Formula Student Car Suspension Design

Transcription

1 Motorsport Engineering Formula Student Car Suspension Design Oliver de Garston Student Number: Dr. Rohitha Weerasinghe 87 Pages Module Code: UFMERY-30-M 0 P a g e

2 I Abstract In July 2015 UWE Formula Student will attend the Formula Student event at Silverstone. The Formula Student competition is between Universities that have built race cars according to Formula SAE rules. Further to my last report where the needs of the suspension system were analysed and modifications made to an existing design, the aim of this work is to design from scratch a suspension system for the University s 2015 Formula Student entry. This design will suit the needs of the event and its performance analysed through computer simulation. This design will be one of the key features of this year s UWE Formula Student entry. The suspension system will be of a classical unequal length double wishbone design. This suspension type has the most adjustability in characteristics and should meet all demands. I P a g e

3 Table of Contents I Abstract... I Table of Contents... II 1 Introduction Project Background Critical Analysis of Previous Work Formula Student Event Suspension Re-design Reasons Rule Design Limitations Resources Solidworks VSusp MSC Adams UWE Formula Student Team Literature Survey Formula Student Competition and Events Acceleration Skid-Pan Autocross Endurance Wheelbase Track Width Instant Centre and Roll Centre Short Swing Arm Length Long Swing Arm Length Medium Swing Arm Length Ultra-Long Swing Arm Length II P a g e

4 3.5 Camber Toe Kingpin Axis and Scrub Radius and Spindle Length Caster Angle and Trail Tie Rod Location and Bump Steer Anti-Features Ackermann Steering Spring Rates Wheel Frequency The Wheel Rate The Coil Rate or Spring Rate The Fitted Rate Anti-Roll Bars New Suspension Design Considerations Regulations Tyres Wheels Hubs and Uprights Geometry Roll Centre Modelled Swing Arm Length Side View Geometry Springs Dampers Anti-roll Bars Steering New Suspension Aims III P a g e

5 5 Suspension Geometry Design Wheelbase Track Width Wheels, Brakes and Offset Upright and Outer Pivot Points Wishbone Lengths and Roll Centre Inboard Pivot Points and Side View Geometry Springs, Bell Cranks and Lever Ratios Anti-roll Bars Steering Geometry Initial Analysis Front Key Parameters Rear Key Parameters Comparison between the Design and the Initial Aims of the Design MSC Adams Model Camber Gain Due to Bump and Droop Camber Gain Due to Roll Roll Centre Movement Final Component Designs for the Formula Student Car Conclusion Recommendations for Further Work Table of Figures Table of Equations Table of Tables References IV P a g e

6 1 Introduction 1.1 Project Background With UWE Formula Student entering their fourth year of competition in the Formula Student Event with their second Class 1 entry. The team has kept high member numbers from last year with over 80 team members being involved. With the author being the senior design specialist for the suspension area, this project is the perfect opportunity to aid the team. Having undertaken this project last year, my knowledge and experience with suspension systems and the design of suspension systems has grown massively from just hands on knowledge available before. Now knowing not only the basic terminology, but also what effects changing key parameters will have on the system, and its elements, as well as the key areas to consider when designing race car suspension. This project still coincides with my work in Formula Student and it has continued to be a great help towards designing the cars suspension. The work done previously showed the key short comings of the original design and found key improvements that could be made and will be used as a base and as a learning exercise for this report. This report aims to cover the complete re-design of the suspension system for the new UWE-FS-15 car that will coincide with a new chassis and powertrain. 1.2 Critical Analysis of Previous Work The starting blocks of this work is to improve upon the work carried out in the previous year. By identifying project areas that were overlooked or inadequate and aiming to improve upon them with a new design, thereby contributing to success at the Formula Student Silverstone event. The following provides a quick rundown of the previous year. The primary goal last year was to analyse an existing design and make minor theoretical improvement to understand their effects on the system. Alongside this the original design was to be manufactured for the 2014 Formula Student entry. It started with an inherited CAD design from P a g e

7 Figure Original Inherited CAD Design This design was then broken down and transferred into Vsusp a 2D suspension analysis software. Figure Original Design in VSusp The basic characteristics of the suspension system were then tabulated and compared against an ideal set of parameters. The suspension system was also analysed in terms of camber change and some graphs were produced. Table Original Design Basic Characteristics Criteria Front Suspension Rear Suspension Ideal Parameter Kingpin Inclination Angle Caster Angle Static Wheel Camber Scrub Radius 28.19mm mm 0mm 10mm Roll Centre Height 14mm 44mm -25mm 50mm Swing Arm Length mm mm Front 1778mm 4572mm Rear 1016mm 1778mm The suspension system was then manufactured by the author and the UWE Formula Student team for the 2014 car. 2 P a g e

8 Figure Wishbone Jig Figure Welded Wishbones Figure Completed Car at Silverstone. It was while manufacturing that a number of problems arose with the suspension, the inconsideration as far as shocks, pushrods and similar items meant the design was far from complete. The design was limitedly improved upon using the Vsusp program, but in order to reduce costs as many original components where kept to reduce potential costs for the team. 3 P a g e

9 Table Inherited Design Vs the Improved Design Criteria Kingpin Inclination Angle Caster Angle Static Wheel Camber Scrub Radius Roll Centre Height Swing Arm Length Current Suspension New Suspension Ideal Parameter Front Suspension Rear Suspension Front Suspension Rear Suspension Front Suspension Rear Suspension mm mm 28.19mm mm 14mm 44mm -22mm 3mm mm mm mm mm 0mm 10mm -25mm 50mm 1250mm 2500mm 0mm 10mm -15mm 60mm 1016mm 1778mm The new design saw improvements in possible damper mounting positions, camber change in bump and droop while sacrificing a small amount of camber stability in roll. As only limited parts of the design could be improved areas such as scrub radius and caster angle could not be changed. Static camber angles for both front and rear were also improved enabling a greater range of adjustment. Overall body roll was also improved by lowering both the front and rear roll centres. This improved design was then converted back into a CAD drawing 4 P a g e

10 Figure Previous Suspension CAD Geometry The author feels that the changes made in Part A where beneficial to the original system and that the goals set out at the start were achieved. Although it would be possible to improve upon this design this year, with the new knowledge learned the author feels that a better approach would be to design a new system from scratch. Working on a new design also allows for improvements to be made to other systems that rely on the suspension, such as the brakes. This was a key area that the car failed at scrutineering last year, and to enable bigger brakes to be fitted, complete outboard geometry changes need to be made. As this year s budget will be more wisely spent and better controlled, it is expected that a larger portion of the budget can be spent on a new suspension system. It is for this reason that a complete redesign is desirable. 1.3 Formula Student Event Formula Student (FS) is Europe's most established educational motorsport competition, run by the Institution of Mechanical Engineers. Backed by industry and high profile engineers such as our Patron Ross Brawn OBE, the competition aims to inspire and develop enterprising and innovative young engineers. Universities from across the globe are challenged to design and build a single-seat racing car in order to compete in static and dynamic events, which demonstrate their understanding and test the performance of the 5 P a g e

11 vehicle. (IMechE, n.d.) Formula Student cars are Formula style open-wheel single-seater race cars, all of which operate a form of double wishbone or multilink suspension due to its easy adjustment ability and that it provides independent control of each wheel. 1.4 Suspension Re-design Reasons The suspension system on the previous UWE Formula Student car was based on the work of the author s predecessor in the team. However due to the nature of the competition and the rules surrounding it, the design must be changed or modified year on year. As the car currently under design has a completely new chassis and drivetrain the suspension must be re-designed alongside this to give the car the best performance characteristics possible. This re-design will be for all components and geometries 1.5 Rule Design Limitations The rules that govern the building of a Formula Student car are largely governed by the regulations set by the FSAE. The ones that directly apply to the suspension geometry itself are listed below: T2.3 Wheelbase The car must have a wheelbase of at least 1525 mm (60 inches). The wheelbase is measured from the centre of ground contact of the front and rear tires with the wheels pointed straight ahead. T2.4 Vehicle Track The smaller track of the vehicle (front or rear) must be no less than 75% of the larger track. T4.2 Cockpit Internal Cross Section: T4.2.1 A free vertical cross section, which allows the template shown in Figure 9 to be passed horizontally through the cockpit to a point 100 mm (4 inches) rearwards of the face of the rearmost pedal when in the inoperative position, must be maintained over its entire length. If the pedals are adjustable, they will be put in their most forward position. 6 P a g e

12 Figure FSAE Cockpit Internal Cross Section Board (IMechE, 2014) T4.2.2 The template, with maximum thickness of 7mm (0.275 inch), will be held vertically and inserted into the cockpit opening rearward of the Front Roll Hoop, as close to the Front Roll Hoop as the car s design will allow. T4.2.3 The only items that may be removed for this test are the steering wheel, and any padding required by Rule T5.8 Driver s Leg Protection that can be easily removed without the use of tools with the driver in the seat. The seat may NOT be removed. T4.2.4 Teams whose cars do not comply with T4.1.1 or T4.2.1will not be given a Technical Inspection Sticker and will NOT be allowed to compete in the dynamic events. NOTE: Cables, wires, hoses, tubes, etc. must not impede the passage of the templates required by T4.1.1 and T4.2. T6.1 Suspension T6.1.1 The car must be equipped with a fully operational suspension system with shock absorbers, front and rear, with usable wheel travel of at least 50.8 mm (2 inches), 25.4 mm (1 inch) jounce and 25.4 mm (1 inch) rebound, with driver seated. The judges reserve the right to disqualify cars which do not represent a serious attempt at an operational suspension system or which demonstrate handling inappropriate for an autocross circuit. T6.1.2 All suspension mounting points must be visible at Technical Inspection, either by direct view or by removing any covers. 7 P a g e

13 T6.2 Ground Clearance Ground clearance must be sufficient to prevent any portion of the car, other than the tires, from touching the ground during track events. Intentional or excessive ground contact of any portion of the car other than the tires will forfeit a run or an entire dynamic event. T6.3 Wheels T6.3.1 The wheels of the car must be mm (8.0 inches) or more in diameter (IMechE, 2014) 2 Resources 2.1 Solidworks 2014 Solidworks is a 3D design software package with functions including FEA analysis, Weldmends, a rendering package as well as surface modelling and basic sketching. 2.2 VSusp Vsusp is an online two-dimensional simulator assuming ideal conditions. It provides an easy way to see what happens to a vehicle s suspension after: It goes into bump/droop or roll Altering the tyre sizes Substituting different length control arms Moving control arm pickup locations Lowering the vehicle Adding spacers at ball joints Changing wheel offset or diameter. And others That can be observed under various conditions include: Roll centre location and movement Tyre camber Scrub radius Front view swing arm length. And others 8 P a g e

