Optimization of Formula Car Double Wishbone Suspension System

2012 FORMULA CAR SUSPENSION SETUP OPTIMIZATION

Debraj Roy, Kulkeerty Singh, Harshit Agarwal, Aman Bansal, Ashutosh Sharma B.Tech (MAE) V Sem, ASET

Abstract

The report intrigues with the variations and optimizations in the suspension design of formula cars, the fastest automobiles. We elaborate the concepts coined with a suspension system setup for a formula car. Suspension is what harnesses the power of the engine, the downforce created by the wings and aerodynamic pack and the grip of the tyres, and allows them all to be combined effectively and translated into a fast on-track package[i]. Suspension systems serve a dual purpose — contributing to the vehicle's handling and braking for good active safety and driving pleasure, and keeping vehicle occupants comfortable and reasonably well isolated from road noise, bumps, and vibrations, etc. These goals are generally at odds, so the tuning of suspensions involves finding the right compromise[ii] The suspension of a modern Formula One car forms the critical interface between the different elements that work together to produce its performance. The analytical part comprises of study of double wishbone setup used nowadays with the effect of roll centre on the car‘s performance. The optimization for a perfect balance between the various criteria affecting the suspension has been scrutinized from different aspects. A brief view on the different options for the suspension setup has been presented. A critical point to the controversial ‗active suspension‘ systems

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Acknowledgements I would like to extend my heartiest gratitude to respected Mr. Vijay Shankar Kumawat, Department Of Mechanical Engineering, Amity School of Engineering & Technology for his visionary guidance and sizable subvention at each and every step of the project. It was his precisionist & rationalist remonstrance that obscured the way for us to work through this project and develop an apical precinct for the task. It was extremely amiable experience to work under a truly devoted and ingenious scholastic. Also, it would be malefic of us if we fail to extend our gratitude to all the colleagues whom we interacted with the time being. We would immensely like to appreciate the support of each other for their generous & receptible nature throughout the work. The fact that this small journey is approaching its end is sorrowful for us as we would have liked to gain more from all the aforementioned delightful personnel. We were also willing to complete a optimisation of the setup from ourown, but shortage of time and material requisites have hindered our willingness. It would be grateful of us to lend our hand in nearby future for any other task in the project and even work on it.

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Table of Contents Abstract……………………………………………………..…………………….1 Acknowledgements……………………………………….……………………....2 Table of Contents…………………………………………..……………………..3 List of Figures….......................................................................................................5 Tables & Graphs……………………………………………….…………………7 Certificate………………………………………….……………….…………...8 1. Introduction…………………………………………………………….9 2. Understanding Basics of Formula Car Suspension…………………...10  Jounce…………………..………………………………………...10  Rebound…………………………………………………………..10  Springs……………………………………………………………11  Sprung Weight…………………………..……………………......11  Unsprung Weight…………………………………………………11  Ride Height……………………………………………………….12  Vehicle Trim Height……………………………………………...13  Setback……………………………………………………………13  Thrust Angle……………………………………………………...13  Caster Angle……………………………………………………...14  Camber Angle…………………………………………………….14  Toe Angle…………………………………………………….…...15  Shock Absorbers, and Travel……………………………….…….16  Wheelbase and Track Width……………………………………...16  Kingpin Inclination & Scrub Radius……………………….…..…16  Damping………………………………………………….……….17  Roll Centre………………………………………………………..19  Anti-Squat………………………………………………………...28  Suspension Travel………………………………………………...28  Anti-Roll Bars…………………………………………………….29 Amity School of Engineering & Technology

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 Shock-Mounting Locations………………………………….……30 3. Mobility of Formula Car Suspension Mechanisms..……………..........33 4. Double Wishbone Suspension for Formula Car...……………………..35  Multi-Link Suspension.…………………………………………….39 5. Optimized Suspension Geometries for Formula Car………………....40  Design Overview………………………………………………….47 o Static Weight……………………………………………….47 o Lateral load transfer due to lateral acceleration……………48 o Longitudinal weight transfer due to negative acceleration...49 o Maximum loads achieved………………………………….50 o Maximum Tractive Forces ………………………………...50 o Factor of Safety Development……………………………...51 o A-Arm Force Calculations…………………………………52 o Front Uprights……………………………………………...54 o Rear Uprights………………………………………………56 o Rockers……………………………………………………..57 o Push rods…………………………………………………...58 o Steering Arms………………………………………………62 6. Process Controls (Troubleshooting)…………………………………..63 7. Safety Considerations……………………………………………........65 8. Manufacturing Considerations………………………………………..66 9. Modifications…………………………………………………………66 10. Conclusion…………………………………………………………….67 11. References…………………………………………………………….68 12. Bibliography…………………………………………………………..69

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Figures Figure 1: Jounce and Rebound……………………………………………………10 Figure 2: Spring Rate Comparison……………………………………………....11 Figure 3: Ride Height[iv]………………………………....……………………….12 Figure 4: Setback & Thrust Angle………………………………………………13 Figure 5: Caster & Camber Angle [v]…………………………………………….15 Figure 6: Toe Angle[vi]…………………………………………….…………….16 Figure 7: Kingpin Inclination & Scrub Radius…………………………………17 Figure 8: Suspension of a Typical Car………………………………………….19 Figure 9: Intersection Point of Poles………………...............................................20 Figure 10: Applying Theorem of Kennedy……………………………………..22 Figure 11: Obtaining Roll Centre….……………………………………………22 Figure 12: Inertial Force…………………………………………………………23 Figure 13: Positioning of CG & RC……………………………………………..24 Figure 14: Roll Moment…………………………………………………………24 Figure 15: Change in Roll Centre on Cornering……………………………..…25 Figure 16: Roll Axis: Side View…………………………………………………26 Figure 17: Anti-Roll Bar[vii]……………………..……………………………….30 Figure 18: Shock Mounting Locations & Wheel Rates….………………………31 Figure 19: Ferrari 663[xiv]………………………………….……………………..33 Figure 20: Double Wishbone Suspension Multi-Link Solidworks Model[xi,xii]…...36 Figure 21: Double Wishbone Suspension Rear View [iv]………………………….38

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Figure 22: Double Wishbone Suspension with Pull Rod Arrangement[viii]..........39 Figure 23: Double Wishbone Suspension Coil Spring Solidworks Model[xiii]….40 Figure 24: Optimized Roll Centre Location………………………….…………43 Figure 25: Tire Data……………………………………………………………..44 Figure 26: Scrub radius………………………………………………………….45 Figure 27: Plot of Relevant Forces………………………………………………48 Figure 28: Tire Force Schematic …………………………………………….…49 Figure 29: Schematic of tire with axes ………………………………………….51 Figure 30: Force Schematic & Truss Design …………………………….……..53 Figure 31: Front Uprights ………………………………………………………55 Figure 32: Front Uprights CATIA V5 Model Static Load Test ..………………56 Figure 33: Rear Uprights ……………………………………………………….56 Figure 34: Rear Uprights CATIA V5 Model Static Load Test ……………….…57 Figure 35: Rockers ………………………………………………………………58 Figure 36: Rebound Damping[10]………………………………………………….59 Figure 37: Compression Damping …………………………………………….….60 Figure 38: Pushrods.………………………………………………………………61 Figure 39: Bell Crank FEA Results[11]………………………………………..…61 Figure 40: Motion Ratio…………………………………………..…………….62 Figure 41: Steering Arms…………………………………………..……………62 Figure 42: Supra SAE AUR Prototype Solidworks Model[ix]………………..…67

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Tables Table 1: Geometries of Double Wishbone SLA Suspension……………..…...41-42 Table 2: Acceleration Data used for Calculations……………………………..….48 Table 3: Vertical Tire Force Calculation…………………..……………………...49 Table 4: Lateral Acceleration Loads…………………..………………………….49 Table 5: Longitudinal Weight Transfer…………..……………………………….50 Table 6: Maximum Achievable Loads …………………..……………………….50 Table 7: Horizontal Tire Force …………………..……………………………….51 Table 8: Material Properities for a 14 inch pin-pin beam …………………..……54

Graphs Graph 1: Roll Centre v/s Displacement………………………..………………….21 Graph 2: Camber v/s Wheel Displacement…………………..…………………...45 Graph 3: Toe-In/Out v/s Wheel Displacement……………..…………………......46 Graph 4: Caster Angle v/s Wheel Displacement………………...……………......47 Graph 5: Kingpin Angle v/s Wheel Displacement……………………………......47

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CERTIFICATE

This is certified that this project report "A Technical Report On Optimization Of Formula Car Double Wishbone Suspension System" is the bona fide work of Debraj Roy, Kulkeerty Singh, Harshit Agarwal, Ashutosh Sharma, Aman Bansal studying in B.Tech(MAE) V Semester of Amity School of Engineering & Technology, Jaipur who carried out the project under my supervision.

Signature of the HOD

Signature of Supervisor

(Mr.Mangal Singh Sisodia)

(Mr. Vijay S. Kumawat)

Lecturer,Mechanical Engg. Deptt.

Lecturer, Mechanical Engg. Deptt.

