti Squat 



Eff

Each method utilizes upward force of brake torque reaction to oppose the downward force of load transfer. This opposition means suspension becomes stiffer and less sensitive with vertical wheel travel and so is less able to absorb the shocks caused by track surface irregularities and load transfers. Under the brakes should wheel hit a bump at a time when the upward force opposing the load transfer is close to the downward force of the

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







transfer, equal and opposite forces will be achieved and the suspension would be effectively blind solid and the tire goes into severe tramp. At the rear,the problem with the vertical load transfer under acceleration is chassis squat with its attendant negative camber.It can be resisted by antisquat suspension linkage. We are resisting the natural downward force of load transfer with the reactive upward thrust so it is possible to loose sensitivity and get into tire patter and the alike if too much antisquat is employed.This will manifest itself as power on over steer. Converging inclination of pivot axes causes front wheel caster to increase with the vertical wheel travel. This increases the steering effort. The parallel but the inclined axes causes the wheel to move forward as well as upwards in reaction to vertical loads. In order to absorb bumps tire should move rearward under impact. This opposition of forces means that suspension becomes stiffer and less sensitive with upward wheel travel and we get into patter once again. One disadvantage found at the front doesn’t exist at the rear-when the pivot axes are inclined upward toward the front ,the bump movement will force the wheel rearward-in the natural direction to absorb the energy of the bump,rather than to oppose it.The fact that the wheelbase changes slightly while all of this is happening doesn’t seem to bother anything.It is,however,necessary to carefully adjust the rear suspension to avoid undesirable bump steer characterstics.

1.5.3  

Conclusion

Anti-dive generally lies between 20-25%. Maximum anti-squat is 20%.

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2. SELECTION OF WHEEL BASE AND TRACKWIDTH  Previous Car dimensions:  Rear Trackwidth : 1250 mm  Front Trackwidth : 1286 mm  FSAE Guidelines: There are no guidelines in place for track width.

2.1   

2.2     

2.3

Salient Features for Larger Rear Track Width Provides for slightly for space for housing the engine in rear – mounted engine cars such as our car Front track width being smaller helps there will be lesser drag force on the car, resulting in better streamlining of the vehicle. It causes the car to undergo slight under steer

Salient Features for Larger Front Track Width Better maneuverability of the car Aids us in changing the direction quickly Since the engine – driven wheels(Rear) are closer, this aids in traction Lesser the rear track width, lesser the transmission power losses from the engine It causes to vehicle to have a slight over steer.

Procedure followed to determine Track Width

Since the larger rear track width points are not applicable for us, it was decided to continue with a larger front track width for the convenience of driver. Lateral Load Transfer Calculations: Lateral Load Transfer between the Tires=[(Lateral acceleration in g's)*(weight)*(CG height)]/(track width) On the Race Track: 1. 2. 3. 4.

Radius of the corner = 4 m Velocity at the corner = 10 m/s Weight = 400 kg CG Height = 250 mm (to be reduced from 298 mm)

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5. Trackwidth = (assumed 1250 mm) From these calculations, It was found that lateral load transfer for the 2 inner tires would be around 1800N. Thus, each tire would take an extra weight of around 90 kg which is within the acceptable range for the tire chosen. It is observed that, “For every 1mm of track width change at a lateral acceleration of 3 g's, the lateral load changes by 1.5N” Hence, we can quite clearly change the track width by 50 -70 mm as compared to the dimensions of the previous car without adversely affecting the lateral load transfer.

2.4

Conclusion

 For maintaining the proper dimensions of the car, it was decided to keep the front track width at .75 to .80 times the wheelbase.  Moreover, the rear track width would be kept slightly smaller at . 90 to .98 times the front track width in order to fully allow for the engine constraints. Considering all the study and calculations, final dimensions were decided as: Wheel Base = 1600mm Front Track Width = 1160mm Rear Track Width = 1140mm

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3. TIRE

AND

RIM SELECTION

3.1 Objective To select best possible tires and rims for the Formula Racing Car considering the following factors:  

Stability of car Economy

3.2 Parameters 3.2.1

Aspect Ratio

The “aspect ratio” of a tire is the ratio of its section height to its section width. The smaller the number the shorter the sidewall and wider the tire. 3.2.1.1 Effects of Aspect Ratio  As the aspect ratio of a tire is lowered, or the width of the tire is increased, the tire footprint area increases. The larger footprint area reduces the average pressure of the contact patch. Since footprint pressure is closely related to hydroplaning resistance, lower aspect ratio tire hydroplaning resistance is not as high as that of high aspect ratio tires.  Lower aspect ratio provides better lateral stability. When a car goes around a turn lateral forces are generated and the tire must resist these forces. Tires with a lower profile have shorter, stiffer sidewalls so they resist cornering forces better.  Lowering aspect ratio would increase a tire's radial stiffness and dimensional stability. This reduces the deflection of a tire and decreases rolling resistance, and thus improves fuel economy, results in improving the tread wear.   Lower aspect ratio tires can successfully use softer tread compounds. It seems this is due to the more uniform stress distribution of these tires as compared to high aspect ratio tires. The use of a softer compound increases the traction of the tire on the track. At high speeds, this is very desirable for vehicle handling.

3.2.2

Hydroplaning Team AXLR8R

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“Hydroplaning” or “aquaplaning” by the tires of a road vehicle occurs when a layer of water builds between the rubber tires of the vehicle and the road surface, leading to the loss of traction and thus preventing the vehicle from responding to control inputs such as steering, braking or accelerating. 3.2.1.1 Effects of Hydroplaning Tire tread wear and contact patch shape The longer and thinner the contact patch, the less likely a tire will hydroplane. Tires that present the greatest risk are wide, lightly loaded, and small in diameter. Deeper tread dissipates water more easily.



Ratio of tire load to inflation pressure Underinflated tires are more prone to hydroplaning, especially as vehicle weight increases.

3.2.3

Traction

Traction is the grip of a tire on the road.

3.2.4

Tire Tread Width

 More the tire Width better is the traction.  Wider tires have more amount of rubber which must be heated; this added material may prevent the tires from reaching the optimum temperature range. More width implies larger contact patch, which means larger area on ground to resist sliding, spinning and losing traction. Thus, cars can negotiate corners at higher speed and accelerate faster as it would be possible with regular tires.

3.2.5 Basic Terminology

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3.2.6

39

Tire Type

Advantages

  Bia s

 

     Rad ial

   

3.2.7  

Strong sidewalls, tough casing Better sidewall puncture resistance Good lateral stability (hill side work) Good in rough terrain and off-road

Good high speed capacity Longer lasting (Up to 50% longer) Wear resistant Low heat build-up Lower rolling resistance Better Fuel Economy Better floatation and larger contact area Less soil compaction Better stability and machine handling

Disadvantages



Poor life expectancy (50% of radial) Lack of flexibility in casing reduces foot print and traction  Tread flexes more, generating more heat and rolling resistance.  Profile of tire increases soil compaction and reduces traction



More prone to puncturing

Spring Rate

As the pressure increases, spring rate of tire increases. As the weight on tire increases, spring rate increases.

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3.3 Load Analysis Total Weight of the car (including the driver) 350 kg or 771.6 lb

W

Maximum Load acts on a tire in case of cornering as well as braking Static weight distribution: Weight on front tires = 140 kg or 308.6 lbs Weight on rear tires = 210 kg or 463 lbs C.G. height = 250 mm or 9.84 inch Wheelbase = 1600 mm or 63 inch Braking acceleration = 1.4 g Track width = 1286 mm or 50.62 inch Longitudinal load transfer in case of braking = acceleration ( g ) × weight ( lbs ) × c . g . height ( inch ) wheelbase (inch)

= 168.7 lbs Therefore, Total weight on front tires = 477.36 lbs Total weight on rear tires = 294.3 lbs Velocity while cornering = 8 m/s

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Turning radius = 4 m Lateral load transfer in case of braking = acceleration ( g ) × weight ( lbs ) × c . g . height ( inch ) trackwidth(inch) = 148.45 lbs Therefore, Load on front outer tire = (477.36/2) + 148.45 = 387.1 lbs Thus, maximum load is possible on front outer tire.

3.4 Considerations for Selection 

 



Rim diameter of the used tires is 13 inch. Tires with large rim diameter will have short sidewalls. Hence a desirable lower aspect ratio. By studying the tire catalogue of different companies, it was observed that tires with rim diameter 10”, 13”, 15” and 16” are available. From which 10” rim diameter is too small for the size of the brake disk. Rim diameter of 15” or 16” is too large as it will increase the weight of tires. Cold tire pressure is 14 psi. Outer diameters of wet and dry tires are same to ensure ride height is not affected by changing the tires. Rim specifications are also taken to be identical for wet and dry tires to ensure they do not affect the hub and the brake disk. Radial Tires are better than Bias Tires.

3.5 Shortlisted Tires Based on our considerations, following tires are shortlisted:3.5.1 Dry Tires Goodyear:

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Product Code

Size

42

O.D .

Trea Secti Recommen Compou Retail Weight d on ded nd Price Widt Width Rim h Item Size O.D Trea Secti Recommen Rim Compou Retail S.A.E. Numb . d on ded Measur nd Price Price er Widt Section Widt Rim ed Item Size O. Trea Rec. Rim Compo Retail S.A.E. 80720.0 20.D. 7.2" 8.7" 6.0-8.0" WET $206. Price 10.6 lbsPrice h Number dh Width Rim Measur und 299x 5" 00 Widt ed 0967.0h MATL 13 No. 44125 19.5 x 19. 6.2" 8.2" 6.06.0" WET $167. $133.6 6.5-10 7" 8.0" 00 0 20.0 20. 7.7" 9.1" 8" WET $219. 11.0lbs Product Size O. Tread Sectio Recommende Compoun Retail Weight x20.0 x 0" 20. 00 44150 7.4" 8.3" 7.07.0" $206. $164.8 Code D. Width n d d WET Price 8.07.5-13 6" 00 0 Width 8.0" Rim 13 43128 21.0 20.5 xx 21. 6.0" 7.2" 7.3" 5.5-6.5" 5.5" WET R25B $203. $186. $148. 44185 21. 6.7" 6.06.0" $162.4 6.0-13 0" 00 6.5-13 2" 8.0" 00 0 80 80720.0 43162 20.5 x 299x 7.0Produc 7.0-13 Size 06813 t Code MATL 43169 20.0 x No. 7.5-13

20. 21. 5" O. 0" D.

807807434434068068MATL MATL No. No.

20. 20 0" .0"

20.0 20.0 x x 8.013 8.0-

20. 6"

7.2" 7.0" Trea d Widt 8.0" h 7.7" 7.7"

8.7" 6.0-8.0" DRY 8.0" 5.5-8.0" 6.0" R25B Sectio Recommend Compou n ed nd Width Rim 9.4" 7.0-9.0" 8.0" R25B 9.1" 9.1"

8" 8"

DRY DRY

$181.0 10.4 lbs $186. $148. 0 Retail 00 Weight 80 Price $198. 00 $184.0 $184. 0 00

11.0lbs 11.0lbs

13

Hoosier:

3.5.2

Wet Tires

Goodyear: Hoosier:

3.6 Selected Tires 3.6.1

Dry Tires

From this study, following conclusions were made:  Tire should have lower aspect ratio which means wider tires with shorter and stiffer sidewalls.  Load carrying capacity of tires should exceed 400 lbs.

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$158. 40


43

Selected Tire is:

We selected the following tires because of following features: 1. Tire has section width of 9.1” which is appreciably wide. 2. Aspect ratio is the smallest among all the shortlisted as width is larger Produc t Code

Size

O. D.

Trea d Widt h

Sectio n Width

Recommend ed Rim

Compou nd

Retail Price

Weight

807434068MATL No.

20.0 x 8.013

20 .0"

7.7"

9.1"

8"

WET

$219. 00

11.0lbs

and side wall thickness is small.

3.6.2

Wet tires

From this study, following conclusions were made:    

Tire should have deeper treads. Outer Diameter of tire should be large. Tire should not be underinflated. Tire tread width should be smaller.

Selected Tire is

NOTE: 



The reason we have selected this tire and not Hoosier, is also that we were unable to find the Tire Curves for the Hoosier which also is very important criteria in deciding the tires. The tires curves are provided by Tire Consortium and there is a large fee involved which justifies our incapability.

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3.7

RIMS

3.7.1

Wheel Offset

Offset is the distance between the imaginary centerline of the wheel (as viewed from behind the wheel as it would roll away from you) and the inside face that bolts up against the wheel hub on the car. A significant reduction in positive offset of the wheels will EFFECTIVELY change the steering geometry's scrub radius, possibly increasing the steering effort and making the car harder to control during turning and cornering. Offset is also important. Positive offset will increase the track (width side to side) of the car, lessening weight transfer and increasing grip. Such wheels are recognized by a concave, deeper look, where the mounting surface of the wheel is further inboard, beyond the centerline. Negative offset is where the mounting surface is outboard of the centerline of the rim, giving the wheel a flatter appearance. Negative offset of wheels means choosing a narrower track, more weight transfer and less grip. Because wheel offset changes the lever-arm length between the center of the tire and the centerline of the steering knuckle, the way bumps, road imperfections and acceleration and braking forces are translated to steering torques (bump-steer, torque-steer, etc) will change depending on wheel offset. Likewise, the wheel bearings will see increased thrust loads if the wheel centerline is moved away from the bearing centerline.

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45

Positive offset

3.7.2

P C D

The term PCD stands for (pitch circle diameter) and is the diameter of a circle drawn through the centre of your wheels bolt holes. PCD is

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measured in millimeters and also indicates the number of studs or bolts the wheel will have. One of the most common fitments has 4 studs and a PCD of 100mm, hence the fitment 4x100. Measuring PCD The other two things to look for when fitting after market wheels is the PCD (Pitch Circle Diameter, ) and spigot size. The PCD is easy to match as this relates to the number of studs we need to hold the wheel on the car. The actual meaning is the diameter of the studs from the centre of the wheel. Calculating PCD

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4 HOLE WHEELS Measure the distance between the centers of 2 OPPOSITE holes OR Measure the distance between the centers of 2 ADJACENT holes and multiply by 1.414

3.7.3

48

5 HOLE WHEELS Measure the distance X between the centers of 2 ADJACENT holes and multiply by 1.7012

Spigot Size

Spigot is the bit in the centre of the hub that we rest the inside centre of the wheel on whilst aligning the studs and screwing back the wheel nuts. On generic after market wheels, the spigot hole inside the wheels is a lot bigger than the spigot on the car. So we need to fit spigot locating rings. These are just rings of aluminum or hard plastic that fit over the spigot on the car and then have a proper snug fit with the spigot hole on the wheel. If the spigot does not take all the weight of the car, chances are one or more studs will break when we drive the car hard or have to brake hard. The wheel nuts are simply there to hold the wheel on, NOT support the

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weight of the car. Also, as there is nothing to centre the wheel, we'll notice the wheels go in and out of balance because as we drive around, they'll move around on the hub. 3.7.4 Conclusion We visited the market to see the common Steel Alloys Rims available. Considering the width of tire, we came to following Conclusion.   

Rim Offset should be negative to get low value of KPI Offset. Out of the all available, offset of -35mm was most common. Rim width = 5.5 in PCD = 100 X 4

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4. ROLL CENTER & MOVEMENT OPTIMIZATION

The points labeled IC are the instant centers for the wheels relative to the chassis. The other instant center in figure, the roll center, is the point that the chassis pivots about relative to the ground.  



The front and rear roll centers define an axis that the chassis will pivot around during cornering. Since the CG is above the roll axis for most race cars, the inertia force associated with cornering creates a torque about the roll center. This torque causes the chassis to roll towards the outside of the corner. Ideally, the amount of chassis roll would be small so that the springs and anti-roll bars used could be a lower stiffness for added tire compliance. However, for a small overturning moment, the CG must be close to the roll axis. This placement would indicate that the roll center would have to be relatively high to be near the CG.

4.1 Effects of height of Roll Center 



Unfortunately, if the roll center is anywhere above or below the ground plane, a “jacking” force will be applied to the chassis during cornering. For example, if the roll center is above ground, this “jacking” force causes the suspension to drop relative to the chassis. Suspension droop is usually undesirable since, depending on the suspension design, it can cause positive camber which can reduce the amount of tire on the ground. Conversely, if the roll center is below the ground plane, the suspension goes into bump, or rises relative to the chassis, when lateral forces are applied to the tires.

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Therefore, it is more desirable to have the roll center close to the ground plane to reduce the amount of chassis vertical movement due to lateral forces. Since the roll center is an instant center, it is important to remember that the roll center will move with suspension travel. Therefore, the migration of the roll center must be checked to ensure that the “jacking” forces and overturning moments follow a relatively linear path for predictable handling. For example, if the roll center crosses the ground plane for any reason during cornering, then the wheels will raise or drop relative to the chassis which might cause inconsistent handling. This has been taken care of with the help of Anti Roll Bars (Refer Section 6).

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5. FINALIZATION OF A ARM POINTS 5.1 Front

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5.1.1

Front A Arm Geometry Team AXLR8R

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54

After various iterations and optimization of the following during Bumpdroop and Roll: a) b) c) d) e) f)

Camber Caster Kpi offset Anti-Dive and Anti-Squat Roll Center position Front view Swing axle arm lengths

Keeping the variation of the above parameters minimum, following set of data was obtained: Double A-arm Vehicle lateral datum

(Y): Vehicle centreline

Vehicle vertical datum

(Z): Ground

Vehicle longitudinal datum (X): Front axle centreline

Chassis pivot points (from vehicle Y, Z, X datum)

LH

- top A-arm chassis pivot (front/rear)

315.00

-Y

300.00

-Z

325.00

-X

135.00 -135.00

- bottom A-arm chassis pivot (front/rear)

319.00

-Y

270.00

-Z

155.00

-X

135.00 -150.00

- top A-arm chassis pivot (virtual/normal)

161.00

-Y

-Z

322.00

-X

0.00

307.50

-6.64

-Z

157.84

-X

0.00

277.11

157.82 0.90

Upright pivot points (from vehicle Y, Z, X datum)

- bottom A-arm upright pivot

307.87

321.85

- bottom A-arm chassis pivot (virtual/normal) - Y

- top A-arm upright pivot

285.00

-Y -Z

361.96

-X

5.74 -Y

546.76

557.33

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277.06


55

-Z

166.36

-X

15.83

- spindle reference point

-Y

610.50

-Z

258.19

-X

-0.46

- spindle / wheel cl point

-Y

575.50

-Z

257.58

-X

0.07

Instant centre Front view swing axle length (at IC point)

1483.38

Front view swing axle height (at IC point)

120.67

Roll centre height

47.18

Roll centre offset

0.00

Side view IC length (at IC point)

3931.36

Side view IC height (at IC point)

243.63

Side view IC height (at rear axle centreline)

99.15

Side view IC angle (from tyre centre) Suspension roll axis

3.55 -6.2%

Brake force split 62% front 38% rear Brake anti-dive %

24.6%

Track (wheel cl on ground)

1160.00

Top A-arm link lengths (front/rear) Top A-arm link lengths (virtual)

242.55

Bottom A-arm link lengths (front/rear) Bottom A-arm link lengths (virtual) Bottom A-arm link lengths (normal)

Tyre contact cl from vehicle cl

274.53

242.64

Top A-arm link lengths (normal)

Tyre contact cl from X datum

281.01

311.27 280.80 280.80 0.00 580.00

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318.89


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Tyre rolling radius (effective radius)

257.62

Tyre diameter (overall)

523.24

Rim width

152.40

Rim mounting offset

-35.00

Wheel mounting spacer

0.00

Wheel toe reference length

330.20

Wheel alignment in straight ahead position Camber angle

-1.00

Upright pivot inclination (kpi) and offset

3.05

Caster angle and trail

3.00

Spindle offset from kingpin axis(side/front view) Static toe (mm) toeout

14.05

24.21 10.71

23.07

-5.00

Ride height ref point (from vehicle Y, Z, X datum)

Front

Rear

Front LH: Rear LH: -Y

0.00

Ride height (ref point to ground)

0.00 -Z

-X

0.00

38.10

38.10

1600.00

Datum reference dimensions Chassis lateral datum

(Y): Chassis centreline

Chassis vertical datum

(Z): Ground

Chassis longitudinal datum (X): Front axle centreline Ride height ref point (from chassis Y, Z, X datum)

Front


0.00

0.00

-Z

38.10

38.10

-X

0.00

1600.00

Chassis pivot points (from chassis Y, Z, X datum)

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LH

Rear


57

- top A-arm (front/rear)

-Y

300.00

-Z

325.00

-X

135.00 -135.00

- bottom A-arm (front/rear)

319.00

-Y

270.00

-Z

155.00

161.00

-X

135.00 -150.00

- tie rod (steering rack)

-Y

315.00

251.43

-Z

186.40

-X

52.00

Upright pivot points (from upright Y, Z, X datum) - top A-arm

-Y

62.00

-Z

105.00

-X

0.00

- bottom A-arm

-Y

55.00

-Z

-90.00

-X

20.00

- tie rod (steering arm)

-Y

97.00

-Z

-52.70

-X

60.00


-Y

0.00

Upright pivot points (from chassis Y, Z, X datum) - top A-arm

-Y

546.76

-Z

361.96

-X

5.74

- bottom A-arm

-Y

557.33

-Z

166.36

-X

15.83


-Y -Z

200.88

-X

58.28


-Y -Z

515.36

610.50

258.19

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285.00

FSAE IIT Delhi Suspension Report -X

5.1.2

58 -0.46

Front Roll and Bump Data

Chassis roll values calculated every 0.25 degrees. Roll left. Full dynamic roll centre. Roll starts at Static.