14 2.3 MSC Adams MSC Software produces a multibody dynamics simulation program called Adams. It is thought of as the most widely used multibody dynamics software available and can help engineers to study the dynamics of moving parts, how loads and forces are distributed throughout mechanical systems. In this report MSC Adams will only be used for simple analysis of the suspension system as it is deemed that the author does not have enough time to be comprehensible enough with the software to run complex simulations. 2.4 UWE Formula Student Team The team will be a great resource to use. They helped the author manufacture the suspension system for last year s car and when the design produced in this project gets implemented into the current car under construction the team will assist in the manufacture and testing as the team will need to carry out these procedures as well. 3 Literature Survey 3.1 Formula Student Competition and Events The Formula student event in July is divided into two separate categories, static and dynamic. The static events consist of: Business Presentation Cost Analysis Engineering Design These events are designed to evaluate the team s ability in organisation, design, costing, delivery and selling their product. The dynamic events are: Acceleration Skid-Pan Autocross Endurance Acceleration The acceleration event is a fairly simple drag race covering a distance of 75 metres. The cars start 0.3m behind the start line, when the cars cross the start line the timer starts and it finishes when they cross the finish line. There are two heats for this event each heat must utilise a different driver and each driver may make two runs, so four runs in total. This event 9 P a g e

15 is the least important as far as suspension design is concerned; the ideal characteristics are to maintain the largest contact patch as possible between the rear tyres and the ground Skid-Pan The objective of the skid-pad event is to measure the car s cornering ability on a flat surface while making a constant-radius turn. (IMechE, 2014) The layout of the skid-pan will consist of two rings with and inner diameter of 15.25m with their centres 18.25m apart. The thickness of the rings will be 3m wide. The layout is shown in Figure Skid-pan layout The procedure for the skid-pan event is that the car will start by entering the right hand circle; it will complete on lap, and then continue on the same circle for a second lap which will be timed. The driver then immediately enters the left hand circles for his third lap staying on this circle for the fourth lap which is timed. The driver then has the option to make an immediate second run. Each team will have two drivers able to do two runs each. The suspension design is critical for this event as the key is to be able to corner at high speed and maintain grip levels. Figure Skid-pan layout (IMechE, 2014) 10 P a g e

16 3.1.3 Autocross The objective of the autocross event is to evaluate the car's manoeuvrability and handling qualities on a tight course without the hindrance of competing cars. The autocross course will combine the performance features of acceleration, braking, and cornering into one event. (IMechE, 2014) The layout of the autocross track is unknown until the event but is designed in a way to keep the speeds from being high, the average speed should be between 25mph and 30mph.The layout is specified as follows: Straights: No longer than 60 m (200 feet) with hairpins at both ends (or) no longer than 45 m (150 feet) with wide turns on the ends. Constant Turns: 23 m (75 feet) to 45 m (148 feet) diameter. Hairpin Turns: Minimum of 9 m (29.5 feet) outside diameter (of the turn). Slaloms: Cones in a straight line with 7.62 m (25 feet) to m (40 feet) spacing. Miscellaneous: Chicanes, multiple turns, decreasing radius turns, etc. The minimum track width will be 3.5 m (11.5 feet). Each team can enter two drivers into this event, each having a maximum of two timed runs, with the best time from each driver being counted. This event relies heavily on the suspension and steering geometry, as a well-balanced easy handling car will make it easier for the driver to push the car to the limit and post competitive times Endurance The Endurance Event is designed to evaluate the overall performance of the car and to test the car s durability and reliability. The car s efficiency will be measured in conjunction with the Endurance Event. The efficiency under competition conditions is important in most vehicle competitions and also shows how well the car has been tuned for the competition. This is a compromise event because the efficiency score and endurance score will be calculated from the same heat. No refuelling will be allowed during an endurance heat. (IMechE, 2014) The layout of the endurance track is also unknown until the event but will be designed for an average speed of 29.8mph with a top speed of 65.2mph. The layout is specified as follows: 11 P a g e

17 Straights: No longer than 77.0 m (252.6 feet) with hairpins at both ends (or) no longer than 61.0 m (200.1 feet) with wide turns on the ends. There will be passing zones at several locations. Constant Turns: 30.0 m (98.4 feet) to 54.0 m (177.2 feet) diameter. Hairpin Turns: Minimum of 9.0 m (29.5 feet) outside diameter (of the turn). Slaloms: Cones in a straight line with 9.0 m (29.5 feet) to 15.0 m (49.2 feet) spacing. Miscellaneous: Chicanes, multiple turns, decreasing radius turns, etc. The standard minimum track width is 4.5 m (14.76 feet). For this event a single 22km heat is made during which the teams will not be permitted to work on their cars. A driver change must be made during a three minute stop at the half way stage of the event. With the track layout being similar to the autocross event this is also a key event where the suspension needs to perform well to get the best results. 3.2 Wheelbase The wheelbase, l, is the distance between the centre point of the front axle and the centre point of the rear axle. The wheelbase and centre of gravity position have a great impact on the wheel loads and axle load distribution. This is shown in Figure A short wheelbase will give a greater load transfer between the front and rear axles than a longer wheelbase during acceleration and braking according to Equations and Figure Side view parameters for longitudinal load transfer calculations. 12 P a g e

18 ax CG l k mg λ Fz1 Fz2 Figure Side view parameters for longitudinal load transfer calculations. Equations Axial Load Distribution Load on the front wheels F f = (l λ) l Load on the rear wheels F r = λ l mg Equations Longitudinal Load Transfer Under Braking (l λ) F z1 = ( mg) + ( k l l A x mg) F z2 = ( λ l mg) (k l A x mg) mg A shorter wheelbase will have the advantage of a smaller turning radius for the same steering input. A longer wheelbase will be able to be fitted with a softer spring set up to increase driver comfort. However a car with too small a wheelbase may act nervously in a straight line and on corner exits. Features to counter this can be built into a suspension setup but these will also affect the longitudinal load transfer. 3.3 Track Width The track width is a major feature when designing a vehicle. Its main influence is on a vehicles tendency to roll and its cornering behaviour. The smaller the track width the larger the lateral load transfer when cornering and the opposite is true for a larger track. This is shown for a rear axle in Equation According to the regulations the smallest width a dynamic event track can be is 3m. A larger track has the advantage of smaller lateral load transfer but a disadvantage in that more lateral movement is needed to avoid obstacles. The amount of lateral load transfer is also affected if the car has anti-roll bars. The amount of lateral load transfer wanted depends on the tyres that have been chosen. 13 P a g e

19 CG ay mg h t/2 t Figure Total Lateral Load Transfer Equation Lateral Load Transfer ΔW = mg Ay h t 3.4 Instant Centre and Roll Centre The instant Centre is the momentary centre which the suspension linkage pivots around. As the suspension geometry changes during suspension movement the instant centre also moves. Instant centres can be constructed in both the front view and the side view of the geometry. When the instant centre is viewed in the front view a line can be drawn from the instant centre to the centre of the tyre contact patch. When done on both sides the point at which these lines intersect is the roll centre of the sprung mass of the car. This means that the instant centres determine the position of the roll centre, so high instant centres will lead to a high roll centre. The roll centre establishes the force between the unsprung and the sprung masses of the car. When the car corners the centrifugal force acting on the centre of gravity can be translated to the roll centre and down to the tyres where the reactive lateral forces are built up. The higher the roll centre is the smaller the rolling moment around the roll centre is. This rolling moment must be restricted by the springs. Horizontal-vertical coupling effect is another factor. If the roll centre is located above the ground the lateral force generated by the tyre generates a moment about the instant centre, which pushes the wheel down and lifts the sprung mass. This effect is called jacking. If the roll centre is below the ground level the force will push the sprung mass down. The lateral force will, regarding the position of the roll centre, imply a vertical deflection. If the roll centre passes through the ground level when the car is rolling there will be a change in the movement direction of the sprung mass. 14 P a g e

20 Centre of Car Roll Centre Instant Centre Roll Centre Centre of Contact Patch FVSA length Figure Instant Centre and Roll Centre Locations The camber change rate is a function only of the front view swing arm length, FVSA length. Front view swing arm length is the length of the line from the wheel centre to the instant centre when viewed from the front. The amount of camber change achieved per mm of ride travel is shown in Equation 3.4.1and Figure Instant Centre and Roll Centre Locations Equation Camber Change Per mm of Ride Travel degrees mm = 1 tan 1 ( FSVA length ) The camber change is not constant throughout the whole ride travel since the instant centre also moves with wheel travel. Varying the swing axel length obviously has a great effect on roll centre location and how the wheel acts in corners and how it reacts in bump and droop Short Swing Arm Length A short swing arm length of between 508 mm and 1016 mm gives a very good roll centre location and keeps the outer wheel vertical during cornering, but has bad camber change effects in bump and droop, going positive in droop and negative in bump Long Swing Arm Length A long swing arm length of between 1778 mm and 4572 mm gives a low roll centre but less control over their sideways movement, minimal scrub, poor outer wheel control going into positive camber, but only small camber change in bump and droop Medium Swing Arm Length A medium swing arm length of between 1016 and 1778 mm is the transitional area between the long and short swing arm lengths and as could be expected is a bit of everything. 15 P a g e

21 3.4.4 Ultra-Long Swing Arm Length An ultra-long swing arm length anything above 4572 mm or near parallel wishbones gives great vertical wheel control with very low roll centres but enormous sideways movement, wheel camber is virtually unaltered in bump and droop but poor wheel control in roll with angles being near equivalent to body roll angles. 3.5 Camber Camber angle is the angle between the vertical plane and the wheel centre plane. Negative camber is defined as when the wheel is tilted inwards at the top relative to the car. The camber angle has influences on the tyres ability to generate lateral forces. A cambered rolling wheel produces a lateral force in the direction of the tilt. This force is referred to as camber thrust when it occurs at zero slip angles. Camber angle also affects the aligning torque due to distortion of the tire. The effect of this is rather small and can be cancelled with increasing slip angle. Camber also leads to a raise in the lateral force produced by the wheel when cornering. This is true in the linear range of the tyre. If the linear range is exceeded, the additive effects of the camber angle decreases; this effect is called roll-off. Therefore the difference in lateral force when comparing a cambered wheel with a non-cambered wheel is small, around 5-10% at maximum slip angle. The difference is much larger at zero slip angles due to the camber thrust. The effects of camber on a tyre are bigger for a bias ply tyre than a radial ply tyre. For radial tyres the camber forces tend to fall off at camber angels above 5 while the maximum force due to camber for a bias ply tyre occurs at smaller angles. 3.6 Toe Toe is the measure of how far inward or outward the leading edge of the tyre is facing, when viewed from the top. Toe adjustment can be used to overcome handling difficulties. Rear toe out can improve the turn in of a car. As the car turns in the load transfer adds more load to the outside wheel and the effect is in and over steer direction. The amount of static toe in the front will depend on factors that include camber, and Ackermann steering geometry. However it follows the same pattern as the rear with toe out encouraging turn initiation. This advantage in steering response provided by toe-out becomes a trade-off with straight-line stability provided by toe-in at the front. Although in racing situations sacrificing a little straight line stability for a shaper turn-in is desirable. Minimum static toe is desirable to reduce rolling resistance and unnecessary tyre heating and tyre wear caused by the tyres working against each other. 16 P a g e