AMITY SCHOOL OF ENGINEERING & TECHNOLOGY NH-11C, Kant Kalwar, RIICO Industrial Area, Jaipur, Rajasthan-302006

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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 and allows relative motion between the two [1] [ii]. Apart from your car's tyres and seats, the suspension is the prime mechanism that separates one‘s rears from the road. It also prevents one‘s car from shaking itself to pieces. No matter how smooth we think the road is, it's a bad, bad place to propel over a ton of metal at high speed. So we rely upon suspension. People who have once travelled on underground trains wish that those vehicles relied on suspension too, but they don't and that's why the ride is so harsh. Actually it's harsh because underground trains have no lateral suspension to speak of. So as the rails deviate side-to-side slightly, so does the entire train, and its passengers. In a car, the rubber in the tyre helps with this little problem, while all the other suspension parts do the rest[i]. It is important for the suspension to keep the road wheel in contact with the road surface as much as possible, because all the forces acting on the vehicle do so through the contact patches of the tires. Thus the suspension protects the vehicle itself and any cargo or luggage from damage and wear. The design of front and rear suspension of a car may be different. In 1901 Mors of Paris first fitted an automobile with shock absorbers. With the advantage of a dampened suspension system on his 'Mors Machine', Henri Fournier won the prestigious Paris-to-Berlin race on the 20th of June 1901. Fournier's superior time was 11 hours 46 min 10 sec, while the best competitor was Léonce Girardot in a Panhard with a time of 12 hours 15 min 40 sec.[2] In 1920, Leyland used torsion bars in a suspension system. In 1922, independent front suspension was pioneered on the Lancia Lambda and became more common in mass market cars from 1932. [3] Unlike road cars, occupant comfort does not enter the equation for formula cars - spring and damper rates have to be very firm to ensure the impact of hitting bumps and kerbs and have to be defused as quickly as possible. The spring absorbs the energy of the impact; the shock absorber releases it on the return stroke, and prevents an oscillating force from building up. Think in terms of catching a ball rather than letting it bounce.[i] Amity School of Engineering & Technology

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Understanding Basics of Formula Car Suspension

 Jounce[4] It is the upward movement or compression of suspension components.  Rebound It is the downward movement or extension of suspension systems.

Jounce

FIG. 1

Rebound

 Springs The most common variety of springs are coil springs, these are usually placed around the damper housing to form a spring-damper unit. A spring is an elastic device that resists movement in its direction of work. The force it exerts is proportional to the movement of one of its ends. Or to put this into a mathematical equation:

Force = Movement * Spring constant A high value for the spring constant makes for a stiff spring, and a low value makes for a soft spring. Amity School of Engineering & Technology

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FIG. 2

Spring Rate Comparison

 Sprung Weight Sprung weight transfer is the weight transferred by only the weight of the vehicle resting on the springs, not the total vehicle weight. Calculating this requires knowing the vehicle's sprung weight (total weight less the unsprung weight), the front and rear roll center heights and the sprung center of gravity height (used to calculate the roll moment arm length). Calculating the front and rear sprung weight transfer will also require knowing the roll couple percentage. The roll axis is the line through the front and rear roll centers that the vehicle rolls around during cornering. The distance from this axis to the sprung center of gravity height is the roll moment arm length. The total sprung weight transfer is equal to the G-force times the sprung weight times the roll moment arm length divided by the effective track width. The front sprung weight transfer is calculated by multiplying the roll couple percentage times the total sprung weight transfer. The rear is the total minus the front transfer.    

Body and frame Engine and transmission Load or cargo Fuel tank  Unsprung Weight

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Unsprung weight transfer is calculated based on the weight of the vehicle's components that are not supported by the springs. This includes    

Wheels and tires Wheel bearings and hubs Axles and steering knuckles Wheel mounted brake components

These components are then (for calculation purposes) assumed to be connected to a vehicle with zero sprung weight. They are then put through the same dynamic loads. The weight transfer for cornering in the front would be equal to the total unsprung front weight times the G-Force times the front unsprung center of gravity height divided by the front track width. The same is true for the rear.

 Ride Height Ride height is the height at which a vehicle‘s sprung components are carried over the vehicle‘s un-sprung components. It is a suspension measurement taken from un-sprung to sprung components. Vehicle ride height is not the same as:  Vehicle trim height  Curb riding height  Side-to-side lean

FIG. 3 Amity School of Engineering & Technology

Ride height Page 12

 Vehicle Trim Height Side-to-side lean is a term used to describe the difference in the height of the vehicle body usually measured from a point on the body to the ground on both sides of the vehicle.

 Setback It is a reference to the difference in side-to-side wheelbase.  Positive Setback :  The RH wheelbase is longer, using the left side as a base.  Negative Setback : The RH wheelbase is shorter, using the left side as a base.

FIG. 4

Setback & Thrust Angle

 Thrust Angle Amity School of Engineering & Technology

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It is the angle between the vehicle's centerline and the thrust-line of the rear axle.  Negative thrust angle- rear wheels point left.  Positive thrust angle - rear wheels point right.  Caster Angle It is the forward or rearward inclination of the steering axis. It acts as a   directional control angle. It would will pull the vehicle to the least positive side. It is sometimes misinterpreted as a tire wear angle which isn‘t so.  Camber Angle Camber describes the angle between the tyre‘s centreline and the vertical plane. It is also a directional control angle and would pull the vehicle to most positive side. It is a ‗Tire wear angle‘. If the wheels of the car lean inwards, the camber angle is said to be negative, if they lean outward, the angle is said to be positive. It is usually measured at ride height, and angles of -0.5 to -3 are the most common.[6] First of all, positive camber is never used, only negative. Negative camber is necessary because when a car turns into a corner, it experiences chassis roll, which increases the tires' camber angle. Also, because most rubber tires are quite flexible, they get a little deformed in the direction of the Centre of the corner. If the car doesn‘t have any negative camber, only the tires' outer edge and sidewall would touch the ground, which isn't beneficial for traction. A tyre‘s coefficient of traction (grip) increases as its contact surface increases, so the ideal situation would be that the tire would stay perpendicular to the ground at all times, and that it wouldn‘t deform under heavy side load. Unfortunately, this isn‘t the case; most of the time one has to find the best compromise. The problem is that if one wants maximum forward traction, he has to set the camber to 0°, and if he wants maximum cornering action he has to set it to a few degrees negative, depending on the softness of the suspension and tire carcass. So one can't have both, but you can try to make the best possible compromise. The easiest way is to set camber so the tires wear evenly across their surface, that way one can be sure every part of the Amity School of Engineering & Technology

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surface is used to the maximum of its potential. Keep in mind that a car with very soft suspension settings and very little camber change will need more negative camber than a car with a very stiff suspension and in very bumpy off-road conditions however, it can be beneficial to use more camber than would be needed for uniform wear across the surface. The excess camber stabilises the car in large bumps and reduces the risk of catching a rut and flipping over. Camber can also be used as an adjustment to attain a desired handling effect, but we definitely won' t recommend this: a non-optimal camber setting always yields less traction, which inevitably makes the car slow.

FIG. 5

Caster & Camber Angle

 Toe Angle It is inward or outward variation of tires from a straight ahead position. Possibilities of toe are in form of ‗Toe In‘ or ‗Toe Out‘. It is not a directional control angle. It is also a ‗Tire wear angle‘ like camber angle.

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FIG. 6

Toe Angle

 Shock absorbers, and travel Shock absorbers and dampers are important elements of suspension and are the key element to supporting and balancing the forces that the arm will be suffering. Functions of Shock Absorbers  Control spring oscillation and rebound  Reduce body sway and lean on turns  Reduce the tendency of a tire to lift off the road  Compression Ratios are expressed in terms of extension/compression with ratios from 50/50 to 80/20 available. A ratio of 70/30 is common.  Wheelbase and Track Width The wheelbase is the distance between the centers of the front and rear wheels. Track width is usually measured from the center point of the tires. The track widths may be different, but the smaller track width cannot be less than 75% of the larger track width. This will provide a stability, but it should not be so wide that it hinders cornering and maneuverability.  Kingpin Inclination and Scrub Radius Amity School of Engineering & Technology

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The first parameter that had to be determined besides track width was kingpin inclination. This is the angle between vertical and the axis running through the upper and lower ball joints. The kingpin inclination affects steering performance and return ability. This is interrelated with the scrub radius and the spindle length, which were minimized for this design. The spindle length is the distance from the kingpin axis to the centerline of the wheel at the wheel axis. The scrub radius is the distance from the kingpin axis to the center of the wheel at the ground. By minimizing the spindle length and scrub radius, the jacking effect when the wheels are steered is minimized. That results in less steering effort on the driver‘s part and less sensitivity to braking inputs.

