2007 Baja Project - Suspension - Motion Research Group

2007 Baja ProjectSuspension1) Table of Contents1) Table of Contents............................................................................................................. i2) List of Tables................................................................................................................. iv3) List of Figures................................................................................................................. v4) List of Equations............................................................................................................ix5) Nomenclature.................................................................................................................. x6) Introduction to Suspension Kinematics and Kinetics..................................................... 16.1) Suspension Kinetics................................................................................................. 16.1.1) Vehicle ride modeling (vertical dynamics) ...................................................... 26.1.2) Vehicle handling............................................................................................. 116.2) Suspension Kinematics.......................................................................................... 186.2.1) Track width and tire scrub.............................................................................. 186.2.2) Instant center and roll center position............................................................. 196.2.3) Camber angle.................................................................................................. 216.2.4) Caster angle and caster trail............................................................................ 246.2.5) Kingpin angle and scrub radius ...................................................................... 256.2.6) Toe angle, roll steer and bump steer............................................................... 276.2.7) Aligning torque or self centering moment...................................................... 306.2.8) Anti-dive/anti-squat........................................................................................ 306.2.9) Motion ratio and wheel rate............................................................................ 336.2.10) Roll stiffness................................................................................................. 346.2.11) Vehicle ride height........................................................................................ 356.2.12) Understeering/Oversteering characteristics of vehicle................................. 356.3) Spring rate determination ...................................................................................... 377) 2007 Suspension Kinematics........................................................................................ 387.1) Choosing the dimensions of the vehicle................................................................ 387.2) Choosing the suspension points............................................................................. 407.3) Choosing the suspension geometry angles ............................................................ 417.4) Choosing the inner suspension points ................................................................... 427.5) Choosing the steering tie rods lengths................................................................... 477.6) Choosing the strut mounting points....................................................................... 487.7) Design front and rear suspension to be consistent................................................. 498) 2007 Suspension kinetics.............................................................................................. 528.1) Handling analysis on 2006 vehicle........................................................................ 52i

2007 Baja ProjectSuspension8.2) Approach to designing 2007 suspension kinetics.................................................. 538.3) 2007 front and rear suspension shocks.................................................................. 548.4) The required spring rates based on the Olley criteria............................................ 548.5) CarSim model for 2007 vehicle............................................................................. 568.6) Necessary combination of Elka Suspensions springs............................................ 648.7) Evaluation of spring rate in CarSim ...................................................................... 658.8) Ride, bounce, pitch and wheel hop frequencies .................................................... 678.9) Prediction of vehicle performance in regards to the dynamic events.................... 729) Suspension Component Design.................................................................................... 749.1) Choice of Materials........................................................................................... 749.2) Front Suspension System.................................................................................. 759.2.1) Control Arms ............................................................................................ 759.2.2) Finite Element Analysis............................................................................ 769.2.3) Joints ......................................................................................................... 789.2.4) Steering tie rod and bump stop ................................................................. 809.3) Rear Suspension System........................................................................................ 829.3.1) Control Arms .................................................................................................. 829.3.2) Finite Element Analysis.................................................................................. 849.3.3) Joints............................................................................................................... 849.4) Installation ............................................................................................................. 8510) Shocks (Dampers & Springs) ..................................................................................... 8810.1) Chosen shocks ..................................................................................................... 8810.2) Adjustable Damping............................................................................................ 8910.3) Progressive spring rates....................................................................................... 9011) Hubs & Uprights......................................................................................................... 9311.1) Background & Research...................................................................................... 9311.2) Concepts & Brainstorming .................................................................................. 9311.3) CATIA Modeling ................................................................................................ 9411.4) FEA...................................................................................................................... 9511.5) Materials & Manufacturing Procedure Used....................................................... 9511.6) Finished Product.................................................................................................. 9511.6.1) Testing .......................................................................................................... 9511.7) Recommendations for Improvements.................................................................. 9612) Tires and Rims............................................................................................................ 9712.1) Background and Research .................................................................................. 97ii

2007 Baja ProjectSuspension12.2) Concepts and Brainstorming .............................................................................. 9712.3) CATIA Modeling ............................................................................................. 10512.4) Additional Analysis .......................................................................................... 10512.5) Materials and Manufacturing Procedures Used................................................ 10612.6) Finished Product............................................................................................... 10612.6.1) Product Assembly and Maintenance ......................................................... 10612.6.2) Testing ........................................................................................................ 10612.7) Recommendations for Improvement ................................................................ 10713) Suspension tuning and testing .................................................................................. 10813.1) Suspension kinematics adjustment and measurement....................................... 10813.2) Dynamic tuning of the suspension..................................................................... 11113.3) Problems during testing..................................................................................... 11214) Strain gage testing .................................................................................................... 11614.1) Background & Research.................................................................................... 11614.2) Concepts & Brainstorming ................................................................................ 11614.3) CATIA Modeling .............................................................................................. 11814.4) FEA.................................................................................................................... 11914.5) Additional Analysis ........................................................................................... 12014.6) Materials & Manufacturing Procedure Used..................................................... 12114.7) Recommendations for Improvements................................................................ 12115) Suspension Prototype ............................................................................................... 12215.1) Background & Research.................................................................................... 12215.2) Concepts & Brainstorming ................................................................................ 12215.3) ADAMS Modeling ............................................................................................ 12315.4) Additional Analysis ........................................................................................... 12715.5) CATIA & FEA .................................................................................................. 12715.6) Materials & Manufacturing Procedure Used..................................................... 12915.7) Finished Product................................................................................................ 13015.7.1) Product Assembly & Maintenance............................................................. 13015.7.2) Testing ........................................................................................................ 13215.8) Recommendations for Improvements................................................................ 13316) References and contacts............................................................................................ 13916.1) Contacts ............................................................................................................. 13916.2) Websites............................................................................................................. 14016.3) Books and professional papers .......................................................................... 141iii

2007 Baja ProjectSuspension17) Appendixes ............................................................................................................... 14317.1) Appendix A........................................................................................................ 143The derivation of the half car model....................................................................... 14317.2) Appendix B........................................................................................................ 145The derivation of the bicycle model........................................................................ 14517.3) Appendix C........................................................................................................ 14817.4) Appendix D........................................................................................................ 154Critical speed calculations of 2006 vehicle............................................................ 15417.5) Appendix E........................................................................................................ 15617.6) Appendix F ........................................................................................................ 157Predicted spring rates............................................................................................. 15717.7) Appendix G........................................................................................................ 158Acceleration Plots................................................................................................... 158Acceleration and Cornering ................................................................................... 160Braking.................................................................................................................... 161Braking and Cornering........................................................................................... 162S Shaped Plots......................................................................................................... 1632007 Jump Performance......................................................................................... 165Cornering................................................................................................................ 16617.8) Appendix H........................................................................................................ 16717.9) Appendix I ......................................................................................................... 18017.10) Appendix J....................................................................................................... 193Spreadsheets to record the data during testing........................................................ 19317.11) Appendix K...................................................................................................... 19717.11.1) Rear suspension assembly Bill of Material: ................................................. 19717.11.2) Front suspension assembly Bill of Material ................................................. 20117.12) Appendix L...................................................................................................... 2052) List of TablesTable 1: Summary of vehicle dimensions......................................................................... 40Table 2: Static Suspension Angles.................................................................................... 42Table 3: Estimated cornering stiffness of the 2006 tires................................................... 52Table 4: Critical speed of 2006 vehicle ............................................................................ 52Table 5: Weight of the vehicle and weight distribution.................................................... 54iv

2007 Baja ProjectSuspensionTable 6: Ride frequencies of the 2005 vehicle.................................................................. 55Table 7: Required spring rates for 2007 vehicle based on Olley criteria.......................... 55Table 8: The main and auxiliary springs required to obtained the appropriate ridefrequencies ................................................................................................................ 64Table 9: Spring rate evaluation results.............................................................................. 66Table 10: The frequencies of the vehicle.......................................................................... 67Table 11: Summary of material properties ....................................................................... 74Table 12: 2003 Testing Data............................................................................................. 97Table 13: Tire Pressure ................................................................................................... 1073) List of FiguresFigure 1: Vehicle axis system............................................................................................. 2Figure 2: The quarter car model.......................................................................................... 3Figure 3: Bounce/pitch model............................................................................................. 5Figure 4: The half car model............................................................................................... 8Figure 5: The front and the rear suspension amplitudes as a function of time ................... 9Figure 6: Eigenvalues verses vehicle speed for an understeering vehicle........................ 15Figure 7: Oversteering and Understeering Vehicle .......................................................... 16Figure 8: The lateral force verses the slip angle ............................................................... 17Figure 9: Vehicle track width ........................................................................................... 19Figure 10: The roll axis of the vehicle.............................................................................. 19Figure 11: The effect of the jacking forces....................................................................... 20Figure 12: Roll center position of a double A-arm type of suspension ............................ 21Figure 13: Definition of camber angle (note in the figure one is looking at the vehiclefrom the front)........................................................................................................... 22Figure 14: The effect camber has on the tire contact patch .............................................. 22Figure 15: The effect of the camber angle on the cornering curve................................... 23Figure 16: Caster angle and caster trail............................................................................. 24Figure 17: Kingpin angle (steering inclination angle) and scrub radius........................... 26Figure 18: Toe angle (note the view in the figure is the top view)................................... 27Figure 19: The necessary steps to locate the tie rod position to have no toe angle changewith suspension travel............................................................................................... 29Figure 20: The pitch center............................................................................................... 31Figure 21: Anti-dive suspension geometry....................................................................... 32v