LH wheel centre height

camber angle fvsax

caster

angle

caster

trail

kpi

angle

kpi

offset

wheel

scrub

axle

tramp

toe mm

roll

offset

0.00 roll -1.00 47.18 1483.38

3.00

24.21

3.05

14.05

0.00

0.00

-5.00

0.00

0.50 roll -0.70 46.77 1447.24

3.07

24.52

2.75

14.04

-0.02

-0.08

-5.09

-44.11

1.00 roll -0.42 45.18 1408.99

3.13

24.79

2.47

14.04

-0.04

-0.12

-5.18

-89.51

1.50 roll -0.16 42.34 1368.63

3.18

25.03

2.21

14.04

-0.06

-0.14

-5.29 -137.97

2.00 roll 0.06 38.11 1326.09

3.22

25.23

1.98

14.03

-0.09

-0.12

-5.42 -191.93

2.50 roll 0.26 32.21 1281.18

3.26

25.39

1.79

14.03

-0.13

-0.07

-5.58 -255.19

RH wheel centre

caster

wheel

axle

toe

roll

scrub

tramp

mm

offset

height

camber

fvsax

angle

angle

caster trail

kpi

kpi

angle

offset

0.00 roll -1.00 47.18 1483.38

3.00

24.21

3.05

14.05

0.00

0.00

-5.00

0.00

0.50 roll -1.31 46.77 1518.65

2.93

23.88

3.36

14.05

0.00

0.09

-4.92

-44.11

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59

1.00 roll -1.64 45.18 1551.65

2.85

23.52

3.69

14.06

0.01

0.23

-4.83

1.50 roll -1.99 42.34 1582.20

2.76

23.12

4.04

14.07

0.01

0.41

-4.75 -137.97

2.00 roll -2.36 38.11 1609.97

2.67

22.68

4.40

14.08

0.02

0.64

-4.65 -191.93

2.50 roll -2.74 32.21 1634.49

2.57

22.20

4.79

14.08

0.02

0.93

-4.55 -255.19

LH wheel camber roll centre height chassis

angle ground

caster

angle fvsax

caster

trail

kpi

angle

kpi

offset

wheel

scrub

axle

-89.51

toe

tramp

mm

rc

offset

37.38 bump 0.00 22.07

-2.57 -15.31

3.59 26.82 1232.02

4.62

14.07

0.91

-0.45

-5.45

35.00 bump 0.00 23.59

-2.46 -11.41

3.55 26.65 1247.74

4.51

14.06

0.97

-0.41

-5.41

30.00 bump 0.00 26.81

-2.23 3.47 26.29 -3.19 1280.91

4.28

14.06

1.05

-0.33

-5.32

25.00 bump 0.00 30.09

-2.02 3.39 25.94 5.09 1314.26

4.06

14.06

1.06

-0.26

-5.25

20.00 bump 0.00 33.41

-1.80 13.41

3.31 25.59 1347.78

3.85

14.06

0.99

-0.19

-5.19

15.00 bump 0.00 36.78

-1.59 21.78

3.23 25.24 1381.46

3.64

14.05

0.86

-0.14

-5.13

10.00 bump 0.00 40.20

-1.39 30.20

3.15 24.89 1415.29

3.44

14.05

0.64

-0.08

-5.08

5.00 bump 0.00 43.66

-1.19 38.66

3.08 24.55 1449.27

Static -1.00 3.00 47.18 47.18 1483.38 5.00 droop 50.75 55.75

-0.81 2.92 1517.62

24.21 23.86

3.24 3.05

14.05

14.05

2.86

14.05

0.36 0.00 -0.43

-0.04 0.00

-5.04

-5.00

0.03

-4.96

10.00 droop 0.00 54.36

-0.63 64.36

2.85 23.52 1551.98

2.67

14.05

-0.94

0.06

-4.93

15.00 droop 0.00 58.03

-0.44 73.03

2.77 23.19 1586.45

2.49

14.05

-1.53

0.08

-4.89

20.00 droop 0.00 61.75

-0.27 81.75

2.70 22.85 1621.04

2.31

14.04

-2.19

0.10

-4.86

25.00 droop 0.00 65.52

-0.09 90.52

2.62 22.51 1655.74

2.14

14.04

-2.93

0.11

-4.82

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0.00 0.00


60

30.00 droop 0.00 69.35

0.08 99.35

2.55 22.18 1690.55

1.97

14.04

-3.74

0.12

-4.77

35.00 droop 0.00 73.24

0.24 108.24

2.47 21.84 1725.47

1.80

14.04

-4.64

0.12

-4.73

37.72 droop 0.00 75.38

0.33 113.09

2.43 21.66 1744.50

1.72

14.04

-5.16

0.12

-4.70

Equivalent suspension travel due to chassis roll RH

LH

0.00 roll

0.00

0.00

0.50 roll

-4.97

5.15

1.00 roll

-9.55

10.69

1.50 roll

-13.72

16.61

2.00 roll

-17.46

22.95

2.50 roll

-20.70

29.73

Side view swing axle and instant centre IC

IC

length

axle

height

height

angle

37.38 bump

3860.26

218.32

90.49

3.24

35.00 bump

3864.64

219.89

91.04

3.26

30.00 bump

3873.91

223.22

92.19

3.30

25.00 bump

3883.26

226.56

93.35

3.34

20.00 bump

3892.69

229.92

94.50

3.38

15.00 bump

3902.21

233.31

95.66

3.42

10.00 bump

3911.83

236.72

96.82

3.46

5.00 bump Static 5.00 droop

3921.54 3931.36

240.16

243.63

3941.29

97.99

99.15

247.14

3.50 3.55

100.33

3.59

10.00 droop

3951.34

250.68

101.51

3.63

15.00 droop

3961.51

254.26

102.69

3.67

20.00 droop

3971.82

257.88

103.88

3.71

25.00 droop

3982.26

261.55

105.09

3.76

30.00 droop

3992.86

265.27

106.30

3.80

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61

35.00 droop

4003.61

269.04

107.52

3.84

37.72 droop

4009.53

271.12

108.19

3.87

LH brake

accel

a-dive% a-lift% 37.38 bump

22.4

0.0

35.00 bump

22.6

0.0

30.00 bump

22.9

0.0

25.00 bump

23.2

0.0

20.00 bump

23.4

0.0

15.00 bump

23.7

0.0

10.00 bump

24.0

0.0


24.3 24.6 24.9

0.0 0.0 0.0

10.00 droop

25.2

0.0

15.00 droop

25.5

0.0

20.00 droop

25.8

0.0

25.00 droop

26.1

0.0

30.00 droop

26.4

0.0

35.00 droop

26.7

0.0

37.72 droop

26.8

0.0

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5.2 Rear

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62


5.2.1

Rear A Arm Geometry Team AXLR8R

63


64

After various iterations and optimization of the following during Bumpdroop and Roll: a) b) c) d) e) f)

Camber Caster Kpi offset Anti-Dive and Anti-Squat Roll Center position Front view Swing axle arm lengths

Keeping the variation of the above parameters minimum, following set of data was obtained: Double A-arm Vehicle lateral datum



(Z): Ground


Chassis pivot points (from vehicle Y, Z, X datum)

LH

- top A-arm chassis pivot (front/rear)

275.00

-Z

-Y

320.00

285.00

315.00

- X -1450.00 -1750.00 - bottom A-arm chassis pivot (front/rear) -Z

172.00

-Y

285.00

275.00

155.00

- X -1450.00 -1750.00 - top A-arm chassis pivot (virtual/normal) -Z

317.50

-Y

280.00

279.97

317.48

- X -1600.00 -1600.96 - bottom A-arm chassis pivot (virtual/normal) - Y -Z

163.50

280.00

164.53

- X -1600.00 -1581.78 Upright pivot points (from vehicle Y, Z, X datum) - top A-arm upright pivot

-Y -Z

542.48

350.19

- X -1610.25

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280.61


65


-Y -Z

542.11

160.16

- X -1590.25 - spindle reference point

-Y -Z

600.53

256.19

- X -1599.72 - spindle / wheel cl point

-Y -Z

565.54

255.58

- X -1600.04 Instant centre Front view swing axle length (at IC point)

1390.71

Front view swing axle height (at IC point)

179.87

Roll centre height

73.72

Roll centre offset

0.00

Side view IC length (at IC point)

4356.42

Side view IC height (at IC point)

408.21

Side view IC height (at front axle centreline)

149.93

Side view IC angle (from tyre centre)

5.35

Suspension roll axis

9.3%

Brake force split 62% front 38% rear Brake anti-lift %

22.8%

Acceleration anti-squat %

22.4%

Track (wheel cl on ground)

1140.00

Top A-arm link lengths (front/rear) Top A-arm link lengths (virtual)

304.77

303.83

264.70

Top A-arm link lengths (normal)

264.70

Bottom A-arm link lengths (front/rear) Bottom A-arm link lengths (virtual) Bottom A-arm link lengths (normal)

293.12 262.31 261.68

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311.28


66

Tyre contact cl from X datum

-1600.00

Tyre contact cl from vehicle cl

570.00

Tyre rolling radius (effective radius)

255.62

Tyre diameter (overall)

523.24

Rim width

152.40

Rim mounting offset

-35.00

Wheel mounting spacer

0.00

Wheel toe reference length

330.20

Wheel alignment in straight ahead position Camber angle

-1.00

Upright inclination angle

0.00

Spindle offset from kingpin axis(side/front view) Static toe (mm) toein

0.00

23.24

3.00

Ride height ref point (from vehicle Y, Z, X datum)

Front

Rear


0.00

Ride height (ref point to ground)

0.00 -Z

-X

0.00

38.10

38.10

1600.00

Datum reference dimensions Chassis lateral datum

(Y): Chassis centreline

Chassis vertical datum

(Z): Ground

Chassis longitudinal datum (X): Front axle centreline

Ride height ref point (from chassis Y, Z, X datum)

Front


0.00

0.00

-Z

38.10

38.10

-X

0.00

1600.00

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Rear


67

Chassis pivot points (from chassis Y, Z, X datum) - top A-arm (front/rear)

-Y -Z

285.00

320.00

LH 275.00

315.00

- X -1450.00 -1750.00 - bottom A-arm (front/rear) -Z

-Y

285.00

172.00

155.00

- X -1450.00 -1750.00 - toe control link

-Y -Z

268.00

241.00

- X -1750.33 Upright pivot points (from upright Y, Z, X datum) - top A-arm

-Y

56.50

-Z

95.00

-X

-10.00

- bottom A-arm

-Y

60.00

-Z

-95.00

-X

10.00

- toe control link

-Y -Z

57.78

2.86

- X -105.00 - spindle reference point

-Y

0.00

Upright pivot points (from chassis Y, Z, X datum) - top A-arm

-Y -Z

542.48

350.19

- X -1610.25 - bottom A-arm

-Y -Z

542.11

160.16

- X -1590.25 - toe control link

-Y -Z

543.67

258.04

- X -1705.24

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275.00


68


-Y -Z

600.53

256.19

- X -1599.72

5.2.2

Rear Roll And Bump Data

SusProg3D July10_R6_Suspension Final 2011.s3d Rear Roll and bump

Chassis roll values calculated every 0.25 degrees. Roll left. Full dynamic roll centre. Roll starts at Static.

LH wheel

camber angle

caster

angle

kpi

angle

wheel

scrub

axle

toe

tramp

mm

roll centre offset

height 73.72

0.00 roll 1390.71

-1.00

0.00

-0.06

0.00

0.00

3.00

0.00

0.50 roll 1387.51

-0.71

-0.06

-0.35

-0.01

-0.28

2.95

-41.43

73.16

1.00 roll 1383.20

-0.43

-0.11

-0.62

-0.02

-0.61

2.91

-83.82

71.07

1.50 roll 1377.56

-0.18

-0.16

-0.88

-0.03

-0.99

2.87 -128.45

67.38

2.00 roll 1370.32

0.06

-0.19

-1.12

-0.05

-1.42

2.85 -176.94

61.94

2.50 roll 1361.16

0.28

-0.22

-1.33

-0.06

-1.89

2.84 -231.62

54.46

RH wheel

camber angle

caster

angle

angle

kpi

wheel

scrub

axle

tramp

toe mm

roll centre offset

height 73.72

0.00 roll 1390.71

-1.00

0.00

-0.06

0.00

0.00

3.00

0.00

0.50 roll 1393.04

-1.30

0.06

0.24

-0.01

0.25

3.05

-41.43

73.16

1.00 roll 1394.62

-1.61

0.14

0.56

-0.02

0.44

3.10

-83.82

71.07

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fvsax

fvsax


69

1.50 roll 1395.64

-1.94

0.22

0.89

-0.03

0.57

3.14 -128.45

67.38

2.00 roll 1396.29

-2.29

0.31

1.23

-0.03

0.62

3.17 -176.94

61.94

2.50 roll 1396.74

-2.65

0.41

1.59

-0.03

0.59

3.19 -231.62

54.46

LH wheel

camber angle

caster

angle

kpi

angle

wheel

scrub

axle

tramp

toe

rc roll centre height

mm

offset chassis

ground

fvsax 35.81 bump -2.50 0.30 1351.57

-0.49

1.44

2.34

-1.07

3.06

0.00

36.10

35.00 bump -2.46 1.94 1353.11

-0.47

1.41

2.34

-1.05

3.06

0.00

36.94

30.00 bump -2.25 12.12 1361.97

-0.41

1.20

2.27

-0.91

3.04

0.00

42.12

25.00 bump -2.04 22.32 1369.69

-0.34

0.98

2.11

-0.77

3.03

0.00

47.32

20.00 bump -1.83 32.54 1376.24

-0.27

0.78

1.87

-0.62

3.02

0.00

52.54

15.00 bump -1.62 42.79 1381.62

-0.20

0.57

1.54

-0.47

3.01

0.00

57.79

10.00 bump -1.41 53.07 1385.83

-0.14

0.36

1.12

-0.32

3.00

0.00

63.07

5.00 bump -1.21 63.37 1388.86 Static 1390.71 5.00 droop 1391.38

-1.00 -0.79

-0.07 0.00

0.15

-0.06

0.07

-0.26

0.60 0.00 -0.69

-0.16 0.00 0.16

3.00 3.00 3.00

0.00 0.00

68.37

73.72

0.00

73.72

79.11

10.00 droop -0.59 94.55 1390.86

0.14

-0.47

-1.48

0.33

3.00

0.00

84.55

15.00 droop -0.38 105.04 1389.16

0.20

-0.67

-2.36

0.50

3.01

0.00

90.04

20.00 droop -0.18 115.59 1386.27

0.27

-0.88

-3.33

0.68

3.02

0.00

95.59

25.00 droop 0.03 126.20 1382.19

0.34

-1.09

-4.40

0.85

3.03

0.00

101.20

30.00 droop 0.24 136.88 1376.94

0.41

-1.30

-5.56

1.03

3.04

0.00

106.88

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84.11


70

35.00 droop 0.45 147.64 1370.51

0.47

-1.50

-6.82

1.22

3.06

0.00

112.64

35.71 droop 0.48 149.17 1369.51

0.48

-1.53

-7.01

1.24

3.06

0.00

113.46

Equivalent suspension travel due to chassis roll RH

LH

0.00 roll

0.00

0.00

0.50 roll

-4.89

5.06

1.00 roll

-9.41

10.48

1.50 roll

-13.56

16.25

2.00 roll

-17.32

22.40

2.50 roll

-20.63

28.96

Side view swing axle and instant centre IC

IC

length

axle

height

height

angle

35.81 bump

4382.91

393.53

143.66

5.13

35.00 bump

4382.19

393.85

143.80

5.14

30.00 bump

4377.86

395.84

144.67

5.17

25.00 bump

4373.76

397.85

145.54

5.20

20.00 bump

4369.89

399.88

146.41

5.23

15.00 bump

4366.23

401.93

147.28

5.26

10.00 bump

4362.78

404.00

148.16

5.29


4359.51 4356.42

406.09

408.21

4353.51

149.04

149.93

410.36

150.82

5.32 5.35 5.38

10.00 droop

4350.75

412.54

151.71

5.42

15.00 droop

4348.14

414.75

152.62

5.45

20.00 droop

4345.68

417.00

153.53

5.48

25.00 droop

4343.34

419.28

154.46

5.51

30.00 droop

4341.13

421.61

155.39

5.55

35.00 droop

4339.03

423.98

156.34

5.58

35.71 droop

4338.74

424.32

156.48

5.59

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71

LH brake

accel

a-lift% a-squat% 35.81 bump

21.8

20.1

35.00 bump

21.9

20.2

30.00 bump

22.0

20.5

25.00 bump

22.1

20.8

20.00 bump

22.3

21.1

15.00 bump

22.4

21.4

10.00 bump

22.5

21.8


22.7 22.8 22.9

22.1 22.4 22.7

10.00 droop

23.1

23.1

15.00 droop

23.2

23.4

20.00 droop

23.3

23.8

25.00 droop

23.5

24.1

30.00 droop

23.6

24.5

35.00 droop

23.8

24.8

35.71 roop

23.8

24.9

5.3 Verification of Susprog Results It has been verified that the Front view swing axle arm length has been given by

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6.

SHOCK ABSORBERS

6.1 Parameters of Study 1. 2. 3. 4. 5. 6. 7. 8.

Bell crank Pushrod/Pull rod Suspension frequency Spring rate Wheel rate Motion ratio Non-linear variation of motion ratio Shock Absorber

6.2 Bell Crank The bell crank is used to convert the direction of reciprocating movement. By varying the angle of the crank piece it can be used to change the angle of movement from 1 degree to 180 degrees. The bell crank aides packaging, it allows the pull rod and the shock displacement to be aligned in different directions. Bell crank can amplify a force "in line” in a limited space. Length of arms and angle between arms will be decided based on analysis on Susprog3D.

6.3 Push Rod/Pull Rod  

Pull rod needs to have larger strength than push rods which acts in compression. Ultimate / Yield strength of pull rod must be greater. The issue isn't the ultimate/yield strength of materials; it’s a buckling issue with the pushrods.

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72


6.4 Ride/Suspension Frequency The first step in choosing spring stiffness is to choose the desired ride frequencies for front and rear. A ride frequency is the undamped natural frequency of the body in ride. The higher the Frequency, the stiffer the ride. So, this parameter can be viewed as normalized ride stiffness. Based on the application, there are ballpark numbers to consider.  0.5 - 1.5 Hz for passenger cars  1.5 - 2.0 Hz for sedan racecars and moderate down force formula cars  3.0 - 5.0+ Hz for high down force racecars

6.4.1   

Produce a softer suspension. More mechanical grip. However, the response will be slower in transient (what drivers report as “lack of support”).

6.4.2  

Effects at Lower frequencies

Effects at Higher frequencies

Create less suspension travel for a given track Allowing lower ride heights, and in turn, lowering the center of gravity.

6.4.3

Deciding the Ride Frequency

Ride frequencies front are rear are generally not the same. In Figure 1, we can see the undamped vertical motion of the chassis with the front ride frequency higher than the rear. The out of phase motion between front and rear vertical motion, caused by the time delay between when the front wheel and rear wheel hit the bump, is accentuated by the frequency

difference. HIGHER FRONT RIDE FREQUENCY

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74

A result of the phase difference is pitching of the body. To reduce the pitch induced by hitting a bump, the rear needs to have a higher natural frequency to “catch up” with the front, as shown in Figure 2. This notion is called producing a “flat ride”, meaning that the induced body pitch from road bumps is minimized. The above theory was originally developed for passenger cars, where comfort takes priority over performance, which leads to low damping ratios, and minimum pitching over bumps. Racecars in general run higher damping ratios, and have a much smaller concern for comfort, leading to some racecars using higher front ride frequencies. The higher damping ratios will reduce the amount of oscillation resultant from road bumps, in return reducing the need for flat ride.