FIG. 7

Kingpin Inclination & Scrub Radius

 Damping Damping is needed to absorb the energy associated with suspension travel. Bumps or lateral or longitudinal acceleration can induce that suspension travel. Without damping, the magnitude of the suspension movement would never stop increasing, leading to a very humorous situation. In terms of energy, damping absorbs most of the energy the car receives as it moves, unlike springs, which store the energy, and Amity School of Engineering & Technology

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release it again. Imagine a car with no damping driving on a bumpy road. The subsequent impacts from the bumps on the tires would make the suspension bounce very intensely, which is not a good thing. Dampers absorb all the excess energy, and allow the tires to stay in contact with the ground as much as possible. This also indicates that the damping should always be matched to the spring ratio: never runs a very stiff spring with very soft damping or a very soft spring with very stiff damping. Small changes however can give interesting results. Damping that‘s a bit on the heavy side will make the car more stable; it will slow down both the vehicle‘s pitch and roll motions, making it feel less twitchy. Damping only alters the speed at which the rolling and pitching motions occur, it does not alter their extent. So if one wants his vehicle to roll less, anti-roll bars, or the springs should be adjusted, but not the dampers. Something you can adjust with the damping rate is the speed at which the suspension rebounds: if a car with soft springs but hard dampers is pushed down, it will rebound very slowly, and a car with stiff springs and light damping will rebound very quickly. The same situation occurs when exiting corners: in the corner, the weight is transferred, and the chassis has rolled and/or dived, but when the steering is straightened out, and the cornering force disappears, the chassis comes back to its original position. The speed at which this happens is controlled by the damping rate. So the car with the soft springs and hard damping will tend to want to continue turning when the steering is straightened. It will also tend to continue running straight when steering is first applied; it will feel generally unresponsive, yet very smooth. The car with firm springs and soft damping will be very responsive: it will follow the driver‘s commands very quickly and aggressively. We may not always be able to use the spring and damping rates one like, because of bumps. Small, high-frequency bumps require soft settings for both damping and springs. We can‘t use such soft settings for big, harsh bumps, because the car would bottom out a lot, so we‘ll need to set our car a little stiffer. On very smooth tracks you can use very stiff settings for both springs and damping. But it‘s not quite as simple as that: even in the simple dampers used in R/C cars, there is a difference between high-speed and low-speed damping. They‘re also independently adjustable. Amity School of Engineering & Technology

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 Roll Centre Predicting how a car will react when forces are applied at the tires is not easy. The force can be absorbed, split, converted into a torque... by all sorts of suspension components. To avoid all of this one can try to find the roll centre of his car and try to predict the reaction of the car from there. A roll centre is an imaginary point in space; look at it as the virtual hinge the car hinges around when its chassis rolls in a corner. It's as if the suspension components force the chassis to pivot around this point in space. Let's look at the theory behind it first. The theorem of Kennedy tells us that if three objects are hinged together, there are at most three poles of movement, and they are always collinear, i.e. they are always on one line. To understand what a pole really is, consider the analogy with the poles of the earth: as earth rotates, the poles stay where they are. In other words, the earth rotates around the imaginary axis that connects the two poles. Now this is a 3-dimensional analogy, in the case of the roll centre we only need two dimensions at first. So a pole of an object (or a group of objects) is like the centre point of a circle it describes.

FIG. 8

Suspension of a typical Car

If we look at the suspension of a typical Formula car, with a lower A-arm and an upper link, we see a bunch of objects that are all hinged together. These objects include the chassis, the upper link, the A-arm, and the hub. For now we consider the hub, the axle and the wheel as one unit. First, let‘s look at the chassis, the upper link and the hub. They are hinged together, so the theorem of Kennedy Amity School of Engineering & Technology

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applies. The pole of the upper link and the hub is the ball joint that connects them, because they both hinge around it. The pole of the upper link and the chassis is also the ball joint that connects them. So if we now look at the chassis, the upper link and the hub, we have already found two of the three poles, so if there is a third one, it should be on the imaginary line that connects the other two. That line is drawn on the next drawing. The same applies to the bottom half of the suspension system, the pole of the lower A-arm and the hub is the outer hinge pin, the pole of the A-arm and the chassis is the inner hinge pin, so if there is a third pole it should be on the line that connects the other two. If the car uses ball links instead of hinge pins, the axis through the centres of the two balls makes up a virtual hinge pin.

FIG. 9

Intersection Point of Poles

If the two lines intersect, the pole of the hub/wheel and the chassis is the intersection point I. The distance from point I to the centreline of the tire is sometimes referred to as 'swing axle length‘, it's as if the hub/wheel is attached to an imaginary swing axle which hinges around point I. Having that long swing axle would be equivalent to having the double wishbone-type suspension, but the actual construction would be very impractical. Nevertheless it serves as a good simplification. The swing axle length, together with the angle, determines the amount of camber change the wheel will experience during the compression of the Amity School of Engineering & Technology

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Wheel Displacement (in)

suspension. A long swing axle length will cause very little camber change as the suspension is compressed, and a very short one will cause a lot. If the upper link and the A-arm are perfectly parallel to each other, the two lines won't intersect, or, in other words, the intersection point I is infinitely far removed from the car. This isn‘t a problem though: just draw the line (in the next drawing) parallel to the two. The two lines should always intersect on the side of the centre of the car, if they intersect on the outside, camber change will be bizarre: it will go from negative to positive back to negative, which is not a good thing for the consistency of the traction. 3 2 1 0 -1 0 -2 -3

2

4

6

8

Roll Centre Height(in)

Graph 1

Roll Centre V/s Wheel Displacement

The wheel and the ground can also move relative to each other; let's assume the wheel can pivot around the point where it touches the ground, which is usually in the middle of the tire carcass. That point is the pole of the tire and the ground. As it is drawn, a problem might arise when the chassis rolls: the tires might also roll, and hence the contact point between the earth and the tire might shift, especially with square-carcass tires that don't flex much. Now we can apply the theorem of Kennedy again: the ground, the wheel and the chassis are hinged together, we have already found the pole of the wheel and the ground, and the pole of the wheel and the chassis. If the pole of the ground and the chassis exists, it should be somewhere on the line that connects the other two poles, drawn in the next drawing.

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FIG. 10

Applying Theorem of Kennedy

The same procedure can be followed for the other half of the suspension, as in the picture below. Again a line will be formed on the pole of the ground and the chassis should be on. The intersection point of the two lines is the pole of the ground and the chassis. That point, the pole of the chassis and the ground is also called the roll centre of the chassis. Theoretically, the ground could rotate around it while the chassis would sit still, but usually it‘s the other way around; the chassis rotates around it while the ground sits still.

FIG.11

Obtaining Roll Centre

The roll centre is also the only point in space where a force could be applied to the chassis that wouldn‘t make it roll. The roll centre will move when the Amity School of Engineering & Technology

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suspension is compressed or lifted, that‘s why it‘s actually an instantaneous roll centre. It moves because the suspension components don‘t move in perfect circles relative to each other, most of the paths of motion are more random. Luckily every path can be described as an infinite series of infinitely small circle segments. So it doesn‘t really matter the chassis doesn‘t roll in a perfect circular motion, just look at it as rolling in a circle around a centre point that moves around all the time. If we want to determine the location of the roll centre of a car, we can either ‗eyeball‘ it by imagining the lines and intersection points, or you can get a really big sheet of paper and make a scale drawing of the car‘s suspension system. Now that we know where the roll centre (RC) is located, let‘ s look at how it influences the handling of the car. Imagine a car, driving in a circle with a constant radius, at a constant speed. An inertial force is pulling the car away from the centre point, but because the car is dynamically balanced, there should be a force equal but opposite, pulling the car towards the centre point. This force is provided by the adhesion of the tires.

FIG.12

Inertial Force

In principle, the inertia force works on all the different masses of the car, in every point, but by determining the centre of gravity (CG) it‘s possible to replace all of the inertia forces by one big force working in the CG. It‘s as if the total mass of the car is packed into one point in space, the CG. If the CG is determined correctly, both conditions should be perfectly equivalent. The forces generated by the tires can be combined to one force, working in the car‘s roll centre. Viewed from the back of the car, it looks like this: Amity School of Engineering & Technology

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FIG.13

Positioning of CG & RC

Two equal, but opposite forces, not working in the same point generate a torque equal to the size of the two forces multiplied by the distance between them. So the bigger that distance, the more efficiently a given pair of forces can generate a torque onto the chassis. That distance is called the roll moment. Note that it is always the vertical distance between the CG and the RC, since the forces always work horizontally.

FIG.14

Roll Moment

The torque generated by the two forces will make the chassis roll, around the roll centre. This rolling motion will continue until the torque generated by the springs is equally big, only opposite. The dampers determine the speed at which this happens. Note that the roll torque is constant, well at least in this example where the turning radius is constant, but the torque supplied by the spring increases as the suspension is compressed. The difference between the two torque‘s, the resultant, is what makes the chassis lean. This resultant decreases because the torque supplied by the spring‘s increases. So the speed at which chassis roll takes place always decreases and it reaches zero when both torques are equal. So for a given spring stiffness a big roll moment will make the chassis roll very far in the Amity School of Engineering & Technology

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corners, and a small roll moment will make the chassis lean over less. This also explains why a vehicle with a high CG has a tendency to lean very far in a corner, and possibly tip over. So at any given time, the size of the roll moment is an indication of the size of the torque that causes the chassis to lean over while cornering. Now, a different problem arises; the location of the roll centre changes when the suspension is compressed or extended, most of the time it moves in the same direction as the chassis, so if the suspension is compressed, the RC drops. When the car corners, and the chassis leans over, the RC usually moves away from the chassis‘ centreline.