2007 Baja ProjectSuspensionFigure 22: Anti-squat suspension geometry ..................................................................... 32Figure 23: Motion ratio..................................................................................................... 33Figure 24: The lateral force verses the vertical force for a given slip angle..................... 36Figure 25: Vehicle Dimensions ........................................................................................ 38Figure 26: Rear end of vehicle.......................................................................................... 39Figure 27: Front and Rear Uprights.................................................................................. 40Figure 28: Wheel hub........................................................................................................ 41Figure 29: ADAMS/Car suspension modeling................................................................. 43Figure 30: Anti Squat Angle............................................................................................. 44Figure 31: Anti Squat Reaction......................................................................................... 44Figure 32: Longitudinal wheel travel................................................................................ 45Figure 33: Roll Center Height and Swing Arm Length.................................................... 46Figure 34: Camber Gain.................................................................................................... 46Figure 35: Steering tie rod length ..................................................................................... 47Figure 36: Tie rod clearance with control arm.................................................................. 48Figure 37: Motion Ratio.................................................................................................... 48Figure 38: Roll Center Lateral Position............................................................................ 50Figure 39: Roll Center Vertical Position .......................................................................... 50Figure 40: Roll Stiffness ................................................................................................... 51Figure 41: Track Width Change ....................................................................................... 51Figure 42: The three interfaces in CarSim........................................................................ 57Figure 43: Vehicle model in CarSim ................................................................................ 57Figure 44: The mass, Inertia and vehicle dimensions screen in CarSim .......................... 58Figure 45: The powertrain model in CarSim .................................................................... 59Figure 46: The brake model in CarSim............................................................................. 60Figure 47: The steering model in CarSim......................................................................... 61Figure 48: The front suspension kinematics model in CarSim......................................... 62Figure 49: The front suspension compliance model in CarSim........................................ 63Figure 50: Motion amplitude ratio for front excitation..................................................... 68Figure 51: Pitch/Excitation amplitude ratio for front excitation....................................... 68Figure 52: Motion of the rear unsprung mass/excitation amplitude for front excitation.. 69Figure 53: Motion of the front unsprung mass/excitation amplitude for front excitation 69Figure 54: Motion amplitude ratio for rear excitation ...................................................... 70Figure 55: Pitch/Excitation amplitude ratio for rear excitation ........................................ 70Figure 56: Motion of the front unsprung mass/excitation amplitude for rear excitation.. 71vi

2007 Baja ProjectSuspensionFigure 57: Motion of the rear unsprung mass/excitation amplitude for rear excitation ... 71Figure 58: The hill created to simulate the hill climb....................................................... 72Figure 59: Suspension and traction course ....................................................................... 73Figure 60: Front lower control arm................................................................................... 75Figure 61: Front upper control arm................................................................................... 76Figure 62: Front lower control arm FEA .......................................................................... 76Figure 63: Front upright FEA ........................................................................................... 77Figure 64: Front suspension assembly FEA ..................................................................... 78Figure 65: Laser cut tabs................................................................................................... 78Figure 66: Pivot joint construction ................................................................................... 79Figure 67: Caster adjustment mechanism......................................................................... 80Figure 68: Camber adjustment mechanism....................................................................... 80Figure 69: Steering tie rod ................................................................................................ 81Figure 70: Steering stop.................................................................................................... 81Figure 71: Schematic of rear lower control arm ............................................................... 82Figure 72: Rear control arms ............................................................................................ 83Figure 73: Aluminum rear upper control arm................................................................... 83Figure 74: Rear suspension assmebly FEA ...................................................................... 84Figure 75: Hiem joint........................................................................................................ 85Figure 76: Upright to control arm pivot............................................................................ 85Figure 77: Front control assembly .................................................................................... 86Figure 78: Rear control assembly ..................................................................................... 87Figure 79: Elka Suspensions coil over shock ................................................................... 88Figure 80: Rebound and compression damping adjustment............................................. 89Figure 81: Suspension springs with the crossovers .......................................................... 91Figure 82: Load versus displacement of Elka Suspension with longer sides of collarsfacing up.................................................................................................................... 92Figure 83: Load versus displacement of Elka Suspension with shorter sides of collarsfacing up.................................................................................................................... 92Figure 84: Final Catia model ............................................................................................ 94Figure 85: Rear Assembly FEA........................................................................................ 95Figure 86: Proposed test setup .......................................................................................... 96Figure 87: Tire internal cord scenarios ............................................................................ 98Figure 88 Tire contact patch reactions.............................................................................. 98Figure 89 Contact patch aligning moment........................................................................ 99vii

2007 Baja ProjectSuspensionFigure 90 Internal Pressure Model.................................................................................... 99Figure 91 Lateral force, traction force affect on slip %.................................................... 99Figure 92 Aligning moment for vertical loads and slip angles....................................... 100Figure 93 Lateral forces for brake forces at different slip angles................................... 101Figure 94 Lateral forces and aligning moments for different traction forces................. 101Figure 95 Vertical and longitudinal reactions for tire roll over a bump ......................... 103Figure 96 Tire natural frequency vibration modes ......................................................... 103Figure 97 Rolling loss factor graph ................................................................................ 104Figure 98 CATIA Model of Rim .................................................................................... 105Figure 99 CATIA Model of Rear Suspension Assembly ............................................... 106Figure 100: Caster angle measurement........................................................................... 109Figure 101: Toe angle measurement............................................................................... 110Figure 102: Camber angle measurement ........................................................................ 111Figure 103: Track with measurement ............................................................................. 112Figure 104: The protection layer on the control arms..................................................... 113Figure 105: The bend in the control arm ........................................................................ 113Figure 106: Angle iron to reinforce the rear control arms .............................................. 114Figure 107: The wear in the bushings............................................................................. 114Figure 108: Timken tapered needle roller bearings ........................................................ 115Figure 109: Strain gauge testing specimen ..................................................................... 117Figure 110: Bending of test specimen ............................................................................ 117Figure 111: Axial test on specimen ............................................................................... 118Figure 112: Specimen modeled in Catia......................................................................... 118Figure 113: 2004 lower control arm model .................................................................... 118Figure 114: 2004 lower control arm FEA for 500 lb loading......................................... 119Figure 115: Cantilever FEA simulation.......................................................................... 119Figure 116: Axial FEA simulation.................................................................................. 120Figure 117: 2007 control arm gauging locations ............................................................ 120Figure 118: Tailing arm and Semi trailing arm .............................................................. 122Figure 119: Semi trailing arm......................................................................................... 123Figure 120: Tailing arm .................................................................................................. 123Figure 121: New semi trailing arm ................................................................................. 124Figure 122: Camber angle comparison........................................................................... 124Figure 123: Roll centre comparison................................................................................ 125Figure 124: Toe angle comparison ................................................................................. 125viii

2007 Baja ProjectSuspensionFigure 125: Anti Squat comparison ................................................................................ 126Figure 126: Wheel travel track comparison.................................................................... 126Figure 127: Prototype Suspension Assembly 1 .............................................................. 128Figure 128: Prototype Suspension Assembly 2 .............................................................. 128Figure 129: Rear Lower Control Arm FEA.................................................................... 129Figure 130: Rear Upper Control Arm FEA .................................................................... 129Figure 131: Prototype front view.................................................................................... 130Figure 132: Prototype back view .................................................................................... 130Figure 133: Prototype top view....................................................................................... 131Figure 134: prototype side view ..................................................................................... 131Figure 135: Joint and axis control................................................................................... 132Figure 136: Camber checking 1...................................................................................... 132Figure 137: Camber checking 2...................................................................................... 133Figure 138: Semi trailing arm 1...................................................................................... 134Figure 139: Semi trailing arm 2...................................................................................... 134Figure 140: Tailing arm 1 ............................................................................................... 135Figure 141: Tailing arm 2 ............................................................................................... 135Figure 142: New Semi trailing arm 1 ............................................................................. 136Figure 143: New Semi trailing arm 2 ............................................................................. 136Figure 144: Other suspension 1 ...................................................................................... 137Figure 145: Other suspension 2 ...................................................................................... 137Figure 146: Other suspension 3 ...................................................................................... 1384) List of EquationsEquation 1: The equations of the quarter car model........................................................... 2Equation 2: The natural frequencies of the unsprung and sprung mass ............................. 3Equation 3: The natural frequency of the both the unsprung and sprung mass in hertz..... 4Equation 4: The amplitudes of displacements of both masses (unsprung and sprung) ...... 4Equation 5: Bounce and pitch equations of motion (neglecting damping)......................... 5Equation 6: Motion ratios at each of the natural frequency................................................ 5Equation 7: Natural frequencies in bounce and in pitch..................................................... 6Equation 8: Equations of motion in bounce and pitch........................................................ 6Equation 9: Bounce and pitch damped natural frequency .................................................. 7ix