HIGHER REAR RIDE FREQUENCY

A higher front ride frequency in a racecar allows  Faster transient response at corner entry.  Less ride height variation on the front (the aerodynamics are usually more pitch sensitive on the front of the car).  Allows for better rear wheel traction (for rear wheel drive cars) on corner exit. The ride frequency split should be chosen based on which is more important on the car you are racing, the track surface, the speed, pitch sensitivity, etc. f=

1 √k 2π m

f = natural frequency (Hz) K = spring rate (N/m) m = mass (kg)

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75

6.5 Spring Rate Spring Rate indicates how much the spring will deflect when a load is applied. Spring rate is measured in pounds per inch (lb/in). Spring rate for a coil is given by: K=

d 4G 8 N D3

Where, wire G is the

d is the diameter, spring's s modulus, s the of wraps s the diameter coil.

hear and N i number and D i of the

Solving the above equation for spring rate and applying to a suspension to calculate spring rate from a chosen

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76

Ride frequency, measured motion ratio, and mass:

Ks = 4π2f2msmMR2 Where, Ks is spring rate (N/m), msm is Sprung mass (kg), f is Ride frequency (Hz) and MR is Motion ratio (Wheel/Spring travel).

6.6 Motion Ratio Motion ratio in suspension of a vehicle describes the amount of shock travel (spring movement) for a given amount of wheel travel. Mathematically it is the ratio of shock travel and wheel travel. The amount of force transmitted to the vehicle chassis reduces with increase in motion ratio. A motion ratio close to one is desired in vehicle for better ride and comfort. Motion Ratio = Wheel Travel ÷ Spring Travel Wheel Rate = Spring Rate ÷ (Motion Ratio)2 Motion ratio affects both spring and shock rates, as well as the effectiveness of the anti-roll bar. The lower the motion ratio that a given spring is working with, the lower the wheel rate will be.

6.7 Wheel Rate Wheel Rate is the change of wheel load, at the center of tire contact, per unit vertical displacement of the sprung mass relative to the wheel at a specified load. Wheel rate for a one corner of a race car can be calculated from two numbers – the rate of the road spring and the motion ratio of the suspension.

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

Wheel rate is always less than spring rate. Hence linear distance travelled by wheel is more than compression or expansion of the spring.



In order to make the contact between the tires contact patches and the track surface as continuous as possible and to avoid shaking the car/or driver apart, racing cars must have some sort of springs. Springs allow the wheels to deflect in reaction to accelerations. When the vehicle is sprung, longitudinal accelerations and load transfer will cause vertical movement of sprung mass and centrifugal acceleration will cause the sprung mass to roll. Road surface irregularities will cause vertical deflection of the unsprung wheels in relation to the chassis. All of these antics cause wheels’ camber to change in relation to road surface. In addition to this, it causes large amount of energy to be stored in the springs as they compress which calls for the need for shock absorbers. The amount of vertical wheel deflection caused by a given acceleration or its resultant load transfer is determined by the wheel’s ride rate





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resistance expressed in pounds of force necessary to cause a deflection of one inch and measured at wheel centerline. The resistance to the chassis roll caused by a given centrifugal acceleration is determined by vehicle’s roll rate resistance expressed in pounds of force necessary to resist one degree of roll generation. This force will come from the compression of the outboard springs in roll and from the resistance of anti-roll bars.

6.8 Roll Gradient The Roll Gradient/Roll Gain/Roll Stiffness is defined as rate of change of vehicle roll angle with steady state lateral acceleration values. It is measured as the degrees of body roll required in a 1-G corner. Dependent Factors: Of all the factors CG height (z-dir) and sprung mass are the most sensitive. 

  

CG location in x and z-directions: This change is attributed to moment arm of CG from roll axis of the vehicle. It increases with increasing distances. Sprung Mass: Roll gradient increases with increasing sprung mass. Diameter of Anti-roll bars: Roll Gradient decrease with increasing diameter of ARB. Stiffness of Tires: Increase in stiffness of ARB and Tires increase the stiffness of vehicle thereby reducing the value of developed roll angle.

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6.9 Damping 6.9.1

What is damping?

In a spring-mass system, any displacement and release of the mass from its equilibrium position will cause the mass to oscillate. If the system were ideal, the mass would continue vibrating at a given frequency (its natural frequency) indefinitely with unchanged amplitude. Introducing damping into the system causes the oscillation to trail off and forces the system to reach a steady state value.

6.9.2

Damping ratio

The damping ratio, usually designated as ζ, is defined as the ratio of actual damping coefficient to the critical damping coefficient. The reason why we work with damping ratios instead of actual damping coefficients is so that we can normalize the discussion for all dampers.

The damping force is generated by the orifice and also the shim disc valves located at the end of the rod. Since both the gas and the oil chambers are separated by the free piston, the oil and nitrogen cannot be mixed. Considering that the damping force of shock absorber corresponds to a resistant force while an object moves within a fluid, viscous damping model can be introduced. In such case, the damping force of absorber is assumed to be proportional to the piston speed where the proportional constant is defined as the damping coefficient. Relation between these quantities is written as follows.

It is difficult to determine by the damping force itself whether the shock absorber is hard (large) or soft (small). Therefore the damping ratio associated with the vehicle gross weight and also the wheel rate is further defined. Using the damping ratio, the strength of the damping force of absorber is evaluated.

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This is the Basic Suspension Analysis Block.

Consider the case when, KB <
Applying the Laplace transform to our equations shows

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Wheel rate Example:

Figure: Effect of damping ratio to a sprung mass system

An undamped system will tend to eternally vibrate at its natural frequency. As the damping ratio is increased from zero, the oscillation trails off as the system approaches a steady state value. Eventually, critical damping is reached- the fastest response time without overshoot. Beyond critical damping, the system is slow responding. An important point to understand that will be useful when tuning the shocks on the car is that once any damping is present, the amount of damping does not change the steady state value- it only changes the amount of time to get there and the overshoot.

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6.9.3

Transmissibility

The transmissibility (TR) is the ratio between output and input amplitude. In our application, the input amplitude will be the height of a road irregularity and the output amplitude is the vertical movement of the car body. For a spring-mass-damper system, transmissibility is actually a function of frequency. When we hit a speed bump going very slowly, the car moves vertically almost as much as the wheels. But if we were to go over the same bump going quickly, the body of the car doesn’t move nearly as much. Depending on the speed at which we hit the speed bump, the car body’s response changes. The cause of this phenomenon is that the response of the system – the car and its suspension – is a function of the frequency of the input. Transmissibility also changes with damping.

6.10 6.10.1

Shock Absorber Introduction

The shock absorber, or snubber, a device that controls unwanted spring motion through a process known as dampening. Shock absorbers slow down and reduce the magnitude of vibratory motions by turning the kinetic energy of suspension movement into heat energy that can be dissipated through hydraulic fluid. These dampen the vertical motion induced by driving your car along a rough surface and so should technically be referred to by their 'proper' name - dampers. If your car only had springs, it would be a travelling deathtrap. Or at least it would be a travelling deathtrap until the incessant vibration caused it to fall apart. Shock absorbers (dampers) perform two functions. 1. They absorb any larger-than-average bumps in the road so that the upward velocity of the wheel over the bump isn't transmitted to the car chassis.

2.

They keep the suspension at as full a travel as possible for the given road conditions - they keep your wheels planted on the road.

Technically they are velocity-sensitive damping devices - in other words, the faster they move, the more resistance there is to that movement. They work in conjunction with the springs. The spring allows movement of the wheel to allow the energy in the road shock to be transformed into kinetic energy of the unsprung mass, whereupon it is dissipated by the

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damper. The damper does this by forcing gas or oil through a constriction valve (a small hole). Adjustable shock absorbers allow you to change the size of this constriction, and thus control the rate of damping. Smaller the constriction, stiffer the suspension.

6.10.2

Shock Absorber Components

The telescopic damper is made up of several key components, each performing a specific role. Brief descriptions of listed components follow, • Body • Piston • Valve • Main Shaft • Adjusters • Reservoir Body The body of a racing telescopic shock absorber performs several unique functions and is composed of several pieces. Primarily, the body must contain the fluid being used to provide the damping force, usually oil. The inner face of the body also forms the sealing surface at the extremity of the piston and the body must be strong enough to withstand the hydrostatic pressures induced by compression and extension of the main shaft. Furthermore, the body must provide support for the main shaft against loadings that contain components misaligned to the plunge axis. In modern racing shock absorbers, the body also provides provision for the coil spring mounting and preload adjustment as well as the mounting point to the chassis. Piston The piston divides the body into two sealed oil chambers. Provision for oil to flow between these two chambers is accommodated for via holes, called ports, in the piston. The shape and size of these ports determine the high speed characteristic of the shock absorber. To facilitate different damper characteristics in both compression and rebound, the ports are positioned such that they are covered by valves in one flow direction. The extremity of the piston accommodates a sliding seal to the inner face of the damper body. The faces of the piston may also be dished to provide preload for the valve stack.

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Valve The role of the valve is to control oil flow through the piston. Valves take the form of annular discs with varying thickness and diameter, and are often stacked on top of each other. This arrangement is known as the valve stack. The valve stack controls the transition from low speed to high speed damping. Main Shaft The main shaft or rod serves to connect the piston to the shock absorber eyelet mount. The eyelet is connected to the vehicles’ suspension, providing freedom for the unsprung mass to move relative to the chassis. In adjustable dampers, the main shaft usually houses the low speed rebound adjuster. The main shaft must have sufficient inertia to withstand buckling loads imposed by road surface inputs. Adjusters Adjusters take two forms, oil metering and valve stack. Oil metering adjusters are used to control the low speed damping characteristics of the shock absorber. Oil metering adjustment is achieved with needle and seat style valves, with the needle moving further from the seat as less damping force is required. Valve stack adjusters control the amount of preload the valve stack sees, and hence, the pressure required to open them. Valve stack adjusters are used to alter the transition to high speed damping. Reservoir Reservoirs are secondary chambers attached to the body of the some dampers via either rigid or flexible couplings. The reservoir provides the ability to add pressurization to the damper, reducing cavitations, while maintaining a minimal overall length. The oil is separated from the gas by a floating piston, which is free to move along the axis of the reservoir and avoids the gas forming an emulsion with the oil. Compression adjusters are also housed in the reservoir in adjustable shock absorbers.

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6.10.3

Working Principle

When the shock is in compression modes, oil is forced from the shock body to reservoir in proportion to the area of the shaft entering the shock body. As the oil enters the reservoir, it must pass through the compression adjuster. When the compression adjuster is fully open the shock is set at full soft, conversely when the compression adjuster is closed (the smallest opening) the shock is at full firm. After the oil passes through the compression adjuster, it enters the reservoir where the floating piston will compress the nitrogen. The floating piston is designed so that aeration will not happen.

Picture depicting various parts of showing parts of shock absorber

When the shock is in rebound modes, the oil in the shock shaft is forced through the shaft. Inside the shaft is a needle. This needle is used to adjust the amount of fluid that can pass by. As the needle is closed it causes firmer rebound damping forces. When the needle is opened further it allows more oil to flow through and that creates softer rebound damping forces. The needle adjustment also effects when the shims on the main piston will open. The damping dynamics of a shock are dependent of the shaft velocities within the shock, in both rebound and compression. Most of the changes within the shock happen within the main shock shaft and body. Shock dynamics are considered under high and low shaft speeds. High shaft speeds occur in bumps, or significant track inconsistencies. Slow shaft speeds occur during cornering, acceleration and braking.

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Low Speed Compression In slow shaft speed compression, oil is displaced into the reservoir in direct proportion to the area of the shaft entering the shock body. The oil passes through the compression adjuster to the external reservoir.

High Speed Compression:

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In fast shaft speeds, oil is displaced into the reservoir through a secondary channel and shim stack. At fast shaft speeds the oil bypasses the slow speed needle. Pressure induced by the high shaft speeds causes the shim stacks that cover holes on the main piston head to flex. When the shim stacks flex, oil passes through the holes on the piston head.

Low Rebound:

Speed

In low speed rebound oil is displaced through the shaft and over the low speed needle.

High Speed

Rebound:

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During fast shaft speed rebound shim stacks located on the main piston head flex in order to allow oil to pass through. Oil bypasses the opening and slow speed needle adjustment.

6.10.4

Adjustments

Problem The vehicle feels unstable, bouncy and non-responsive The vehicle feels hard and bumpy The vehicle feels soft, has low riding position and a tendency to bottom easily in long dips The vehicle feels harsh and has low grip

6.10.5

Conclusions Team AXLR8R

Solution Increase Damping Reduce Damping Increase Damping Reduce Damping


RULE: The car must be equipped with a fully operational suspension system with shock absorbers, front and rear, with usable wheel travel of at least 50.8 mm (2 inches), 25.4 mm (1 inch) jounce and 25.4 mm (1 inch) rebound, with driver seated. After doing all the study, following conclusions are made: Ride Frequency: It should be close to 3 Hz.(good for Formula Cars). Motion Ratio: For better ride and comfort, the motion ratio should be close to 1. Lower motion ratio gives a soft suspension: forces are transferred to body. Higher motion ratio produces stiff suspension Stroke length: The presence of dampers/shocks in Formula SAE suspension designs is articulated in chassis section of the competition rules of FSAE. Specifications on permissible suspension travel are also outlined in the clause: To be on safer side, we are designing the Shock movement upto 37-38mm (1.5”). Since the motion ratio should be close to 1 and considerations of wheel bump and droop are 37-38mm, stroke length must be around 75 mm. Damping Ratio: It lies between 0.65-0.70. For the least oscillating motion of the sprung mass on encountering with a bump or droop, the damping ratio is chosen to be in the given range.

Figure. Effect of damping ratio to a sprung mass system

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The damping must be considerably higher for road holding and control of the unsprung mass motion. Data has shown that for racecars, a good range of damping ratio is between 0.65 and 0.70.

Figure.

Transmissibility for different damping ratios

For maximum grip, we want to minimize the change in forces that the springs are seeing. This is achieved with minimal body movement. Thus, we want the lowest transmissibility possible. At low frequencies, from the plot that we want higher damping ratios. Corresponding low frequencies to low shock speeds, and high frequencies to high shock speeds, we can see that we need high damping ratios for low speeds and low damping.

6.10.6

Calculations

Front Sprung Mass = 57kg

Ride Frequency = 2.79 Hz

Ks = =(1.0^2)* 2.79 *2.79 *484/49*4*57 = 17.53 N/mm ~ 100 lb/in Critical Damping coeff. =2*SQRT(Ks*57/(1^2)) = 1999 Ns/m Damping Coeff= 0.65*Critical Damping Coeff. = 1300 Ns/m Rear

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Sprung Mass = 92kg

Ride Frequency = 2.88 Hz

Ks = =(0.992^2)* 2.88 *2.88 *484/49*4*92 = 29.78 N/mm ~ 170 lb/in Critical Damping coeff. =2*SQRT(Ks*92/(0.992^2)) = 3134 Ns/m Damping Coeff= 0.65*Critical Damping Coeff. = 2037 Ns/m

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6.10.7

Shortlisted Shock Absorbers

Koni 2812 MK2

The 2812 MK II Series is a mono-tube damper specifically designed for competition purposes, featuring externally adjustable compression and rebound. This shock can be rebuilt by the racer. Spring seats are available for 2”, 2.25” and 2.5” ID springs. In addition, 3 different top mounting eye lengths are available. A steel cap is available for the upper eye so that custom mounts can be fabricated as well. For stroke length below 60mm:

Refer 2812 LB for greater Damper length with same stroke length. 3012 The 3012 series features a threaded aluminum-body, external double adjustability and a high pressure gas mono-tube design, ensuring optimum performance. The monotube design allows for independent adjustments to the rebound and compression forces. All damping adjustments are made at the piston, eliminating the additional weight and packaging complications of an external reservoir. The 3012 series offers one of the broadest adjustment ranges in the industry, eliminating the need of constant revalving procedures from track to track.

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95

Elka Suspension 

High-Speed Compression adjustment

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Low-Speed Compression adjustment



Rebound adjustment



Spring Preload adjustment

Shock

$450 /ea.

Hi-Tensile Steel Alloy Springs

$45 /ea.

Optional Titanium Springs

$295 /ea.

2-Piece Mounting Hardware Set: 2 aluminum reducers 3-Piece Mounting Hardware Set: 1 stainless sleeve + 2 aluminum spacers

$10 /set $15 /set

Available Sizes below 60mm stroke length: 

7.5" ETE x 2.0" stroke (190.5mm / 50.8mm)



7.875" ETE x 2.0" stroke (200.3mm / 50.8mm)



7.875" ETE x 2.25" stroke (200.3mm / 57.2mm) Specs:

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BODY DIAMETER: 25mm



SHAFT DIAMETER: 14mm



RESERVOIR DIAMETER: 34mm



SPRING: 35mm inner diameter, 55mm outside diameter



DU BUSHINGS: 12.7mm (1/2" standard)

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Penske Design Benefits • User revalvable and rebuildable • Available valving kit enables user to create desired damping characteristics • External rebound and compression adjustments • Piggyback reservoir with 360-degree clocking • Monotube design for lower hysteresis • Solid model of damper available with purchase • Legendary Penske reliability

Design Specs 50 mm Stroke Length • Compressed — 156mm • Extended — 206mm Piston OD — 25mm Body OD — 32mm Fasteners — 6mm Springs — ID —34mm OD — 40mm Weight • Shock only—412g • Shock and Spring—535g Price $675 per shock

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Risse Racing Jupiter 5

350$

Jupiter 5R

400$

Jupiter 7R

600$

Difference between Jupiter 5 and 5R is the convenience in adjustability. In 5R we can adjust the compression etc. easily as the adjustment knob is protruding outside (away from shock absorber). Difference between Jupiter 5R and 7R is material used in the body of the damper. 7R series is light weight.

Öhlins TTX 25 FSAE Specifications: Overall length = 200 mm Stroke = 57 mm Weight = approx. 448 g (~1 lb) without spring Spherical Bearing dimensions: ID = 8 mm Ball Width = 8 mm OD = 15 mm Springs: 150lb/in to 650lb/in in 50lb increments

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6.10.8

Finalised Shocker

Penske 7800 On the basis of desired Damping as shown in calculations, Penske Shocks satisfies the requirement. We have gone through all the damping curves of different companies. Penske suits the best. Picture shows the F vs v curve of the damper at specific position of the adjusters.

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7. ANTI ROLL BARS 7.1 Introduction A sway bar (also stabilizer bar, anti-sway bar, roll bar, or anti-roll bar, ARB) is an automobile suspension device. It connects opposite (left/right) wheels together through short lever arms linked by a torsion spring. A sway bar increases the suspension's roll stiffness—its resistance to roll in turns, independent of its spring rate in the vertical direction.

7.1.1

Main Functions

Anti-roll bars provide basically two main functions:1. The first function is the reduction of body lean. The reduction of body lean is dependent on the total roll stiffness of the vehicle. Increasing the total roll stiffness of a vehicle does not change the steady state total load (weight) transfer from the inside wheels to the outside wheels, it only reduces body lean. The total lateral load transfer is determined by the CG height and track width. Weight Transfer=lateral

acceleration∗weight∗CG height track width

2. The other function of anti-roll bars is to tune the handling balance of a car. Understeer or over steer behaviour can be tuned out by changing the proportion of the total roll stiffness that comes from the front and rear axles.

7.2 Body Roll During the course of cornering, lateral forces pass through the CG, which creates a torque as the roll axis generally do not pass through the CG which cause the outside suspension to compress while the other side lifts and extends. More technically, one side moves into jounce while the other moves into rebound.

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7.2.1 Negative Aspects of Body Roll Firstly, it disrupts the driver. Secondly, due to body roll, angle of tire w.r.t ground changes, which changes camber angle and also caster angle, which ultimately affects tire traction. More specifically, outer tire experiences increased positive camber and inner tire undergoes negative camber.

7.2.2

Ways to Prevent Body Roll

Prevention of body roll is important as it causes detrimental effects to the handling of the car. One method to achieve this is through the use of stiffer springs. A stiffer spring will compress less than a softer spring when subjected to an equal amount of force. And less compression of the suspension on the outside edge will result in less body roll. However, stiffer springs require the use of stronger dampers (struts or shock absorbers) and have an immediate and substantial effect on ride quality and also too much spring stiffness will harshly affect the damping characteristics which in turn will result in loss of traction. Another option is to use “anti roll bar” along with the springs. The use of anti-roll bars allows to reduce roll without making the suspension's springs stiffer in the vertical plane, which allows improved body control with less compromise of ride quality.

7.3 Types of Anti Roll Bar There are basically two types of ‘anti roll bar’ assembly -U shaped anti roll bar -T shaped anti roll bar Both of them have same function, just their mode of functioning are different in some aspects.

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7.3.1

U-shaped Anti Roll Bar

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7.3.1.1Some Relevant Terms Effective length or Active length- The part of anti roll bar rod which actually undergoes torsion motion. Actual Arm length- It is the actual length of lever arm(moment arm). Effective Arm length- It is the perpendicular distance between anti drop link and anti roll bar rod. Nominal length- It is the actual length of anti roll bar rod which also includes the welding or fixation portion of lever arm with anti roll bar rod.

7.3.2

T-shaped Anti Roll Bar

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We decided to use U shaped anti roll bar considering the chassis space constraint in the front as well as rear. Actually rear posed more problems. Another reason being its principles and installation were relatively easy to understand and apply.