FIG.15

Change in RC on cornering

Most R/C cars allow for the length and position of the upper link to be changed, and thus change the roll characteristics of the car. The following generalizations apply in most cases. An upper link that is parallel to the lower Aarm will make the RC sit very low when the car is at normal ride height, hence the initial body roll when entering a corner will be big. An upper link that is angled down will make the RC sit up higher, making the initial roll moment smaller, which makes that particular end of the car feel very aggressive entering the corner. A very long upper link will make that the roll moment stays more or less the same size when the chassis leans over; that end of the chassis will roll very deeply into the suspension travel. If not a lot of camber is used, this can make the tires slide Amity School of Engineering & Technology

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because of excessive positive camber. A short upper link will make that the roll moment becomes a lot smaller when the chassis leans; the chassis won‘t roll very far. Until now, we‘ve ignored the fact that there are two independent suspension systems in a car; there‘s one in the front and one in the rear. They both have their own roll centre. Because the ‗chassis‘ parts of both systems are connected by a rigid structure, the chassis, they will influence each other. Some people tend to forget this when they‘ re making adjustments to their cars; they start adjusting one end without even considering what the other end is doing. Needless to say this can lead to anomalies in the car‘s handling. Having a very flexible chassis can hide those anomalies somewhat, but it‘s a far cry from a real solution. Anyway, the front part of the chassis is forced to hinge on the front RC, and the rear part is forced to hinge on the rear RC. If the chassis is rigid, it will be forced to hinge on the axis that connects both RC‘s, that axis is called the roll axis.

FIG.16

Roll Axis: Side View

The position of the roll axis relative to the cars CG tells a lot about the cornering power of the car; it predicts how the car will react when taking a turn. If the roll axis is angled down towards the front, the front will roll deeper into its suspension travel than the rear, giving the car a ‗nose down‘ attitude in the corner. Because the rear roll moment is small relative to the front, the rear won‘t roll very far; hence the chassis will stay close to ride height. Note that with a car with very little negative suspension travel (droop) the chassis will drop more efficiently when the car leans over. With the nose of the car low and the back up high, a bigger percentage of the cars weight will be supported by the front tires, more tire pressure means more grip, so the car will have a lot of grip in the front, making it Amity School of Engineering & Technology

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oversteer. A roll axis that is angled down towards the rear will promote understeer. Remember that the position of the roll centres is a dynamic condition, so the roll axis can actually tilt when the car goes through bumps or takes a corner, so it‘s possible for a car to understeer when entering the corner, when chassis roll is less pronounced, and oversteer in the middle of the corner because the front RC has dropped down a lot. This example illustrates how roll centre characteristics can be used to tune a car to meet specific handling requests, from either the driver or the track. In general, we could say that the angle of the upper link relative to the Aarm determines where the roll centre is with the chassis in its neutral position, and that the length of the upper link determines how much the height of the RC changes as the chassis rolls. A long, parallel link will locate the RC very low, and it will stay very low as the car corners. Hence, the car (well at least that end of the car) will roll a lot. An upper link that‘s angled down and very short will locate the RC very high and it will stay high as the chassis rolls. So the chassis will roll very little. Alternatively, a short, parallel link will make the car roll a lot at first, but as it rolls, the tendency will diminish. So it will roll very fast at first, but it will stop quickly. And a long link that‘s angled down will reduce the car‘s tendency to roll initially, but as the chassis rolls it won‘t make much of a difference anymore. In terms of car handling, this means that the end where the link is angled down the most (highest RC) has the most grip initially, when turning in, or exiting the corner, and that the end with the lowest RC when the chassis is rolled will have the most grip in the middle of the corner. So if you need a little more steering in the middle of the corners, lengthen the front upper link a little. (Be sure to adjust camber afterwards) If you‘d like more aggressive turn-in, and more low-speed steering, either set the rear upper link at less of an angle, or increase the front link‘s angle a little. Now you might ask yourself: what‘s the best, a high RC or a low one? It all depends on the rest of the car and the track. One thing is for sure: on a bumpy track, the RC is better placed a little higher; it will prevent the car from rolling from side to side a lot as it takes the bumps, and it will also make it possible to use Amity School of Engineering & Technology

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softer springs which allow the tires to stay in contact with the bumpy soil. On smooth tracks, one can use a very low RC, combined with tiff springs, to increase the car‘s responsiveness and jumping ability.  Anti-squat It describes the angle of the rear hinge-pins relative to the horizontal plane. Its purpose is to make the car squat less when accelerating. (Squatting is when the rear of the car drops down when the car accelerates) More anti-squat will give more ‗driving traction‘: there will be more pressure on the rear tires as you accelerate, especially the first few meters. At the same time, it will give more onpower steering, because the car isn‘t squatting much. The disadvantage is that the car has an increased tendency to become unstable entering corners, especially in the rear. Reducing the anti-squat angle has the opposite effect: a lot less on power steering, and more rear traction when the car isn‘t accelerating as much anymore. The car will also be a lot more stable entering corners. It also affects the car‘s ability to handle bumps: more anti-squat will cause the car to bounce more when accelerating through bumps, but it will increase the car‘s ability to absorb the bumps when coasting. Reducing the anti-squat does the opposite: it improves the car‘s ability to soak up the bumps under power, but reduces it while coasting.  Suspension Travel The amount of negative suspension travel (downtravel) a car has can have a huge effect on its handling; it influences both the mount of roll and the amount of pitch the chassis will experience. With a lot of downtravel, as the chassis rolls into a turn, the height of the CG doesn‘t change very much. With almost no downtravel, as it rolls into a turn, the chassis is pulled down as it rolls, effectively lowering the CG. So, if one end of the car has less downtravel than the other, that end will be forced down more in a turn, which makes for more grip at that end, especially in the middle part of the turn, where weight transfer is more pronounced. Very little downtravel at the front will give a lot of steering, especially when entering a corner at high speed, or very violently. Very little downtravel at the rear will give a lot, and consistent traction throughout the turn. Amity School of Engineering & Technology

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But that isn‘t all there is to it: the amount of suspension travel also influences the car‘s longitudinal balance, i.e. when braking and accelerating. An end with a lot of downtravel will be able to rise a lot, so chassis pitch will be more pronounced, which in turn will provide more weight transfer. For example: if the front end has a lot of downtravel, it will rise a lot during hard acceleration, transferring a lot of weight onto the rear axle. So the car will have very little onpower steering, but a lot of rear traction. A lot of downtravel at both ends, combined with soft springs, can lead to excessive weight transfer: on-power understeer, and off-power oversteer. The cure is simple: either reduce downtravel, or use stiffer springs. There are also some disadvantages of having very little suspension travel: the bump handling and the car‘s jumping ability may suffer, it will bottom out very easily.  Anti-roll Bars Anti-roll bars are like ‗sideways springs‘, they only work laterally. Here‘s how they work: if one side of the suspension is compressed, one end of the bar is lifted. The other end will also go up, pulling the other side of the suspension up also, basically giving more resistance to chassis roll. How far and how strongly the other side will be pulled up depends on the stiffness and the thickness of the bar used: a thin bar will flex a lot, so it won‘t pull the other side up very far, letting the chassis roll deeply into its suspension travel. Note that the bar only works when one side of the suspension is extended further than the other, like when the car is cornering. When both sides are equally far compressed; like, when the car is braking, the bar has no effect. So anti-roll bars only affect the lateral balance of the car, not the longitudinal balance. Unfortunately, anti-roll bars aren‘t the only things affecting the car‘ s roll stiffness; they work in conjunction with the springs and dampers. Suppose we add an anti-roll bar at the rear of the car without changing any of the other settings. When the car enters a turn, the chassis starts to roll. Normally, the suspension on the outside of the turn would compress, and the one on the inside would extend, making for a lot more pressure on the outside tire. With the anti-roll bar however, the suspension on the inside will be Amity School of Engineering & Technology

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compressed, so the chassis will roll less, and the rear of the car will sit lower than normal. So the rear has more weight on it, and it‘s distributed more evenly over the two tires. This makes for a little more and more consistent traction. Remember that this is in the beginning of the turn; the situation is different in the middle of the turn. Normally, without the anti-roll bar, the chassis would stop rolling when the roll torque is fully absorbed by the outside spring. But with the anti-roll bar, some of that torque is absorbed by the anti-roll bar, and used to compress the inside suspension. So the outside suspension won‘t be compressed as much as it normally would, making the rear of the chassis sit up higher than normal, so less weight is on the rear of the car, and more at on the front. It‘s as if suddenly the rear has become stiffer, making for more steering and a little less rear traction.

FIG.17

Anti-Roll bar

Rear traction is more consistent however, because the weight is distributed more evenly over the rear tires, unless the track is really bumpy, that is; anti-roll bars can really mess up a car‘s rough track handling, so they‘re rarely used on bumpy tracks. Adding an anti-roll bar at the front of the car has a similar, but opposite effect: it decreases steering, but makes it much smoother and more consistent. Amity School of Engineering & Technology

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 Shock mounting locations Most R/C vehicles have several possible mounting points for the shock absorbers, both at the upper mount (area 1) and at the A-arm (area 3). By mounting the shocks in a different position, spring action can be altered. The question is: how will this affect the handling, or the ‗feel‘ of the car? To understand this, first you need to know about wheel rates. A wheel rate is an equivalent spring rate at the wheel; it‘s the spring rate of a spring that would give the same stiffness as the current one, if it was to be attached right at the centreline of the wheel. After all, that‘s where the traction forces act: at the wheel.