2007 Baja ProjectSuspensionEquation 10: The half car model equations ........................................................................ 8Equation 11: Sprung and unsprung mass.......................................................................... 10Equation 12: The equations used in the bicycle model..................................................... 11Equation 13: Equations of motion in steady state cornering ............................................ 12Equation 14: Vehicle yaw rate as a function of the steering angle................................... 12Equation 15: The cornering radius as a function of the kinematic cornering radius ........ 12Equation 16: The kinematic turning radius....................................................................... 12Equation 17: Body slip angle............................................................................................ 13Equation 18: The body slip angle as a function of the steering angle .............................. 13Equation 19: The limit of the β/δ ratio for an understeering vehicle................................ 13Equation 20: Critical speed of an oversteering vehicle .................................................... 14Equation 21: Characteristic speed of an understeering vehicle ........................................ 14Equation 22: Solution to the transients associated with the bicycle model ...................... 15Equation 23: Magic tire Formula...................................................................................... 17Equation 24: Tire cornering stiffness................................................................................ 18Equation 25: Condition for proper Ackermann steering................................................... 29Equation 26: Aligning moment......................................................................................... 30Equation 27 : Wheel rate................................................................................................... 34Equation 28: Roll stiffness as a function of ride rate........................................................ 34Equation 29: 3 cases to determine whether the vehicle will oversteer or understeer basedon the bicycle model ................................................................................................. 35Equation 30: Ride frequency ............................................................................................ 37Equation 31: The spring rate of 4 springs in series........................................................... 64Equation 32: Caster angle from measurements .............................................................. 108Equation 33: Toe angle measurement............................................................................. 1105) NomenclatureRR0mrr&uabC fC rActual cornering radiusLow speed cornering radius (kinematic), obtained when cornering without lateralslip.Mass of the vehicleYaw rateRate of change of vehicle yaw rateVehicle’s forward velocityDistance between the center of mass and the front axleDistance between the center of mass and the rear axleThe cornering stiffness of both of the front tiresThe cornering stiffness of both of the rear tiresx

2007 Baja ProjectSuspensionα f Front tire slip angleα r Rear tire slip angleF z Normal load at the tireF y Lateral Force at the tireµ yz Lateral force coefficientγ Camber angleC Cornering stiffnessE Tire belt compression modulusb t Tire belt thicknessw Tire belt widthr t Rim radiuss Sidewall vertical deflection when loaded (unitized percent)a t Tire aspect ratio (height/width)a lat Lateral accelerationδ Steering angleδ * Limit steering angle (based on a lateral acceleration of 0.5g’s)v Lateral velocityv& Rate of change of the lateral velocityI Yaw inertiaβ Body slip angleF f Lateral force on both of the front tiresF r Lateral force on both of the rear tiresx The coordinate direction from the center of gravity to the front of the car. Alsothis coordinate rotates with the vehicle, rotating frame of reference.y The coordinate direction from the center of gravity to the side of the vehicle (thelateral direction). Also this coordinate rotates with the vehicle, rotating frame ofreference.u t Forward velocity of the tirev t Lateral velocity of the tireα f Front tire slip angleα r Rear tire slip anglevt f Lateral velocity of the front tirev tr Lateral velocity of the rear tireut fr Forward velocity of the front right tireut fl Forward velocity of the front left tiret w Vehicle widtht TimemsMeters per secondm Meters per second squared2sgdegGravity Constant (9.81m/s^2)Degreerad Radians/secondsxi

2007 Baja ProjectSuspensionsec, s Secondm MeterX Displacement of the vehicle in the x direction (forward)Y Displacement of the vehicle in the y direction (lateral)m Mass of the vehiclea Distance between the center of mass and the front axleb Distance between the center of mass and the rear axleI Pitch inertiat Timek f Front suspension spring constant (for both of the front suspensions)k r Rear suspension spring constant (for both of the rear suspensions)C f Front damping coefficient (for both of the front suspensions)C r Rear damping coefficient (for both of the rear suspensions)k tf Front tire spring constant (for both of the front tires)k tr Rear tire spring constant (for both of the rear tires)m s Sprung massm u Unsprung massm uf Portion of the unsprung mass associated with the front of the vehiclem ur Portion of the unsprung mass associated with the rear of the vehicler y Radius of gyration in pitchZ s Vertical motion of the vehicle bodyθ Vehicle pitch motionZ f Vertical motion associated with the unsprung mass at the front of the vehicleZ r Vertical motion associated with the unsprung mass at the rear of the vehicleh f Disturbance (excitation) motion at the front of the vehicleh r Disturbance (excitation) motion at the rear of the vehicleϖ n Natural frequencyϖ Frequency of excitationξ Damping ratiof 1 Approximate body motion frequencyf 2 Approximate wheel hop frequencym 2sdeg Degreerad Radians/secondssec, s Secondm MeterH z Hertzlb Poundin InchesN Newton’s per metermxii

2007 Baja ProjectSuspensionN Newton’s per meter per secondmsxiii

2007 Baja ProjectSuspension6) Introduction to Suspension Kinematics and KineticsVehicle dynamics is the study of all forms of transportation (trains, airplanes,boats, and automobiles). However vehicle dynamics as we know it is the study of theperformance of the automobile in all of its motions (ride, acceleration, cornering, andbaking). The vehicles suspension plays a key roll in each of these motions. The study ofa vehicles suspension can be broken into two major categories: suspension kinetics andsuspension kinematics. Suspension kinetics is a dynamic and a vibration analysis on thevehicle and suspension systems. Suspension kinematics involves analyzing the motion ofthe tires as the suspension compresses and extends. Each of these two divisions will beanalyzed in depth in the following sections.6.1) Suspension KineticsSuspension kinetics is an analysis that is important to the overall performance ofthe vehicle because it is what determines if the vehicle is capable of absorbing groundloads; it is what judges the comfort of the driver, it is what determines if the vehicle willroll or not; and it is what determines the resonant frequency of the chassis, the shock andthe tire; it is what determines the handling performance of the vehicle. The vehicle willsee a wide range of vibrations because of the speeds it travels and the boundaries ittravels on, thus it is important to analyze the resonant frequency of the suspensioncomponents and the chassis. The ride quality (or vertical dynamics) of a vehicle can beanalyzed using the half car model. The handling performance of the vehicle can beanalyzed using the bicycle model. However before each of these models are consideredit is important to define the vehicle axis and the appropriate rotations about each of theaxis.The conventional axis system is placed at the center of mass of the vehicle withthe x axis pointing towards the front of the vehicle, the y axis pointing towards the rightside of the vehicle, and the z axis pointing towards the bottom of the vehicle. The x axisis known as the longitudinal axis, the y axis is known as the lateral axis, and the z axis isknown as the vertical axis. The rotation about the x axis is know as roll, the rotationabout the y axis is known as pitch and the rotation about the z axis is known as yaw(Figure 1: Vehicle axis system).Vehicle ride modeling is the study of the motions transmitted to the vehiclechassis, and thus the motions felt by the passengers in the vehicle. The motionstransmitted to the vehicle chassis come from the vibration of the suspension as it absorbsthe motion coming from the disturbance at the ground. It is these vibrations that causethe passengers to feel uncomfortable when they are riding in a vehicle. Therefore,vehicle ride problems arise from the vibrations of the vehicle body (chassis). One of themain objectives of the suspension system is to control the vibrations of the vehicle bodyin order to provide a comfortable ride for the driver.1

2007 Baja ProjectSuspensionFigure 1: Vehicle axis system6.1.1) Vehicle ride modeling (vertical dynamics)Mechanical vibrations in a vehicle represent a very complex field, and usuallyrequire multiple degrees of freedom to accurately predict the vertical performance of thevehicle. However, there exist two simplified models which when combined give anaccurate approximation as to the ride quality of the vehicle. These include the quarter carmodel (corner model) (used to predict the motion of a single suspension unit) and thebounce/pitch model (used to predict the motions of the sprung mass of the vehicle).These models combined produce the half car model (four degrees of freedom model).The vertical performance of the vehicle is directly linked to the sprung mass, theunsprung mass, the pitch inertia, the suspension stiffness, the tire stiffness, the dampingin the tires, the damping in the suspension units, and the excitation frequency. Before thehalf car model is introduced, the quarter car model and the bounce/pitch models will beintroduced.The quarter car model is a model that models the motion of a single suspensionsystem (it models one corner of the car) (Figure 2: The quarter car model). The sprungmass in this model represents some portion of the total sprung mass of the system. Thetire is excited because of the shape of the path it is following (the shape is not flat,especially for an off road track). Applying Newton’s 2 nd law of motion the equations ofmotion that govern the quarter car model are as follows (Equation 1: The equations of thequarter car model).m && zm && zu2+ C( z&1− z&2) + ks( z1− z2) =( z&2− z&1) + ks( z2− z1) + Ctz&2+ ktz2= Ctz&0+ ktz0s 1+ Cs0sEquation 1: The equations of the quarter car model2

2007 Baja ProjectSuspensionFigure 2: The quarter car modelThis is a two degree of freedom system, thus there will be two natural frequencies (theunsprung and sprung mass will each have a resonant frequency). The wheel hopfrequency is the frequency associated with the unsprung mass it is usually around 10Hz.The body motion frequency is the frequency associated with the sprung mass and it isusually around 1 to 1.25 Hz. Note, the damping ratios in most suspension systems isrelatively low, therefore the majority of the time the undamped natural frequency will bereally close to the damped natural frequency thus the damped natural frequency is usuallycalculated by neglecting any damping in the system. The following equation can be usedto calculate the natural frequencies of the system. Note the natural frequencies arecalculated by neglecting damping in the system and neglecting any excitations (Equation2: The natural frequencies of the unsprung and sprung mass).⎡ms0 ⎤⎡&&z1⎤ ⎡ ks⎢+0⎥⎢⎥ ⎢⎣ mu⎦⎣&&z2⎦ ⎣−k2det[ k −ϖM ] = 0sk− kss+ kt⎤⎡z⎥⎢⎦⎣z12⎤ ⎡0⎤⎥ = ⎢0⎥⎦ ⎣ ⎦Equation 2: The natural frequencies of the unsprung and sprung massNote the above equation in matrix form leads to an eigenvalue problem by assuming thedisplacement of each mass to be harmonic (z = Zcos(ωt)). By solving the determinantwill lead to the natural frequencies of both masses in the system. The frequencies can beapproximated by the following equations (Equation 3: The natural frequency of the boththe unsprung and sprung mass in hertz).3