7.4 Principles 

The basis principle applies to both U shaped anti roll bar as well as T shaped anti roll bars. They are constructed out of a U-shaped piece of steel that connects to the body at two points, and at the left and right sides of the suspension. If the left and right wheels move together, the bar just rotates about its mounting points and does not bend. If the wheels move relative to each other, the bar is subjected to torsion and forced to twist.



The bar resists the torsion through its stiffness. The stiffness of an antiroll bar is based on the fourth power of its radius, the stiffness of the

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material, the inverse of the length of the lever arms (i.e., the shorter the lever arm, the stiffer the bar), the geometry of the mounting points, and the rigidity of the bar's mounting points. Some anti-roll have adjustable lever arm, allowing their stiffness to be altered by increasing or reducing the length of the lever arms. The stiffer the bar, the more force required to move the left and right wheels relative to each other. This increases the amount of force required to make the body roll.

7.5 Factors that Determine Stiffness There are two primary factors that determine an anti-roll bar's torsional stiffness: the 1. 2.

Diameter of the bar The length of the bar's moment arm.

Torsional (or twisting) motion of the bar is actually governed by the equation: twist=

2× Torque ×length π ×d 4 × material modlus

And since the diameter is in the denominator, as diameter gets larger, the amount of twist gets smaller. It means that torsional rigidity is a function of the diameter to the fourth power. This is why a very small increase in diameter makes a large increase in torsional rigidity. For hollow bars, we calculate the rate of a solid bar of the outer diameter and the rate of a solid bar of the inner diameter. Then, the rate of the smaller bar is subtracted from the larger bar.

7.6 Components of U- shaped anti roll bar

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Anti Roll Bar rod (tubular or solid) This is the principal component as it undergoes torsion movement. Its mechanical properties like shear modulus, young’s modulus is the one which matters the most in calculations. Lever arm It is basically a moment arm fixed to the anti roll bar rod and is free to rotate with respect to anti drop link. Usually, it does not contribute to stiffness of anti roll bar, but in case of bladed type lever arm, they contribute towards the total stiffness.

Anti Drop Link

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It is basically a rod simply joined to lever arm and the torsion motion actuator (e.g. bell crank or a-arm) through nut-bolts so that it can rotate freely on both ends.

Anti Roll bar Bushes

They're used on anti-roll bar links and mountings. It's vitally important for car's handling. Good and efficient bushes improve a cars' road holding and chassis performance by controlling the amount of unwanted movement in the suspension. This gives the tyres greater contact with the road, improving safety and performance.

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Polyurethane can be used for mounting the anti roll bar with the chassis. The rubber is a little too soft and deteriorates with age. It also perishes in the cold and splits in the heat. Nylatron is a self lubricating oil filled hard nylon which reduces wear on these parts. 7.7

Tubular Anti Roll Bar

Testing has found the tube is the strongest shape and while maintaining a proportionate wall thickness a tubular sway bar will provide only 5% less stiffness for one made out of solid metal in the same diameter but will have a significantly lower weight, sometimes a reduction as much as 1020lbs. This has no heavy polar impact since it is so low on the chassis but will impact braking/acceleration respectively. Centre portion of the anti roll bar rod contribute nothing significant but weight to the performance of the vehicle. Holes must not be drilled to make it softer. It may break the bar during the course of its torsion movement.

7.8 Some important Parameters to be used in Calculations 7.8.1

Roll Gradient

The roll gradient is the degrees of body roll required in a 1-G corner. Chassis stiffness should be 10 times the roll stiffness /roll gradient of the suspension at a minimum. Optimizing the roll angle during a handling manoeuvre can be achieved by one of the following methods: 1. Lowering the CG height of the vehicle will increase the SSF (Static Stability Factor), increasing the tendency of the vehicle to slide before it will roll. A lower CG point can be obtained by semi-active, slow-active or active suspension systems with ride height control.

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SSF=

110

t 2h

t = track width of the car.

h = height of the centre of gravity. 2. Increasing the suspension stiffness and/or damping will reduce the body roll of the vehicle, thereby increasing vertical load transfer on the tyres and decreasing the lateral force between the tyres and the road. This can be achieved with passive, semi active or active suspension systems.

7.8.2

TLLTD

Another significant terminology is TLLTD. TLLTD stands for Tire Lateral Load Transfer Distribution. It simply measures the front-to-rear balance of how lateral load is transferred in a cornering manoeuvre. It is commonly used to compare the rate of lateral traction loss between the front and rear tires. In other words, a vehicle with say, 70% TLLTD will transfer 70% of its sprung weight at the front of the vehicle during cornering.

7.8.2.1 Anti-Roll Bars And TLLTD  The most prevalent misconception is that a firmer anti-roll bar would lead to better camber control, which would lead to better traction. So, if we add a firmer anti-roll bar to the front, traction loss diminishes, so understeer is reduced. But its opposite is true.  TLLTD can be described as the relative demand of side-to-side energy control that is placed upon the tires. Because a firmer anti-roll bar allows less deflection, it will transfer side-to-side energy (lateral loads) at a faster rate. As the rate of lateral load transfer increases, additional demands are placed upon the tire. So if we install a firmer anti-roll bar in the front, then we increase the distribution of lateral load transfer

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toward the front tires. This increases the front TLLTD value, which will result in additional understeer, holding all else constant.  If we analyse the situation more critically, this means that for absolute understeer ,more front tire lateral load transfer should be there as compared to the rear one(basically front should first lose traction ). So if we install a firmer anti-roll bar in the front than the rear, then we increase the distribution of lateral load transfer toward the front tires. This increases the front TLLTD value, but it cannot be assured that absolute TLLTD value is greater than 50%.It depends on static weight distribution also. Now, it can be understood that although the full form of TLLTD is “Total Lateral Load Transfer Distribution”, we define it as transfer percentage of its sprung weight at the front of the vehicle during cornering as because it ultimately leads to transfer of side-toside energy (lateral loads).  The same logic also holds true in the rear. A firmer anti-roll bar in the rear will increase the rate of lateral load transfer, placing more demand upon the rear tires, accelerating lateral traction loss and creating more oversteer, holding all else constant.  With a stiff front anti roll bar, the outside tire will have a much higher load than the inside front tire in a corner. In this situation, the outside front tire is overloaded and the inside front tire is only lightly loaded. This pair of tires will generate less side force than the more evenly loaded rear tires and thus, the front end will stick less than the rear, making the car understeer.  In general, more load transfer, more quickly that tire loses traction. Putting simply, there is only so much force that a tire can handle. When we ask more of the tire than the tire can deliver, it "saturates," or loses traction. If the rear tires saturate before the front tires, then we call this oversteer or lose--this means that the rear of the car tends to swing around faster than the front, causing a spin.

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 In reality, a car with a 50 percent TLLTD is literally on the constant brink of oversteer. And there are many factors that can quickly and easily take the car from the brink into a full-scale, out-of-control, spinning-in-circles disaster. A front TLLTD value greater than 50 percent indicates that the front tires lose traction more quickly than the rear tires--resulting in understeer. And a front TLLTD value lower than 50 percent indicates that the rear tires tend to lose traction more quickly than the front--resulting in oversteer.  Since our car is slightly over steered, so TLLTD value should be <50%.



In general, a value 5% forward of the front/rear weight distribution is used for racy cars, which is also known as ‘MAGIC NUMBER’.

7.8.3

Points Concerning Ride Frequency

 A ride frequency is the undamped natural frequency of the body in ride. The higher the frequency, the stiffer the ride.  The limit of how low our ride rate frequency can go for a FSAE car (standard setup) depends on the travel you have in your system before the cars nose hits the ground, the softer the spring the less they influence negatively the vertical tire load fluctuations of the tire, however this might also make necessary for you to adjust our ride height higher in order to not hit the ground with the chassis/nose during braking, making the CG height rise.  The first step in choosing spring stiffness is to choose your desired ride frequencies, front and rear.  Lower frequencies produce a softer suspension with more mechanical grip, however the response will be slower in transient (i.e. “lack of support”). Higher frequencies create less suspension travel for a given track, allowing lower ride heights, and in turn, lowering the centre of gravity.  Ride frequencies front and rear are generally not the same; there are several theories to provide a baseline. For example, passenger cars

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have higher rear ride frequency for flat and comfortable ride. Whereas on the other hand, race cars have higher front frequency mainly because of higher damping ratios, and have a much smaller concern for comfort.  The out of phase motion between front and rear vertical motion, caused by the time delay between when the front wheel and rear wheel hit the bump, is accentuated by the frequency difference. A result of the phase difference is pitching of the body. To reduce the pitch induced by hitting a bump, the rear needs to have a higher natural frequency to “catch up” with the front. This notion is called producing a “flat ride”, meaning that the induced body pitch from road bumps is minimized. The above theory was originally developed for passenger cars, where comfort takes priority over performance, which leads to low damping ratios, and minimum pitching over bumps.  A higher front ride frequency in a race car allows  Faster transient response at corner entry  Less ride height variation on the front (the aerodynamics are usually more pitch sensitive on the front of the car)  Allows for better rear wheel traction (for rear wheel drive cars) on corner exit.  The ride frequency split should be chosen based on which is more important on the car we are racing, the track surface, the speed, pitch sensitivity, etc.  Also, the ride frequency should be greater than 1.8 Hz as because we can’t reduce roll of a soft setup with harder anti roll bars because it will have very bad damping characteristics during cornering.  Too much high ride frequency makes the car skittish.

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114

 The spring frequency is a function of the sprung weight acting at the wheel, and the vertical stiffness, wheel rate or effective stiffness acting at the wheel.  Exact number of roll stiffness distribution will depend on exact weight distribution, tire sizes front and rear, roll centre height, etc.  Also, variation in natural frequency should be less than 0.4Hz. Generally 10% difference between the front and rear ride frequency should be there.  Another thing to be noted that as you go faster, the frequency increase and we will reach a frequency where the body movement reaches a maximum, this is the resonant frequency. At this frequency the transmissibility is maximum and higher than one.  With reference to FSAE forums it was analyzed that 3 Hz is the upper extreme value of the ride frequency used in FSAE cars.

7.9 Calculation Theory of Anti Roll Bars 7.9.1 Formulas for Required ARB Stiffness Required Equation for calculating spring rate:

Ks = 4 fr2m MR2 sm

Ks = Spring rate (N/m) msm = Sprung mass(on one wheel) (kg) fr = Ride frequency (Hz) MR = Motion ratio (Wheel/Spring travel) Similar to choosing ride frequencies for bump travel, the roll stiffness must be chosen next. The normalized roll stiffness number is the roll gradient, expressed in degrees of body roll per “g” of lateral acceleration. The Magic Number is expressed as the percentage of the roll gradient taken by the front suspension of the car.

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115

As a baseline, use 5% higher Magic Number than the static front weight distribution. Roll gradients are degrees of body roll per g of lateral acceleration. Roll rates are Newton-meters of torque per degree of body roll or ARB twist. The following equations do not take into account roll due to the tires. Roll gradient of ride springs:

 r / Ay = -W x H KF + KR H = Cg to Roll axis dist (m) W = Vehicle weight (N) r/Ay = Roll gradient from ride springs (deg/g)

KF = tf)KLFKRF 180(KLF+KRF)

KF = Front roll rate (Nm/deg roll) tf = Front track width (m) KLF = LF Wheel rate (N/m) KRF = RF Wheel rate (N/m)

Remember that wheel rate is spring rate/ MR2 ; the effect of the spring at the wheel

KR = tr)KLRKRR 180(KLR+KRR)

KR = Rear roll rate (Nm/deg roll)

tr = Rear track width (m) KLR = LR Wheel rate (N/m) KRR = RR Wheel rate (N/m) Total ARB roll rate needed to increase the roll stiffness of the vehicle to the desired roll Gradient:

KA =

KDESKT(t/2)

−¿

Team AXLR8R

KW(t/2)


116

180 [KT(t/2)/180 – KDES]

180

KA = Total ARB roll rate needed (Nm/deg roll) KDES = Desired total roll rate (Nm/deg roll) KW = Wheel rate (N/m) KT = Tire rate (N/m) t = Average track width between front and rear (m)

KDES = WH (/Ay)

W = Weight of vehicle (N) H = Vertical distance from roll centre axis to Cg (m) /Ay = Desired total roll gradient, chosen earlier (deg/g)

Front and Rear Anti-Roll Bar stiffness:

KFA = KANmagMRFA/100 KFA = FARB roll rate (Nm/deg twist) KA = Total roll rate (Nm/deg roll) Nmag = Magic Number (%) MRFA = FARB Motion ratio

KRA = KA(100-Nmag)MRRA/100 KRA = RARB roll rate (Nm/deg twist) KA = Total roll rate (Nm/deg roll) Nmag = Magic Number (%) MRRA = RARB Motion ratio

The chassis also acts as a torsional spring in roll. It is worth comparing the roll rate of the suspension to the roll rate of the chassis- if the chassis twists as much as the suspension, it could be a larger area of concern than the suspension. With steady state roll angles different front to rear, or different roll frequencies front to rear, chassis torsion will be induced. Now, we got the required front and rear roll stiffness of the anti roll bars to be used.

Team AXLR8R


We now design the anti roll bar of the desired stiffness rate (Nm/degree twist). If we carefully analyse the desired roll stiffness rate then it can be interpretated that, for one degree twist of anti roll bar, we must apply a definite amount of torque(i.e. force onto the attachment point of lever arm and drop link, times the effective lever arm length). So, we could change the following variables till the arrangement suits our requirement.       

Inner diameter of the anti roll bar. Outer diameter of the anti roll bar. Active arm length. Lever arm length. Motion ratio of the anti roll bar. Angle b/w lever arm and anti roll bar. Angle b/w lever arm and drop link.

7.9.2

Spring Rate Calculations

Torsion bar Rates:

θ=

TL −(1) JG

T JG = −(2) θ L

J=

π d4 ( ) −3 32 4

T πd G ( ) = −4 θ 32 L

Team AXLR8R

117


Let the deflection at the end= δ

118

δ θ= −( 5 ) r

Since, T=F*r, using this and eq.5 in eq. 4 we get: F ×r π d 4 G = δ 32 L r Then the deflection rate at the free end is found F π d4 G = =k δ 32 L r 2 The deflection rate at the wheel now can be found by thorough analysis of the motion ratio. 

Torsion Bar Calculations : If Steel is used: E= 30,000,000 psi K≅

2,200,000 d 4 2 Lr

L=Bar length

d= Bar diameter r= lever arm length

Anti Roll Analysis The Deflection Rate at the wheel is based on the motion ratio between the wheel and the bar end r2 versus r1. 2 r2 ¯ ¿ 2 r1 K wh =K ¿ r1 = length of the attachment arm r2 = the pivot to attachment length r1/r2=motion ratio of the anti roll bar 2 π d 4 G r2 K wh = × 32 L r 2 r 12

Team AXLR8R


The roll stiffness has previously been defined as: 2 T t k K ∅= = θ (2 ×57.3) The Stabilizer contribution to roll stiffness is now: 2 π d 4 G r2 t2k ¯ ∅ ¿= × × 32 L r 2 r 12 (2 ×57.3) K¿

7.9.3 Approximations Done (With Reference to RCVD) 2

2

K r =4 π fr msm

1.

But, we considered “4 fr2msm” as the Wheel rate instead of Ride Rate. K w=

KR KT K T −K R

Where, Kw= wheel center rate, lb./in. KR = ride rate, lb./in. KT = tire vertical rate, lb./in. Figure shows the installation ratio as a function of wheel ride position for a typical double wishbone suspension.

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119


If the linkage ratio is not constant, we need to know how it varies in order to relate the rates t one another. A detailed analysis of the problem yields the formula:

K w =F s

∆ IR + K s (IR)2 ∆δ

If the linkage ratio is not constant, we need to know how it varies in order to relate the rates to one another. A detailed analysis of the problem yields the formula: K w=

Fs + K s ¿ (IR)2 ∆ δ ×∆ IR Where

Kw = wheel rate, lb. /in Fs = spring force, lb Ks = spring rate, lb./in IR = installation ratio or motion ratio

1/( ∆ δ × ∆ IR )

= change of reciprocal of installation ratio with

wheel displacement The first term in the above formula is called the geometric rate. As is seen in the formula, if the change of installation ratio with wheel displacement is zero, then the wheel rate is related to the spring rate only by the installation ratio squared with no geometric rate term , or

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120


Kw = Ks/ (IR) 2 For race cars that are stiffly sprung this is usually a sufficiently accurate approximation. However as the ride rates or ride frequencies decrease, the error in using this approximation can become very significant. As is seen, the installation ratio changes considerably, especially as the suspension goes into jounce. We can find the change of installation ratio from this figure and then calculate the true wheel rate and its component part (i.e. the geometric rate and the spring rate divided by the squared installation ratio) for various rates. The following table shows some observations. The geometric rate for this suspension is negative and nearly constant for all three spring rates.

Effect of Installation Ratio with Different Spring Rate

7.10

Materials of Anti Roll Bars

 Basically it’s a calculation based issue. After calculating roll stiffness required from the anti roll bars, material can be decided considering its shear modulus, young’s modulus and other factors into account; the most important one is availability.  Commonly, AISI 4140 chrome molybdenum steel, high carbon steel, 4130 steel alloys are used. But, it is not a hard and fast rule to use them only.

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7.11

Reasons For Using Lever type ARB rather

than Bent type  Basically torsion is not going to be produced in the lever arm .So there is no need to use the material which we used for making the torsion bar. Light material but strong enough to handle the tension and compression could be used for manufacturing lever arm.  Also, larger anti roll bar (bent type) is required for producing the same stiffness as caused by the lever arm type anti roll bar.  Offset could be set to zero in case of bent type anti roll bar but it’s quite hard to achieve in bent type anti roll bar.

7.12

Where to Install

One important thing to understand is that the work and effect of anti roll bar is independent of the location where we install it , keeping the other parameters same. •First of all is the space constraints i.e. due to compactness of the chassis and other components, anti roll bar cannot be installed anywhere. •Further, it should be considered that the anti roll bar must not come in touch with any of the chassis part and other vehicle components while its rolling action as because it would lead to sudden unpredictable change in the behaviour and response of the car and would thus result in detrimental consequences. •Anti roll bar should be kept as low as possible so as to lower the C.G. height of the car. Final setup is decided with the help of designing and optimization of anti roll bars with other components on the ‘SusProg3D software’.

7.13

Drawbacks of Using Anti Roll Bar Team AXLR8R

122


Because an anti-roll bar connects wheels on the opposite sides of the vehicle together, the bar will transmit the force of one-wheel bumps to the opposite wheel. On rough or broken pavement, anti-roll bars can produce jarring, side-to-side body motions (a "waddling" sensation), which increase in severity with the diameter and stiffness of the sway bars. Excessive roll stiffness, typically achieved by configuring an anti-roll bar too aggressively, will cause the inside wheels to lift off the ground during very hard cornering. The inside rear wheel should be prevented from lifting during high speed turns. This is a significant issue because the car’s differential is only able to distribute power to the road when both rear wheels can maintain some traction. Ideally, the car should see no more than 80% lateral weight transfer.

7.14 



  

Conclusions

In the nutshell, it can be concluded that anti roll bar is a sort of compromise between damping characteristics and controlling the rolling of the car. It’s not compulsory to use anti roll bar. If desired roll stiffness and sufficient damping is achieved through shockers, then there is no need to use anti roll bars. Apart from reduction in body lean, anti roll bar is also being used to affect the oversteer and understeer behaviour of the car. Tubular anti roll bar rod is a much better and efficient option as compared to solid rods. It's important that the anti-roll bar should not be pre-loaded when the car is resting at its static ride height with the driver on board, since pre-loading causes a difference in handling between right and left turns. Pre-loading of the anti-roll bar occurs when the bar has to be twisted to connect the end links to the suspension. This problem is a result of a mismatch in the geometry of the anti-roll bar and the mounting points of the end links on the suspension. Pre-loading can be avoided by using adjustable-length end links to dial-in the precise length required to avoid twisting of the anti-roll bar. If the anti-roll bar attaches directly to the suspension without using end links, the bar itself must be re bent to the proper position.

7.14.1

Installation Team AXLR8R

123


 

124

Finally, it can be concluded that front ARB should be installed underneath the chassis in accordance with other components. Front as well as rear ARB is to be attached through the bell crank by which ARB motion ratio could also be varied. Basically, ARB should be as low as possible to lower the CG height.

7.15

Future Prospects

During cornering, it is desirable that the stiffness of the stabilizer bar be increased. If the stabilizer bar is too compliant, the vehicle will not respond well during cornering, increasing the likelihood of rolling over. However if the stabilizer bar is too stiff, the ride and handling will be compromised during normal vehicle operation. Therefore, it is desirable that the stiffness

of the stabilizer

bar be variable to

adjust for

changing driving

conditions.



Another option

is to use active

anti roll bar.