FIG.18

Shock Mounting Locations & Wheel Rates

A wheel rate is defined as (motion ratio)² * spring rate * sin(spring angle), and motion ratio is the distance between the lower shock mounting position and the inner hinge pin divided by the distance between the inner hinge pin and the tyre‘s centreline. The spring angle is the angle between the shock and the lower A-arm. Wheel rate = spring rate * (D1/D2)² * sin a Amity School of Engineering & Technology

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This formula tells us two things: 1. The more the shocks are inclined, the softer the wheel rate. 2. The closer the bottoms of the shocks are mounted to the middle of the chassis, the softer the spring rate. Note that if we change the lower shock mounting location, we change both the shock angle and the motion ratio, but it's usually the change in motion ratio that has the biggest effect. This also shows in the formula: the motion ratio is squared, and the spring angle isn‘t. The amount of suspension travel also changes, which can also affect the car's handling. The shock angle isn't constant either: it gets bigger as the suspension is compressed. This effect is more pronounced as the shocks are more laid down, so the more inclined the shocks are, the more progressive the wheel rate will be. So think of the top mounting positions as a means of fine-tuning spring and damper rates, and changing the progressiveness. Keep in mind this isn't perfectly correct: if the centreline of the tire doesn't intersect with the outer hinge pin, a considerable part of the forces acting on the tire are transmitted to the chassis along the upper link. Nevertheless, it's a very good approximation. Since the shocks' angle changes their progressiveness, it also influences the shaft speed: if the shock is laid down (progressive), shaft speed will increase as the shock is compressed, if it is close to vertical (linear), shaft speed won't vary a lot with suspension travel. Obviously, this affects high-speed damping too; it affects when the transition from low-speed to high-speed damping occurs. It will occur earlier when the shock is closer to vertical, because when it is inclined, it takes some time (and some positive suspension travel) for the shaft to ' speed up', and reach the same shaft speed. So inclining the shocks more has more or less the same effect as using a piston with slightly bigger holes, and mounting it more upright has the same effect as using a piston with slightly smaller holes. We find that changing the lower mounting location of the shocks comes in handy sometimes when we want to change the amount of negative suspension travel, but we don't feel like altering the length of the shock, or when we need the springs to be just a little stiffer or softer. Changing the top mounting location is a Amity School of Engineering & Technology

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very subtle adjustment, we like to change it after all of the other, more important adjustments have been made, and the car is handling more or less the way we want it to. It's especially helpful to alter the 'feel' of the steering entering corners. Now we don't know if this applies when the springs' action is very progressive, but the more the shocks are stood up (less inclined), the more direct their action will be entering the corner. For instance: if the front shocks are close to vertical, and the rears are somewhat laid down, the car will have a lot of turn-in steering; it will be very responsive. If the rears are close to vertical, and the fronts are more laid down, the car won't have a lot of turn-in, but it will have more steering in the middle of the turn; it will 'square' . In some cases, the rear might actually begin to slide. It works much in the same way as having stiff springs or heavy damping: if you have stiff springs, or heavy damping up front, the initial reaction when you enter a turn will be very strong. In the middle part of the corner the car will probably understeer, but it's the initial reaction that gives the car a 'responsive' character. Even roll centre works this way: a very high roll centre in the front will make the car turn in very aggressively, but understeer in the middle of the corner. It's nice if one likes an aggressive car one can ' throw' into the corners, but we doubt it‘s the fastest way round the track. Conversely, if the rear roll centre is set very high, the car will turn in very gently, and possibly oversteer after that.

FIG.19 5

Ferrari 663

Mobility of Formula Suspension Mechanisms Suspension systems are in general three-dimensional mechanisms and as such are difficult to analyze fully without the aid of computer packages. Their analysis is complicated by the inclusion of many compliant bushes which effectively result in links having variable lengths. Amity School of Engineering & Technology

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Notwithstanding these complications it is possible to gain an appreciation of the capabilities and limitations of various mechanisms used in suspension design by neglecting bush compliances and concentrating on the basic motion of suspension mechanisms. A fundamental requirement of a suspension mechanism is the need to guide the motion of each wheel along a (unique) vertical path relative to the vehicle body without significant change in camber. This requirement has been addressed by employing various single degree of freedom (SDOF) mechanisms which have straight line motion throughout the deflection of the suspension. Despite the apparent complexity of some suspension systems, a basic understanding of their kinematics can be derived from a two-dimensional analysis, i.e. by considering the motion in a vertical transverse plane through wheel centre. Fundamental to this analysis is an understanding of how the number of degrees of freedom (mobilityin mechanisms parlance) of a mechanism are related to the number of links and the types of kinematic constraint imposed on them. In general the aim is for a SDOF or a mobility of one. Mechanisms which have a mobility of zero are structures, i.e. not designed for motion, while those having two degrees of freedom require two prescribed inputs to position them uniquely. This is not desirable for suspensions. Most of the kinematic connections between the members of a suspension mechanism can be reduced down to the kinematic pairs. Each has an associated number of degrees of freedom and can be classified as lower pairs (connections having a SDOF) or higher pairs (more than one DOF). It has been shown that the mobility M, of a plane mechanism forming a closed kinematic chain, is related to the number of links n, the number of lower pairs jl and the number of higher pairs jh. According to the Kutzbach criterion: M= 3(n –1) – jh-2jl For spatial (three dimensional) mechanisms there is an equivalent equation. The use of equation can be illustrated with reference to the double wishbone and MacPherson strut suspensions. Both suspensions can be seen to represent a single closed kinematic chain. In the case of the double wishbone suspension, there are four links, AB, BC, CD and DA forming a four-bar chain , i.e. n= 4. Each of the four joints are of the revolute type (lower pairs) and hence jl = 4. There are no Amity School of Engineering & Technology

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higher pairs and therefore jh = 0. Substituting into above equation gives M = 3 ×(4 –1) –0 ×(2 ×4) = 1, i.e. a SDOF mechanism. In the kinematically equivalent mechanism for the MacPherson strut thetelescopic damper is replaced with an extension of the wheel attachment to pass through a trunnion (a 2DOF joint) at C. The mechanism thus has three links AB, BC and CA, i.e. n= 3. There are two lower pairs (one at A and one at B) and one upper pair (at C). This gives jl = 2 and jh = 1. Hence M= 3 ×(3 –1) –1 –(2 ×2) = 1, i.e. a SDOF mechanism. While mobility analysis is useful for checking for the appropriate number of degrees of freedom, it does not help in developing the geometry of a mechanism to provide the desired motion.For suspension mechanisms this process is called position synthesis and requires the use of specialized graphical and analytical techniques, aided by computer software. This departure from the well established suspension types is only required when it is necessary to produce enhanced suspension characteristics, e.g. to produce changes in camber and toe under certain operating conditions to improve handling.

Double Wishbone Suspension for Formula Car The autocross course is constructed of several components that are typically found in formula racing: straight-aways, slaloms, constant radius turns, hairpin turns, chicanes, multiple turns, and varying radius turns. The suspension of a Formula One car has all of the same components as the suspension of a road car. Those components include springs, dampers, arms and anti-sway bars. To keep things simple here, we'll say that almost all Formula One cars feature double wishbone suspensions. Before any race, a team will tweak suspension settings to ensure that the car can brake and corner safely, yet still deliver responsiveness of handling. Following the ban on computer-controlled 'active' suspension in the 1990s, all of the Formula car's suspension functions must be carried out without electronic intervention. The cars feature 'multi-link' suspension front and rear, broadly equivalent to the double wishbone layout of some road cars, with unequal length suspension arms top and bottom to allow the best possible control of the camber Amity School of Engineering & Technology

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angle the wheel takes during cornering. As centrifugal force causes the body to roll, the longer effective radius of the lower suspension arms means that the bottom of the tyre (viewed from ahead) slants out further than the top, vital for maximising the grip yielded by the tyre. A double wishbone (or upper and lower A-arm) suspension is an independent suspension design using two (occasionally parallel) wishbone-shaped arms to locate the wheel. Each wishbone or arm has two mounting points to the chassis and one joint at the knuckle. The shock absorber and coil spring mount to the wishbones to control vertical movement. Double wishbone designs allow the engineer to carefully control the motion of the wheel throughout suspension travel, controlling such parameters as camber angle, caster angle, toe pattern, roll center height, scrub radius, scuff and more.

FIG.20

Double Wishbone Suspension Coil Spring Solidworks Model

The double-wishbone suspension can also be referred to as "double A-arms," though the arms themselves can be A-shaped, L-shaped, or even a single bar linkage. The upper arm is usually shorter to induce negative camber as the suspension jounces (rises), and often this arrangement is titled an "SLA" or "short long arms" suspension. When the vehicle is in a turn, body roll results in positive

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camber gain on the lightly loaded inside wheel, while the heavily loaded outer wheel gains negative camber. Between the outboard end of the arms is a knuckle with a spindle (the kingpin), hub, or upright which carries the wheel bearing and wheel. To resist fore-aft loads such as acceleration and braking, the arms require two bushings or ball joints at the body. At the knuckle end, single ball joints are typically used, in which case the steering loads have to be taken via a steering arm, and the wishbones look A- or Lshaped. An L-shaped arm is generally preferred on passenger vehicles because it allows a better compromise of handling and comfort to be tuned in. The bushing inline with the wheel can be kept relatively stiff to effectively handle cornering loads while the off-line joint can be softer to allow the wheel to recess under foreaft impact loads. For a rear suspension, a pair of joints can be used at both ends of the arm, making them more H-shaped in plan view. Alternatively, a fixed-length driveshaft can perform the function of a wishbone as long as the shape of the other wishbone provides control of the upright. In elevation view, the suspension is a 4bar link, and it is easy to work out the camber gain and other parameters for a given set of bushing or ball-joint locations. The various bushings or ball joints do not have to be on horizontal axes, parallel to the vehicle centre line. If they are set at an angle, then antidive and antisquat geometry can be dialed in. In many formula cars, the springs and dampers are relocated inside the bodywork. The suspension uses a bellcrank to transfer the forces at the knuckle end of the suspension to the internal spring and damper. This is then known as a "push rod" if bump travel "pushes" on the rod (and subsequently the rod must be joined to the bottom of the upright and angled upward). As the wheel rises, the push rod compresses the internal spring via a pivot or pivoting system. The opposite arrangement, a "pull rod," will pull on the rod during bump travel, and the rod must be attached to the top of the upright, angled downward.