2007 Baja ProjectSuspensionff12==12π12πkkksssmmksut+ kt+ kt(body motion)(wheel hop)Equation 3: The natural frequency of the both the unsprung and sprung mass in hertzSome important observations can be made by solving the above equations. The firstobservation is that the sprung mass is well isolated at high frequency, however it will bepoorly isolated at low frequencies, and in some cases, at low frequencies the amplitude ofthe sprung mass can be amplified in such a way that it is greater than that of theexcitation amplitude.Damping will have an effect on the amplitudes of motion even though it does nothave a significant effect on the natural frequencies. The easiest way to solve for theamplitudes is to use a complex number approach (assume z = Ze iωt ). If this is taken intoconsideration the equations of motion will be as follows (Equation 4: The amplitudes ofdisplacements of both masses (unsprung and sprung)).2[ −ϖM + iϖC+ k]⎧z⎨⎩z12⎫⎬ =⎭⎧z1⎫ i⎨ ⎬e⎩z2⎭ϖt⎡ 0 ⎤ i= ⎢ Z0ekti t⎥⎣ + ϖ ⎦2−1⎡ 0 ⎤[ −ϖM + iϖC+ k] Z0⎢⎣kt+ iϖt⎥⎦Equation 4: The amplitudes of displacements of both masses (unsprung and sprung)Note, the result will be a complex number because of the phase lag between the motionand the disturbance (this is because of the damping in the system, note the i term next tothe C in the equation of motion above). The amplitude is simply the sum of the squaresfo the real and imaginary parts of the answer obtain from the above equation22( Z = real + imaginary ). The usual way to solve the equations to obtain theamplitudes is to assume the excitation is one, and calculate the amplitudes of theunsprung and sprung mass with respect to this input over a wide range of frequencies.This will allow the amplitude ratios to be obtained over a wide range of frequencies. Thedifference between the motion of the sprung and unsprung mass represents thesuspension shock travel, and the distance between the travel of the unsprung mass and theexcitation is the tire deflection. Tire deflection is a measure of handling because it is thenormal force that generates the necessary friction to propel the vehicle forward (ie if thenormal force is fluctuating up and down the tire is being prevented from griping theroad). Therefore, it can be seen that a stiffer suspension will hurt the tires capability fromgripping the road. The unsprung mass has almost no effect at low frequencies, but athigher frequencies a lower unsprung mass will lead to lower tire deflections and thusbetter handling performance of the vehicle. At mid range frequencies, a lower spring rateϖt4

2007 Baja ProjectSuspensionleads to a reduction in tire deflections, and thus improves tire grip. However, a lowerspring rate allows for increased body motions which are detrimental to vehicle handling.The bounce/pitch suspension model models the vehicle motions separately fromthe wheel motions (Figure 3: Bounce/pitch model).Figure 3: Bounce/pitch modelThe equations of motion that govern this system can be obtained by applying Newton’ssecond law of motion in both pitch and bounce to the system (note damping will be firstneglected so that the natural frequency can be obtained) (Equation 5: Bounce and pitchequations of motion (neglecting damping)).m && z + kms2sryf&& θ −2s yI = m r( z − aθ) + kr( z + bθ) = 0k a( z − aθ) + k b( z + bθ)fr= 0Equation 5: Bounce and pitch equations of motion (neglecting damping)The equations of motion are coupled as can be seen above. If it is assumed that thedisplacements are harmonic then the natural frequencies can be obtained (z = Zcos(ωt)and θ=Θ cos(ωt)). The following is the equation that would be obtained from assumingthe motions are harmonic for the natural frequencies (Equation 7: Natural frequencies inbounce and in pitch). The motion ratios can be obtained at each of these frequencies bysubstituting each of the results back into the equation of motion (Equation 6).ZΘZΘD2=ϖ − D21221D2=ϖ − D1Equation 6: Motion ratios at each of the natural frequency5

2007 Baja ProjectSuspensionϖDDD1,2123=1=ms1=ms121=m r( D + D ) ± ( D − D )1( k + k )2( k b − k a)2s yfr142 2( k a + k b )frfr132D+rEquation 7: Natural frequencies in bounce and in pitchThe bounce and pitch natural frequencies are usually very close to one another. They areusually between 1 to 1.5 Hz. The bounce and pitch equations of motion can be re writtento include damping in the equation of motion (damping is important when it is desired toobtained the amplitudes of motion) (Equation 8: Equations of motion in bounce andpitch).⎧&&z⎫⎧z&⎫ ⎧ z ⎫M ⎨&&⎬ + C⎨⎬ + K ⎨ ⎬ = 0⎩θ&⎭ ⎩θ⎭ ⎩θ⎭⎧&&z⎫− ⎧z&1 ⎫ −1⎧ z ⎫⎨&&⎬ = −MC⎨⎬ − M K ⎨ ⎬⎩θ&⎭ ⎩θ⎭ ⎩θ⎭⎡ms0 ⎤M = ⎢2 ⎥⎣ 0 msry⎦⎡ kf+ krbkr− akf ⎤K = ⎢2 2 ⎥⎣bkr− akfb kr+ a kf ⎦⎡ Cf+ CrbCr− aCf ⎤C = ⎢2 2 ⎥⎣bCr− aCfb Cr+ a Cf ⎦Equation 8: Equations of motion in bounce and pitchThe above equations of motion can be solved to obtain the natural frequencies andamplitude ratios, as well as the amplitudes for a given frequency. This can be done byreducing the equations from second order to first order (Equation 9: Bounce and pitchdamped natural frequency).222y6

2007 Baja ProjectSuspension⎧z&⎫⎪ ⎪& θ⎡ 02⎨ ⎬ =z⎢⎪&&⎪ ⎣−M⎪&&⎩θ⎪⎭Assumez = Zest⎧ z ⎫ ⎧ z ⎫⎪ ⎪ ⎪ ⎪θstθ⎨ ⎬se= [ A]⎨ ⎬e⎪ sz ⎪ ⎪ sz ⎪⎪⎩sθ⎪⎭⎪⎩sθ⎪⎭⎧ z ⎫⎪ ⎪θ⎨ ⎬ = 0⎪ sz ⎪⎪⎩sθ⎪⎭s = eigenvalue[ Is − A]x2−1K& θ = Θe[ A]I− Mst2x2−1st⎧z⎫⎪ ⎪⎤θ⎬ =C⎥⎨⎦⎪z&⎪⎪ &⎩θ⎪⎭[ A]⎧z⎫⎪ ⎪θ⎨ ⎬⎪z&⎪⎪ &⎩θ⎪⎭Equation 9: Bounce and pitch damped natural frequencyIt is important to note that the eigenvalues will be complex numbers because of the phasechange; however the natural frequency is just the sum of squares of the real andimaginary values. The damping ratio is the negative of the real part divided by thenatural frequency (ζ=-a/ωn). The amplitudes at all frequencies can be solved byassuming a value for either the pitch angle or the bounce and then solving the other valueover a wide range of frequencies.The bounce/pitch model and the quarter car model are two of the most powerfulmodels to predict the vertical motion of the vehicle. These two models can be combinedto create the half car model. This model couples the motions of the front and rearsuspension through the motion of the sprung mass (both bounce and pitch). This modelallows the wheel hop frequencies to be obtained for both the front and rear suspensions atthe same time. As well as the pitch and body motion frequencies can be obtained. Thehalf car model predicts the motions of the both the front and both the rear suspensionunits at once. There are certain assumptions used in this model, and these include that thetires on either side of the vehicle have the same effect on the dynamics, and the width ofthe vehicle is assumed to be constant. Also, it is assumed that the springs are linear, andthat the damping can be modeled as viscous dampers. The model consists of fourcoupled equations used to find the motions associated with the sprung mass and both theunsprung masses (Equation 10: The half car model equations) (Figure 4: The half carmodel) (Appendix A).7

⎡m⎢⎢0⎢ 0⎢⎣ 0s⎡⎢+ ⎢⎢⎢⎣0I00( kf+ kr) ( akf− bkr)2 2( akf− bkr) ( a kf+ b kr)− kf− km0r00uf0 ⎤⎧Z&&s⎫⎡⎪ ⎪0⎥ ⎢&&⎥θ⎨ ⎬ + ⎢0 ⎥⎪Z&&f⎪⎢⎥⎪ ⎪⎢mur⎦⎩Z&&r⎭⎣− akfbkr( Cf+ Cr) ( aCf− bCr)2 2( aCf− bCr) ( a Cf+ b Cr)− Cf− Cr− kf− akf( kf+ ktf)0( kr+ ktr)Equation 10: The half car model equations2007 Baja ProjectSuspension− Cf− Cr⎤⎧Z&s⎫⎪ ⎪− aC⎥f bCr&⎥θ⎨ ⎬− aCfCf0 ⎥⎪Z&f⎪⎥bCr0 Cr⎦⎪⎩Z&r⎪⎭− kr⎤⎧Zs⎫⎧ 0 ⎫bk⎥⎪⎪ ⎪ ⎪r⎥θ0⎨ ⎬ = ⎨( )( )( )( )⎪ ⎪ ⎬0 ⎥ ff tf⎪Z⎪ ⎪ h k⎥⎦⎪⎩Zr⎪⎭⎪⎩ hrktr⎭Figure 4: The half car modelThe following is a discussion on the important parameters that are applied in the half carmodel.The Suspension Stiffness and DampingThe suspension stiffness is one of the most important parameters whenconsidering the vertical performance of the vehicle. It is generally best to have amoderate spring rates. This is because low spring rates reduce the tire deflection whichincreases the tire grip, however it also allows for increased body motions (in roll and inpitch) which are harmful to the overall handling performance of the vehicle. Theopposite is true for high spring rates. Therefore, there should be a compromise betweenimplementing high and low suspension stiffness’. Also, according to Maurrie Olley thefollowing set of rules should be followed when designing a suspension system for thecomfort of the passenger, and they are:1. Front suspension should have a 30% lower ride rate than rear suspension8