Active Anti Roll

bar is new high

tech system

which is now

being used in

costly Another

passenger cars. advancement

that can be

made in future is

“bladed lever

arm” through

which effective

torsion stiffness

can be altered

by just rotating



the bladed lever arm. No need for hole/s on the lever arm.

Team AXLR8R


125

8. SHOCKER AND ANTI ROLL BAR RESULTS FROM SUSPROG3D 8.1 Front 8.1.1

Shocker and Anti Roll Bar Geometry

Vehicle lateral datum



(Z): Ground


LH and RH side identical

Wheel rate N/mm

Motion

lb/in

ratio

Shockabsorber Coil spring

100.18

219.00

0.999

183.62 1048.50

Spring

deflection

0.999 17.54

Antirollbar

Length

122.33

-13.19 nsp

1.016

Pushrod and bellcrank - Pushrod mounting (A-arm)

-Y -Z

195.00

-X

0.00

- Pushrod length

500.00

437.76 Shock

- bellcrank pivots - Y

P1 Bellcrank P2 Pushrod Rollbar

273.77

-Z

669.92

-X

0.00

270.00

580.00

270.00

580.00

0.00 -100.00

- Pushrod arm length & offset

336.72

601.17 0.00

547.85 0.00

70.00

- shockabsorber arm length & offset - Pushrod pivot to shockabsorber pivot

90.00 93.22

Team AXLR8R

320.66

0.00 0.00


126

- angle between arms

70.00

- anti-clockwise rotation in bump (LH) - antirollbar link arm length & offset

60.00

- Pushrod pivot to antirollbar link pivot

-55.68


0.00

-50.00

Shockabsorber - shockabsorber mounting (chassis)

-Y

-Z

680.00

-X

0.00

- length - compressed (full bump) -

static

-

extended (full droop)

55.00

182.00 219.00 257.00

- stroke

74.99

- motion ratio (static)

1.00

Corner weight (unsprung)

13.000 kg

Corner weight (sprung)

28.66 lb

57.000 kg

Corner weight (total)

125.66 lb

70.000 kg

Suspension frequency

154.32 lb

167.53 cpm

Coil spring - spring seat (shockabsorber shaft)

0.00 mm

- spring seat (shockabsorber body)

96.67 mm

- spring rate

17.51 N/mm

- static load

558.49 N

0.000 in 3.806 in

100.00 lb/in 56.950 kg

- static length

122.33 mm

4.816 in

- free length

109.14 mm

4.297 in

- compressed length

0.00 mm

Team AXLR8R

0.000 in

125.55 lb

FSAE IIT Delhi Suspension Report - preload

127

-51.18 mm

-2.015 in

17.51 N/mm

100.00 lb/in

Coil spring parameters - spring rate - type of ends

Closed and ground

- total number of coils

7.00

- number of active coils - coil ID

5.00 38.00 mm

1.496 in

- wire dia

6.03 mm

0.237 in

- free length

109.14 mm

4.297 in

- solid length

39.18 mm

1.542 in

- solid load

2144.22 N

- torsional stress (corrected) - static

218.650 kg

468.51 MPa

- full bump 940.57 MPa - solid

1321.16 MPa

191618.44 psi

- arm length (actual)

130.00

- arm length (effective)

130.00

- arm length (offset)

0.00

- drop link length

332.00

- antirollbar mounting (chassis)

-Y

-Z

250.00

115.00

- X -100.00 - arb arm/link pivot

-Y

67951.08 psi

136417.80 psi

Anti-roll bar

312.50

-Z

216.48

-X

-18.75

Anti-roll bar config is u-bar, actuated from bellcrank.

Team AXLR8R

482.04 lb


128

Shape is bar & lever.Style A (LH side). - active length

615.00 mm

- outside diameter

24.213 in

26.70 mm

- inside diameter

1.051 in

22.48 mm

- spring rate (nominal; Cf = 1.00)

0.885 in

189.36 N/mm

1081.28 lb/in

Chassis pivot points (from chassis Y, Z, X datum) - shockabsorber mounting

-Y -Z

680.00

-X

0.00

- bellcrank pivot (P1)

-Y

55.00

270.00

-Z

580.00

-X

0.00

- bellcrank pivot axis (P2 offset from P1) -Z

LH

-Y

0.00

0.00

- X -100.00 - antirollbar mounting

-Y -Z

250.00

115.00

- X -100.00 A-arm pivot points (Y from chassis pivot, Z from plane, X from apex normal) - Pushrod mounting

8.1.2

-Y -Z

30.12

-X

-13.40

223.61

Roll Data

Roll starts at Static. LH and RH side identical Wheel rate N/mm

lb/in

Motion ratio

Length

Spring

deflection

Shockabsorber

Team AXLR8R

Bellcrank rotation


129

37.38 bump

1.038

182.00

24.42

35.00 bump

1.031

184.30

22.79

30.00 bump

1.020

189.17

19.42

25.00 bump

1.012

194.09

16.10

20.00 bump

1.007

199.04

12.83

15.00 bump

1.004

204.01

9.59

10.00 bump

1.001

209.00

6.38

5.00 bump

1.000

Static

0.999

5.00 droop

214.00

3.19

219.00

0.998

0.00

224.01

-3.19

10.00 droop

0.997

229.02

-6.39

15.00 droop

0.996

234.03

-9.61

20.00 droop

0.994

239.06

-12.87

25.00 droop

0.992

244.09

-16.16

30.00 droop

0.988

249.15

-19.52

35.00 droop

0.982

254.22

-22.95

37.72 droop

0.979

257.00

-24.86

Coil spring 37.38 bump

16.26

92.85

1.038

85.33

23.81

35.00 bump

16.47

94.07

1.031

87.63

21.51

30.00 bump

16.83

96.12

1.020

92.50

16.64

25.00 bump

17.09

97.58

1.012

97.42

11.72

20.00 bump

17.27

98.60

1.007

102.37

6.77

15.00 bump

17.39

99.29

1.004

107.34

1.80

10.00 bump

17.47

99.74

1.001

112.33

-3.19 nsp

100.02

1.000

117.33

-8.18 nsp

5.00 bump Static

17.52 17.54

100.18

0.999

122.33

Team AXLR8R

-13.19 nsp


5.00 droop

17.57

130

100.34

0.998

127.34

-18.19 nsp

10.00 droop

17.60

100.51

0.997

132.35

-23.20 nsp

15.00 droop

17.64

100.75

0.996

137.36

-28.22 nsp

20.00 droop

17.71

101.12

0.994

142.39

-33.24 nsp

25.00 droop

17.80

101.66

0.992

147.42

-38.28 nsp

30.00 droop

17.94

102.47

0.988

152.48

-43.33 nsp

35.00 droop

18.15

103.62

0.982

157.55

-48.41 nsp

37.72 droop

18.29

104.44

0.979

160.33

-51.18 nsp

LH side: Wheel rate N/mm

Motion

lb/in

Length

ratio

Spring

deflection

Bellcrank rotation

Shockabsorber 0.00 roll

0.999

219.00

0.00

0.50 roll

1.000

213.84

3.29

1.00 roll

1.001

208.30

6.83

1.50 roll

1.004

202.38

10.65

2.00 roll

1.010

196.07

14.78

2.50 roll

1.021

189.36

19.29

Coil spring 0.00 roll

17.54

100.18

0.999

122.33

-13.19 nsp

0.50 roll

17.53

100.08

1.000

117.17

-8.02 nsp

1.00 roll

17.48

99.79

1.001

111.63

1.50 roll

17.37

99.17

1.004

105.71

2.00 roll

17.16

98.00

1.010

99.40

9.74

2.50 roll

16.80

95.92

1.021

92.69

16.45

Team AXLR8R

-2.49 nsp 3.43


131

Antirollbar 0.00 roll

183.62 1048.50

1.016

0.50 roll

231.93 1324.38

0.904

1.00 roll

313.20 1788.40

0.778

1.50 roll

480.30 2742.58

0.628

2.00 roll

1034.52 5907.25

2.50 roll

275.63 1573.89

0.428 0.829

RH side: Wheel rate N/mm

lb/in

Motion

Length

ratio

Spring

deflection

Bellcrank rotation


0.999

219.00

0.00

0.50 roll

0.999

223.97

-3.16

1.00 roll

0.999

228.55

-6.09

1.50 roll

0.999

232.72

-8.76

2.00 roll

0.999

236.45

-11.17

2.50 roll

0.999

239.68

-13.27


17.54

100.18

0.999

122.33

-13.19 nsp

0.50 roll

17.55

100.19

0.999

127.30

-18.15 nsp

1.00 roll

17.54

100.15

0.999

131.88

-22.73 nsp

1.50 roll

17.53

100.13

0.999

136.05

-26.91 nsp

2.00 roll

17.53

100.12

0.999

139.78

-30.63 nsp

2.50 roll

17.54

100.14

0.999

143.01

-33.86 nsp

Antirollbar

Team AXLR8R


132

0.00 roll

183.62 1048.50

0.50 roll

150.40

858.82

1.122

1.00 roll

126.86

724.40

1.222

1.50 roll

109.38

624.60

1.316

2.00 roll

96.07

2.50 oll

85.88

548.56 490.39

1.016

1.404 1.485

Team AXLR8R


Team AXLR8R

133


Team AXLR8R

134


8.2

135

Rear

8.2.1

Shocker and Anti Roll Bar Geometry




(Z): Ground



Wheel rate N/mm

Motion

lb/in

ratio

Shockabsorber Coil spring

152.37

219.00

0.992

245.48 1401.73

Spring

deflection

0.992 26.68

Antirollbar

Length

169.00

-12.48 nsp

1.062

Pushrod and bellcrank - Pushrod mounting (A-arm)

-Y -Z

490.00

195.00

- X -1580.00 - Pushrod length

212.46 Shock

- bellcrank pivots - Y -Z

P1 Bellcrank P2 Pushrod Rollbar

238.81

399.77

310.00

340.00

371.25

418.53

338.32

322.19

268.64

377.98

- X -1503.12 -1540.00 -1549.03 -1502.84 -1490.28 - Pushrod arm length & offset

50.00

- shockabsorber arm length & offset - Pushrod pivot to shockabsorber pivot - angle between arms

0.00

100.00

0.00

126.18 110.00

- anti-clockwise rotation in bump (LH) - antirollbar link arm length & offset

75.00

Team AXLR8R

0.00


136

- Pushrod pivot to antirollbar link pivot

90.14


90.00

Shockabsorber - shockabsorber mounting (chassis) -Z

-Y

245.00

370.00

- X -1720.00 - length - compressed (full bump) -

static

-

extended (full droop)

182.01 219.00 256.99

- stroke

74.97

- motion ratio (static)

0.99

Corner weight (unsprung)

13.000 kg

Corner weight (sprung)

28.66 lb

92.000 kg

Corner weight (total)

202.83 lb

105.000 kg

Suspension frequency

231.49 lb

162.63 cpm

Coil spring - spring seat (shockabsorber shaft)

0.00 mm

- spring seat (shockabsorber body)

50.00 mm

- spring rate - static load

26.27 N/mm 895.15 N

0.000 in 1.969 in

150.00 lb/in 91.280 kg

- static length

169.00 mm

6.654 in

- free length

156.52 mm

6.162 in

- compressed length - preload

0.00 mm -50.47 mm

0.000 in -1.987 in

Coil spring parameters - spring rate

26.27 N/mm

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150.00 lb/in

201.24 lb


137

- type of ends

Closed and ground

- total number of coils

7.00

- number of active coils - coil ID

5.00 38.00 mm

1.496 in

- wire dia

6.84 mm

0.269 in

- free length

156.52 mm

6.162 in

- solid length

44.47 mm

1.751 in

- solid load

5396.38 N

- torsional stress (corrected) - static

550.277 kg

538.59 MPa

- full bump 66.13 MPa - solid

78115.86 psi

154629.45 psi

2364.87 MPa

342995.44 psi

Anti-roll bar - arm length (actual)

200.00

- arm length (effective)

200.00

- arm length (offset)

0.00

- drop link length

180.00

- antirollbar mounting (chassis)

-Y

-Z

250.00

110.00

- X -1320.00 - arb arm/link pivot

-Y -Z

319.00

309.67

- X -1331.54

Anti-roll bar config is u-bar, actuated from bellcrank. Shape is bar & lever.Style A (LH side). - active length

630.00 mm

1213.15 lb

24.803 in

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FSAE IIT Delhi Suspension Report - outside diameter

138 33.40 mm

- inside diameter

1.315 in

24.30 mm

- spring rate (nominal; Cf = 1.00)

0.957 in

276.71 N/mm

Chassis pivot points (from chassis Y, Z, X datum) - shockabsorber mounting

-Y -Z

1580.06 lb/in

LH

245.00

370.00

- X -1720.00 - bellcrank pivot (P1)

-Y -Z

310.00

340.00

- X -1540.00 - bellcrank pivot axis (P2 offset from P1) -Z

78.53

-X

-9.03

- antirollbar mounting

-Y -Z

-Y

61.25

250.00

110.00

- X -1320.00 A-arm pivot points (Y from chassis pivot, Z from plane, X from apex normal) - Pushrod mounting

8.2.2

-Y -Z

33.42

-X

10.47

208.69

Roll Data




(Z): Ground


Roll starts at Static.

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139


Wheel rate N/mm

Motion

lb/in

ratio

Length

Spring

deflection

Bellcrank rotation

Shockabsorber 35.81 bump

0.925

182.01

22.46

35.00 bump

0.928

182.89

21.95

30.00 bump

0.944

188.24

18.83

25.00 bump

0.958

193.50

15.73

20.00 bump

0.971

198.69

12.63

15.00 bump

0.980

203.82

9.53

10.00 bump

0.987

208.90

6.40

5.00 bump

0.991

Static

0.992

5.00 droop

213.96

219.00

0.990

3.23 0.00

224.04

-3.31

10.00 droop

0.983

229.12

-6.72

15.00 droop

0.971

234.24

-10.28

20.00 droop

0.953

239.44

-14.02

25.00 droop

0.926

244.77

-18.01

30.00 droop

0.889

250.30

-22.34

35.00 droop

0.836

256.13

-27.17

35.71 droop

0.826

256.98

-27.91

Coil spring 35.81 bump

30.70

175.29

0.925

132.01

24.51

35.00 bump

30.51

174.23

0.928

132.89

23.63

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140

30.00 bump

29.47

168.29

0.944

138.24

18.28

25.00 bump

28.60

163.31

0.958

143.50

13.02

20.00 bump

27.89

159.26

0.971

148.69

7.83

15.00 bump

27.34

156.11

0.980

153.82

2.70

10.00 bump

26.95

153.89

0.987

158.90

5.00 bump

26.73

Static

26.68

5.00 droop

152.63

152.37

26.81

0.991

0.992

153.10

-2.39 nsp

163.96

169.00

0.990

-7.44 nsp

-12.48 nsp

174.04

-17.53 nsp

10.00 droop

27.18

155.21

0.983

179.12

-22.60 nsp

15.00 droop

27.86

159.06

0.971

184.24

-27.72 nsp

20.00 droop

28.94

165.24

0.953

189.44

-32.92 nsp

25.00 droop

30.62

174.82

0.926

194.77

-38.26 nsp

30.00 droop

33.25

189.84

0.889

200.30

-43.78 nsp

35.00 droop

37.62

214.82

0.836

206.13

-49.61 nsp

35.71 droop

38.47

219.69

0.826

206.98

-50.47 nsp

LH side: Wheel rate N/mm

lb/in

Motion ratio

Length

Spring

deflection

Bellcrank rotation


0.992

219.00

0.00

0.50 roll

0.990

213.89

3.27

1.00 roll

0.984

208.40

6.71

1.50 roll

0.974

202.49

10.34

2.00 roll

0.960

196.11

14.17

2.50 roll

0.942

189.20

18.27

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141


26.68

152.37

0.992

169.00

-12.48 nsp

0.50 roll

26.82

153.12

0.990

163.89

-7.37 nsp

1.00 roll

27.14

154.99

0.984

158.40

-1.88 nsp

1.50 roll

27.69

158.13

0.974

152.49

4.03

2.00 roll

28.50

162.74

0.960

146.11

10.40

2.50 roll

29.61

169.09

0.942

139.20

17.32


245.48 1401.73

1.062

0.50 roll

255.21 1457.28

1.041

1.00 roll

266.88 1523.91

1.018

1.50 roll

281.08 1605.01

0.992

2.00 roll

298.67 1705.47

0.963

2.50 roll

320.97 1832.77

0.929

RH side: Wheel rate N/mm

lb/in

Motion ratio

Length

Spring

deflection

Bellcrank rotation


0.992

219.00

0.00

0.50 roll

0.991

223.92

-3.23

1.00 roll

0.987

228.49

-6.30

1.50 roll

0.979

232.71

-9.21

2.00 roll

0.970

236.55

-11.92

2.50 roll

0.958

239.97

-14.41

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142


26.68

152.37

0.992

169.00

-12.48 nsp

0.50 roll

26.74

152.69

0.991

173.92

-17.40 nsp

1.00 roll

26.98

154.05

0.987

178.49

-21.97 nsp

1.50 roll

27.38

156.37

0.979

182.71

-26.19 nsp

2.00 roll

27.94

159.56

0.970

186.55

-30.03 nsp

2.50 roll

28.63

163.46

0.958

189.97

-33.45 nsp


245.48 1401.73

1.062

0.50 roll

237.00 1353.29

1.081

1.00 roll

229.76 1311.99

1.097

1.50 roll

223.53 1276.41

1.113

2.00 roll

218.13 1245.53

1.126

2.50 roll

213.43 1218.74

1.139

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143


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144


145

8.3 Final Calculations 8.3.1

Spring rate

Ks = 4 fr2m MR2 sm

Ks = Spring rate (N/m) msm = Sprung mass(on one wheel) (kg) fr = Ride frequency (Hz) MR = Motion ratio (Wheel/Spring travel) Front MR= 0.999 fr = 167.53 revolutions/ minute msm = 57 kg Ks = 4*484/49*(167.53/60)2*0.9992*57 = 17522.5691 N/m Rear MR= 0.992 fr = 162.63 revolutions/ minute msm = 92 kg Ks = 4*484/49*(162.63/60)2*0.9922*92 = 26279.6313 N/m Desired roll gradient = 0.8 degree/g

8.3.2

Roll gradient of ride springs

r / Ay = -W x H KF + KR H = Cg to Roll axis dist (m) W = Vehicle weight (N) r/Ay = Roll gradient from ride springs (deg/g) H = 0.2 m W= 350*9.81 N

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KF = tf)KLFKRF 180(KLF+KRF)

146

KF = Front roll rate (Nm/deg roll) tf = Front track width (m) KLF = LF Wheel rate (N/m) KRF = RF Wheel rate (N/m)

tf = 1.16 m KLF = KRF = 17522N/ m KF = 22/7*(1.162)/360/(0.9992)* KLF = 206.255208 Nm/deg roll

KR = tr)KLRKRR 180(KLR+KRR)

KR = Rear roll rate (Nm/deg roll)

tr = Rear track width (m) KLR = LR Wheel rate (N/m) KRR = RR Wheel rate (N/m) tr = 1.14 m KLR = KRR = 26705.20413 N/mm KR = 22/7*(1.142)/360/ (0.9922)* KLR = 302.989631 Nm/deg roll r/Ay =350*9.81*0.2/ (302.989631+206.255208) = 1.348467274 deg/g

8.3.3 Total ARB roll rate needed to increase the roll stiffness to the desired roll gradient

KA =

KDESKT(t/2)

−¿

180 [KT(t/2)/180 – KDES]

KW(t/2)

180

KA = Total ARB roll rate needed (Nm/deg roll) KDES = Desired total roll rate (Nm/deg roll) KW = Wheel rate (N/m) KT = Tire rate (N/m)

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147

t = Average track width between front and rear (m) KT = 1000 lb/inch t = 1.15 m

KDES = WH (/Ay) W = Weight of vehicle (N) H = Vertical distance from roll centre axis to Cg (m) /Ay = Desired total roll gradient, chosen earlier (deg/g) KDES = 350 * 9.81*0.2/0.8 = 858.375 Nm/ deg roll Front KA=(22/7/180*(350*9.81*0.2/0.8)*1000*386.4/2.2*(1.15*1.15/2)/ ((1000*386.4/2.2*(1.15*1.15/2)*22/7/180)-(350*9.81*0.2/0.8)))22/7/180/2*(1.15*1.15)*( 17522.5691 /0.9992) = 1285.702394 Nm/deg roll Rear KA=(22/7/180*(350*9.81*0.2/0.8)*1000*386.4/2.2*(1.15*1.15/2)/ ((1000*386.4/2.2*(1.15*1.15/2)*22/7/180)-(350*9.81*0.2/0.8)))22/7/180/2*(1.15*1.15)*( 26279.6313 /0.9922) = 1180.088254 Nm/deg roll

8.3.4

Front and Rear Anti-Roll Bar stiffness

KFA = KANmagMRFA/100 KFA = FARB roll rate (Nm/deg twist) KA = Total roll rate (Nm/deg roll) Nmag = Magic Number (%) MRFA = FARB Motion ratio Nmag = 5 % MRFA = 1.016 KFA = 1285.702 *45*(1.0162)/100 = 597.2283049 Nm/deg twist

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KRA = KA(100-Nmag)MRRA/100 KRA = RARB roll rate (Nm/deg twist) KA = Total roll rate (Nm/deg roll) Nmag = Magic Number (%) MRRA = RARB Motion ratio MRRA = 1.062 KFA = 1180.088254 *55*(1.0622)/100 = 732.0255009 Nm/deg twist Now, we have got the required front and rear Anti Roll Bar stiffness based on the optimum G calculations. This is basically a theoretical value of the required dimensions. We have to achieve this value through actual anti roll bar setup. This is the practical value of the required dimensions to be achieved.