22 3.7 Kingpin Axis and Scrub Radius and Spindle Length The kingpin axis is determined by the positions of the upper and lower joints on the wheel end of the wishbones. This axis is not necessarily centred on the tyre contact patch. Viewing from the front the axis is called the kingpin inclination angle and the distance from the centre of the tyre contact patch to the axle centre is called the scrub radius. The distance from the kingpin axis to the wheel centre plane is measured horizontally at the axle height and is called the spindle length. Figure Kingpin Axis, Scrub Radius and Castorshows the kingpin geometry. Kingpin Axis Wheel Offset Kingpin Inclination Upper Joint Side View Wheel Flange plane Spindle Length (+) Upper Joint Lower Joint Kingpin Offset Caster (+) Lower Joint Mechanical Trail Scrub Radius (-) Forward Figure Kingpin Axis, Scrub Radius and Castor There are a number of effects that can occur due to the values of these factors. If the spindle length is positive, the car will be raised up as the wheels are turned and this results in an increase of the steering moment at the steering wheel. The larger the kingpin inclination angle is, the more the car will be raised, regardless of which way the front wheels are turned. If there is no caster present, this effect is symmetrical from side to side. The raising of the car has a self-aligning effect on the steering at low speeds. Kingpin inclination affects the steer camber. When a wheel is turned it will lean out at the top, towards positive camber if the kingpin inclination angle is positive. The amount of this is small but not to be neglected if the track includes tight turns. If the acceleration or braking force is different on the left and right side this will introduce a steering torque proportional to the scrub radius, which will be felt by the driver at the steering wheel. 17 P a g e

23 Typical Kingpin angles are between 0 and 10. Too much king pin angle, and the tyre tends to flop from side to side as it is steered, this causes the tyre contact patch to run up the edge of the tyre as it is turned. In regards to scrub radius, the smaller the distance the less kick back is felt and the less effort is needed to steer the car, however the larger a scrub radius the more the driver feels bumps, brake pulsations and steering feedback. This is ideal in race cars or performance cars. Mark Ortiz of Racecar Engineering states, I would aim for a scrub radius anywhere from one to four inches (25 to 100mm) more for low-speed tracks, less for high-speed. (Ortiz, 2015) All three of these factors are interrelated and a compromise is needed. To have a specific scrub radius the outer ball joints are in fixed positions; this then fixes the kingpin angle automatically. If a specific kingpin angle is desired then the scrub radius will not necessarily be what is wanted. As the car is rear wheel drive, a minimum kingpin angle is desired and a compromise in scrub radius will have to be taken. 3.8 Caster Angle and Trail When viewing from the side the kingpin inclination is called the castor angle. If the kingpin axis doesn t pass through the centre of the wheel then there is a side view kingpin offset present. The distance from the kingpin axis to the centre of the tyre contact patch is called the trail or caster offset. See Figure Kingpin Axis, Scrub Radius and Castorfor the side view geometry. The caster angle and trail is important when designing the suspension geometry. With caster present the tyre aligns itself behind the pivot as it travels. More trail means that the tyre side force has a larger moment arm to act on the kingpin axis; this produces more self-centring effect and the primary source of self-centring moment about the kingpin axis. There are a number of effects that can occur due to the values of these factors. Caster angle will cause the wheel to rise and fall with steering input. This effect is opposite from side to side and causes roll and weight transfer, leading to an over steering effect. Caster angle has a positive effect on steer-camber. With positive caster angle the outside wheel will camber in a negative direction and the inner wheel in a positive direction, causing both wheels to lean into the turn. The size of the mechanical trail due to caster may not be too large compared to the pneumatic trail from the tyre. The pneumatic trail will approach zero as the tyre reaches the slip limit. This will result in lowering the self-centring torque that is 18 P a g e

24 present due to the lever arm between the tyres rotation point at the ground and the point of attack for the lateral force. This will be a signal to the driver that the tyre is near its breakaway point. This breakaway signal may be lost if the mechanical trail is large compared to the pneumatic trail. 3.9 Tie Rod Location and Bump Steer The location of the tie rods is an important factor. The location should be such that bump steer effects are kept to a minimum. Bump steer is the change in toe angle due to wheel travel. A car with too much bump steer will have the tendency to change its movement direction when the front wheels run over an obstacle. The effects of this can be hazardous when running on a track over the corner curbs. In order to accomplish zero bump steer the tie rod must fall between an imaginary line that runs from the upper outer ball joint through the lower outer ball joint and an imaginary line that runs through the upper wishbone pivots and the lower wishbone pivots. In addition, the centreline of the tie rod must intersect with the instant centre created by the upper wishbone and the lower wishbone. This layout is shown below in Figure Diagram showing ideal tie rod locations. The simplest way to minimise bump steer is to locate the tie rod in the same plane as either the upper or lower wishbones. Another factor to look out for is the camber compliance under lateral force. If the tie rods are located either above and behind or below and in front of the wheel centre the effect on the steering will be in the understeer direction. If the wishbones are stiff enough the effects will be small and thereby minimize the risk of over steering effects due to compliance in the wishbones. The length of the lever arm from the outer tie rod end to the upper joint determine together with the steering rack ratio the total ratio from the steering wheel s angle to the wheels steering angle. Centre of Car Instant Centre FVSA length Figure Diagram showing ideal tie rod locations 19 P a g e

25 3.10 Anti-Features The anti-effect in a suspension describes the longitudinal to vertical force coupling between the sprung and unsprung masses. It results from the angle of the side view swing arm. Antifeatures do not change the steady-state load transfer at the tyre contact patch; it is only present during acceleration and breaking. The longitudinal weight transfer during steady acceleration or breaking is a function of wheelbase, centre of gravity height and acceleration or breaking forces as shown in Figure Braking Force l CG h +ΔFz -ΔFz Figure Basic Brake Force Braking Force=W(ax/g) Moment=W(ax/g)(% front braking)(svsa height) Svsa length CG θf IC Svsa height IC θr Figure Anti Force s The anti-features changes the amount of load going through the springs and the pitch angle of the car. Anti-features are measured in percent. A front axle with 100% anti dive will not deflect during braking, no load will go through the springs, and a front axle with 0% anti dive will deflect according to the stiffness of the springs fitted; the entire load is going through the springs. It is possible to have negative anti effects. This will result in a gain of deflection. 20 P a g e

26 Equation will give the percentage of anti-dive in the front of the car with outboard brakes. Equation Anti-Dive Equation % Anti dive Front = W ( a x height g )(% front braking)(svsa svsa length ) W ( a x g ) ( h l ) = (% front braking)(tanθ F )( l h ) By substituting % front braking with % rear braking and tan(θf) with tan(θr) in Equation the amount of anti-lift can be calculated. Anti-squat is similar however the acceleration on the centre of gravity position is now in the opposite direction. Equation Anti-Squat Equation % Anti squat = tanθr ( h l ) 100 The way in which the suspension reacts to brake and drive torque alters how to calculate the amount of Anti present. If the control arms react to torque, either from the brakes or from drive torque, the anti s are calculated by instant centre location relative to the tyre contact patch. If the suspension doesn t react to drive or brake torque, but only the forward or rearward force, then the anti s are calculated by the instant centre location relative to the wheel centre. For a rear wheel driven car there are 3 different types of anti-features: Anti-dive, which reduces the bump deflection during forward braking. Anti-lift, which reduces the droop travel in forward braking. Anti-squat, which reduces the bump travel during forward acceleration Ackermann Steering In low speed turns, where external forces due to acceleration are negligible, the steering angle needed to make a turn with radius R is called the Ackermann Steering Angle, δa, and can be calculated by using Equation Equation Ackermann Steering δ a = l R If both front wheels are tangents to concentric circles about the same turning centre, which lies on a line through the rear axle, the vehicle is said to have Ackermann steering. This results in the outer wheel having a smaller steering angle than the inner wheel. If the outer wheel has a larger steering angle this is called reverse Ackermann and if both wheels have the 21 P a g e

27 same steering angle, the vehicle has parallel steer. Passenger cars have a steering geometry between Ackermann and parallel steering while it s common among race cars to use reverse Ackermann. By using Ackermann steering on passenger cars, or other vehicles exposed to low lateral accelerations, it is ensured that all wheels roll freely with no slip angles because the wheels are steered to track a common turn centre. Race cars are often operated at high lateral accelerations and therefore all tyres operate at significant slip angles and the loads on the turn s inner wheels are much less than the turn s outer wheels due to the cornering force. Using a low speed steering geometry on a race car would cause the turn s inner tyre to be dragged along at a much higher slip angle than needed and this would only result in raises in tyre temperature and slowing of the car due to slip angle induced drag. Therefore race cars often use parallel steer or even reverse Ackermann. The different types of Ackermann are shown in Equation Figure Ackermann Steering (Milliken & Milliken, 1995) 3.12 Spring Rates Wheel Frequency The wheel frequency is the natural frequency of the suspension or wheel in either cycles per minute (CPM) or per second (Hz). An ideal value would be found at around Hz or 100 CPM 150 CPM for racing cars without wings or ground effect. With anything lower being for road cars and above this for high downforce cars, as this effectively increases the sprung weight. Tiny ground clearances will mean that even higher frequencies will be essential, however hard the ride will become, with the tyre taking over more and more of the spring s job. Figures of CPM are needed, with Natural frequency s reaching as high as 500 CPM at the peak of the ground effect era. It is usual to find the rear frequency to be about 10% higher than the front. This is to avoid a nose up nose down oscillation caused 22 P a g e