2007 Baja ProjectSuspension2. Pitch and bounce frequencies should be close together, bounce frequency shouldbe 1.2 times the pitch frequency3. Neither the bounce nor the roll frequency should be greater than 1.3Hz.The reason for this is that the front of the vehicle will ride over the bump (ordisturbance) first creating an excitation in the front suspension, and then seconds later therear suspension will ride over the bump creating an excitation in the rear suspension. Ifthe two suspension rates are identical the phase lag between the front and the rearsuspensions will create an undesirable motion in pitch. There have been studies that haveshown that the driver/passenger is/are very uncomfortable in pitch motion, it tends tocause neck muscle strains. Therefore, by increasing the suspension rate in the rearsuspension allows for the rear of the vehicle to “catch up” to the front of the vehicle(Figure 5: The front and the rear suspension amplitudes as a function of time).Figure 5: The front and the rear suspension amplitudes as a function of timeIt can be seen from the figure above that there exists a phase lag between the front andthe rear excitations, and that by having a rear suspension rate higher than the frontsuspension rate allows for the rear excitation to catch up to the front excitation.The Tire Stiffness and DampingThe tires stiffness and the tires viscous damping coefficient are important to theride quality of the vehicle, but more importantly to the handling performance of thevehicle. In typical passenger car vehicles the stiffness of the tires is of an order ofmagnitude greater than the suspension stiffness. It is typically the tire deflection that isimportant for the handling performance of the vehicle, because the tire deflection is oneof the parameters in which decides the tires grip capabilities. As the deflection of the tireincreases, the grip capabilities of the tire will decrease. It is very important to not allowthe tire to lose contact with the ground, because if it does the car will not be controllable9

2007 Baja ProjectSuspensionin handling. Typically, the damping coefficient of the tires is neglected because it isgenerally very low compared to the other parameters in the system, and neglecting itresults in a small error in the analysisThe Sprung and Unsprung MassThe mass of the vehicle is an important parameter in the analysis of the verticaldynamics of the vehicle. The mass of the vehicle is one of the main parameters in whichwill decide the deflections of both the front and the rear tires, and the suspension unitswhen they are excited. The mass of the vehicle is divided into two parts the sprung massand the unsprung mass. The sprung mass consists of everything the suspension unitshave to support, and these include the chasis, and the engine. The unsprung massconsists of everything the tires have to support, and these include the front and rear axles.Typically the sprung mass is of an order of magnitude greater than the unsprung mass.Therefore the following formula can be used to calculate the sprung mass and theunsprung mass based on the mass of the vehicle (Equation 11: Sprung and unsprungmass).m = ms+ mum = 10mu+ mu⎛ 0.4535924kg3290lbs⎜mlbsmu= =⎝1111ms =( 10)( 135.67kg) = 1356.65kg⎞⎟⎠= 135.67kgEquation 11: Sprung and unsprung massWhen implementing the half car model the unsprung mass has to be further divided intothe unsprung mass supported by the front tires of the vehicle, and the unsprung masssupported by the rear tires of the vehicle.The Pitch InertiaThe pitch inertia is the inertia that arises in the rotation of the front and rear of thevehicle with respect to the center of mass. The pitch inertia is usually calculated usingthe radius of gyration. It is important in the study of the ride quality of the vehiclebecause it is one of the significant parameters in which determine the amount ofdeflection a vehicle will have in pitch. Generally, in order to have good ride quality inpitch the radius of gyration should be around 1.2m, and the ratio of the radius of gyrationsquared to the location of the front axle from the center of mass times the location of thery 2rear axles from the center of mass (( a)( b)) should be between 0.8 and 1.2. Thesevalues provide a desirable ride in pitch because the center of oscillations in pitch and rollwill be close to the front and the rear axle, thus allowing the motion in pitch created atone axle to somewhat cancel out the motion in pitch created at the other axle, and10

2007 Baja ProjectSuspensiontherefore minimizing the overall motion in pitch felt by the driver.The half car model leads to a good prediction of the vertical performance of thevehicle or the ride quality of the vehicle.6.1.2) Vehicle handlingThe Handling performance of an automobile is important to the all aroundperformance of the vehicle. The handling performance will determine how the car willexecute in turning corners; its lateral performance. There are many important parametersthat determine the lateral performance of a vehicle, these include but are not limited tothe location of the center of mass, tire cornering stiffness, the steering angle, the lateralvelocity, the forward vehicle velocity, the lateral acceleration, the rotational speed (yawrate), the body slip angle, and the tire slip angle. The model usually used to predict thelateral performance of the vehicle is the linear bicycle model.There are certain assumptions used in this model, and these include that the tireson either side of the vehicle have the same effect on the dynamics, and the width of thevehicle is assumed to be constant. The model consists of two coupled equations used tofind the lateral acceleration and the rate of change of the vehicles yaw rate whileassuming the forward vehicle speed is held constant (its in the control of the driver)(Equation 12: The equations used in the bicycle model) (Note, for a clarification of themodel see the derivation in Appendix B).⎡m⎢⎣ 0⎡0⎤⎧v&⎫ ⎢⎨ ⎬ + ⎢I⎥⎦⎩r&⎭ ⎢⎣( Cf+ Cr) ( aCf− bCr)u2 2( aCf− bCr) ( a Cf+ b Cr)uuu⎤+ mu⎥⎧v⎫⎧ Cf⎫⎥⎨⎬ = ⎨ ⎬δ⎥⎩r⎭⎩aCf⎭⎦Equation 12: The equations used in the bicycle modelOnce the above equations of motion are solved for the yaw rate, lateral velocity, lateraldisplacement and the vehicle yaw several other parameters can be solved for, and certaincharacteristics of the vehicle can be determined. Also certain cases can be analyzed indetail, and one such case is steady state cornering (lateral acceleration and rate of changeof the yaw rate are equal to zero) (Equation 13: Equations of motion in steady statecornering). Solving the equations of motion in steady state leads to the followingimportant equations (Equation 14: Vehicle yaw rate as a function of the steering angle)(Equation 15: The cornering radius as a function of the kinematic cornering radius).11

2007 Baja ProjectSuspension⎡⎢⎢⎢⎣( Cf+ Cr) ( aCf− bCr)u2 2( aCf− bCr) ( a Cf+ b Cr)uuu⎤+ mu⎥⎧v⎫⎧ Cf⎫⎥⎨⎬ = ⎨ ⎬δ⎥⎩r⎭⎩aCf⎭⎦Equation 13: Equations of motion in steady state corneringrδ=2a + b −muu( aC − bC )( a + b) CfCrEquation 14: Vehicle yaw rate as a function of the steering angleRR0mu= 1−2( aC − bC )2( a + b) CfCrEquation 15: The cornering radius as a function of the kinematic cornering radiusThe second equation (equation 15) is important because it describes the path theundersteer/oversteer characteristics of the vehicle. If the vehicle was cornering with nolateral slipping than the vehicle would corner about a perfect circular path with a radiusof R 0 (R 0 is known as the kinematic turning radius) (Equation 16: The kinematic turningradius).ffrrEquation 16: The kinematic turning radiusThe kinematic turning radius is the radius in which the driver is aiming for the vehicle tofollow. Examination of equation 15 reveals that if aC f < bC r than the vehicle willundersteer. If the vehicle understeers, the radius of the path will increase with vehicle12

2007 Baja ProjectSuspensionspeed. In order to maintain the desired path of the vehicle the driver will have to increasethe steering angle with vehicle speed. If aC f > bC r the vehicle oversteers, and thecornering radius will decrease with vehicle speed. The driver will have to decrease thesteering angle as the speed of the vehicle increases in order to maintain the desired pathof the vehicle. If aC f = bC r the vehicle neutral steers and will turn on the kinematicturning radius. The radius of curvature will be independent of vehicle speed. It is alsoimportant to note that understeer/oversteer characteristics is also affecting by theinclination of the roll axis and the front and rear suspension roll stiffness as will be seenin the suspension kinematics section. The cornering stiffness of the driving wheels willchange as the traction (driving) force increases (as the traction force increases the lateralforce will decrease (friction circle)). For a front wheel drive vehicle this effect is to forcethe vehicle to understeer, and for a rear wheel drive to force the vehicle to oversteer.When the vehicle is cornering it does not point in the direction it is traveling in,this is known as body slip. The vehicle will experience a body slip angle (Equation 17:Body slip angle).vtan β ≈ β =uEquation 17: Body slip angleUsing the steady state bicycle model the body slip angle can be solved for as a functionof the steering angle (Equation 18: The body slip angle as a function of the steeringangle).βδb −=2mua + b −2amuC( a + b)( aC − bC )( a + b) CfCrEquation 18: The body slip angle as a function of the steering angleAt low speeds, the β/δ ratio will be positive which indicates that the rear wheels will trackinside the front wheels. However, at high speeds the opposite will be true; the rearwheels will track outside the front wheels. For an understeering vehicle the β/δ ratio willtend to a limit; at high speeds it will be a constant (Equation 19: The limit of the β/δ ratiofor an understeering vehicle).frrβδlim it=aCaCff− bCrEquation 19: The limit of the β/δ ratio for an understeering vehicleAn oversteering vehicle will have larger slip angles than an understeering vehicle, and theβ/δ ratio will tend to infinity at a critical vehicle speed. The vehicle will become unstable13