Theoretical Nominal rate (front) = 597.2283049*2*57.3*1.0162/0.6152/1000 = 186.7936827 N/mm Theoretical Nominal rate (rear) = 732.0255009*2*57.3*1.0622/0.632/1000 = 238.3849111 N/mm Practical Nominal Rate, achieved by the set up of ARB = 4

F πd G = =k δ 32 L r 2

Front Nominal Rate d = d2 – d1 = outer diameter – inner diameter = (26.70 – 22.48)mm G = shear modulus of ARB rod = 86 GPa L = active length of ARB rod = 0.615 m r = effective lever arm length = 0.130 m k = 189.36 N/mm, which is pretty much close to the required value of 186.7936827 N/mm.

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149

Rear Nominal Rate d = d2 – d1 = outer diameter – inner diameter = (30.0 – 24.00)mm G = shear modulus of ARB rod = 86 GPa L = active length of ARB rod = 0.67 m r = effective lever arm length = 0.144 m k = 235.71 N/mm, which is pretty much close to the required value of 238.3849111 N/mm. Maximum Force on the lever arm F=k× δ

δ

= maximum perpendicular deflection of anti drop link = 33.40 mm bump or droop /MRARB

Maximum Force on front lever arm = 186.7936827 * 33.4 / 1.016 = 6140.658 N Maximum Force on rear lever arm = 238.3849111 * 33.4 / 1.062 = 7497.228 N

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8.4 Final Damping Curve

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151

9. FORCE CALCULATIONS 9.1 Front TOTAL MASS OF THE CAR = 350 kg. Static mass distribution = 40:60(rear). CG HEIGHT = 10 inch. (A =Front, B=Rear, +x= forward, +y=inward, +z=upward) Ft = tire forces. Fu= upright forces.

L=lower

Fk=front a-arm forces.

U=upper

Fm=rear a-arm forces.

X,y,z = signifies directions e.g. Fku,Fml,Ftx,Fuz...

FRONT TIRE (OUTER) Braking acceleration = 1.4 g Bump acceleration = 1 g Lateral acceleration = 1.9 g Front track width = 1160mm Rear track width =1140mm Wheel base = 1600mm =63 inch Static mass=57 kg (sprung) + 13 kg (unsprung). Longitudinal mass transfer (due to braking) = (1.4g*350*10)/63g = (25.92*2) kg Apparent mass of the tire = 57+13+ 25.92=95.92 kg Lateral weight transfer = 95.92*2*1.9g*10/40.76g + 13g/g (due to bump acceleration) = 89.44 kg (40.76=constant depending upon car dimensions)

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152

Total mass of the tire =95.92+89.44 = 198.36 kg

 Ftx = 198.36*1.4*9.81 = 2777 N  Fty =198.36*1.9 *9.81 = 3692.2 N  Ftz =198.36 *9.81 = 2073.44 N Forces on upright attachment points with A-arms:Based on force balance equations in three directions & moment balance equation along three axes. Fux +Flx =|Ftx| direction Fuy + Fly = -|Fty| direction

Ftx=2777 N along –ve x Fty=3692.2 N along –ve y

Fuz + Flz = -|Ftz| z direction

Ftz=2073.44 N along +ve

Mx =0 Taking moment along x- axis passing through lower upright a-arm mounting point.

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153

-Fuy(362-166.36)-Fty(166.36)-900(166.36-105.09)+Ftz(580557.33)=0 => Fuy= -2881.8 N => Fly= 7474 N My = 0 Taking moment along y- axis passing through lower upright aarm mounting point. => Fux(362-166.36)+Ftx(166.36)+Ftz(15.8)=0 => Fux = -2528.83 N => Flx= 5305.83 N Mz =0 Taking moment along z- axis passing through lower upright a-arm mounting point. It can be assumed that under extreme conditions, all the vertical forces of the tire passes through the push rod.  Fp = -Fz/0.912 = 2261.62 N  Fuz = - 10 N  Flz = - 2062.6 N Flx = 5305.83 N

Fux = -2528.83 N

Fly = 7474 N Flz = -2083.44 N

Fuy = Fuz =

10 N

A-ARM forces:UPPER

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-2881.8 N


K=front

a-arm

154

m =rear a-arm

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155

ANGLES: b1u= 27.64= angle of front upper a-arm with vertical plane as shown in figure. b2u= 31.27= angle of rear upper a-arm with vertical plane as shown in figure. a1u= 7.5= angle of front upper a-arm with horizontal plane passing through upper a-arm pivot point. a2u= 8.9= angle of rear upper a-arm with horizontal plane passing through upper a-arm pivot point. => Fm*cos(a2u)*cos(b2u)+Fk*cos(a1u)*cos(b1u) = 2881.8 => Fm*0.844+Fk*0.878 = 2881.8 => Fk*cos(a1u)*sin(b1u)-Fm*cos(a2u)*sin(b2u) = 2528.33 => Fk*0.46-Fm*0.513= 2528.33 Fku = 4707.23 N Fku = force on front upper a-arm Fmu = -1066.28N Fmu = force on rear upper a-arm

LOWER K=front

a-arm

m =rear a-arm

ANGLES: b1l= 22.53= angle of front lower a-arm with vertical plane as shown in figure. b2l= 31.33= angle of rear lower a-arm with vertical plane as shown in figure. b3=0=angle of push rod with vertical plane.

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a1l=2.1 = angle of front lower a-arm with horizontal plane passing through lower a arm pivot point. a2l= 1= angle of rear lower a-arm with horizontal plane passing through lower a-arm pivot point. a3=69.43=angle of push rod with horizontal plane.

=> Fm*cos(a2l)*cos(b2l)+Fk*cos(a1l)*cos(b1l)+Fp*cos(a3)*cos(b3) = -7474 => Fm*0.854+Fk*0.923+Fp*0.351 = -7474 => Fk*cos(a1l)*sin(b1l)-Fm*cos(a2l)*sin(b2l)+Fp*cos(a3)*sin(b3) = -5305.83 => Fk*0.383-Fm*0.51988+Fp*0 = -5305.83 =>- Fk*sin(a1l)-Fm*sin(a2l) +Fp*sin(a3)= 2083.44 => -Fk*0.0366-Fm*0.017+Fp*0.9362 = 2083.44 Fkl = force on front lower a-arm = -10847.033 N Fml = force on rear lower a-arm = 2214.77 N

PUSH ROD Force = 1841.583 N (by solving equations) or 2216.6 N (assuming that all the vertical tire forces passes through push rod).

9.2 REAR TIRE (OUTER) Forward acceleration =0 .724m/s2 (from torque acceleration readings at various gears) Bump acceleration = 1 g Lateral acceleration = 1.9 g Front track width = 1160mm

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157

Rear track width =1140mm Wheel base = 1600mm =63 inch Static mass= 92 kg(sprung) + 13 kg (unsprung) Longitudinal mass transfer (due to braking) = (7.24*350*10)/63g = (20.11*2) kg Apparent mass of the tire = 92+13+ 20.11=125.11 kg Lateral mass transfer = 250*1.9g*10/44.882g +13g/g (due to bump acceleration) = 118kg upon car dimensions)

(44.882=constant depending

Total mass of the tire =250 kg

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 Ftx =250*7.24 = 1800 N  Fty =250*1.9*9.81 = 4660 N  Ftz =250*9.81 = 2450 N

158

along +ve x direction along –ve y direction along +ve z direction

Forces on upright attachment points with A-arms:Based on force balance equations in three directions & moment balance equation along three axes. Fux +Flx = -|Ftx| Fuy + Fly = |Fty| Fuz + Flz = |Ftz| Mx =0 Taking moment along x- axis passing through lower upright aarm mounting point.

 -Fuy(350.19-160.16)-Fty(160.16)+Ftz(600.5-542.2) =0  Fuy = -3172 N  Fly = 7832 N My = 0 Taking moment along y- axis passing through lower upright a-arm mounting point.

   

Fux(350.19-160.16) –Ftx(160.16)+Ftz(1600-1590.08) = 0 190 Fux+20 Fuz =263696. Fuz = -4685 N Flz = 2300 N

Mz =0 Taking moment along z- axis passing through lower upright aarm mounting point.

 Fux(600.5-542.2)-Fuy(1610.08-1590.08)+Fty(1600-1590.08)=0  Fux = -1880 N  Flx = 80 N Flx = 80 N Fly = 7832 N

Fux = -1880 N Fuy = - 3172 N

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Flz = 2300 N

159

Fuz = -4685 N

A-ARM forces:UPPER K=front

m =rear

ANGLES:

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b1u=31.86 = angle of front upper a-arm with vertical plane as shown in figure. b2u=27.63 = angle of rear upper a-arm with vertical plane as shown in figure. a1u=5.66 = angle of front upper a-arm with horizontal plane passing through upper a-arm pivot point.

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161

a2u=6.60 = angle of rear upper a-arm with horizontal plane passing through upper a-arm pivot point.

=> Fm*cos(a2u)*cos(b2u)+Fk*cos(a1u)*cos(b1u) = 3172 => Fm*0.88+Fk*0.845 = 3172 => Fk*cos(a1u)*sin(b1u)-Fm*cos(a2u)*sin(b2u) = 1880 => Fk*0.5252-Fm*0.460= 1880 Fku =3659 N Fku = force on front upper a-arm Fmu =90.88 N Fmu = force on rear upper a-arm LOWER K=front

a-arm

m =rear a-arm

ANGLES: b1l=28.56 86 = angle of front lower a-arm with vertical plane as shown in figure. b2l=30.9 = angle of rear lower a-arm with vertical plane as shown in figure. b3=23.23=angle of push rod with vertical plane. a1l=7.25 = angle of front lower a-arm with horizontal plane passing through lower a-arm pivot point. a2l=1.115 = angle of rear lower a-arm with horizontal plane passing through lower a-arm pivot point. a3=26.83=angle of push rod with horizontal plane.

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=> Fm*cos(a2l)*cos(b2l)+Fk*cos(a1l)*cos(b1l)+Fp*cos(a3)*cos(b3) = -7832 => Fm*0.85+Fk*0.87+Fp*0.82 = -7832 => Fk*cos(a1l)*sin(b1l)-Fm*cos(a2l)*sin(b2l)+Fp*cos(a3)*sin(b3) = -80 => Fk*0.47-Fm*0.51+Fp*0.35 = - 80 => Fk*sin(a1l)-Fm*sin(a2l) +Fp*sin(a3)= -2300 => Fk*0.126-Fm*0.02+Fp*0.455 = -2300 Fkl = force on front lower a-arm =-504.018N Fml = force on rear lower a-arm = -3795.41N PUSH ROD Force, Fp = -3730 N(assuming that all vertical tire forces passes through push rod) or -5082.21 N (by solving equation) Approximations : Toe rod force contribution at the rear = 0. Assumed Kpi & Caster angle to be 0 at front. No shifting of contact patch at front (considered tire forces passing through the centre of contact patch).

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10.

BEARING SELECTION

To design a rolling bearing arrangement two criteria are most important: 1. Selecting suitable bearing type. 2. Selecting appropriate size according to requirements. The type of bearing depends largely on the type of loads that the bearing has to undergo. The bearings are to be used between the upright and the hub connected to the wheels which will experience both radial and axial loads. According to this requirement, the bearing type selected was angular contact bearing as it can handle both radial and axial loads. To support axial loads in both directions, the double row type of angular contact bearings was finalized.

SKF double row angular contact ball bearings correspond in design to two single row angular contact ball bearings but take up less axial space. They can accommodate radial loads as well as axial loads acting in both directions. They provide stiff bearing arrangements and are able to accommodate tilting moments.

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164

Once, this was decided we looked up the SKF catalogue for the different sizes and types available in the Double row angular contact bearing category. The inner diameter of the bearing was fixed as 30 mm.

Angular contact ball bearings, double row Product information

Principal dimensions

Basic load ratings dynamic static

d

C

D

B

mm 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 35 35 35 35 35 35

C0

kN 62 62 62 62 62 62 62 62 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72

23,8 23,8 23,8 23,8 23,8 23,8 23,8 23,8 30,2 30,2 30,2 30,2 30,2 30,2 30,2 30,2 30,2 30,2 30,2 27 27 27 27 27 27

30 30 30 30 30 30,3 30,3 30,3 41,5 41,5 41,5 41,5 41,5 41,5 41,5 41,5 46,8 46,8 46,8 40 40 40 40 40 40

20,4 20,4 20,4 20,4 20,4 28 28 28 27,5 27,5 27,5 27,5 27,5 27,5 27,5 27,5 43 43 43 28 28 28 28 28 28

Tolerances , see also text Axial internal clearance, a), b), see also text Recommended fits Shaft and housing tolerances Fatigue load limit Pu

Speed ratings Reference Limiting speed speed

kN

r/min

0,865 0,865 0,865 0,865 0,865 1,2 1,2 1,2 1,16 1,16 1,16 1,16 1,16 1,16 1,16 1,16 1,83 1,83 1,83 1,18 1,18 1,18 1,18 1,18 1,18

Mass

Designation

* - SKF Explorer bearing

10000 10000 10000 10000 9500 9500 9000 9000 9000 9000 9000 9000 8500 8500 9000 9000 9000 9000

kg 10000 10000 10000 7500 10000 10000 7500 10000 9000 6300 9000 9000 9000 9000 6300 9000 9000 6300 9000 9000 6300 6300 9000 9000 9000

0,29 0,29 0,29 0,27 0,27 0,35 0,35 0,35 0,59 0,52 0,52 0,52 0,53 0,59 0,53 0,52 0,59 0,59 0,59 0,40 0,44 0,44 0,44 0,44 0,44

3206 A-2ZTN9/MT33 * 3206 ATN9 * 5206 A * 5206 A-2RS1 * 5206 A-2Z * 5206 E 5206 E-2RS1 5206 E-2Z 3306 A * 3306 A-2RS1TN9/MT33 * 3306 A-2Z/MT33 * 3306 A-2ZTN9/MT33 * 3306 ATN9 * 5306 A * 5306 A-2RS1 * 5306 A-2Z * 5306 E 5306 E-2RS1 5306 E-2Z 3207 A * 3207 A-2RS1/MT33 * 3207 A-2RS1TN9/MT33 * 3207 A-2Z/MT33 * 3207 A-2ZTN9/MT33 * 3207 ATN9 *

The Bearing number 3306-ATN9 was then finalized.

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Its dynamic load constant (C) = 41500 N. Load ratings and life - Dynamic bearing loads and life

The basic dynamic load rating C is used for calculations involving dynamically stressed bearings, i.e. a bearing that rotates under load. It expresses the bearing load that will give an ISO 281:1990 basic rating life of 1 000 000 revolutions. It is assumed that the load is constant in magnitude and direction and is radial for radial bearings and axial, centrically acting, for thrust bearings. The basic dynamic load ratings for SKF bearings are determined in accordance with the procedures outlined in ISO 281:1990. The load ratings given in this catalogue apply to chromium steel bearings, heat-treated to a minimum hardness of 58 HRC, and operating under normal conditions. SKF Explorer class bearings account among others, for improvements in material and manufacturing techniques applied by SKF and apply update factors to calculate the basic dynamic load ratings according to ISO 281:1990. The life of a rolling bearing is defined as – the number of revolutions or – the number of operating hours at a given speed

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Which the bearing is capable of enduring before the first sign of metal fatigue (flaking, spalling) occurs on one of its rings or rolling elements. Practical experience shows that seemingly identical bearings operating under identical conditions have different individual endurance lives. A clearer definition of the term "life" is therefore essential for the calculation of the bearing size. All information presented by SKF on dynamic load ratings is based on the life that 90% of a sufficiently large group of apparently identical bearings can be expected to attain or exceed. There are several other types of bearing life. One of these is "service life", which represents the actual life of a bearing in real operating conditions before it fails. Note that individual bearing life can only be predicted statistically. Life calculations refer only to a bearing population and a given degree of reliability, i.e. 90%, furthermore field failures are not generally caused by fatigue, but are more often caused by contamination, wear, misalignment, corrosion, or as a result of cage, lubrication or seal failure. Another "life" is the "specification life". This is the life specified by an authority, for example, based on hypothetical load and speed data supplied by the same authority. It is generally a requisite L10 basic rating life and based on experience gained from similar applications. The load according to our specifications are as follows: Axial load (Fa) = 2100 N Radial load (Fr) = 3700 N Assuming that the bearing will run throughout its life at this load and adding a constant static load of 1000 N for the weight of suspension parts to the radial loads assembly and 400 N to the axial load. Fa = 2500 N Fr = 4700 N

Equivalent dynamic bearing load

P = Fr + Y1*Fa ;

Fa/Fr <= e

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P = X1*Fr + Y2*Fa ;

Fa/Fr > e

e=0.8 Y1=0.78

Fa/Fr = 0.53 <0.8 P= Fr + Y1*Fa P= 6650 N

Bearing life L10 = (C/P)3 for ball bearings = 5.17 million revolutions

Wheel Radius = .254 m Therefore, life in terms of Km = (2*3.14*.254)*5.17*1000000/1000 = 8245 Km This is sufficiently good for a racing car like ours which has to be in operation for around only 1000 or so Km.

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11.

DESIGNING

The Designing process followed the following procedure: 1. Estimation of the forces acting on the component. 2. Choosing the right material. 3. Designing the CAD model on SolidWorks considering the geometric requirements. 4. Stress analysis of the model using Simulation Express Analysis Wizard in SolidWorks considering all the loads as estimated. 5. Optimization of the design: This step includes modifying the model by removal of extra material that is not adding to the strength but only to the weight.

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11.1 11.1.1

Hub Estimation of Forces

The forces acting on the Hub at different points are determined by balancing forces and moments and by considering certain assumptions. The forces acting on the hub are same as the forces on the tire. The determination of forces has been done in the section 8.1:

The final magnitudes of the forces are found to be: FRONT HUB -

Forces acting on the rim mounting studs: FX = 2777 N FY = 3692.2 N FZ = 2073.44 N



Forces acting on the brake disk mountings F= 1300N on each mounting, tangentially

REAR HUB -

Forces acting on the rim mounting studs: FX = 1800 N FY = 4660 N FZ = 2450 N



Forces acting on the brake disk mountings F= 1300N on each mounting, tangentially

11.1.2

Choosing the material

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170

The material chosen for both the Hubs is AISI 4140, which is a high yield strength material as compared to aluminium thus giving the required strength. Properties of AISI 4140: Yield Strength: 900 MPa (Approx.) Density: 7850 Kg/m3 

In Comparison with other options of material available:

Property

AISI 4140

AISI 1020

Al 6351

Yield Strength

900 MPa

350 MPa

150 MPa

Density

7850 Kg/m3

7850 Kg/m3

2700 Kg/m3



AISI 4140 has same density as that of Mild Steel (AISI 1020) but has



almost thrice of its yield strength. AISI 4140 is heavier than Al6351 with its density being 3 times of that



of Al but its yield strength is also 6 times of yield strength of Al. Because of this superiority in property, AISI 4140 is preferred. Its properties are used in giving high structural strength to the upright



with minimization of the weight. As the uprights would be manufactured by CNC milling operation, it is ensured that AISI 4140 is easily machinable.

11.1.3

Designing the CAD model on SolidWorks Team AXLR8R


171

For making the CAD model of Hub we need to consider the geometric constraints which are bearing size, rim width, rim offset and PCD of rim. Besides these certain things are kept in mind while deciding the other basic dimensions of the hub: -

Before starting the design of the hub, size of the bearing is known. The hub dimensions depend on dimensions of the brake disk. For designing the brake disk mountings, the orientation of the holes of the brake disk is carefully considered. While varying the width of the hub, we have to do analysis of the whole tire assembly, as the mounting points of upright are fixed. The designing of the rim mountings in the hub depend on the rim offset, rim width and PCD of the rim.

 Features of the design, same for both front and rear hubs: - For mounting of the rim, 4 holes have been provided in which studs will be fixed and then the rim will mount on these studs. - A step of 2mm is given in the housing for the bearing made to prevent the axial movement of the bearing. - The dimension of the diameter of the shaft is chosen with proper tolerances as the bearing is in interference fit with the shaft.