28 by the front wheels when rising over a bump first, followed shortly by the rears. For an inboard mounted coil there are effectively three rates to any spring. Equation Wheel Frequency Wheel Rate N m Wheel Frequency Hz = 4π 2 Sprung Mass kg The Wheel Rate The first rate is the wheel rate or how strong the spring appears to be at the wheel, however adding 100N of spring rate will not necessarily add 100N to the wheel rate unless the spring is mounted directly on the axle. Anytime there are linkages such as wishbones and pushrods, the linkage ratios need to be considered, and for this the calculation involves squaring the leverage ratios. Equation Wheel Rate Wheel Rate N m = 4π2 Wheel Frequency 2 Sprung Mass kg Equation Alternative Wheel Rate or Wheel Rate N mm = Coil Rate N mm Suspension Leverage The Coil Rate or Spring Rate Second is the coil rate, or amount the spring compresses under a given load (in lbs./ in. or N./ mm.) usually this its etched or painted on the springs by the manufacturer. If this is unavailable or missing, the rate can be determined by measuring the springs and using the following Equation Equation Measuring Spring Rate Coil Rate = Gd 4 8ND 3 Where G is the average torsional modules of steel, d is the wire diameter in inches, N is the number of coils and D is the mean coil diameter in inches. The coil rate can also be worked out from the wheel frequency and motion ratio as seen in Equation Equation Coil Rate The Fitted Rate Coil Rate N/m = 4π 2 Wheel Frequency (Hz) 2 Sprung Mass (kg) Motion Ratio 2 The third is the fitted rate or how strong the spring appears to be on the car, taking into account the leverage on it exerted by the suspension linkage. A coil mounted to a longer 23 P a g e

29 suspension linkage will be crushed more than the same coil mounted on a shorter suspension linkage. Equation Fitted Rate 3.13 Anti-Roll Bars Fitted Rate N mm = Coil Rate N mm Motion Ratio An anti-roll bar, also referred to as a stabilizer or sway bar, is a bar or tube which connects some part of the left and right sides of the suspension system. The primary function of an anti-roll bar is to control and limit the body roll of the vehicle during cornering by adding to the roll resistance of the suspension springs. This is for a higher overall roll resistance, as the primary purpose of the spring is to maintain maximum contact of the tyre to the road surface and therefore we must settle for the roll resistance provided, which is rarely enough. The antiroll bar adds to the roll resistance without resorting to an overly stiff spring. A properly selected anti-roll bar will reduce body roll in corners for improved cornering traction, but will not increase the harshness of the ride, or reduce the effectiveness of the tyre to maintain good road surface contact. A secondary function is that they can be used to tune the vehicles handling balance, as the anti-roll rate not only determines the amount the chassis rolls during cornering, but the relative anti-roll rates front to rear, determine the weight transfer characteristics of the race car. Many race car engineers refer to the relative roll stiffness as the magic number. Changing the relative anti-roll rate front to rear is the single most effective way of establishing a balanced race car. By changing the relative anti-roll rate and hence their relative weight transfer, the overall mechanical grip can be sacrificed at one end of the race car to improve the other, until a balance is achieved. The following equations are used to calculate the roll gradient of the ride springs and thus the deficit that the anti-roll bar needs to deal with. Equation Roll Gradient From Ride Springs Equation φ r A y = W H K φf + K φr Where φ r A y = the roll gradient from the ride springs in deg/g, H = Cg to roll axis distance in m, W is the vehicle weight and K φf and K φr are the front and rear roll rates respectively in Nm/deg Equation Front Roll Rate Due to Springs Equation K φf = π (t f 2 ) K LF K RF 180 (K LF + K RF ) 24 P a g e

30 Where t f = front track width in m and K LF and K RF are the front left and right wheel rates respectively in N/m. This equation is similar for the rear. Equation Rear Roll Rate Due to Springs Equation K φr = π (t R 2 ) K LR K RR 180 (K LR + K RR ) Next the total anti-roll bar roll rate needed to increase the roll stiffness of the vehicle to the desired roll gradient should be calculated. Equation Total ARB Roll Rate Needed Equation K φa = π 180 ( K φdes K T (t 2 /2) [K T (t 2 /2) π 180 K φdes] ) πk W (t 2 /2) 180 Where K φa = the total ARB roll rate needed in Nm/deg roll, K φdes = the desired total roll rate in Nm/deg roll. K W = the average wheel rate in N/m and K T =the Tyre Rate in N/m. t is the average track width of the vehicle in m. Equation Desired Total Roll Gradient Equation K φdes = W H/ ( φ A y ) Where φ A y = the desired total roll gradient, chosen by the user in deg/g. It is then possible to calculate the front and rear anti-roll bar stiffness. Equation FARB Stiffness Equation K φfa = K φa N mag MR FA 2 Where K φfa = the Front ARB roll rate in Nm/deg twist, N mag =the roll gradient distribution in % and MR FA = the FARB motion ratio. The roll gradient distribution is 5% more than the 100 static front load percentage. Again this equation is similar for the rear. Equation RARB Stiffness Equation K φra = K φa (100 N mag ) MR RA Now these equations can be used to calculate the anti-roll bar stiffness. 4 New Suspension Design Considerations Having read much literature on the subject it is clear there are many approaches to designing a suspension system, the chosen method for this report is what the author believes is the most effective and follows both the advice in Race Car Vehicle Dynamics (Milliken & Milliken, 1995) and a modified priority list set out in Competition Car Suspension (Staniforth, 1999): 1. Regulations 25 P a g e

31 2. Track Width 3. Tyres 4. Wheels 5. Hubs and uprights 6. Geometry 7. Roll centre 8. Instantaneous roll centre/ swing arm length 9. Springs 10. Dampers 11. Anti-roll bars 12. Steering 4.1 Regulations Reading the regulations is step one. It is no use to arrive in the first scrutineering bay with a world beater that is just slightly the wrong size. (Staniforth, 1999) This sounds like a basic concept but even the best teams get this wrong. The regulations that govern the design of the suspension for the Formula Student car have been covered earlier in section 1.5 and can be found in the 2015 Formula SAE Rule book. (IMechE, 2014) In most cases to get the most out of the regulations they must be stretched to the limit. However considering the performance of the team last year at Silverstone. The decision has been made to play reasonably conservative all round to ensure that the scrutineering process goes without a hitch. 4.2 Tyres 13 inch diameter tyres are likely to be the first choice, whether new or slightly scuffed due to their enormous availability and variety. A larger diameter is usually employed only because vehicle size or power forces this option, which is not a factor with the UWE Formula Student car. The smaller 10 inch mini size tyre suffers from a lack of choice in width, construction and tread compounds which also rules out this option. The most desirable from a weight and inertia point of view is the 12 inch tyre however this is a very rare size and can be extremely expensive and hard to find. As tyre sizes are usually limited by the sanctioning body rules, the general rule is to use all the tyre that the rules will let you get away with. So for these reasons the 13 inch tyre is to be chosen. Avon manufacture a range of suitable tyres 26 P a g e

32 for the FSAE competition. For various reasons the tyre choice is out of the authors control, due to the team budget and last year s lack of tyre usage it has been decided that the previous year s tyres will be recycled. To this end the tyre choice is therefore the Avon FSAE 7.2x20x13. This has a width of 183 mm and an outside diameter of 521 mm. 4.3 Wheels Although wheels are not really part of the suspension, except as tyre carriers, wheels are nonetheless the vital link between the geometry and the tyre contact patch and as such need to have properties of strength, lightness and reliability. The wheel size will totally depend on the tyre size and the desired PCD or type of stud pattern of the hub flange. It is far easier to obtain a wheel with the correct offset and PCD than to alter a hub and flange to suit the wrong wheel. The specific wheel manufacturer also needs to be known and a cross section of the wheel is desired to be able to optimise full usage of the space inside the wheel. At this stage the brake calliper placement and wheel offset are worked out together to make sure that the calliper clears the inside surface of the wheel. Once the calliper is located this then automatically positions the brake rotor. 4.4 Hubs and Uprights Although technically these are two separate items, together with their bearings, spacers and seals, they are so closely inter-related as to be considered a single component. The key design areas are the wheel and brake attachment points and the positions of the upper and lower outboard suspension pickups and later the steering pickup. The lower suspension point should be positioned first, as close to the brake disc as possible and as low as possible without contacting the wheel rim in the full range of movement for the suspension. The upper suspension point should then be positioned to give the desired king pin inclination angle, caster angle and as far away from the lower suspension mount as possible to reduce loading. This will however dictate the scrub radius. The two main criteria for the outboard pickup points are that; a) They do not contact the wheel rim b) The further outboard they can be positioned the more the leverage of the wheel against links can be reduced. Some ideal characteristics that are needed from the outboard suspension pickup points are a kingpin inclination angle of between 0 and 8, a scrub radius lower than 40 mm but not 27 P a g e

33 negative. A caster angle between 3 and 7, with a static camber angle around -2 with adjustment between 0 and -4. However due to the relationship between kingpin angle and scrub radius there may need to be some compromise between the two values. 4.5 Geometry Any decision on springs, anti-roll bars, weight transfer or wheel frequency cannot be made until the lengths, angles and pick up positions of the wishbones have been finalised. But the basic concept of stay low where centre of gravity and roll centre are concerned is a vital one. You have to have at least one firm base on which to begin creating your suspension design, and nothing I have been involved with over some years has shaken my conviction that the best, and possibly the only, reliable starting point is the roll centre. You have to cling onto something (Staniforth, 1999) Where the roll centre is located statically in various designs of suspension, this can most clearly be seen in drawings rather than attempting an explanation in words. See section 3.4 for a clearer definition of roll centre. As this point will dictate how the chassis suspension pick up points move, and hence what the wheel and tyre will then do, the importance of controlling its position in space, should this be possible is paramount. The trouble with theoretical concepts compared to reality is that they alter once cornering and other forces come into play, because the static data on which they are based alters. The dynamic roll centre can and does move up, down and side to side. With roll itself being a function of an equally invisible point, the centre of gravity, it can be seen how variations and uncertainties rapidly multiply. Leverages alter, the car s attitude alters, weight transfer from inner to outer wheels alters, and at the end of the line, the tyre contact patches start distorting under complex and varying series of loads. This is where wishbone lengths, wishbone angles and chassis mounts are all chosen as well as pushrod and bell crank positions. There are four options to make a start finding a suitable geometry: 1. Copy exactly a successful design already running, this is obviously only if you have access and permission to do this. To make this work every point that moves must be reproduced precisely in space as once you diverge from the original shortcoming begin to creep in. this is obviously not an option in this report as the basis of it is to design a suspension system. 2. Draw the proposed layout, then re-draw and re-draw with gradual movements of wheel and chassis bump, roll and droop. This is not a practical application as one drawing soon turns into hundreds as you go through variation after variation. 28 P a g e