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FIG.21

Double Wishbone Suspension Rear View

Locating the spring and damper inboard increases the total mass of the suspension, but reduces the unsprung mass, and also allows the designer to make the suspension more aerodynamic. Modern Formula car suspension is minutely adjustable. Initial set-up for a track will be made according to weather conditions (wet weather settings are far softer) and experience from previous years, which will determine basic spring and damper settings. These rates can then be altered according to driver preference and tyre performance, as can the suspension geometry under specific circumstances. Set-up depends on the aerodynamic requirements of the track, weather conditions and driver preference for understeer or oversteer - this being nothing more complicated than whether the front or back of the car loses grip first at the limits of adhesion.

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FIG.22

Double Wishbone Suspension With Pull Rod Arrangement

 Multi-Link Suspension This is the latest incarnation of the double wishbone system. The basic principle of it is the same, but instead of solid upper and lower wishbones, each 'arm' of the wishbone is a separate item. These are joined at the top and bottom of the spindle thus forming the wishbone shape. The super-weird thing about this is that as the spindle turns for steering, it alters the geometry of the suspension by torquing all four suspension arms. They have complex pivot systems designed to allow this to happen.

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FIG.23

Double Wishbone Suspension Multi-link Solidworks Model

Car manufacturers claim that this system gives even better road-holding properties, because all the various joints make the suspension almost infinitely adjustable. There are a lot of variations on this theme appearing at the moment, with huge differences in the numbers and complexities of joints, numbers of arms, positioning of the parts etc. but they are all fundamentally the same. Note that in this system the spring is separate from the shock absorber.

Optimised Suspension Geometries for Formula Car Choosing which system best suits our project involves a number of factors, from which we select an SLA (short-long arm) set-up. The first factor was in our application where, in this type of autocross race, the SLA design is very popular Amity School of Engineering & Technology

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and suits the track conditions well. The rack and pinion steering system since it was the most common for an SLA setup and it kept us within budget. There are seven different geometric configurations possible for a front SLA suspension system. In order to narrow down our choices, we tested wheel displacement verses both camber and roll center. We decided that these two characteristics were the most important factors since they are essential in the handling of the car. After reviewing our results, we were able to narrow our system down to three possibilities. In the following table, all seven SLA geometries are illustrated. The geometric setup shown third is the suspension system that is generally usied.[5]

Suspension Set-Up

Wheel Displacement

Camber

Roll Center Negative

None Positive

Always Negative

Always Positive

Always Positive

Positive Majority of the Displacements

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Always Negative

Negative Majority of the Displacements

TABLE 1

Geometries of Double Wishbone SLA Suspension

One of the most difficult parts of designing a suspension system is compromising. There is no optimum suspension for all conditions; therefore, for every improvement there is a sacrifice. The key is to decide what is most important for your particular application. In our case, we had to account for a race on a smooth track that contains many tight turns but can be subject to a variety of weather conditions. To fulfill our goal of maintaining the largest accelerations possible, we examined the many components of a suspension design (the definitions of these terms are conveniently defined during the discussion). The first heavily debated design component examined was the roll axis, a line that connects the front and rear roll centers, around which the car body rotates when lateral forces are applied. The roll center is defined as the effective center that the body will appear to rotate about. For roll centers with small radii, one could image a box suspended by two short strings at two corners suspended as something of a pendulum. The longer the string, the larger the pendulum, and the more minute the angular displacements the box will achieve. As shown below, the body roll Theta 1 is greater than Theta 2 with a longer roll center located below ground level.

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Fig 24

Optimised Roll Centre Location

A small amount of negative camber is desirable in a turn, as determined through a tire manufacturer‘s data.

However, the geometry must be such that the camber is zero for straight driving. If camber exists even when the car is not turning, the tire patch area is reduced and maximum possible traction is not attained. This also leads to uneven tire wear results. The desirable aspect of camber is that it can be used to increase tire patch area when the vehicle experiences body roll. To achieve this effect, camber must be positive when wheel displacement is negative (wheel droop), and negative when wheel displacement is positive (jounce). Below is a graph for a formula car suspension system. It achieves slightly more than a degree of camber per inch of displacement. Comparing this slope to the tire data in, the results support that an increase in lateral force can be achieved.

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Fig 25

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Tire Data

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Wheel Displacement (in)

-4

-2

3 2 1 0 -1 0 -2 -3

2

4

Camber (degrees)

Graph 2

Camber v/s Wheel Displacement

Many complications are added to the suspension geometry where the steering control arms and rack are located. One of the biggest effects it can cause is ―toe-in/out‖, commonly known as ―bump steer‖. ―Toe-in‖ is when the front of the tires angle in towards each other, and ―toe-out‖ is when they angle away from each other. It is undesirable to have the tires independently steer the vehicle when the vehicle hits bump. This characteristic complicates tuning the vehicle by adding responses that are unpredictable to the driver. Both kinds of toe are a result of the position of the steering linkages. Since we are using an existing steering rack, its position has several constraints. To steer the vehicle, the control arms must be a distance from the axis about which the tire turns specifically the king pin inclination (KPI) to induce a moment, thus turning the car. As the figure below demonstrates, the kingpin inclination affects scrub radius, which is pre-determined by re-using the vertical uprights.

Fig 26 Amity School of Engineering & Technology

Scrub radius Page 45

Wheel Displacement (in)

Bump steer is a very difficult characteristic to accommodate. In a majority of geometries tested, the amount of bump steer cannot be zero for all wheel displacements. Therefore, we designed our suspension system with a minimal amount of Toe-In/Toe-Out by placing the rack where the pivots for inner and outer tie rod match the control arm pivot axis. In standard formula car designs, there has been as much as 3.5 degrees of toe-out over a 2-inch wheel displacement. Our results were a considerable improvement since our design has less than a 0.4degree angle over 4-inch wheel displacement. This amount will not noticeably affect the handling of the vehicle.

-0.4

-0.3

-0.2

3 2 1 0 -0.1 -1 0 -2 -3

0.1

0.2

Toe-In/Out (degrees)

Graph 3

Toe-In/Out v/s Wheel Displacement

Another aspect that must be considered is the caster angle. The combination of the caster angle and kingpin inclination greatly affects the handling of the car. Both are very important since they influence the steering forces during lateral acceleration and the self-centering effect of the steering. As with Toe, it is desirable to minimize both the caster angle and the kingpin angle for all wheel displacements. The combination of the two has a large effect on the rate of camber change during wheel displacement. The final design uses pneumatic trail to provide steering center effect at higher speeds. Pneumatic trail differs from the mechanical trail defined by the KPI and caster angle by specific tire characteristics. Pneumatic trail is a result of the tire patch area shape. The patch area roughly forms a triangle, thus providing a wedge effect with the ground and provides a horizontal centering force. Both types of trails act as weather vanes to the steering wheel but have varying effects at over a given range of speed. Mechanical trail is dominant at low speeds while pneumatic Amity School of Engineering & Technology

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Wheel Displacement (in)

trail at high speeds. Skid warning is also maintained by minimizing mechanical trail, and since the effect of pneumatic trail is non-linear with vehicle speed, the driver will be able to sense when there is a significant decrease in pneumatic trail. This provides an important source of driver feedback at higher speeds, and the vehicle will exhibit under steer and feel ―loose‖.