FRONT HUB

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Brakes Disk mountings

FRONT VIEW OF FRONT LEFT HUB

The rim will mount on this step. This is to prevent the static load of rim + tire weight to come on the studs.

Holes have been provided. In these holes studs will be fixed & rim will mount on the studs

Dimension of the shaft so decided for the interference fit with the bearing

SIDE VIEW OF FRONT LEFT UPRIGHT

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A step of 2mm is given to avoid axial movement of the bearing

THREE-D VIEW OF FRONT LEFT HUB

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174

REAR HUB

Brake Disk mounting

FRONT VIEW OF REAR LEFT HUB

SIDE VIEW OF REAR LEFT UPRIGHT

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A step of 2mm Dimension of the shaft decided given to prevent such thataxial the it is in 176 interferenceoffit with movement the bearing

FSAE IIT Delhi Suspension Report 3-D VIEW OF REAR LEFT HUB

The rim will mount on this step. This is to prevent the static load of rim + tire weight to come on the studs.

Holes have been provided. In these holes studs will be fixed & rim will mount on the studs

3-D VIEW OF REAR LEFT HUB

11.1.4 STRESS ANALYSIS EXPRESS ANALYSIS WIZARD

OF THE

CAD

MODEL ON

SIMULATION

After the modeling of the Cad, the analysis of the hub under the loading scenario of the forces as calculated in 10.1.1. The analysis is done in the Simulation Express Analysis Wizard in SolidWorks. The Fixture and forces are specified by us in the wizard. It itself does the required meshing and by Finite Element Analysis, calculates the minimum Factor of Safety present in the component. Simulation Xpress uses the maximum von Mises stress criterion to calculate the factors of safety. This criterion states that a ductile material starts to yield when the equivalent stress (von Mises stress) reaches the yield strength of the material. The yield strength is defined as a material property. Simulation Xpress calculates the factor of safety at a point by dividing the yield strength by the equivalent stress at that point. The Factor of safety for the stress analysis is chosen in the range of 1.72.2. Analysis of FRONT HUB

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THE VON MISES STRESS ANALYSIS

Von Mises stress analysis of front upright showing factor of safety (FOS) = 1.74. In some tiny portions, yellow shades are there otherwise most of the region shows only blue and green. Blue and green regions that these areas are absolutely safe and stresses are here are well below their yield strength.

Analysis of REAR UPRIGHT

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Von Mises stress analysis of front upright showing factor of safety (FOS) = 2.20 Material used is AISI 4140 due to its high yield strength. Also, only in some tiny portions, yellow shades are there otherwise in most of the area it is only blue and green. Every possible effort has been made to cut out the extra material, keeping FOS in mind. It would be manufactured using CNC machines for its intricate details and least possible error.

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11.1.5 Optimization of the Design by removing excess material. After the design, the analysis of that design is done under the loading scenarios as estimated and on the basis of the analysis only optimization of the design is initiated. The minimum Factor of Safety and Weight of the component are taken as prime consideration for design optimization. The weight is reduced and then the value of minimum FOS present in the component is checked by Simulation Express Analysis Wizard. The value of the FOS should lie in the range as taken; in our case we have taken a range of FOS as 1.5-1.8 as optimum. If the FOS of any region is very high than the optimum range then the action taken is removal of material. In the region with very low FOS, some material is added. The material removal is done by addition of features like trusses and slots. The material addition is done by addition of features like fillet and bridging. The mass of the component is taken into account at every step of material removal and addition. After every operation of material removal or addition, the weight of the component is checked and the analysis is re-run to check the minimum factor of safety. In the following optimized designs of front and rear uprights, every possible effort has been reduce the weight to the minimum maintaining optimum factor of safety to enable the design to withstand the different loads and stresses which would be there in actual conditions and are difficult to be considered virtually.

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180

FRONT HUB

Support members introduced to bear the loads as well as adding less to the weight.

Excess material removal

3-D VIEW OF OPTIMIZED DESIGN OF FRONT LEFT UPRIGHT

Every possible effort has been made to cut out the extra material, keeping FOS in mind. The mass of the final design is 476 grams. It would be manufactured using CNC machines for its intricate details and least possible error.

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182

REAR HUB

Support members introduced to bear the loads as well as adding less to the weight.

Removing excess material

3-D VIEW OF REAR LEFT UPRIGHT

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11.2 11.2.1

Upright Estimation of Forces

The forces acting on the upright at different mounting points are determined by balancing forces and moments and by considering certain assumptions. This determination of forces has been done in the section 8.1: The final magnitudes of the forces are found to be: FRONT UPRIGHT  

Forces acting on the a-arm mountings: On upper mount Fx= -2528.83 N Fy= -2881.8 N Fz = 10 N



On lower mount Fx= 5305.83 N Fy= 7474 N Fz = -2083.44 N



Forces acting on the tie-rod mount Fy= 1500N



Forces acting on the brake caliper mountings F= 3000N on each mounting, tangentially

REAR UPRIGHT  

Forces acting on the a-arm mountings: On upper mount Fx= -1800 N Fy= -3172 N Fz = -4685 N



On lower mount Fx= 80 N Fy= 7832 N Fz = 2300 N Forces acting on the toe-rod mount Fy= 500 N



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

185

Forces acting on the brake caliper mountings F= 3000N on each mounting, tangentially

11.2.2


The material chosen for both the uprights is AISI 4140, which is a high yield strength material as compared to aluminium thus giving the required strength. Properties of AISI 4140: Yield Strength : 900 MPa (Approx.) Density : 7850 Kg/m3 


Property

AISI 4140

AISI 1020

Al 6351

Yield Strength

900 MPa

350 MPa

150 MPa

Density

7850 Kg/m3

7850 Kg/m3

2700 Kg/m3

  



AISI 4140 has same density as that of Mild Steel (AISI 1020) but has almost thrice of its yield strength. AISI 4140 is heavier than Al6351 with its density being 3 times of that of Al but its yield strength is also 6 times of yield strength of Al. Because of this superiority in property, AISI 4140 is preferred. Its properties are used in giving high structural strength to the upright with minimization of the weight. As the uprights would be manufactured by CNC milling operation, it is ensured that AISI 4140 is easily machinable.

11.2.3

Designing the CAD model on SolidWorks

For making the CAD model of upright we need to consider the geometric constraints which are due to the mounting points of a-arms, tie-rod and

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186

brake caliper. Besides these certain things are kept in mind while deciding the other basic dimensions of the uprights: -

-



The Hub is designed before starting the design of the upright to do analysis of the whole tire assembly. This analysis would help in starting the designing of the upright. The mounting of the brake disk should be known before hand to decide the required clearance between the upright and the brake disk. For the length of the upright, care is taken to consider the inner diameter of the rim. Any mounting designed on the upright should not collide with the rim. The thickness of the upright is determined by considering the bearing thickness. Mounting points of the brake caliper is decided by analyzing the design of the brake caliper. We make sure a good amount of clearance between brake caliper and the rim. From this clearance, we decide the radial distance of the mounting point from the center of the upright. The distance between both holes is taken from the caliper design. Mountings points on the upright

FRONT UPRIGHT - top A-arm upright pivot

Y

546.76 Z X


Y

361.96 5.74

557.33 Z X


Y

166.36 15.83 533.08 Z

105.09

X

61.23

REAR UPRIGHT - top A-arm upright pivot

Y

542.48 Z 350.19 X -1610.25

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Y

541.11 Z

160.16

X -1590.25 - tie rod (steering arm)

Y

543.67 Z

258.04

X -1705.24

 -

-

-

Features of the design, same for both front and rear uprights: In the front upright, it was not possible to include tie rod mounting bracket as part of the upright as a single part, so the upright was divided into two parts and the bracket will be attached externally to the single piece upright by strong weldments. The upper a-arm mounting bracket is tilted according to the plane of the a-arms to prevent the collision of the arms with upright in case of bump and droop. A step of 2mm is given in the housing for the bearing made in the upright to prevent the axial movement of the bearing. The dimension of the diameter of the housing is chosen with proper tolerances as the bearing is in interference fit with the housing.

FRONT UPRIGHT

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188

Brakes Caliper mountings

Separate Attachment for Tie rod mounting

FRONT VIEW OF FRONT LEFT UPRIGHT

Tilted Bracket for Upper Aarm Mounting

Bracket for Lower A-arm Mounting SIDE VIEW OF FRONT LEFT UPRIGHT

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Housing for bearing which is in interference fit with upright. A step of 2mm is given to avoid axial movement of the bearing

THREE-D VIEW OF FRONT LEFT UPRIGHT

Two holes provided for adjustment of tie rod for two different cornering radii of 6m and 8m.

SEPARATE ATTACHMENT BRACKET FOR TIE-ROD MOUNTING

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REAR UPRIGHT

Brake calipers mountings

bracket for lower a-arm mounting

FRONT VIEW OF REAR LEFT UPRIGHT

Tilted bracket for upper a-arm mounting

Ends of the bracket for lower a-arm mounting is tapered SIDE VIEW OF REAR LEFT UPRIGHT

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Housing for bearing in which bearing is in interference fit with upright.

Separate Toe-rod mounting bracket

A step of 2mm given for bearing


SEPARATE TOE-ROD MOUNTING BRACKET

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11.2.4 Stress analysis of the CAD model on Simulation Express Analysis Wizard After the modeling of the Cad of the upright, the next task done is the analysis of the upright under the loading scenario of the forces as calculated in 10.1.1. The analysis is done in the Simulation Express Analysis Wizard in SolidWorks. The Fixture and forces are specified by us in the wizard. It itself does the required meshing and by Finite Element Analysis, calculates the minimum Factor of Safety present in the component. Simulation Xpress uses the maximum von Mises stress criterion to calculate the factors of safety. This criterion states that a ductile material starts to yield when the equivalent stress (von Mises stress) reaches the yield strength of the material. The yield strength is defined as a material property. Simulation Xpress calculates the factor of safety at a point by dividing the yield strength by the equivalent stress at that point. The Factor of safety for the stress analysis is chosen in the range of 1.51.8. Analysis of FRONT UPRIGHT


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Von Mises stress analysis of front upright showing factor of safety (FOS) = 1.78. In some tiny portions, yellow shades are there otherwise most of the region shows only blue and green. Blue and green regions that these areas are absolutely safe and stresses are here are well below their yield strength.

Analysis of REAR UPRIGHT


Von Mises stress analysis of front upright showing factor of safety (FOS) = 1.54. Material used is AISI 4140 due to its high yield strength. Also, only in some tiny portions, yellow shades are there otherwise in most of the area it is only blue and green. Every possible effort has been made to cut out the extra material, keeping FOS in mind. It would be manufactured using CNC machines for its intricate details and least possible error.

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11.2.5 Optimization of the Design by removing excess material After the design, the analysis of that design is done under the loading scenarios as estimated and on the basis of the analysis only optimization of the design is initiated. The minimum Factor of Safety and Weight of the component are taken as prime consideration for design optimization. The weight is reduced and then the value of minimum FOS present in the component is checked by Simulation Express Analysis Wizard. The value of the FOS should lie in the range as taken; in our case we have taken a range of FOS as 1.5-1.8 as optimum. If the FOS of any region is very high than the optimum range then the action taken is removal of material. In the region with very low FOS, some material is added. The material removal is done by addition of features like trusses and slots. The material addition is done by addition of features like fillet and bridging. The mass of the component is taken into account at every step of material removal and addition. After every operation of material removal or addition, the weight of the component is checked and the analysis is re-run to check the minimum factor of safety. In the following optimized designs of front and rear uprights, every possible effort has been reduce the weight to the minimum maintaining optimum factor of safety to enable the design to withstand the different loads and stresses which would be there in actual conditions and are difficult to be considered virtually.

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195

FRONT UPRIGHT

Stress members introduced to bear the loads as well as adding less to the weight.

removing excess material

Excess material removal by addition of features like slots

3-D VIEW OF OPTIMIZED DESIGN OF FRONT LEFT UPRIGHT


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197

REAR UPRIGHT

Trusses introduced to bear the loads as well as adding less to the




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11.3

Bell crank

Bell crank plays an important role as it transfers the force due to the weight of the vehicle to the shock absorbers in case of bump and droop. In the designing of a bell crank, the focus is on giving it structural strength and designing it in minimum amount of material. In its designing, the difficult part was to tackle the multi-planar forces acting on it from shockers, push rod and Anti roll bars. 11.3.1

Estimation of Forces

The forces acting on the Bell crank at different mounting points are determined by balancing forces and moments and by considering certain assumptions. This determination of forces has been done in the section 8.1: The final magnitudes of the forces are found to be: FRONT BELLCRANK FP (force applied by the pushrod) = 2261.62 N FARB = 3000 N Fshocks = 1600 N

REAR BELLCRANK FP (force applied by the pushrod) = -3730 N FARB = 3000 N Fshocks = 2500 N

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11.3.2

199


The material chosen for Bell crank is AISI 1020. It has been decided to improve the yield strength and other properties of the material by hardening it by heat treatment. This step increases the yield strength of the material up to 1.5 times of its original yield strength. The strength of the bell crank is taken to be high to tackle the multi-planar forces acting on it from the anti roll bars, shockers and push rod. Yield Strength : ~500 MPa (Approx.) Density : 7850 Kg/m3 


Property

Hardened AISI 1020

Al 6351

Yield Strength

~500 MPa

150 MPa

Density

7850 Kg/m3

2700 Kg/m3



  

Heat Hardened AISI 1020 is heavier than Al6351 with its density being 3 times of that of Al but its yield strength is also times of yield strength of Al. Its properties are used in giving high structural strength to the bell crank with minimization of the weight. AISI 1020 can be easily welded, which is an essential property required by us. AISI 4140 was also considered, but its unavailability in form of plates was a hindrance in using it.

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11.3.3

200


For making the CAD model of Bell crank we need to consider the geometric constraints which are due to the mounting points of pushrod, Anti Roll Bar & Shock absorber on bell crank and mounting point of bell crank on chassis. Besides these certain things are kept in mind while deciding the other basic dimensions of the bell crank: -

Firstly, the middle plane of the bell crank is identified from which the designing will start. The thickness of the bell crank is so chosen such that either pushrod or Anti Roll Bar will not collide with it in case of bump or droop.

Bell Crank Pivot Points: 

Front Bell Crank

Shock Absorber mounting on Bell crank -

Y

273.77

Z 669.92 X 0 Anti Roll Bar mounting on Bell crank -

Y

320.66

Z 547.85 X 0 Pushrod mounting on Bell crank -

Y

336.72

Z 601.17 X 0 Bell crank mounting on Chassis -

Y

270.00

Z 580.00 X 0

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

201

Rear Bell Crank

Shock Absorber mounting on Bell crank -

Y

238.81

Z 399.77 X -1503.12 Anti Roll Bar mounting on Bell crank -

Y

268.64

Z 377.98 X -1490.28 Pushrod mounting on Bell crank -

Y

338.32

Z 322.19 X -1502.84 Bell crank mounting on Chassis -

Y

310.00

Z

340.00 X

-1540.00

Features of the Design: The following features have been incorporated in design of both front and rear bell crank: -

The bell crank is designed keeping in account that the attachment of bell crank with chassis will be done by double row deep groove

-

bearing. As the bell crank rotates about the pivot point at its chassis mounting, the use of double groove bearing enables the free rotation of the bell

-

crank about the pivot axis. For incorporating this in design, housing is modeled in the bell crank

-

which holds the bearing by means of interference fit. At certain places of high stresses, side support is given in between the plates to prevent the deformation under loads.

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FRONT BELLCRANK

202

Damper mounting on Bell crank

Anti Roll Bar mounting on Bell crank Bell crank mounting on chassis

Pushrod mounting on Bell crank

FRONT VIEW OF THE FRONT LEFT BELL CRANK

Designed in form of plates with optimum clearance

Housing made to accommodate the deep groove bearing

Side supports given to prevent the deformation of plates under loads

3-D VIEW OF THE FRONT LEFT BELL CRANK

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3-D MODEL OF FRONT REAR BELL CRANK WITH THE BEARING

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204

REAR BELLCRANK Damper mounting point on the Bell crank

Bell crank mounting point on the Chassis

Anti Roll Bar mounting point on the Bell crank

Pushrod mounting point on the Bell crank FRONT VIEW OF REAR LEFT BELL CRANK

Housing made to accommodate the deep groove bearing

3-D VIEW OF REAR LEFT BELL CRANK

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205

Designed in form of plates with optimum clearance

Side supports given to prevent the deformation of plates under loads


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206

OF THE

CAD

MODEL ON

SIMULATION

The analysis of the bell crank under the loading scenario of the forces as calculated in 10.1.1. The analysis is done in the Simulation Express Analysis Wizard in SolidWorks. The Fixture and forces are specified by us in the wizard. It itself does the required meshing and by Finite Element Analysis, calculates the minimum Factor of Safety present in the component. Simulation Xpress uses the maximum von Mises stress criterion to calculate the factors of safety. This criterion states that a ductile material starts to yield when the equivalent stress (von Mises stress) reaches the yield strength of the material. The yield strength is defined as a material property. Simulation Xpress calculates the factor of safety at a point by dividing the yield strength by the equivalent stress at that point. The Factor of safety for the stress analysis is chosen in the range of 1.51.8. Analysis of FRONT BELL CRANK

VON MISES STRESS ANALYSIS OF FRONT LEFT BELL CRANK

Von Mises stress analysis of front bell crank showing factor of safety (FOS) = 1.73.

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Material used is AISI 1020, whose yield strength would be further improved by heat treatment. Also, only in some tiny portions, yellow shades are there otherwise it’s only blue and green. Every possible effort has been made to cut out the extra material, keeping FOS in mind. Analysis of REAR BELL CRANK

VON MISES STRESS ANALYSIS OF REAR LEFT BELL CRANK

Von mises stress analysis showing FOS = 1.68 Material used is AISI 1020, whose yield strength would be further improved by heat treatment. Also, only in some tiny portions, yellow shades are there otherwise it’s only blue and green. Every possible effort has been made to cut out the extra material, keeping FOS in mind.

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11.3.5 Optimization of the Design by removing excess material. After the design, the analysis of that design is done under the loading scenarios as estimated and on the basis of the analysis only optimization of the design is initiated. The minimum Factor of Safety and Weight of the component are taken as prime consideration for design optimization. The weight is reduced and then the value of minimum FOS present in the component is checked by Simulation Express Analysis Wizard. The value of the FOS should lie in the range as taken; in our case we have taken a range of FOS as 1.5-1.8 as optimum. If the FOS of any region is very high than the optimum range then the action taken is removal of material. In the region with very low FOS, some material is added. The material removal is done by addition of features like trusses and slots. The material addition is done by addition of features like fillet and bridging. The mass of the component is taken into account at every step of material removal and addition. After every operation of material removal or addition, the weight of the component is checked and the analysis is re-run to check the minimum factor of safety. In the following optimized designs of front and rear Bell crank, every possible effort has been reduce the weight to the minimum maintaining optimum factor of safety to enable the design to withstand the different loads and stresses which would be there in actual conditions and are difficult to be considered virtually.

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209

FRONT BELL CRANK

Excess material removal by addition of features like slots Trusses introduced to bear the loads as well as adding less to the

3-D MODEL OF FRONT REAR BELL CRANK WITH THE BEARING

Every possible effort has been made to cut out the extra material, keeping the optimum FOS in mind. The mass of the final design is 280 grams.

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210

REAR BELL CRANK

Removing excess material Trusses introduced to bear the loads as well as adding less to the


Every possible effort has been made to cut out the extra material, keeping the optimum FOS in mind. The mass of the final design is 269 grams.

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11.4

A-Arms

A-arm play an important role as it transfers the force due to the weight of the vehicle to the shock absorbers in case of bump and droop. In the designing of A-arms, the focus is on giving it structural strength and designing it in minimum amount of material. 11.4.1

Estimation of Forces

The forces acting on the A-arms are determined by balancing forces and moments and by considering certain assumptions. This determination of forces has been done in the section 8.1: The final magnitudes of the forces are found to be: FRONT A-arms Fku = 4707.23 N Fku = force on front upper a-arm Fmu = -1066.28N Fmu = force on rear upper a-arm Fkl = force on front lower a-arm = -10847.033 N Fml = force on rear lower a-arm = 2214.77 N

REAR A-arms Fku =3659 N Fku = force on front upper a-arm Fmu =90.88 N Fmu = force on rear upper a-arm Fkl = force on front lower a-arm =-504.018N Fml = force on rear lower a-arm = -3795.41N

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11.4.2

212


The material chosen for the A-arms is AISI 316 Stainless Steel. Properties of AISI 316: Tensile Strength: 580 MPa (Approx.) Density: 8000 Kg/m3 


Property

AISI 316 SS

AISI 1020

AISI 304 SS

Tensile Strength

580 MPa

420 MPa

500MPa

Density

8000 Kg/m3

7850 Kg/m3

8000 Kg/m3

  

AISI 316 Stainless Steel is easily available in form of tubes and it has higher value of tensile strength than other options available. No major difference in density of the above specified materials so, with respect to weight nothing is problem. It is ensured that AISI 316 SS is easily machinable and appropriate welding options are there.