34 3. Use a computer program to vary a mathematical model of your idea. This is by far the most practical as a computer has the ability to do millions of repetitive calculations at high speed in search of your solution. The computer does all the repetitive drawing for you it is just up to the engineer to analyse the results and decide what works and what doesn t. 4. Use of the string computer, by making a working model of the unequal wishbone design to scale and to giving it freedom to move, and using string as a way of indicating in small increments what the roll centre might be doing. 4.6 Roll Centre Racing cars have roll centres located around an area within 25 mm below the ground and 50 mm above the ground. Low roll centres give less weight transfer to the outer wheel, smaller or no jacking effect but high potential roll angles. Front and rear roll centres are conventionally at different heights to give a tilted roll axis with the lowest centre at the lowest or lightest end of the vehicle. So for this application the front roll centre will be positioned lower than the rear. 4.7 Modelled Swing Arm Length The swing arm length that is believed to be best for the front of this application is in the range between the longer end of a medium swing arm length and the shorter end of a long swing arm length. This equates to a desired region of around between 1500 mm and 2500 mm as this can give camber gain of between 0.05 per mm and 0.02 per mm, which over the full range of suspension travel should give a camber change due to roll of between 0.3 and 0.7. At the rear medium swing arm length of between 1016 mm and 1778 mm will give a camber change of between 0.03 per mm and 0.05 per mm, which over the full range of rear suspension travel should give a camber gain due to roll of between 0.5 and Side View Geometry The side view geometry involves any anti systems present, due to the nature of the event and the weight of the car it is deemed that no anti-dive is necessary. A small amount of anti-squat however is a preferred choice. To this end it is viewed that 30% anti-squat is a good amount, this will be designed into the rear of the suspension system. 29 P a g e

35 4.9 Springs For this report the aim is to have the natural frequency in the Hz or CPM boundary. With the rear being about 10% higher than the front. So if we say the rear has the maximum frequency of 150 CPM or 2.5 Hz, 90% of this value is 135 CPM or 2.25 Hz. These will be the desired natural frequencies of the car. As the car has yet to be designed the leverage ratios are yet to be known so spring and coil rates cannot be deduced until such time Dampers The precise relationship between a damper, the coil surrounding it and the rest of the car is an extremely subtle and sensitive one, even in this day and age often being fine-tuned by testing and seat of the pants feel once the car is running. (Staniforth, 1999) So long as the leverages are the same within the damper coil system, in terms of the actual rate or strength of that coil, ignoring inclinations, wheel rate, etc. The bump resistance of a damper is always less than the rebound, by a ratio for a circuit racing car of around 2:1 or even 1.5:1 compared to an average road car of about 3:1. This figure has come about as a result of the sacrifice of comfort in search of grip with travel being contained to around 2 inches or less for circuit vehicles with instantaneous loads from bumps or kerbing being many times higher. With the team saving money by reusing existing dampers from last year provided by Protec Shocks there is little that can be changed in this area. However the data for the bump and rebound of the dampers is available and both fully adjustable for that seat of the pants adjustment once the car is running. The bump and rebound graphs are shown below in Error! Reference source not found. and Error! Reference source not found. 30 P a g e

36 Figure Front Damper Bump and Rebound Graph Figure Rear Damper Bump and Rebound Graph 4.11 Anti-roll Bars This is another area where working backward towards what is wanted is the best route, by first finding the roll moment of the whole car. It then must be assessed how much the springs contribute to roll stiffness. Using these two figures it will then be possible to decide what further roll stiffness is required to limit roll with a target of around 1 for a single seater at 1G cornering force as a maximum. Before any calculating can be done it needs to be decided how and where they are best fitted. Criteria are that they do not interfere with the chassis clearance board or drivetrain components, they must be accessible for change or adjustment with freedom to move full travel without fouling. The standard link from bar to suspension makes use of rod ends at each joint with left/right hand threads to allow accurate setting of length without totally dismantling the unit. The mounting location will decide the length of bar and maximum and minimum space for any adjustable lever arm. After this is done then length and lever arm dimensions are now known and a given stiffness requirement can at last be calculated, to determine the bars diameter and wall thickness Steering We must now decide where to locate the rack and pinion, there are two factors to consider, making sure not to foul on the chassis clearance board and the avoidance of excessive bump steer. Bump steer is the phenomena in which either or both front wheels will start pointing themselves in varying directions as they rise and fall without the driver turning the steering wheel. This is as bad as it sounds and at its worst can introduce straight line instability and 31 P a g e

37 highly unwanted uncertainty in cornering feel. Only after the location of all inboard and outboard suspension pickup points has been finalised can the rack position and its required length be determined. The best solution is usually with rack end pivots coinciding exactly with the top wishbone pickup point, although with this the track rod end must also match the vertical height of the top outboard pickup point, however due to the clearance boards this is not generally feasible unless the inboard suspension mountings are mounted sufficiently far apart. To this end rack placement and reducing bump steer becomes trickier. Minimising bump steer is a priority when it comes to steering so this will be the aim of the steering joint locations. Parallel or more Ackermann steering geometry is also the desired aim although in reality this is of little importance New Suspension Aims The aims the author wants to achieve with a new suspension design are as follows: A kingpin inclination angle of between 0 and 8 A scrub radius between 0 mm and 100 mm A caster angle between 3 and 7 Static camber of around -2 but adjustable between 0 and -4 Camber gain of between 0.2 and 0.5 at the front axle Camber gain of between 0.5 and 0.8 at the rear axle A maximum roll of about 2 A roll centre height between 25 mm below ground and 50 mm above ground at the front and marginally higher at the rear Controlled and predictable movement of the roll axis A swing arm length of between 1250 mm and 2500 mm at the front A swing arm length of between 1016 mm and 1778 mm at the rear Minimal bump steer 50% - 65% of the roll stiffness on the rear axle This ideal setup has come about through reading of reference material and talking to people in the motorsport industry. 32 P a g e

38 5 Suspension Geometry Design 5.1 Wheelbase The first key parameters that set the overall size of the system are the wheelbase and the front and rear track. As discussed previously these play a great part in the load transfer and the cornering ability of the vehicle. The rules state the smallest wheelbase maybe 1525 mm, getting as close to this as possible is the ideal target however many factors play into this. A key one is the chassis obviously needs to accommodate the driver, engine, drivetrain and ancillaries, this therefore makes the chassis a certain length, the rear wheels are ideally set in line with the drivetrain to make transferring power as stable as possible without loading up the CV joints to much under extreme angles. Working forward from this enough space must be provided for the engine and engine ancillaries, the main roll hoop will come after this point along with the fuel tank, firewall, driver s seat and the driver. The cockpit must have a certain opening size so this dictates a minimum cockpit size. This and an allowable driver s arm length then places the front roll hoop. It s at this point we think of a front wheel centre point. Another thing to consider is the length of the driver s legs as well as room for pedals, as depending on where the front suspension is located changes the amount of overhang of the front bodywork and nosecone. Too much overhang means the nose has a large sweeping radius in a turn where as too little means the driver does not have enough room or the wheelbase is too long. The key here is to strike a perfect balance between them. Table shows the estimated lengths of the assemblies within the car, this is to give an idea of where the front suspension should be located. Table Estimated Assembly Lengths Assembly Length (mm) Drivetrain 250 Engine 330 Ancillaries 150 Cockpit 730 Driver s Legs 500 Pedals 290 Crash Structure 250 Total 2500 Going off the values in Table the estimated total length of vehicle is 2500 mm or 2.5 metres. As the rear suspension ideally sits in line with the middle of the drivetrain assembly this value can be halved to 125 mm. This makes the total length from rear driveline to tip of 33 P a g e

39 the nose as 2375 mm. From this value we can work out our wheel base on percentage overhang. Table below shows the wheelbase in mm for different percentage nose overhangs, the table starts at 15% as any less than this and the suspension would be floating ahead of the chassis, and it does not go past 40% because as you can see this value is smaller than the allowed wheelbase as described in the rules in Section 1.5. For this reason and to make the numbers easier to work with, adjusted values have been produced also seen in Table Table Wheelbase for Percentage Nose Overhang Percentage Nose Overhang (%) Wheelbase (mm) Adjusted Wheelbase Values (mm) From these values and a rough centre of gravity location it is possible to then do some simple calculations to determine rough axial and wheel loads and longitudinal weight transfer from Equations and Equations The centre of gravity location is taken to be roughly a quarter of the way into the cockpit forward of the rear roll hoop or 800 mm in front of the rear axle line and 400 mm off the floor. The braking G is taken to be 1.5G. Table Axial Wheel Loads at Rest and Under 1.25G Braking Wheelbase (m) Front Load (N) Rear Load (N) Front Load Under Braking (N) Rear Load Under Braking (N) P a g e

40 Load (N) Formula Student Car Suspension Design Front Load Rear Load Front Weight Under 1.25G Braking Rear Weight Under 1.25 Braking Wheelbase (m) Figure Graph of Wheelbase vs Loads and Braking Loads From Table it is obvious that the longer the wheelbase is the less load transfer from the rear to the front axle occurs under braking. This would suggest that a longer wheelbase is better, however longer wheelbases naturally have a larger turning radius. Looking at the static wheel loads, there is a clear spread and correlation as expected, an idea weight spread for a Formula Student car is around 50/50 front to rear, with excess weight being towards the rear, if there does happen to be a spread this will help with traction on the drive wheels. For this reason a wheelbase of metres or 1675 mm is the chosen wheelbase because it produces a near 50/50 weight split, with approximately 47.5% to the front and therefore 52.5% to the rear. The load transfer for this wheelbase is a little worse than expected but is within an acceptable range. 5.2 Track Width The track width of the front and rear axle are key parameters in the cornering performance of the vehicle, looking back to Section it tells us the minimum circuit width is 3.5m, and minimum outer corner diameter is 9m. Too narrow a track will result in high lateral load transfer as given by Equation Lateral Load TransferAlthough too large a track will result in the Formula Student car having to move more lateral distance to negotiate obstacles. Figure Weight Transfer during Cornering For Different Track Widths the linear relationship between track width and weight transfer. 35 P a g e

41 Weight Transferred (N) Formula Student Car Suspension Design Lateral Acceleration Force 0.9m Track Width 1m Track Width 1.1m Track Width 1.2m Track Width 1.3m Track Width 1.4m Track Width Figure Weight Transfer during Cornering For Different Track Widths As revealed earlier in Section 1.5, The smaller track of the vehicle (front or rear) must be no less than 75% of the larger track. (IMechE, 2014) To prevent corner exit understeer it is desirable to have a smaller rear track, as this reduces the push on effect induced by the rear tyres under acceleration. Another advantage to a smaller rear track although not related to the performance of the vehicle, is that with a smaller rear track there is less chance of the driver hitting the course cones trying to negotiate a corner with his rear wheels once they are past his field of view. For these reasons the middle range of track widths has been chosen, it is believed that 1.4m and 1.3m wide are slightly too wide leaving minimal room either side to manoeuvre around the course. For this reason 1.2m or 1200m has been chosen for the front track, and 1.1 m or 1100 mm chosen for the rear track. A smaller rear track could be chosen but the author believes that closer to a square profile is the slightly better option. 5.1 Wheels, Brakes and Offset Now that overall dimensions for the vehicle have been decided, the process can start to move inboard. The next components that need to be decided upon and constrained together are the wheels, the brake calliper and disk, and then the wheel offset. Although this year the team has greater use of the budget than previous year, it has been decided to be smarter with the money and spend it in key areas, this means that wheels and tyres are being reused from last year. This sets the geometry of the wheels, their diameter and tyre size. Figure shows the CAD geometry of the chosen wheels, they are the Team Dynamics Pro Race wheels. They were originally chosen for their lightness, price and the fact that they are easily obtainable. 36 P a g e