-0.04

Wheel Displacement (in)

Graph 4

-4

3 2 1 0 -0.02 -1 0 0.02 0.04 -2 -3 Caster Angle (degrees)

0.06

Caster Angle v/s Wheel Displacement

-2

3 2 1 0 -1 0 -2 -3

2

4

Kingpin Angle (degrees)

Graph 5

Kingpin Angle v/s Wheel Displacement

 Design Overview Static weight The load transfer calculations use the following parameters to model the forces generated. The static forces are calculated using a driver weight of 80 Kg, vehicle weight of 240Kg estimated from existing vehicles, front-to-rear weight distribution

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50/50, and left-to-right weight distribution 50/50. The height of the CG is estimated from the average of the moment of inertias of major components. Height of CG =11”

Wheel Base (WB) = 65”

Weight Driver (WD) = 80 kg

Front Track – 50”

Weight Vehicle (WV) = 240 kg

Rear Track – 51.6”

Total Vehicle Weight (TVW) = WD + WV = 320

Front Static Roll Center = 4

Front Bias = 0.5

Rear Static Roll Center = 6

Rear Bias = 0.5

Positive Acceleration = 1.5

Left Bias = 0.5

Negative Acceleration = 1.5

Right Bias - 0.5

Lateral Acceleration = 1.5

Table 2

Acceleration Data used for Calculations

Lateral load transfer due to lateral acceleration

Fig 27

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Plot of Relevant Forces

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The lateral forces generated act through the center of gravity and are summed as a torque, or moment, to determine the vertical force on a tire. The moments are summed about the roll center axis when roll centers are determined at a static height. The two moments are summed to find Ftire and then split front to rear by multiplying by the bias ratio. The lateral acceleration has been set to a high value of 1.5 times the force of gravity, 1.5 g‘s. This number is used as a safety factor since the car will not encounter more than 1.2 g‘s of force. Front

Rear

L1 = Lcg – Lrc,f = 6

L3 = Lcg – Lrc,r = 4

L5 = 11

L2 = front track/2 = 25

L4 = rear track/2 = 25.8

L6 = WB*front bias = 32.5

F1 = a1*(Fz,sfl + Fz,sfr) =521.25

F2 = a1*(Fz,srl + Fz,srr) = 521.25

L7 = WB*rear bias = 32.5

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

Table 3

Vertical Tire Force Calculation

Fz, Lateral Acceleration Loads, steady state Front, 1 tire = 51.30413 Rear, 1 tire = 51.30413

Table 4

Lateral Acceleration Loads

Longitudinal weight transfer due to negative acceleration

Fig 28 Amity School of Engineering & Technology

Tire Force Schematic

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The rear-to-front weight transfer due to braking is a sum of moments about the y-axis and is defined by the intersection of the x-coordinate of the CG projected on the ground. Fz, Longitudinal weight transfer, negative acceleration, steady state Front = 264.6346

Front Left = 132.3173

Front Right = 132.3173

Rear = -264.635

Rear Left = -132.317

Rear Right = -132.317

Table 5

Longitudinal Weight Transfer

Maximum loads achieved The maximum vertical loads that could be reached correspond to the combined forces of negative and lateral accelerations with the static weight of the vehicle. Fz, Maximum achievable loads; lateral + negative accelerations static + lateral + negative Front Left = 357.3714

Front Right = 357.3714

Rear Left = 92.73683

Rear Right = 92.73683

Table 6

Maximum Achievable Loads

Maximum Tractive Forces The traction generated by a tire (Fx,y) is a function of vertical force exerted on a tire and the coefficient of friction () between the tire and ground. The coefficient of friction is a function of many variables including velocity, temperature, and tire wear. Wet, dry, and/or sandy surface conditions also serve as variables. The coefficient is estimated to be high at 1.5 so that the x and y components of the forces developed are high, since these forces will be used when determining component materials and dimensions as an added margin of safety. Amity School of Engineering & Technology

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Fig 29

Schematic of tire with axes Horizontal tire force, Fx,y (lbs)

Fy: Cornering = u*(static + lateral acceleration loads) Front Left = 337.5812

Front Right = 337.5812

Rear Left = 337.5812

Rear Right = 337.5812

Fx,y: Cornering & braking=u*(static + lateral + negative acceleration loads) Front Left = 536.0572

Front Right = 536.05716

Rear Left = 139.1052

Rear Right = 139.10524

Fx: Braking = u*(static + negative acceleration loads) Front Left = 459.101

Front Right = 459.10096

Rear Left = 62.14904

Rear Right = 62.149038

Table 7

Horizontal Tire Force

Factor of Safety Development To determine the factor of safety we will assume worst-case scenarios for the loading of each component. Specifically the vehicle is under hard braking and hits a pothole or cone. This example exhibits a realistic case for a high performance Amity School of Engineering & Technology

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vehicle and parking lot track condition. The following is part of the analysis of the design of a front pushrod element. The following forces are developed in the push-rod member during full spring compression and max damping setting on the Fox Racing shock: F=n*(k*x + c*velocity) Where, k is the spring constant, x is displacement, c is the damping coefficient, and n is the rocker ratio. The damping force is obtained through the manufacturer‘s supply of damper dyno charts and the spring rate is 39.55 N/m with maximum x displacement of two inches. To use a worst case scenario we will assume the vehicle bottoms out, that is max displacement of two inches is achieved, the damping is set at max 12 clicks closed, and the rocker ratio is three. F  3(39.55 * 2  409)  1464.3N

The pushrod is under buckling in a pin-pin configuration, thus using BernoulliEuler technique: Pcrit 

EI L2

(1)

Using this method with an aluminum ¾‖ diameter pushrod member 14‖ long will result in a factor of safety of four. For this worst-case scenario prediction, we are able to find a factor of safety by dividing the maximum load/static load to essentially get a factor of safety for each member. Where the factor of safety was less than three, the member was re-designed until this criterion was met.

A-Arm Force Calculations In order to compute the thickness necessary for each arm, the maximum forces had to be computed. After the forces were found, we used the largest one to calculate the diameter needed. A factor of safety of three was used. The relationship between the force in the arm and its area is as follows: 

Amity School of Engineering & Technology

P Mc  A I

(2) Page 52

The area can then be used to compute the needed diameter. The forces were found using standard static analysis equations. The four defining equations are as follows:

F

0

F

0

x

y

F

z

M

0

o

0

(3) (4) (5) (6)

They state that the sum of the forces in x, y, and z directions must be zero. The last equation states that the sum of the moments about any point in the system must be equal to zero. The figure below shows the forces involved and their relationship to each other.

Fig 30

Force Schematic & Truss Design

According to the force equations, we determined that the maximum force in any arm of the A-arms was 4009N. Our computations were completed using just a basic A-Arm with no truss braces. Therefore, when we discuss the maximum force in any of the arms, we mean the two major arms of the A-Arm. The truss design Amity School of Engineering & Technology

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was incorporated to cut down on the moments acting on the arm. Since that force was the maximum attained for any member, we used it for all calculations. This insured that all members would be able to handle the maximum possible force encountered. Using the maximum forces, the diameter needed for the A-arms was then calculated. The A-arms were treated as a pin-pin beam, since they are connected with ball joints on each end. Ball joints do not act against moments, similar to the behavior of a pin. The Bernoulli-Euler buckling criterion is given in Eq.1, where I is the moment of inertia. For a round member: 1 I   r4 2

(7)

Using equation 2, we determined the thickness needed for each type of material that we had considered. Also shown is the weight of an arm of the needed diameter. The results are shown in the figure below for the 14-inch arm. The results are based on a maximum force of 4009N and a factor of safety of 3. Therefore, the force calculated for a pin-pin beam is less than 12.027 kN of force. Material

Modulus of Elasticity Diameter

Weight

Aluminum 172.34 GPa

1.62 cm

2.02N

AZ91

146.14 GPa

1.82 cm

1.66N

Steel

308.167 GPa

1.242 cm

3.32N

Table 8

Material Properities for a 14 inch pin-pin beam

Front Uprights One of the critical factors we used to determine the best material was the strength to weight ratio of each material. We computed this by dividing the amount of force in the member by the weight required to hold that load. This determined that AZ91 alloy magnesium is the best of the three materials. In the end, other factors weighed into the decision of what material to use and AZ91 was not selected for the steering arms or the push rods. Further detail on this topic is Amity School of Engineering & Technology

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discussed in the steering arm and push rod sections. AZ91 was selected for the front and rear uprights as well as the A-Arms.

Fig 31

Front Uprights

The front uprights are usually made of AZ91 magnesium to cut down on the weight of the vehicle. We modified the design heavily to incorporate a more adjustable steering arm. The uprights are the centerpieces of the suspension system; they transfer the forces from the tire to the A-arms. Their geometry is very important to the handling characteristics of the car. Magnesium was used for the uprights since they are a part that is cast to the specific form that is needed. Casting was an excellent option since the uprights are not a simple shape that can be easily machined. They also can be cast very close to the exact shape needed. This leads to minimal machining which saves both cost and time. Amity School of Engineering & Technology

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Fig 32

Front Uprights CATIA V5 Model Static Load Test

Rear Uprights

Fig 33 Amity School of Engineering & Technology

Rear Uprights Page 56

The rear upright must only travel within the range that the drive shafts of rear differential can handle. The suspension characteristics of the rear end were modified, but this was done in other ways. If the mounting points on the body are different a different geometrical configuration is obtained. We did this to customize the handling characteristics, as we wanted them. Magnesium was used for the same reasons discussed in the front upright section.

Fig 34

Rear Uprights CATIA V5 Model Static Load Test

Rockers The rocker design is a prototype at a design level rather than a final model. The final model is based on the dynamic vehicle testing to optimize the wheel to shock travel ratio that can be changed from 1.3:3 to 3:1.8 in .5 increments. The design permits the use of a single two-inch travel spring and damper unit to perform in a spring rate range of 16.95N/m to 65.87N/m while retaining the required two inches of wheel travel. This variable system is a design common to some teams and combines manufacturing time savings with material cost savings by using only one rocker to do the same work as six individually cast rockers.