2007 Baja ProjectSuspensionat the critical vehicle speed (Equation 20: Critical speed of an oversteering vehicle).ucritical=CfCr( a + b)( − bC )m aCfr2Equation 20: Critical speed of an oversteering vehicleIf the critical speed is reached the driver is capable of stabilizing the vehicle with steeringinputs. The r/δ ratio will also go to infinity at the critical speed for an oversteeringvehicle; however for an understeering vehicle the r/δ ratio will reach a maximum at thecharacteristic speed (the highest amount of yaw rate for a given steering angle will occurat this speed) (Equation 21: Characteristic speed of an understeering vehicle).ucharacteristic=CfCr( a + b)( − aC )m bCrf2Equation 21: Characteristic speed of an understeering vehicleThe transient effects of vehicle cornering can be considered by solving the bicyclemodel with zero steering angle; the model is solved assuming that the driver is not goingto react (the steering angle is zero). It is important that the transient effects die out overtime; that is the amplitude of vehicle oscillations tends to zero over time. If it does not goto zero, then the vehicle will be unstable. It is best to use an eigenvalue approach whensolving the bicycle model to analyze the transient effects of the vehicle (Equation 22:Solution to the transients associated with the bicycle model). If s is smaller than zero thevehicle will be stable. Analyzing the equation that determines the value of s will indicatethat if C is greater than zero than the vehicle will always be stable. This occurs for anundersteering vehicle. An understeering vehicle will always be stable. However, for anoversteering vehicle the value of C will become negative at the critical speed. This isimplying that an oversteering vehicle will be stable up until the critical speed, but oncethe critical speed is reached the vehicle will become unstable. It is also important to notethat the solution can take on real and complex solutions. We are generally looking forour vehicle to have a stable response (want s to be negative or a complex number with aas being negative) indicating that the yaw rate and lateral velocity will decayexponentially to zero. If we have an unstable response the yaw rate and the lateralvelocity will increase when excited causing the vehicle to loose control. It is generallybetter to design the vehicle so that it is an overall understeering vehicle because it isguaranteed to be stable. Negative eigenvalues are basically indicating that the system iscapable of correcting itself (allow for the yaw rate and the lateral velocity to decay backto zero) if excited without any input from the driver. The only difference between thereal and the imaginary parts is that in the imaginary part of the eigenvectors will fluctuateas they decay to zero, a frequency will exist (Figure 6: Eigenvalues verses vehicle speedfor an understeering vehicle).14

2007 Baja ProjectSuspensionMx&+ Cx = 0⎧v⎫x = ⎨ ⎬⎩r⎭assume x = XeMsXest( Ms + C)Xdet( Ms + C)A = mIuB =C =+ CXe( aC − bC )⎡ Cf+ Crf r ⎤⎢ms++ mu ⎥Ms + C = ⎢u u2 2 ⎥⎢ ( aCf− bCr) ( a Cf+ b Cr)Is⎥⎢+⎣ uu ⎥⎦Solving the determinant leads to the following22 2mu( a Cf+ b Cr) + Iu( Cf+ Cr)22( a + b) C C − mu ( aC − bC )2− B ± B − 4ACs =2Ast= 0fst= 0= 0rfrEquation 22: Solution to the transients associated with the bicycle modelFigure 6: Eigenvalues verses vehicle speed for an understeering vehicleThe eigenvectors are the associated response of the vehicle when it is operating at that15

2007 Baja ProjectSuspensionparticular eigenvalue. As previously mentioned, these eigenvectors allow for the vehicleto be a stable vehicle. Also as the vehicle’s speed is increased the –s value decreases,indicating that the yaw rate and lateral velocity will approach zero at a slower rate. Thatis as the vehicle’s speed increases it’ll take a longer time for the yaw rate and the lateralvelocity to approach zero.The tire cornering stiffnessThe tire cornering stiffness is an important parameter in determining the handlingperformance of the vehicle. It is to some extent arbitrary; each tire has its own stiffness,and the tires on a vehicle can be changed. Therefore the cornering stiffness can bechosen by the user to precisely predict turning (cornering) characteristics of the vehicle.It is this parameter that will determine whether the car is an understeering (the actualcornering radius increases with vehicle speed) or an oversteering (the actual corneringradius decreases with vehicle speed) automobile because the center of mass of the vehicleis a fixed parameter (Figure 7: Oversteering and Understeering Vehicle). It is generallybetter to have an understeering vehicle, because the vehicle is normally more stable. Inan oversteering case, the vehicle oversteers the turn, and the driver will be forced todecrease the steering angle as he/she turns in order to stay on the desired path (the paththe vehicle takes when there is no lateral slipping).Figure 7: Oversteering and Understeering VehicleThere are also more chances that the vehicle spins on the spot (about its own z-axis). Inan understeering case, the car understeers and the driver is forced to increase the steeringangle in order to stay on the desired path. There are several ways to determine the tirescornering stiffness. Two of these ways are by using the magic tire model and second byusing an estimation given the tires dimensions.Magic tire modelThe stiffness can be estimated as the slope of the linear range on the lateral forceverses slip angle diagram, which can be obtained from the magic tire model (Figure 8:The lateral force verses the slip angle, on the following page).16

2007 Baja ProjectSuspensionFigure 8: The lateral force verses the slip angleHowever, tests will have to be done on the tire in order to determine the necessarycoefficients to apply the magic tire formula (Equation 23: Magic tire Formula).Fy = DsinC = a110D = µ yzFµ yz = a1Fz+ aE = a6Fz+ a7111{ C arctan[ B( 1−E)( α + Sh) + E arctan( B( α + Sh))]}⎡ ⎛ FBCD = a3sin⎢2arctan⎜⎣ ⎝ aB = BCDCDSh= a8γ+ a9Fz+ a10Sav= a2= a11γFz+ az12Fz+ aFz+ a11213z4⎞⎤⎟⎥⎠⎦( 1−a5γ)+ SvEquation 23: Magic tire FormulaTire Cornering Stiffness Obtained from the Tire GeometryThe tire cornering stiffness can also be obtained from the geometry of the tire byassuming that the tire is a cantilever beam. This cantilever beam is acted on by a selfaligningmoment and a shearing stress which act together to generate contact patch twistduring cornering. With some manipulation of the tire slip angle (deflection) obtainedfrom the cantilever beam an expression for the cornering stiffness can be obtained(Equation 24: Tire cornering stiffness).17

C =2[( rt+ wat)]⎡ ⎡ ⎛⎢sin⎢arccos⎜1−⎢⎣⎣ ⎝2swat3Ebtw⎞⎤⎤⎛⎡⎜⎛⎟⎥⎥π − sin⎢arccos⎜1−⎝2007 Baja ProjectSuspensionswat⎞⎤⎞⎟⎥( r ) ⎜( ) ⎟ t + wat⎠⎦⎥⎦⎣ ⎝ rt+ wat⎠⎦⎠6.2) Suspension KinematicsEquation 24: Tire cornering stiffnessSuspension kinematics is the study of the motions of the tire. It describes theorientation of the tire as a function of wheel travel and steering angle. The motions of thetire are highly dependent on the type of suspension. In general there are two types ofsuspension systems; solid axles and independent suspensions. A solid axle suspension isa suspension where the movement of one wheel is transmitted to the other wheel causingthem to move together. This type of suspension is essentially a dependent suspension,the motion of the two wheels are correlated to one another. The biggest advantage of thistype is that the camber angle is not affected by vehicle body roll. The majordisadvantage of this type of suspension is the vibrations which are induced into thesystem if the solid axle suspension also incorporates vehicle steering. Independentsuspension systems allow the left and right wheels to move independently; the movementof one wheel will have no effect on the other wheel. The advantages of independent typeof suspensions are: they provide better resistance to steering vibrations; they provide ahigh suspension roll stiffness; steering geometry is easily controlled; suspensiongeometry is easily controlled; and they allow for higher wheel travel. The majordisadvantages are: the camber angle changes quite a bit over suspension travel; increasedunsprung mass; and the high cost of the system.The study of suspension kinematics allows for several different suspensionparameters to be determined throughout suspension travel and steering angle. Some ofthe most important parameters include: roll center position and instant center, camberangle, caster angle, toe angle, tire scrub, kingpin angle, scrub radius, caster trail, aligningmoment, vehicle ride height, track width, wheel rates, roll stiffness, roll axis,understeer/oversteer characteristics, roll steer, bump steer, motion ratio, and antidive/anti-squat.The following will be a discussion of each of these parameters.6.2.1) Track width and tire scrubThe track width is a measure of the distance between the center of the tire contactpatches at the front and rear of the vehicle (Figure 9: Vehicle track width). The trackwidth will change as the wheels travel through the suspension travel, and this change isknown as tire scrub. The change in the track width is a measure of the location of theinstant center of motion of the suspension. As the track width is changing the tires areforced to push out or pull in at the ground, and thus the tires are forced to scrub againstthe ground. Typically, if the suspension is in compression the tires will scrub out, and ifthe suspension is in rebound the tires will scrub in. Tire scrub (track width change)18