42 Figure Wheel CAD Geometry These wheels can come in a range of offsets, however the offset brought forward from last year is 35 mm. Although the specific offset of the wheel is not adjustable, it is possible to include a spacer to decrease this offset value. Figure Front Wheel with Brake Calliper and Disc Figure Rear Wheel with Brake Calliper and Disc Figure and Figure show the front and rear wheel with corresponding brake callipers inserted. Both brake callipers are supplied by AP Racing as well as their corresponding discs. The front callipers are 2 piston radial mounted callipers from there Pro range, they are the smallest in this range but should provide significant stopping power. As the rear wheel will take less load under braking smaller callipers are needed to induce wheel locking. For this reason, smaller lug callipers from the 2 piston range are being used on the rear of the vehicle. To minimise the size of the hubs and the weight of the hubs a 20 mm spacer will be used on each wheel to bring the offset down to 15 mm. Figure shows the wheel with the offset spacer. 37 P a g e

43 Figure Wheel with Spacer to Reduce Offset 5.2 Upright and Outer Pivot Points The next stage in the design involves placing the lower pivot point as close to the brake rotor as possible. This involves selecting spherical bearings, estimating a clearance distance and estimating a minimum upright thickness. The spherical bearings are being supplied by Autosport Bearings, they are a miniature 5/16 th high misalignment spherical bearing perfect for motorsport applications. The reason for using imperial measurements for some motorsport components is due to the grade of bolt that is used. All key critical components will use N.A.S Bolts. These, as the name will reveal are made to National Aviation Standard this is an American marking of quality and standard, (hence the imperial measurements), and are the premium bolt on the market and a motorsport staple. The size of the bearing then dictates the holder. The bearing holder has an outer diameter of 28 mm so half this value to get the minimum distance to the wishbone bracket inner face, adding a 10 mm minimum thickness to the upright makes a minimum distance so far of 24 mm. It must be remembered that the medium camber value is -2 but the maximum value is -4, because of this the suspension system must be designed to -4 and then shimmed out on the outer mountings to achieve a value of -2. Adding 5 mm for the wishbone bracket wall thickness makes 29 mm. Adding an extra 4mm clearance for shims, makes a total maximum distance of around 33 mm. To this the distance from the inside edge of the brake disc to the wheel/hub flange is added and rounded up with extra disc clearance, this makes a minimum distance of 70 mm. This is near 38 P a g e

44 enough the same for the rear suspension, the distance from wheel/hub flange to the inside face of the disc is about 1 mm less, so these values will also be used. Figure Distance from Wheel/Hub Flange to Inside Face of Disc. Now their lateral position is sorted out the next step is their vertical position. On race cars it should be made as low as possible for structural reasons. (Milliken & Milliken, 1995) Following this advice the lower pivot point shall be placed a comfortably close distance to the lower edge of the wheel rim. The maximum inside diameter of the wheel rim is 322 mm, so if we round this to 320 mm, we have 160 mm either side of the centre to play with. According to Section 1.5 the wheel must have a minimum suspension travel of at least 50.8 mm travel. As this is technically 25.4 mm in each direction, and if a degree of safety is inbuilt we can say that we have a minimum clearance of 30 mm. Although this seems extreme, a major aim of the team this year is to pass scrutineering first time so everything is being designed with an added safety factor. To this end the lower ball joint is to be located 120 mm outward of the centre. 39 P a g e

45 Figure Lower Pivot Point For the upper pivot point there is more to consider. For the rear the tie-rods will be located in the same plane as the upper wishbones to eliminated bump steer. This is easily done as there is no steering rack across the internals of the car to dictate the location of the inner pivots. The front however is slightly different; the ideal situation would see the tie-rods in the same plane as the upper front wishbone. Although this may not be feasible due to the clearance board in Figure 1.5.1, we can still design the possibility into the outer geometry. With an ideal distance from the centre for each of the upper pivots as around 100 mm two different pivot heights were looked at to give some clearance indications. Figure and Figure show the horizontal clearance on the inside of the wheel rim and different vertical heights, 120 mm gives an even spread between the centre and the upper and lower pivots but it doesn t leave much horizontal room for the potential two upper pivot points. 110 mm was tried and this gave what is deemed to be sufficient clearance for the pivots not to contact the sides of the wheel centre. This value of 110 mm is used from here onwards for the upper pivots vertical height. 40 P a g e

46 Figure Upper Pivot Point Clearance 1 Figure Upper Pivot Point Clearance 2 To ease the manufacture of the uprights and to make them cheaper, and to reduce the costs of the build the kingpin inclination angle must be similar to the middle camber angle, there is some tolerance to this value, but it means that out kingpin inclination needs to be around the - 2 area. To keep the numbers even, an upper pivot point distance to the hub flange of 80 mm was trialled and this gave a KPI value of As this value is within the desired range of values it is acceptable, however this limited KPI value means that the scrub radius is going to be higher. Figure and Figure shows the KPI angle and a scrub radius of mm at 0 camber. Figure Upper Pivot Point and KPI Angle. Figure Scrub Radius at 0 Camber 5.3 Wishbone Lengths and Roll Centre Although this section is about wishbone lengths and roll centre, the wishbone lengths aren t so much chosen, as worked out. In our instance it is more a case of working out the minimum chassis width, dictated somewhat by Figure Picking front view inboard pickup points 41 P a g e

47 from there that, give a desired roll centre. Playing around with the wishbone lengths enables us to dial in to our desired track width and maximum camber angles. To gauge the minimum chassis distance to the centre line for the front of car the width of the profile board was halved and then multiplied by a factor of 1.2 to give a safety value. To this was then added to the outside diameter of the chassis tubing and this value was rounded up to give a whole number with some extra clearance for wishbone brackets. Equation Distance from Centre Line to Chassis Outer Calculation that this value was 240 mm. This value is to be used for the bottom inner wishbone pickup point. Equation Distance from Centre Line to Chassis Outer Calculation = = = 240 To calculate the rear value, an estimated transmission and engine size was found and a safety value added to this to ensure that there was no chance of interference. This minimum value was found to be 225 mm. It s at this stage that we move over from Solidworks to using VSusp, this is because this piece of software calculates the roll centre and other characteristics for us. By inputting all the values we have so far into the software we can find out the values that we have missing. These are the ride heights, front and rear, the distance from chassis centre to the upper inboard pivot point, and the vertical heights from the bottom of the chassis for both the top and bottom inboard pivot points. The first box to fill out is the front and rear ride heights. The rear ride height wants to be higher than the front, this doesn t just marginally help with the longitudinal roll centre gradient, it has also been requested by the Aerodynamics section of the team to help with under body flow and make possible space for a rear diffuser. The suspension must have a minimum travel distance of 25.4 mm in each direction, and as the underside of the car is not allowed to scrape along the ground at any point the ride height must be higher than this. The value chosen was 40 mm for the front and 60 mm for the rear. This gives a rake gradient of Last year there was minimal vertical height between the wishbones. This led to build problems when it became time to install the spring and damper system, as there was not enough room or the desired angles to install pushrods for an inboard system and a less than ideal location for an outboard spring and damper assembly. To this end the installed shock length was used as a guide to ensure sufficient room, this is around 225 mm. This however is 42 P a g e

48 perfectly vertical, as the pushrods will be angled, this value is shortened to around 190 mm. This value was taken as the minimum vertical wishbone distance. If at this point we consider the chassis as square, and have chassis outer to centre line equal for the top and bottom mounting points, this enables us to get a baseline wishbone length for our desired track value. We can now play around with a few values to get ball park roll centre and swing arm length values. These values are; the chassis bottom to lower wishbone distance, chassis centre line to upper wishbone mount distance and the two wishbone lengths. These values will also dictate our baseline camber. For the front suspension the height from the bottom of the chassis to the top wishbone mounting was increased to 270 mm. This gave a greater height for the top longitudinal chassis bar, this is thought to make bell crank and push rod positioning easier. The rear was raised slightly to 240 mm. This is due to differential size and position, making driveline design easier and shaft inputs to the wheels more linear. This corresponded with moving the lower wishbone mounting point up 75 mm and 60 mm, front and rear respectively. Figure Front Suspension Unrefined Figure Front Suspension Refined Figure Rear Suspension Unrefined Figure Rear Suspension Refined The centre line to upper wishbone mounting point and wishbone lengths were then refined to give the desired roll centres, instant centres, front view swing arm lengths and camber angles. This change can be seen in Figure 5.3.1, Figure 5.3.2, Figure Figure With the 43 P a g e

49 refined design complete we can produce a table of the parameters and the outputs produced. Table shows these parameters. Table Output Parameters Lower Upper Upper Wishbone Front View Camber Final Wishbone Length (mm) Wishbone Length (mm) Mounting Horizontal Distance from the Swing Arm Length (mm) Angle ( ) Track Width (mm) Centre Line (mm) Front Rear Some of these parameters plus the roll centre and instant centre locations can be seen in the whole views for both the front and rear suspension shown in Figure and Figure Figure Whole Front Suspension Front View Figure Whole Rear Suspension Front View As can be seen from Figure and Figure both roll centres are quite low with 9 mm and 25 mm, shown in the green boxes. The instant centre locations are shown in the pink 44 P a g e

50 boxes with swing arm length shown as well. The exact track width is also shown, this however will change slightly with camber changes. 5.4 Inboard Pivot Points and Side View Geometry Now we know all the outboard pivot point locations, wishbone lengths and inboard pivot point locations. We can now build a more detailed cad drawing, this is then used to produce the final inboard pivot locations. As long as the inner pivots for each wishbone are collinear through the designed centre from Section 5.3. It s at this stage that any anti-dive or anti-squat can be introduced. Starting with the front suspension the front view of the wishbone and hub pivot points is drawn. Figure Front Geometry Front View Drawing This is then repeated for the opposite side. 45 P a g e