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Fig 35

Rockers

Push rods The pushrods are the member that transmits the vertical force of the tire to the spring/damper unit. As a result this member is subject to buckling loads in a pin-pin configuration. If weight was the only factor we considered then we would have used AZ91 for the push rods. We ended up using aluminum push rods for a number of reasons. A major reason is the availability of materials. Aluminum is readily available, but magnesium would have to be cast to a specific length. The availability factor also leads us to aluminum since we want components that can easily be repaired or replaced at the race. Repairs are very difficult with magnesium since it is not a weldable metal. Aluminum allowed us more versatility since we could make new arms quickly. We wanted to be able to change the rod lengths if needed to adjust the system. Aluminum is much less expensive than magnesium.

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Fig 36

Rebound Damping

The push rod design is based on keeping the system highly adjustable. The push rod is a rod with a left-handed thread on one side and a right-handed thread on the other. With this setup twisting one way enlarges the length of the rod and twisting the other decreases the length. A nut is tightened on each end to prevent it from adjusting while racing due to vibrations. The steering arms are designed with this same setup.

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Fig 37

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Compression Damping

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Fig 38

Fig 39

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Pushrods

Bell Crank FEA Results

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Fig 40

Motion Ratio

Steering Arms

Fig 41 Amity School of Engineering & Technology

Steering Arms Page 62

Like the pushrods, the steering arms are loaded to buckle in the pin-pin configuration as well. The force developed in this configuration is tabulated in the A-Arm force calculations section. The diameter on the rod is calculated using modulus of aluminum and required length of 12‖.

Process Controls (Troubleshooting) Process controls are the events that can be attributed to some malfunction or undesirable handling effect. For example, if the nose of the vehicle dives during braking, the cause of this problem could be attributed, but not limited to, low front damping, too soft spring rate, or high center of gravity. The process sheet is divided into front and rear suspension, steering components, and possible solutions to the problems listed. The method behind the sheet is to limit total time wasted during competition trying to tune the car to the current track conditions, or analyzing a problem. Stiff Movement  Probable Cause: High spring rate  Possible Solution: Reduce spring pre-load, adjust rocker ratio, and replace spring with different spring rates High Friction  Possible Solution: Re-grease rocker and damper bushings, inspect links for stiff rod-ends, verify misalignment angle to be less than 11, re-torque rocker bolts to 27.1163 Nm and verify rocker clearance for .050‖ clearance High Compression Damping  Readjust damping with 12 click knob one or two clicks lighter Nose Dive  Probable Cause: Light front spring rate Amity School of Engineering & Technology

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 Possible Solution: Adjust pre-load, replace springs with higher rate, adjust rocker ratio Light Front Damping  Possible Solution: Adjust damping compression with incremental knob High Center of Gravity  Possible Solution: None; may be more prominent with excessively large drivers Front Brakes Over-Biased  Possible Solution: Adjust bias proportioning valve Rear Steer  Probable Cause: Differential torque bias  Possible Solution: The Torsen differential bias can be adjusted with different shims, otherwise a common behavior with torque-sensing differentials  Probable Cause: Improper rear alignment  Possible Solution: Calibrate using caster/camber and toe-in/out device Vehicle Pulls to One Side  Probable Cause: Torque bias in differential, see rear steer Over/Under steer  Probable Cause: Ackerman angle  Possible Solution: Increase the Ackerman steering angle if the vehicle under-steers, decrease for over-steer Excessive Steering Force Amity School of Engineering & Technology

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 Probable Cause: Binding rack  Possible Solution: Re-grease rack and inspect for component wear  Probable Cause: Rod-end misalignment  Possible Solution: Verify that misalignment angle does not exceed 11 Steering Arm to Short  Possible Solution: Recalculate equivalent Ackerman angle and manufacture new are with greater length Improper Rack Ratio  Possible Solution: Re-cut new rack and pinion or replace rack with lower ratio

Safety Considerations The suspension system of a vehicle is critical to the safety of the occupant or occupants of that vehicle. In our case this is a very important issue since our vehicle is very small and is capable of large accelerations and decelerations. The vehicle safety issues are minimized by various rules. The rules have many requirements and restrictions to make the vehicle as safe as possible. One critical aspect of this project is the factor of safety used. The appropriate factor of safety can be determined by three different methods. The most detailed method would be to conduct a full detailed study of the situation using modeling and equations. Another method is too used ―Back of the envelope calculations‖, which are best done with worst case scenario numbers used. The final method is to use standard practice values. This is common since it only requires a little research and the values found usually have been tested to confirm their validity.

We used this method combined with ―Back of the envelope

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calculations‖ to verify the validity. The standard factor of safety for the formula suspensions systems is three.

Manufacturing considerations The use of magnesium for some of the suspension components is also a safety consideration due to its low ignition temperature. The safety issue is more with machining rather than the actual use on the car. A good analogy of this is the danger of throwing a match on sawdust compared with throwing a match on a log. There is just not enough heat to ignite the solid body and this is the case with the magnesium also. The solution to machining magnesium safely is quite simply to work at low feed rates, low tool rpm‘s, and use sharp tools. In addition to these steps one should monitor the temperature of the part during machining. If the part is getting too hot to touch for more than a moment then a break should be taken to give the part time to cool. If a fire were to break out water must not be used to extinguish this, in fact water will usually make it worst. A powder that is specially formulated to extinguish magnesium fires must be thrown on it.

Modifications We had made a few major modifications of the design in our system. The modifications were for various reasons, which include safety, aesthetics, interference issues, and ease of manufacture. The design of the front uprights was modified in order to increase the turning ability of the car. Material was removed from the top of the upright where the oversteer stops and steering mounts were going to be. The stops were placed directly on the rack. The steering mounts are located on the side of the upright so they don‘t interfere with the turning of the tire. The height of the steering rack was modified to allow for more room for the driver. At the original location, the driver would have difficulty getting his feet into the vehicle. We added two inches changing the clearance from 7 to 9 inches. Luckily this change only modified the suspension dynamics minimally. In fact, none of the changes are large enough to be noticeable to the performance of the car.

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Conclusion This project was a combination of many smaller design projects involving interdisciplinary teamwork. The finished projects were incorporated into the racecar built by the Supra SAE Chapter at Amity School of Engineering & Technology. The overall goal of the project was to create and intergrate components into a highly competitive vehicle. The suspension portion of the project was designed specifically as a mechanical engineering senior design project. The goal of the suspension team was to incorporate a system that is both reliable and adjustable. In the design, both driving conditions and different drivers were accounted for in creating a versatile car. The suspension had to maintain the maximum accelerations in the lateral, positive, and negative during the Supra SAE challenge. The major restriction was the use of many advanced parts due to budget constraints. The overall goals of our project were met by producing a working vehicle design. As a result of the design process, we have learned a great deal about different engineering disciplines. All of the mechanical systems are interrelated, especially the suspension system. We think Amity University Rajasthan will be well represented at this year‘s SAE student design competition.

Fig 42

Supra SAE AUR Prototype Solidworks Model

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References 1. Reza N. Jazar (2008). Vehicle Dynamics: Theory and Applications. Spring. p. 455. Retrieved 2012-06-24. 2. "The Washington Times, Sunday 30 June 1901". Chroniclingamerica.loc.gov. Retrieved 2012-08-16. 3. Jain, K.K.; R.B. Asthana. Automobile Engineering. London: Tata McGrawHill. pp. 293–294. ISBN 0-07-044529-X. 4. Jones, D. Suspension Systems. Brookhaven College, AUMT 1316, 2011:p. 1-7 5. Bilmanis,A.; Hotaling R.; Mangual J. Suspension, Steering, & Engine Control System Design Final Report. Senior Design Project 2000-2001 6. Hughes,C.; Understanding Suspension.©eSoft 7. Smith,J.H. An Introduction to Modern Vehicle Design p292-347.©Reed Educational and Professional Publishing Ltd 2002 8. Bosch, Robert. Automotive Handbook. Bosch; Stuttgart, Germany. 4th ED, 1996. 9. Milliken, William and Douglas. Race Car Vehicle Dynamics. Society of Automotive Engineers; Warrendale, PA, 1995. 10. Staniforth, Allan. Altair SuspensionGen User’s Manual. Altair Computing Inc.; Troy, MI. Version 1.13, 1998. 11. Jawad, A.B; Baumann, J.; Design of Formula SAE Suspension. Lawrence Technological University, SAE Technical Paper. 2002-01-3310

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Bibliography i. ii. iii. iv.

http://www.formula1.com/inside_f1/understanding_the_sport/5285.html

v. vi.

http://www.rockcrawler.com/techreports/glossary/camber.jpg

vii. viii. ix. x. xi. xii. xiii. xiv. xv.

http://en.wikipedia.org/wiki/Suspension_vehicle http://www.carbibles.com/suspension_bible.html#ixzz2DGB2bnzZ http://www.competitionx.com/wp-content/uploads/2010/09/rc-tuning-rideheight.jpg http://driftjapan.com/blog/wp-content/uploads/2007/11/toe-in-vs-toeout.jpg http://www.automation-drive.com/EX/05-13-06/art_AntiRollBar.gif http://www.uwracing.com/cars/wr-211/chassis http://www.uwracing.com/cars/210 http://allenbergracingschool.com/programs/images/formula_specs_2.jpg http://www.carbibles.com/images/coilspring1.jpg http://www.carbibles.com/images/coilspring2.jpg http://www.carbibles.com/images/multilink.jpg http://www.racecar-engineering.com/wpcontent/uploads/2012/02/upFerrrlead.jpg www.engineeringtoolbox.com

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