2007 Baja ProjectSuspensioncauses the rolling tires to slip and therefore generates lateral forces. Thus if one wheelgoes over a bump (causes the tire to scrub) there will be a disturbance in the lateraldirection; one side of the vehicle can start to see a larger lateral force than the other andthe vehicle may begin to yaw. Therefore it is important that the change in the track widthbe kept to a minimum.Figure 9: Vehicle track width6.2.2) Instant center and roll center positionThe instant center is the point the wheel rotates about relative to the vehiclechassis. It is a function of the geometry of the suspension system. The instant center isimportant because it defines the position of the roll center. The roll center position is aposition where the lateral forces developed at the wheels are transmitted to the vehiclesprung mass. This point will affect the behavior of both the sprung and unsprung massand thus effects the vehicles cornering characteristics. The roll center is defined as thepoint in the transverse vertical plane where the lateral forces may be applied to the sprungmass without producing any suspension roll. The definition of roll center derives fromthe fact that a vehicle will posses a roll axis (Figure 10: The roll axis of the vehicle).Figure 10: The roll axis of the vehicleThe roll axis is the instantaneous axis where the unsprung mass will rotate relative to thesprung mass when a pure couple (moment) is applied to the unsprung mass. The rollcenter is the intersection of the roll axis with the vertical plane at the front and rear of the19

2007 Baja ProjectSuspensionvehicle. Typically, the roll center position is located based on the suspension geometryand then the roll axis is located by defining a line which connects the two roll centerstogether. The roll axis is also the instantaneous axis in which the whole vehicle rotateswith respect to the ground.The amount of body roll depends on the height of the center of mass relative tothe roll center position. Therefore raising the roll center position closer to the center ofmass is equivalent to increasing the roll stiffness of the suspension. However, as the rollcenter position is increased (roll center height measured from ground level is increased)the amount of jacking forces will increase. The jacking forces are the forces that willtravel through the suspension components to the vehicle body; it is the force that is notabsorb by the suspension system. Thus as the amount of jacking forces increase, theamount of forces absorbed by the shock will decrease. Forces generated at the tire havetwo paths into the vehicle: a flexible path and a stiff path. The stiff path is through thesuspension components and the flexible path is through the suspension spring (Figure 11:The effect of the jacking forces).Figure 11: The effect of the jacking forcesThus as the roll center is increased, the forces traveling through the stiff path willincrease and the forces traveling through the springs will decrease causing less springcompression. The jacking forces will tend to lift the vehicle as it corners. Therefore,there should be a balance in roll center height between suspension roll stiffness and thejacking forces seen by the frame. It is important to note that the roll center is a fictitiouspoint. Forces that are traveling from the ground to the chassis will not pass through thispoint. The location of this point will not be able to determine the suspension rollstiffness, nor will it be able to determine the magnitude of the jacking forces. This pointis strictly there to give a relative idea of the roll characteristics of the vehicle.The roll center position is calculated differently for each type of suspensionsystem. The procedure for calculating the roll center position will be outlined for thedouble A-arm type of suspension only (if it is desired to learn how to calculate the rollcenter position for a different suspension system, than it is advised to look in vehicledynamics text book). The first step is to locate the instant center. This is accomplishedby drawing a line that passes through each of the A-Arms when looking at the vehicle in20

2007 Baja ProjectSuspensionthe front view. The intersection of these lines represents the instant center. The secondstep is to draw a line form the center of the tires contact patch to the instant center. Thepoint where the line drawn in step two intersects the center line of the vehicle representsthe roll center position (Figure 12: Roll center position of a double A-arm type ofsuspension).Figure 12: Roll center position of a double A-arm type of suspension6.2.3) Camber angleThe camber angle is defined as the inclination of the tire with respect to the roadsurface in the vertical plane (when looking at the vehicle from the front view). Negativecamber occurs when the top of tire points in towards the vehicle, and positive camberoccurs when the top of the tire points out away from the vehicle (chassis) (Figure 13:Definition of camber angle (note in the figure one is looking at the vehicle from thefront)). Camber on a wheel will produce a lateral force which is known as camber thrust.A rolling tire that is cambered will produce a lateral force which is in the direction thetire is tilting in. When the camber angle is generating a lateral force with no slip anglepresent it is known as camber thrust. Camber force or camber thrust is a function of thefollowing parameters: tire type, tire geometry, pressure, tread pattern, camber angle, slipangles, traction or braking force, and the tire dimensions.Camber thrust is easily understood by examining the contact patch of a tire. If thecontact patch of the tire is examined when the vehicle is not moving with no camberangle, it will be an oval shape which represents the area the tire is in contact with theground. If he contact patch is examined when the vehicle is not moving with a camberangle the contact patch will be an oval shape but will be curved in the direction of the tiltof the tire.21

2007 Baja ProjectSuspensionFigure 13: Definition of camber angle (note in the figure one is looking at the vehicle from the front)If the contact patch is examined when the vehicle is moving with no sideslip angle andwith a camber angle the contact will be an oval shape that will not be distorted or curved(Figure 14: The effect camber has on the tire contact patch).Figure 14: The effect camber has on the tire contact patchThe camber thrust is the amount of force required to straighten out the contact patch sothat it is perfectly oval. Therefore, there are two things which generate a lateral force;camber angle and slip angle. The lateral force generated by a slip angle will be greaterthan the lateral force generated by a camber angle; that is the lateral force generated from1 degree of slip angle will be greater than the lateral force generated from 1 degree ofcamber angle. The cornering stiffness (∆Fy/∆α) is generally five to six times greater thanthe camber stiffness (∆Fy/∆γ). Thus, the effective cornering stiffness of a tire is theaddition of the cornering stiffness and the camber stiffness and it is this value that shouldbe used to predict the handling dynamics of a vehicle. For a tire that has a positivecamber angle the effect is to decrease the effective cornering stiffness, and for a tire thathas a negative camber angle, the effect is to increase the effective cornering stiffness.Therefore, the peak lateral force is increased by adding negative camber to the tires22

2007 Baja ProjectSuspensionwhich is a good thing; the lateral capabilities of the tire are increased (Figure 15: Theeffect of the camber angle on the cornering curve).Figure 15: The effect of the camber angle on the cornering curveAs can be seen in the figure above, the effective cornering stiffness of the tire doesincrease as the tire is cambered in the negative direction.The camber angle at which the maximum amount of lateral force will occur willchange with the initial lateral load (lateral load at 0 degree camber). As the initial loadincreases the maximum load will occur at a later negative camber angle. Typically themaximum amount of lateral force or maximum (Fy/Fz) will occur at a camber anglebetween -2 and -7 degrees.When a vehicle corners it will roll and thus will force the tires to camber by thesame amount on both sides; the tires will camber at the roll angle on both sides, one willcamber out and one will camber in. However, as the vehicle rolls, there will be weighttransfer from the left to the right and thus the suspension on one side of the vehicle willbe in jounce while the suspension on the other side will be in rebound. Therefore therewill be a change in the camber angle from the movement of the tire with respect to theframe. Thus, the total camber angle when the vehicle is cornering is the addition of theroll angle and the camber angle obtained from the kinematics of the suspension. Theamount of lateral force generated during roll will depend on both the roll angle and theangle generated from the kinematics of the suspension; that is the amount of camberthrust generated will depend on the roll angle.In general, it is best to go with a static negative camber angle because it improvesthe effective cornering stiffness of the tire and it increase the maximum lateral force or23

2007 Baja ProjectSuspensionthe Fy/Fz ratio. However too much of a negative camber angle is undesirable becauseeventually it will start to decrease both the cornering stiffness and the Fy/Fz ratio. Also,a large camber angle (negative or positive) increases tire wear which is undesirable. Forbest performance the camber angle should remain between -2 and -7 degrees throughoutthe suspension travel.6.2.4) Caster angle and caster trailThe caster angle is defined as the angle between the steering axis and the verticalplane viewed from the side of the tire. The caster trail is defined as the distance at theground between the center of the contact patch (also known as wheel contact point) thepoint at which the steering axis intersects the ground (Figure 16: Caster angle and castertrail).Figure 16: Caster angle and caster trailThe caster angle is positive when the steering axis (the steering axis is defined as a linethat passes through the ball joints on the upper and lower control arms) is inclined in sucha way as it points to the front of the vehicle; a good way to remember positive casterangle is from the forks of a motorcycle (they are always inclined to the front). The casterangle defined in the figure above is a positive caster angle. Positive caster trail occurswhen the steering axis intersects the ground at a point that is in front of the center of thecontact patch. The caster trail defined in the figure above is a positive caster trail.It is important that the caster angle and caster trail be positive because both ofthese quantities will effect the aligning moment. The aligning moment is the momentthat will act against the driver as he/she is trying to steer the vehicle. It is important that24