51 Figure Whole Front View Geometry Drawing Now that the initial wishbone geometry is drawn out its time to decide how far apart the inner pivot parts for each wishbone will be. This can be decided by thinking how much space between the points is needed, and also by ideal chassis structure distances. The distances were 150 mm from the centre line, so a total wishbone width of 300 mm. At this point any desired caster can be introduced as well. By moving the lower wishbone outer pivot point forward 20 mm from the centre line a caster angle of 5.55 was achieved. This was in the range of values that was considered to be good, and near enough in the middle of the range. Figure Initial Front Suspension Wishbone Layout Drawing 46 P a g e

52 This was then transferred to the opposite side. The next step is to create some construction lines to define the horizontal position of the pivot points. This was done to give a forward taper to the geometry which would then transfer to the chassis, oversized bulkhead dimensions were used for this which can be seen in Figure This allows for the nose to taper down to the size needed to attach the standard impact attenuator. Lines then extended out towards the rear, these will act as markers for the front roll hoop sizing. Figure Front Suspension Drawing with Front Bulkhead Dimensions Lines are then drawn between these markers to act as locating points for the chassis drawing when designing the front roll hoop. As no anti-dive is to be designed into the system the wishbone pivot points will remain parallel to the ground plane. 47 P a g e

53 Figure Front Wishbone Drawing with Front Roll Hoop Dimensions The first part of this process was then repeated with the rear front view geometry. However the upper wishbone outer pivot was shifted forward 75 mm. This was to enable the rear toe arm to sit an equal distance behind the wheel centre. This means that the lower wishbone rear leg is only 75 mm behind the wishbone centre line.. Figure Initial Rear Wishbone Layout Drawing To make the chassis simpler the rear wishbone needs to taper out towards the main roll hoop, to this end more construction lines were added to constrain the inner pivot points. The sizing 48 P a g e

54 for the main roll hoop can be seen in Figure Along with the longitudinal distances from the rear of the chassis and the front. Also included is an estimated centre of gravity point. Figure Rear Wishbone Drawing with Main Roll Hoop Dimensions Lines are then extended from the wishbones through the main roll hoop guide and beyond until they meet in the vertical axis. This is the starting point to dial in some of the anti-squat feature. Figure Rear Wishbone Drawing with Anti-Squat Lines 49 P a g e

55 Viewing this drawing from the side view, the anti-squat lines make a bit more sense. If we look back to Section 3.10 we will remember that the % anti-squat if defined by the point at which the line from the side view instant centre and the contact patch intersect the vertical line for the centre of gravity. As the desired amount of anti-squat is 30% the lines must intersect at 1/3.33 of the way up the centre of gravity line. The angle of the wishbones can then be adjusted by altering the forward most distance value seen in Figure m gave a desired amount of upward slope but not excessive. By changing the angle and taper of the rear wishbones we change the shape of the rear of the chassis so this needs to be double checked to make sure that there is still enough room for the drivetrain systems to fit within the leftover space. Figure Rear Wishbone Drawing with Anti-Squat Dimensions These two drawings are then combined to create a whole suspension drawing shown in Figure Whole Wishbone Geometry Drawing Figure Whole Wishbone Geometry Drawing It s at this point that the chassis can be designed fully around the wishbone geometry. 50 P a g e

56 Figure Wishbone Geometry with Chassis 5.5 Springs, Bell Cranks and Lever Ratios Now that the chassis has been designed shock placement and bell crank ratios can be worked out, but first a pushrod mounting point on the lower wishbones should be decided. This will give us our pushrod lever ratio as well as a rough idea of where the upper end of the pushrod will be located. This point needs to clear the bearing housing and any upright or mounting bracket. It should be fairly close to the pivot point to aid in the transfer of forces. This distance is to be 50 mm as this will allow 28 mm for the wishbone pivot housing and an additional 22 mm for the pushrod mount and bearing. The mounting point is also elevated 15 mm above the top of the wishbone this is to give clearance for a rose joint spherical bearing and mount. The initial front pushrod is shown in Figure Initial Front PushrodThe top pivot point is initially situated 40 mm forward of the centre line of the upper wishbone, this is to aid with bell crank rotation and also increase space for bell crank itself. 51 P a g e

57 Figure Initial Front Pushrod The same strategy is used for the rear pushrod. However the lower pushrod bearing is not only offset 50 mm laterally, it is also offset 20 mm longitudinally forward this is to give clearance room around a 20 mm diameter driveshaft that sits along the centre line of the lower wishbone, with the pushrod being 12 mm diameter, 4 mm clearance is deemed to be sufficient. 52 P a g e

58 Figure Initial Rear Pushrod Whilst matching the initial front design to the chassis it became obvious that any design would encroach on the cockpit internal cross section seen in Figure For this reason a new point higher up on the chassis was then chosen and a new chassis bar installed for this purpose. As seen in Figure 5.5.3, Figure This increased the angle of the pushrod to above the horizontal. This not only increased the amount of space in the chassis for the shock and bell crank, it also increases the direct load path, as the pushrod is more vertical. 53 P a g e

59 Figure Extended Front Pushrod Figure Extended Front Pushrod with Chassis To work out the lever ratio for the wishbone we start with a free body diagram mm 50mm Figure Front Wishbone Free Body Diagram From this diagram we can then deduct the equation to work out our wishbone ratio. 54 P a g e

60 Equation Front Wishbone Ratio Equation Wishbone Ratio = 245 cos(41.17) = So if we want 60 mm of total vertical travel, the pushrod will have a total of mm of movement. This will then need to be translated into shock movement via the bell crank. The shock has a maximum travel of 50 mm, and full advantage of this distance should be used. The rear pushrod was then lined up with the chassis and its fit was good so there were no changes made at this point. Figure Rear Pushrod with Chassis Using the same free body diagram technique the wishbone lever ration can be found for the rear mm 50mm Figure Rear Wishbone Free Body Diagram From this diagram we can then deduct the equation to work out our wishbone ratio. 55 P a g e

61 Equation Rear Wishbone Ratio Equation Wishbone Ratio = 210 cos(39.77) = So this time 60 mm of wheel travel will equate to mm of pushrod travel. Again a bell crank will have to transfer this movement to the shock absorber. The next order is to sort out a shock mount on the chassis and to know the at rest shock length, this length is 225 mm. The front shocks will mount in the corner of the chassis where the front roll hoop meets the new chassis bar that the bell crank will mount to. The rear shocks will mount to the top of the differential assembly between the rear legs of the chassis. Figure Front Rough Shock Placement Figure Rear Rough Shock Placement Now the shock is roughly positioned, a bell crank pivot point can be set out for both the front and the rear. The pivot points are located in line with the centre of the upper wishbone for the front and in line with the pushrod mount on the rear. The reason the front pivot is staggered behind the pushrod point is to help the rotation of the bell crank, because the shock is longitudinal rather than lateral the motion of the pushrod needs to be rotated, this extra offset ensures that there is greater ability to rotate. A rough bell crank shape was then drawn around the pivot point, connecting the shock and pushrod. Initial dimensions were then chosen to give a starting ratio. This was then drawn out in a separate Solidworks drawing, these would act as bell crank calculators to assist with working out the ratios. Figure and Figure show the final bell crank ratios for both front and rear respectively, they also show the final pushrod lengths. 56 P a g e

62 Figure Front Bellcrank Ratio Calulator Figure Rear Bellcrank Ratio Calculator The front and rear bell crank calculators were then put through their range of motion with the output shock length being recorded to confirm the desired motion ratios for each. As will be seen the motion ratio is not quite constant so an average motion ratio will be used over the whole range. 57 P a g e

63 Table Front Bell Crank Motion Table Pushrod Offset Pushrod Change Shock length Shock Difference Shock Change Motion Ratio Shock Difference Shock Change Shock Length Figure Front Bell Crank Motion Chart The table and the graph show that the motion ratio is not a perfectly linear relationship therefore an average motion ratio is used for the front bell crank. This was found to be 1.32:1. 58 P a g e

64 Table 5.5.2Rear Bell Crank Motion Table Pushrod Offset Pushrod Change Shock length Shock Difference Shock Change Motion Ratio Shock Difference Shock Change Shock Length Figure Rear Bell Crank Motion Chart 59 P a g e

65 Again the Motion Ratio is not linear, but this time it is less linear. The ratio for the rear bell crank is 1.18:1 The two bell crank profiles for the front and rear can then be designed for the system. They must be able to take a bearing at the pivot and be strong enough to withstand the forces exerted on the suspension. Figure Finalised Front Bell Crank Figure Finalised Rear Bell Crank 60 P a g e

66 Now that the front and rear bell crank ratios are known they can be combined with the wishbone ratios to give the suspension leverage ratio. Front Suspension Leverage Ratio = = Rear Suspension Leverage Ratio = =0.732 Now that we know the leverage ratios we can work out the coil rate and the fitted rate for the front and rear springs using equations in Section Desired wheel frequencies were decided in Section 4.9, so it is also possible to work out the rough corner masses from the longitudinal loads splits in Section 5.1. An estimated unsprung mass for the front and rear was also included to give the sprung mass for each corner. Table Spring Rate Variables Table Front Rear Wheel Frequency (Hz) Corner Mass (Kg) Corner Unsprung Mass (Kg) Corner Sprung Mass (Kg) Motion Ratio Front Spring Rate = 4π = N/m = N/mm Rear Spring Rate = 4π = N/m = N/mm 5.6 Anti-roll Bars Now the ride frequencies for bump travel are set, the roll gradient for the desired springs can be calculated. Using the equations from Section 3.13 the anti-roll bar stiffness that is needed can be calculated. First solving for K φf and K φr. K φf = π (t f 2 ) K LF K RF 180 (K LF + K RF ) K φr = π (t R 2 ) K LR K RR 180 (K LR + K RR ) For these two equations we need to know the wheel rates front and rear. Equation Alternative Wheel Rateis used here. K F = = N/m K R = = N/m 61 P a g e

67 Inserting these values into the front and rear roll rate equations. K φf = π (1.22 ) ( ) K φr = π (1.12 ) ( ) Now the total roll gradient of the ride springs is worked out. = φ r A y = W H K φf + K φr = deg/g Now the desired total roll rate needs to be equated. = K φdes = W H/ ( φ A y ) = Nm/ deg roll = Nm/ deg roll = 1270 Nm/ deg roll This is used to work out the total ARB roll rate needed to increase the roll stiffness of the vehicle to the desired roll gradient. K φa = K φa = π 180 ( K φdes K T (t 2 /2) [K T (t 2 /2) π 180 K φdes] ) πk W (t 2 /2) 180 π 180 ( ( /2) [ ( /2) π ]) π ( /2) 180 K φa = Nm/ deg roll Lastly the front and rear ARB stiffness s can be calculated. K φfa = K φa N mag MR FA K φra = K φa (100 N mag ) MR RA 2 K φfa = K φra = ( ) = Nm/deg = Nm/deg 62 P a g e