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11.4.3

213


For making the CAD model of A-arms we need to consider the geometric constraints which are due to the mounting points of A-arms on upright and chassis. Besides these certain things are kept in mind while designing the a-arm assembly: -

Deciding how a-arms will be mounted to the upright as then only we can design mounting of a-arm on upright.

A-arm mounting Points: 

Front A-arms

Chassis pivot points (from vehicle Y, Z, X datum) - top A-arm chassis pivot (front/rear) 315.00

LH -Y

-Z

300.00

325.00 -X

319.00

135.00

-135.00 - bottom A-arm chassis pivot (front/rear)

-Y

270.00

285.00

-Z

155.00

-X

135.00

161.00 -150.00 Upright pivot points (from vehicle Y, Z, X datum) - top A-arm upright pivot

-Y


-Y

546.76 -Z

361.96

-X

5.74

557.33 -Z

-X

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15.83




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Rear A-arms

Chassis pivot points (from vehicle Y, Z, X datum) - top A-arm chassis pivot (front/rear) 275.00

LH -Y

285.00

-Z

320.00

315.00 - X -1450.00 -1750.00 - bottom A-arm chassis pivot (front/rear)

-Y

285.00 -Z

275.00

172.00

155.00 - X -1450.00 -1750.00 Upright pivot points (from vehicle Y, Z, X datum) - top A-arm upright pivot

-Y

542.41 -Z

350.19

- X -1610.08 - bottom A-arm upright pivot

-Y

542.17 -Z

160.16

- X -1590.08

Features of the Design: The following features have been incorporated in design of both front and rear A-arms -

For the mounting of A-arms on the upright, we are using a spherical bearing. Housing is made separately of the same material as that of a-arms which will house the spherical bearing.

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The housing will be welded to the a-arms. The dimensions of the housing are chosen to minimize the material. Slots are made in the end of the a-arm so that it fits into the housing and then can be welded. This will give strength to the joint. Slot made in the end of the a-arm to join with the housing

FRONT VIEW OF THE A-ARMS

Welding of the housing and the a-arm The Spherical bearing will fit here by interference fit.

3-D VIEW OF THE A-ARM + HOUSING

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3-D VIEW OF THE SEPARATE HOUSING


OF THE

CAD

MODEL ON

SIMULATION

The analysis of the A-arms is done under the loading scenario of the forces as calculated in 10.4.1. The Factor of safety for the stress analysis is chosen in the range of 1.51.8.

Factor of Safety = 1.63

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11.5 11.5.1

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Anti Roll Bar Estimation of Forces

When we talk of force analysis of Anti Roll Bars, we basically refer to the torque on lever arm ends through anti drop link and torsion stress on anti roll bar rod. Forces on anti drop link are mainly compressive or tensional. The forces acting on the lever arm at its two opposite mounting points with anti drop link are determined by SusProg 3D calculations optimizing forces and also the required anti roll bar stiffness. This determination of forces has been done in the section 8.1: The final magnitudes of the forces are found to be: FRONT ANTI ROLL BAR FRONT ANTI ROLL BAR STIFFNESS = 597.2283049 Nm/deg twist

Nominal Rate = 186.7936827 N/mm Maximum Force on anti drop link at an angle of 144.56 degrees = 6140.658 N Mounting Points Bell crank and anti drop link x

0.00

Y

320.66

Z

547.85

Anti drop link and Lever arm x

-18.75

Y

312.50

Z

216.48

Lever arm and ARB rod x

-100.00

Y

307.50

Z

115.00

Inner diameter rod ARB rod = 22.48 mm Outer diameter rod ARB rod = 26.70 mm

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REAR ANTI ROLL BAR REAR ANTI ROLL BAR STIFFNESS = 732.0255009 Nm/deg twist Nominal Rate = 238.3849111 N/mm Maximum Force on anti drop link at an angle of 144.56 degrees = 7497.228 N

Mounting Points Bell crank and anti drop link x

-1490.28

Y

268.64

Z

377.98

Anti drop link and Lever arm x

-1320.00

Y

315.00

Z

110.00

Lever arm and ARB rod x

-1331.54

Y

319.00

Z

309.67

Inner diameter rod ARB rod = 24.30 mm Outer diameter rod ARB rod = 33.40 mm

11.5.2


The material chosen for both the anti roll bar rod is AISI 304, which has high shear modulus as compared to aluminium and other steel family alloys thus giving high torsion resistance. Properties of AISI 304 are: Yield Strength: 215 MPa (Approx.) Shear modulus: 86 GPa Density: 7850 Kg/m3 


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Property

AISI 4140

AISI 304

AlSI 4130

Shear modulus

80 GPa

86 GPa

80 GPa

Yield Strength

900 MPa

215 MPa

435 MPa

Density

7850 Kg/m3

8000 Kg/m3

7850 Kg/m3





 

AISI 304 has same density as that of AISI 4140 and AISI 4130 but has more torsional resistance, which is the most critical and prominent factor in deciding its material. As far as shear modulus (which is about times the young’s modulus) is concerned, young’s modulus of AISI 304 is definitely less as compared to that of AISI 4140 and AISI 4130 but is sufficient from our design point of view requirement. Moreover, AISI 304 is available in tubular form but AISI 4140 is available in solid rods and AISI 4130 is not available in the market. Because of this superiority in property, AISI 304 is preferred. Its properties are used in giving high torsional resistance and comparable young’s modulus.

Material selection for lever arm Yield Strength: ~500 MPa (Approx.) Density: 7850 Kg/m3 


Property

Hardened AISI 1020

Al 6351

Yield Strength

~500 MPa

150 MPa

Density

7850 Kg/m3

2700 Kg/m3



 

Heat Hardened AISI 1020 is heavier than Al 6351 with its density being 3 times of that of Al but its yield strength is also times of yield strength of Al. Its properties are used in giving high structural strength to the lever arm with minimization of the weight. AISI 1020 can be easily welded.

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11.5.3


For making the CAD model of Lever arm, certain things have to be kept in mind like angle at which anti drop link would apply force to the lever arm. Five holes have been made in the lever arm, two on either sides of the hole obtained from the calculations. Lever arm is fixed to the ARB though strong weldments. The circular cylinder of lever arm joining the ARB rod is being made comparatively bigger as it has to withstand the weldments too. Slots have been made in the lever arm to reduce the excessive material contributing only to the weight. Inner diameter of the bigger cylindrical portion of the lever arm is equal to the outer diameter of the ARB rod. Diameter of the smaller holes to which anti drop link would be screwed is equal to 8 mm. 

Features of the design, same for both front and rear Anti Roll Bar:

In rear lever arm, there is a step of 1 mm to provide optimum thickness to the portion of hole. Anti drop link is attached to tube adapter and rod ends so as to increase or decrease its effective length. Anti Roll Bar rod is being attached to the chassis through anti roll bar bushes so that athe ARB rod would only undergo torsion motion. Polyurathene bushes would be used instead of rubber due to the fact that rubber may contribute to the torsional resistance of ARB rod due to its comparatively soft and sticky nature.

Stress analysis of the CAD model on Simulation Express Analysis Wizard

11.5.4

After the modeling of the Cad of the LEVER arm, the next task done is the analysis of the upright under the loading scenario of the forces as calculated in 10.1.1. The analysis is done in the Simulation Express Analysis Wizard in SolidWorks. The Fixture and forces are specified by us in the wizard. It itself does the required meshing and by Finite Element Analysis, calculates the minimum Factor of Safety present in the component. The Factor of safety for the stress analysis is chosen in the range of 1.5-1.8.

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Analysis of FRONT lever arm Hole to which anti drop link will be screwed through bolt Cylindrical surface to which ARB rod will be welded

FOS =1.7


Von Mises stress analysis of front upright showing factor of safety (FOS) = 1.70. Mass = 107.90 gm Material is hardened AISI 1020 alloy steel. In some tiny portions, yellow shades are there otherwise most of the region shows only blue and green. Blue and green regions that these areas are absolutely safe and stresses are here are well below their yield strength. It would be manufactured using CNC machines for its intricate details and least possible error.

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Analysis of REAR lever arm

FOS = 1.558


Von Mises stress analysis of front upright showing factor of safety (FOS) = 1.558 Mass = 232.60 gm Material is hardened AISI 1020 alloy steel.

11.5.5 Optimization of the Design by removing excess material After the design, the analysis of that design is done under the loading scenarios as estimated and on the basis of the analysis only optimization of the design is initiated. The FOS and weight of the component are taken as prime consideration for design optimization. The weight is reduced and

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then the value of minimum FOS present in the component is checked by Simulation Express Analysis Wizard. The value of the FOS should lie in the range as taken; in our case we have taken a range of 1.5-1.8 as optimum. If the FOS of any region is very high than the optimum range then next action taken is removal of material. In the region with lower FOS, material is added. The material removal is done by addition of features like slots. The material addition is done by addition of features like fillet. The mass of the component is taken into account at every step of material removal and addition.

ARB rod will be welded into it

Slots being made to reduce excess materials

Anti drop link will be attached here

Front Lever Arm

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Rear Lever Arm Step of 1 mm

Rear Lever Arm

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Front Anti Roll Bar Assembly

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Rear Anti Roll Bar Assembly

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11.6

228

Miscellaneous

11.6.1

Pushrod

PUSHROD ASSEMBLY WITH TUBE ADAPTER AND ROD-ENDS

Pushrod directly connects a-arms with the bell crank thus transferring the force from the tires to the dampers via bell crank in case of bump or droop.  -

The force in the pushrod is calculated in section 8.1 Fp (Front) = 2261 N Fp(rear) = -3730 N



Material used for rod is AISI 316 Stainless Steel as used for a-arms, due to its easy availability and good properties.



The Designing involves consideration of features like length of the rod, inner and outer diameter.



After stress analysis and optimization of the design, the inner and outer diameters of the rod are finalized.

Inner diameter = 16mm.

11.6.2

Outer diameter = 19mm.

Tube Adapter Team AXLR8R


Tube Adapters are used at the ends of a-arm rods and push rods to join them to rod-ends. The material of the Tube Adapter is same as that of rod, which is AISI 316 Stainless steel. The Tube Adapter will be welded to the rod.

11.6.3

Brackets Team AXLR8R

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Brackets are used to mount different components. They are welded to the component on which the other part is going to mount.    -

The forces acting on the brackets are same as the force acting on the part mounted on them. The material of the brackets is AISI 4140 Steel for its very high strength. The Brackets are designed considering the following : Required dimensions of the bracket. It should have enough clearance from the part. It should be profiled for easy and better weldments.

LEFT FRONT PUSHROD BRACKET

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LEFT FRONT SHOCKER BRACKET

LEFT FRONT BELL CRANK BRACKET

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LEFT REAR BELL CRANK BRACKET

LEFT REAR PUSHROD BRACKET

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LEFT REAR SHOCKER BRACKET

LEFT FRONT UPPER FRONT A-ARM BRACKET

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11.6.4

Rod-ends

Rod end is used at the end of tube adapter. Nut-bolts are screwed into it. It is also used to change the effective length of the rod.

11.6.5 

Bearings

Deep Groove bearing to be used in Bell crank mounting to chassis

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

Spherical Bearing to be used in A-arm mounting to Upright

11.6.6

Wheel and tire

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11.6.7

Shocker

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11.7 11.7.1

237

Assemblies Front Wheel Assembly

FRONT WHEEL ASSEMBLY

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11.7.2

238

Rear Wheel Assembly

Rear Wheel Assembly

11.7.3

Front Pushrod-bell crank-Shocker Assembly

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11.7.4

Rear bell crank-Shocker Assembly

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FUTURE SCOPE ACTIVE Suspension A passive suspension system has the ability to store energy via a spring and to dissipate it via a damper. Its parameters are generally fixed, being chosen to achieve a certain level of compromise between road holding, load carrying and comfort. An active suspension system has the ability to store, dissipate and to introduce energy to the system. It may vary its parameters depending upon operating conditions and can have knowledge other than the strut deflection the passive system is limited to. The basic idea is to use a computer, sensors, a pump, and hydraulic cylinders at each corner to get the car to do things never before possible, such as leaning into a curve like a motorcycle, compensating for the dive of braking and the squat of acceleration, and raising and lowering its wheels individually to make pavement imperfections seem to disappear. It's even been suggested that a single tire could be lifted off the road for changing. Active suspension systems (also known as Computerized Ride Control) consist of the following components: a computer or two (sometimes called an electronic control unit, or ECU, for short), adjustable shocks and springs, a series of sensors at each wheel and throughout the car, and an actuator or servo atop each shock and spring. The components may vary slightly from manufacturer to manufacturer, but these are the basic parts that make up an active suspension system. Active or adaptive suspension is an automotive technology that controls the vertical movement of the wheels via an onboard system rather than the movement being determined entirely by the surface on which the car is driving. The system therefore virtually eliminates body roll and pitch variation in many driving situations including cornering, accelerating, and braking. This technology allows car manufacturers to achieve a higher degree of both ride quality and car handling by keeping the tires perpendicular to the road in corners, allowing for much higher levels of grip and control.

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An onboard computer detects body movement from sensors located throughout the vehicle and, using data calculated by opportune control techniques, controls the action of the suspension. Active suspensions can be generally divided into two main classes: pure active suspensions and semi-active suspensions.

Arrangement of an active suspension shows a typical arrangement of the active suspension. In general, it is composed of: 

Sensors – various sensors are installed around the vehicle to monitor the vehicle conditions and driver activities.



Electronic control unit (ECU) – all the sensor signals are fed to a microcomputer, also known as ECU. With the aid of a programmed map memory, calculations are made as to what adjustment should be made to the suspension.



Actuators – the instructions from ECU are converted into electrical signals and directed to various actuators to control the suspension. Hydraulic actuators are most often used for their compact volume and light weight.

Pure Active Suspensions

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The first to be separate actuators independent force on improve the riding drawbacks of this are high cost, added the apparatus needed the need for rather and repairs on some

243

introduced, use which can exert an the suspension to characteristics. The design (at least today) complication/mass of for its operation, and frequent maintenance implementations.

Different from semi-active suspensions, a fully active suspension does not change the damper characteristics, but add a force generator in parallel with the passive damper and spring as shown.

Therefore, the suspension can not only dissipate energy, but also inject energy into the system. That is why we call it fully active suspension. Normally the power of the force generator is supplied by the engine; therefore, compared with semi-active suspensions, active suspensions have higher cost and power consumptions. But as a return, it has better performance than semi-active ones. Depending on the response speed of the actuator, there are fast active and slow active suspensions. Slow active suspensions have low cost and power consumption, but the performance is not as good as fast active ones.

Semi-active Suspension These systems can only change the viscous damping coefficient of the shock absorber, and do not add energy to the suspension system.

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Though limited in their intervention (for example, the control force can never have different direction than that of the current speed of the suspension), semi-active suspensions are less expensive to design and consume far less energy. In recent times, research in semi-active suspensions has continued to advance with respect to their capabilities, narrowing the gap between semi-active and fully active suspension systems. The term semi-active suspension is often used to refer to a controlled damper under closed-loop control, which means the control is realized by varying the damper’s damping rate as shown.



A semi-active suspension is energy. According to configurations, semi-active the following categories.

only capable of dissipating different damper dampers can be classified into

Dampers with controllable orifice The damping force in a shock absorber is generated when the oil flow through the hydraulic orifices in the damper valve of the shock absorber. The smaller the orifice is, the larger damping force can be generated. Therefore, we can control the opening of the orifice to adjust the shocker’s damping force.

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Dampers with controllable fluid:

If the hydraulic orifice is fixed, we can vary the oil viscosity to control the damping force. The bigger the oil viscosity is, the larger damping force can be generated. ER (Electro rheological) or MR (Magneto-rheological) fluid can be used for this purpose. There are polarizable particles of a few microns in the oil. When electrical of magnetic field is applied to the oil, the particles will be polarized and distributed in a sequential order as shown.

Work principle of electro-rheological & magneto rheological dampers: Particles in an MR/ER fluid left without & right with applied magnetic/electrical field. As a result, the oil viscosity changes, depending on the strength of the electrical/magnetic field.

ANTI ROLL BAR During cornering, it is desirable that the stiffness of the stabilizer bar be increased. If the stabilizer bar is too compliant, the vehicle will not respond well

during

cornering, increasing

the

likelihood of

rolling

over.

However

if the

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stabilizer bar is too stiff, the ride and handling will be compromised during normal vehicle operation. Therefore, it is desirable that the stiffness of the stabilizer bar be variable to adjust for changing driving conditions. 

Another option is to use active anti roll bar. Active Anti Roll bar is new



high tech system which is now being used in costly passenger cars. Another advancement that can be made in future is “bladed lever arm” through which effective torsion stiffness can be altered by just rotating the bladed lever arm. No need for hole/s on the lever arm.

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REFERENCES Books    

Race Car Vehicle Dynamics (RCVD) by William F. Milliken And Douglas L. Milliken Tune To Win by Caroll Smith Fundamentals of vehicle dynamics - Thomas d Gillespie The Automotive Chassis.

Internet                 

  

http://www.lumenique.com/Cars/mcoupe/modifications/antirollbars.h tm fsae.com/eve/forums/a/tpc/f/125607348/m/510101683 http://www.carbibles.com/suspension_bible.html http://www.jaytorborg.com/anti-roll_bars.htm en.wikipedia.org/wiki/Camber angle www.ozebiz.com.au/racetech/theory/align.html http://www.roversd1.nl/sd1web/suspension.html www.rctek.com/technical/handling/camber_angle_basics.html http://autoracing.suite101.com/article.cfm/race_car_wheel_camber_ angles http://www.blackboots.co.uk/tech-cambertheory.php http://www.blackboots.co.uk/tech-camberbasics.php http://www.blackboots.co.uk/tech-kingpininclination.php http://www.rctek.com/technical/handling/caster_angle_camber_chan ge.html http://www.gtsparkplugs.com/WheelOffsetCalc.html http://www.rx7club.com/showthread.php?t=619446 http://www.miata.net/garage/offset.htm Optimum pdf -http://www.optimumg.com/OptimumGWebSite/Documents/TechTips/ Springs&Dampers_Tech_Tip_1.pdf http://www.optimumg.com/OptimumGWebSite/Documents/TechTips/ Springs&Dampers_Tech_Tip_2.pdf http://www.optimumg.com/OptimumGWebSite/Documents/TechTips/ Springs&Dampers_Tech_Tip_3.pdf http://www.optimumg.com/OptimumGWebSite/Documents/TechTips/ Springs&Dampers_Tech_Tip_4.pdf

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        

 

        

http://www.optimumg.com/OptimumGWebSite/Documents/TechTips/ Springs&Dampers_Tech_Tip_5.pdf http://www.optimumg.com/OptimumGWebSite/Documents/TechTips/ Springs&Dampers_Tech_Tip_6.pdf FSAE Forums http://fsae.com/groupee?s=763607348&cdra=Y http://www.fd3s.net/anti-sway_bars.html#INT http://journals.pepublishing.com/content/b330304481r6m03l/fulltext .pdf http://www.kangaloosh.com/cms/Welcome/Gettingstarted/Basicman ual/tabid/60/Default.aspx http://www.patentstorm.us/patents/6651991/description.html http://docs.google.com/viewer?a=v&q=cache:eccEhkUlzsJ:www.fisita.com/students/congress/sc08papers/f2008sc012.p df+application+of+active+anti+roll+bar+systems+for+enhancing +yaw+stability&hl=en&gl=in&pid=bl&srcid=ADGEESgukNEhjNnP36 5nm37ptvZ2IC9isIgeHsHelKlWK3d81D_OMBvkX78auu814mlW1nzTgVv2pS3g-54QE7erQmcbVa6BCWT5SFvSebh1HQAVa4l0tDwdY0yDpFFZfwZqilPZa8&s ig=AHIEtbRO1BXeBT_P433gBdnMmpB-MXCudg http://www.f1technical.net/forum/viewtopic.php? f=11&t=7716&sid=46cd9d560bcc128ad4930769996e5f55 http://www.authorstream.com/Presentation/ydv_navdeep-175373leaf-spring-lecture-05-springrelations-pjz-science-technology-pptpowerpoint/ http://insideracingtechnology.com/tirebkexerpt2.htm http://en.wikipedia.org/wiki/Kingpin_(automotive_part) http://en.wikipedia.org/wiki/Suspension_(vehicle) http://www.circletrack.com/techarticles/antidive_suspension_tech_pa rameters/index.html http://en.wikipedia.org/wiki/Slip_angle http://www.auto-ware.com/setup/slp_hndl.htm http://home.scarlet.be/~be067749/58/c1/index.htm en.wikipedia.org/wiki/Understeer en.wikipedia.org/wiki/Oversteer

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FSAE Suspension report

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