68 5.7 Steering Geometry The last design step is the positioning of the steering arms and steering rack. Looking back at Section 3.9 we know the ideal position is to have the steering arm inclined towards the instant centre. So to start, the instant centre is drawn into the CAD model. The steering rack then needs to be chosen and roughly positioned so it doesn t interfere with the cockpit internal cross section board. Last year s steering rack is to be used to save costs for the team. The steering rack length is known already and unchangeable. The length from pivot to pivot on the steering rack is mm. After assessing a few positions, it became clear that the only area that would work would be in front of the lower wishbone centre line, and just above the wishbone itself. This gave clearance to the steering arm during suspension travel and also kept the steering rack out the way of the cockpit internal cross section board. This also meant the steering pivot on the upright would be in one of the two preferred understeer areas for camber compliance under lateral force, also talked about in Section 3.9. Then to bring the steering pivot on the upright forward, away from the wheel centre the steering rack was moved forward as close to the pedals as comfortably possible, this distance was found to be 80 mm. Now this was set, a line was drawn from the instant centre through the steering rack pivot and out to a line intersecting the upper and lower wishbone pivots. Now the height from the lower pivot to the steering pivot is adjusted until the steering rack is as low as possible. This distance was found to be 30 mm. Figure shows this drawing, the steering rack is shown as the horizontal dotted line in the centre and the two steering arms are the solid black lines. This position is designed to give minimal bump steer effect. Figure Steering Arm Location 63 P a g e

69 6 Initial Analysis In this first analysis the key parameters of the basic geometry for the front and rear suspension has been compared to the ideal parameters in Section Front Key Parameters Having done the initial analysis of the front suspension system a number of key values can be noted to compare against the ideal conditions, these are: A kingpin inclination angle of 2.49 A camber angle of A scrub radius of mm An instant centre inclination angle of A roll centre height of 9 mm An instant centre length of 1032 mm and a height of 24 mm A swing arm length of 1629 mm A front track of mm A caster angle of 4.97 A kingpin offset of 10 mm 6.2 Rear Key Parameters Having done the design of the rear suspension system a number of key values can be noted to compare against the ideal parameters, these are: A kingpin inclination angle of 2.49 A camber angle of A scrub radius of mm An instant centre inclination angle of A roll centre height of 25 mm An instant centre length of 771 mm and a height of -59 mm A swing arm length of mm A front track of mm 6.3 Comparison between the Design and the Initial Aims of the Design The new design parameters were then compared to the initial aims of the design. 64 P a g e

70 To compare the new suspension design to the initial parameters set as aims discussed earlier in Section 4.13 a table was drawn up showing the values for the main parameters that were found from the 2D simulation software and 3D CAD drawings. Table Comparison Table Criteria Kingpin Inclination Angle Caster Angle Static Wheel Camber Scrub Radius Roll Centre Height Swing Arm Length Current Suspension Front Rear Suspension Suspension Ideal Parameter Front Rear Suspension Suspension mm mm 9 mm 25 mm 1629 mm 1316 mm 0mm 100mm -25mm 50mm 1250mm 2500mm 0mm 100mm -15mm 60mm 1016mm 1778mm From this initial table it is clear to see that all the values are within the desired limits other than the static wheel camber. This value is higher to enable the camber of the suspension system to be dialled in with adjustable top upright mount spacers. 6.4 MSC Adams Model In order to analyse the suspension system, it was transferred to the MSC Adams software package. As stated earlier in Section 2.3, MSC Adams is a multibody dynamics software package. A basic assembly was downloaded from the MSC Software website, each individual subsystem was then modified using the hard point adjustment tool to give the required geometry. The dynamic parameters such as spring and damper rates were also adjusted; a standard Formula Student tyre model was also used with this system. The front suspension assembly can be seen in Figure P a g e

71 Figure MSC Adams Front Suspension Assembly The upper and lower wishbone can be seen in light blue and red respectively, while the pushrod is in black and the steering arm in white. The anti-roll bar is in grey across the back, while the shocks are in yellow longitudinally at the top. This same process and colour scheme were used for the rear suspension assembly seen in Figure Except this time the driveline is also in grey. 66 P a g e

72 Figure MSC Adams Rear Suspension Assembly Once the suspension assemblies for both front and rear were created, a centre of gravity and relative sprung mass were positioned and defined within the full assembly. This full assembly can be seen in Figure This assembly along with the Vsusp model from the suspension design stage where used to do some analysis to the suspension geometry, and its performance characteristics. Figure MSC Adams Full Suspension Assembly 67 P a g e

73 Camber (deg) Camber Change (deg/mm) Formula Student Car Suspension Design 6.5 Camber Gain Due to Bump and Droop A graph of camber change due to bump and droop of the front and rear wheels can be produced to aid vehicle analysis. For this graph the static camber value has been adjusted to simulate the adjustment on the actual product, so static camber is now set to -2 for both the front and rear. For the front we have a swing arm length of 1629 mm, from this we would expect the camber change to be fairly average. The graph in Figure Error! Reference source not found.error! Reference source not found.shows a camber change of 1.75 for a suspension travel of 50 mm which is roughly the full travel of the suspension system. The camber angle of the wheel stays within the desired static camber range of 0 to -4. This result can be verified using a simple equation noted earlier, Equation Equation Front Camber Change per mm of Travel degrees mm = 1 tan 1 ( 1629 ) = per mm And from the graph we can work out that the camber change per mm of travel is equal to This value is very close to the value from Equation For the rear the swing arm length is 1316 mm and we would expect the camber change to similar to the front. The graph in Figure shows a camber change of 2.19 for a suspension travel of 50 mm which is roughly the full travel of the suspension system. Again this result can be verified using a simple equation noted earlier in Equation Equation Rear Camber Change per mm of Travel degrees mm = 1 tan 1 ( 1316 ) = per mm And from the graph we can work out that the camber change per mm of travel is equal to This value is again very close to the value from Equation Figure Graph of Camber Change for the Front and Rear Suspension Bump (mm) Front Rear Front Difference Rear Difference Linear (Front) Linear (Rear) 68 P a g e

74 Camber Angle (deg) Formula Student Car Suspension Design 6.6 Camber Gain Due to Roll The initial suspension aims targeted a camber gain due to roll angle of between per degree at the front axle and per degree at the rear axle. Figure shows the camber change due to roll angle for the front and rear suspension geometry Front Camber Rear Camber Roll Angle (deg) Figure Camber Change Due to Roll Angle From the graph it is obvious to see that both camber changes are very similar. It is also noticeable that the front camber change is more than that of the rear. This instantly suggests that one of these parameters will not sit in the required area. By calculating the camber change per degree of roll we can find out which camber change is outside its ideal parameters. The front camber change has a range of 3.14 over the 5 of roll angle. Equation Front Camber Change per Degree of Roll Front Camber Change per Degree of Roll = = The rear camber change has a range of 2.88 over the 5 of roll angle. Equation Rear Camber Change per Degree of Roll Rear Camber Change per Degree of Roll = = From these simple calculations we can see that the front camber change due to roll is outside its ideal parameter of between per degree of body roll. The rear however is within the desired range of between per degree of body roll 69 P a g e

75 Roll Centre Height (mm) Roll Cnentre X Location (mm) Formula Student Car Suspension Design 6.7 Roll Centre Movement A key feature of the suspension aims was controlled and predictable movement of the roll axis. To look to see if this was achieved the effects of bump/droop and roll on the roll centre was investigated. The effects of roll angle on the X and Y location of the roll axis was looked at first Front Roll Centre Height Rear Roll Centre Height Front Roll Centre X Location Roll Angle (deg) Rear Roll Centre X Location Figure Roll Centre Location Due to Roll Angle From the graph we can see that the effects of roll have a stable and controlled movement. The roll centre height has a nice symmetrical arc for both the front and the rear. The roll centre moves a maximum of 36 mm at the front and 13 mm at the rear over a 5 roll motion, this equates to very little movement for both the front and the rear. Table Roll Axis Vertical Movement Due to Roll Angle Front Rear Total Movement (mm) Movement per Degree (mm) The X location of the roll axis however has a greater range of movement; this is due to the shallow instant centre inclination angle of the geometry. Although the movements are large, they are reasonably linear, this means that the motion of the roll axis is predictable, and expected. Table Roll Axis X Location Due to Roll Angle Front Rear Total Movement (mm) Movement per Degree (mm) P a g e

76 Roll Centre Height (mm) Roll Cnentre X Location (mm) Formula Student Car Suspension Design The movement of the roll centre due to single wheel bump was then investigated, for this the left wheel was moved vertically 25 mm in each direction to simulate the full movement of the suspension system. Figure shows the roll centre height and X location of the roll centre during the suspension movement Front Roll Centre Height Rear Roll Centre Height Front Roll Centre X Location Bump (mm) Rear Roll Centre X Location Figure Roll Centre Location Due to Bump Looking at the graph we can see some big movements of the roll centre. The more controlled of the two is the rear roll centre, as this just starts to ramp up at the limit of the suspension travel meaning that a majority of the movement is fairly linear, and only starts to increase after 10 mm of bump. Again the X location movement is quite large. The front roll centre movement is more erratic, this is due again to the shallow instant centre inclination angle. In droop, both the vertical movement and the X location of the front roll centre are linear and quite controlled, it s when the wheel goes into bump that things start to get irregular. The roll centre X location is the most unstable with the roll centre moving out to mm from the centre, while the vertical movement travels to -716 mm. this movement is not very desirable, but is a compromise that is traded off to get the small amount of camber change due to bump and droop that we see in Section 6.5. This erratic behaviour is not so as important as it might seem, due to the nature of the Formula Student competition, and the use of inexperienced drivers. This large roll centre movement could appear as a slight change is driving characteristics and may go unnoticed by an inexperienced driver, as they are not in tune with the system. 71 P a g e

77 6.8 Final Component Designs for the Formula Student Car During the writing of this report, a vast majority of the main components for the system were designed by the author. These included the front and rear uprights, the bell cranks as seen in Section 5.5, the wishbones, wishbone mounting brackets, hubs, brake disc bells, as well as selecting all the bearings for the system to enable to UWE Formula Student Team to build the current design in May of 2015 to be part of the 2015 UWE Formula Student entry at Silverstone. Below are a few images of the completed system to give an idea of the whole design. Figure Full Suspension CAD Assembly Figure Full Front CAD Assembly 72 P a g e Figure Full Rear CAD Assembly

78 Figure Whole CAD Assembly without Chassis Figure Front Suspension Corner Figure Rear Suspension Corner 73 P a g e