2007 Baja ProjectSuspensionthis moment acts against the driver so that when the driver lets go of the steering wheel itwill correct itself; the moment will force the tire to re straighten itself.Caster trail is important because it defines how much of a moment will be appliedto the steering axis; as the caster trail increases, the moment arm increases and thus themoment acting on the steering axis will increase. It is this moment that is acting to selfcenter the tire if the caster trail is positive. However, if the caster trail is too large thedriver will have a difficult time trying to turn the wheels about the steering axis.Caster angle will cause the wheel to rise or fall during steering. Caster anglecauses the wheel to displace up or down as the wheel is turning about the steering axis.Therefore, if the caster geometry is the same on both sides the vehicle will roll as it isbeing steered; one side will toe out and one side will toe in, thus one side will lift and oneside will fall causing the vehicle to roll. The caster angle also affects the camber angle asthe wheel is turned about the steering axis. With the same positive caster angle on bothwheels the outside tire in a turn will camber in a negative direction and the inside tire willcamber in a positive direction. This effect is a bit desirable because it allows the vehicleto lean into the turn. Therefore, it is desirable to have a small positive caster angle and asmall to moderate caster trail to produce desirable results. The caster angle should not beincreased too much because it will cause too much camber angle change with steer andwill cause to tire to raise or fall too much with steer.6.2.5) Kingpin angle and scrub radiusThe kingpin angle is the angle between the steering axis and the vertical planewhen viewing the tire from the front. The scrub radius is the distance measured at theground level between the center of the contact patch and the point where the steering axisintercepts the ground. The scrub radius is measured when looking at the wheel from thefront plane (Figure 17: Kingpin angle (steering inclination angle) and scrub radius). Apositive kingpin angle occurs when the steering axis points outward; note the kingpinangle defined in the figure is positive. A positive scrub radius occurs when the steeringaxis intercepts the ground at the inside of the tire; note the scrub radius shown in thefigure is a positive scrub radius.It is important that the kingpin angle and scrub radius are positive because both ofthese quantities will effect the aligning moment. The aligning moment is the momentthat will act against the driver as he/she is trying to steer the vehicle. It is important thatthis moment acts against the driver so that when the driver lets go of the steering wheel itwill correct itself; the moment will force the tire to re straighten itself.The effect of a positive kingpin angle is to raise the wheel as the wheel is turnedabout the kingpin axis. The greater the kingpin angle is the more the wheel will rise as itis being steered. Note, the wheel will rise regardless of the direction it is being turned. Itis to be noted that the greater the distance between the ball joints for a given kingpinangle the greater the amount of lift that will occur. Essentially, the kingpin angle and thelength between the ball joints is trying to raise the wheel so that it can center the steering25

2007 Baja ProjectSuspensionaxis to provide less scrub while steering.Figure 17: Kingpin angle (steering inclination angle) and scrub radiusThe kingpin angle affects the camber angle as the wheel is steered about the steering axis.With a positive kingpin angle, the tire will lean out as it is steered about the steering axis.Therefore, the greater the steering angle, the greater the amount of positive cambergenerated, and the greater the kingpin angle the greater the amount of change in thecamber angle. When a wheel is rolling over a bump, the effective rolling radius of thetire will change, thus resulting in changes in the effective rolling speed of the tire. Thechange in the rolling speed of the tire will give rise to a longitudinal force acting at thewheel center, and this causes a kickback into the steering system. The reaction forcescaused by the change in the rolling speed will try to force the wheel to toe, and thus causea shock to the driver, and the driver will have to react quickly in order to correct thischange in toe angle. The amount of kickback is proportional to the distance between theball joints, the greater the distance, the greater the amount of kickback.Driving and braking forces will introduce a torque about the steering axis, and thistorque will be proportional to the moment arm, the scrub radius. If the driving andbraking forces are different on either side of the vehicle than the driver will feel a netsteering torque acting to steer the vehicle. The amount the tire scrubs against the groundas the wheel turns is dependent on the scrub radius. If one the wheels losses tractionwhen the vehicle is braking then the opposing wheel will toe an amount that isdetermined by the compliance in the steering system. This will tend to steer the car in astraight line even though the braking forces are the same on both sides. Note the lasteffect described will only occur when the scrub radius is negative. In general, a smallnegative scrub radius is desired, however if the scrub radius is negative than the kingpinangle will be have to be large in order to ensure the aligning torque is positive.Typically, a small positive scrub radius is used on vehicles with a small to moderatekingpin angle is used. If the distance between the ball joints is large then a smallerkingpin angle is used and if the distance is small then moderate kingpin angles are used.26

2007 Baja ProjectSuspension6.2.6) Toe angle, roll steer and bump steerThe toe angle is defined as the angle between the longitudinal axis of the vehicleand a line passing through the center of the tire when viewed from the top (Figure 18:Toe angle).Figure 18: Toe angle (note the view in the figure is the top view)Toe in occurs when the front of the tire points in towards the vehicle, and tow out occurswhen the front of the tire points away from the vehicle. The concept of toe in and toe outis outlined in the figure above. The toe angle is a measure of the initial steer of thevehicle. There will be usually some elastic deformation of the suspension under drivingor braking that will cause changes in the toe angle. Therefore, it is common practice toput an initial toe angle on the suspension system so that the deformation in the systemwill force the tire to straighten when the vehicle is driving or braking. The tire is usuallytoed so that the tire will be straight when the vehicle is propelling forward. However, ifthe braking acceleration is much higher than the driving acceleration then the tire will beinitially toed in so that it will straighten itself when the vehicle is braking.It is important to recognize that the suspension and steering systems are coupled.As the suspension goes through its travel, so does the tie rod and it is important that thetire does not toe with suspension travel. The inside point of the tie rod is fixed (the pointat the steering rack) so that if the length of the tie rod is not at the correct length and thetie rod does not have the same instant center as the suspension system then as the27

2007 Baja ProjectSuspensionsuspension travels and thus the tie rod travels (but not at the appropriate path) it will forcethe tire to rotate about the steering axis. Bump steer by definition is toe angle changewith suspension travel. If one tire goes over a bump and experiences a toe angle changethe vehicle will steer. This condition is very troublesome for the driver because thedriver will consistently have to correct the vehicle as the vehicle travels over changes inroad conditions. Roll steer occurs when a vehicle rolls and there is weight transfer andthus the suspension on the inside compresses and the suspension on the outside goes intorebound. The net effect is that one side of the vehicle will toe in and one side of thevehicle will toe out, thus forcing the vehicle to steer as it rolls. The steering geometrycan be chosen such that the more the vehicle rolls the more it will steer or the less it willsteer. Therefore, the oversteer/understeer characteristics can be controlled by the rollsteer effect. However, most of the time the suspension geometry and tie rod position andlength are chosen to minimize toe angle change with suspension travel, and thusminimizing the effects of roll steer and bump steer.The following is a discussion of how to choose the position and the length of thetie rod in order to have no change in toe angle with suspension travel. This is a veryimportant concept and needs to be considered when designing the suspension andsteering systems. The tie rod should lie on a line passing through the instant center of thesuspension system, and on this line a proper length can be chosen. The following is a listof the proper steps to take in order to choose the proper tie rod position and length.1. Draw a line that passes through the steering axis (this line will pass through theball joints of the upper and lower control arms)2. Draw a line that passes through the joints of the A-arms at the inside section ofthe A-arms3. Extend the lines drawn in steps 1 and 2 until they intercept, denote theinterception point as P24. Locate the instant center of the suspension system, and denote it as P1 or IC5. Draw a line that goes from the outer tie rod point to the instant center, note the tierod must lie on this line6. Draw a line that passes through the outer tie rod point and the outer point of theupper control arm (the ball joint)7. Calculate the angle between the line passing through the tie rod ends to the IC(the line from step 5) and the line passing through the lower control arm points tothe IC, and denote this angle α8. Draw a line that connects the IC to P29. Draw a line that is at an angle of α from the line drawn in step 8 and that startsfrom the IC; draw this line until it intercepts the line drawn in step 6, denote theinterception point as P310. Draw a line that passes through P3 and the inner point of the upper control armand extend it until it intercepts the line from step 511. The interception point from step 10 locates the point where the inner tie rod pointmust lie to have no toe angle change with wheel travelThe following figure will help clarify the steps (Figure 19: The necessary steps to locatethe tie rod position to have no toe angle change with suspension travel).28

2007 Baja ProjectSuspensionFigure 19: The necessary steps to locate the tie rod position to have no toe angle change withsuspension travelThere is essentially two things that can be changed in order to deviate from theideal position and length. The first is to change the tie rod length and the second is toraise or lower the steering rack. If the tie rod is shortened the deflection of thesuspension will cause toe out, and if it is lengthened the deflection of the suspension willcause toe in. If the steering rack is raised the tire will toe in when it is in compressionand will toe out when it is in rebound (roll steer behavior). The opposite is true if thesteering rack is lowered.In order for the wheels to roll without slip (especially at low speeds) there must betoe out with steer. Therefore the toe angle must change with the steering angle. This canbe seen on most steering angle versus toe angle curves. It is not a linear relationshipbetween the two. This effect is usually known as Ackermann steering; the effect thatthere must be some toe out with steer. For proper Ackermann steering to be designedinto the suspension system the following relationship must be true (Equation 25:Condition for proper Ackermann steering).cot( δo) − cot( δi) =ljEquation 25: Condition for proper Ackermann steeringIf Ackermann geometry is introduced into the suspension system, then there will be anincrease in the slip angles at the outer tires when the vehicle is turning. Therefore, usinghigher slip angles at the outer tire tends to generate more lateral forces with less steerangles and rolling losses. The location of the rack position in respect to the longitudinalposition effects the amount of Ackermann steering generated. Therefore the height of therack and the size of the rack will be chosen first in order to optimize the bump steer androll steer characteristics of the suspension system. The longitudinal position of the rackwill be chosen last in order to obtain the desired amount of Ackermann steering. Most of29

2007 Baja ProjectSuspensionthe time a little bit of Ackermann steering is designed into the suspension system.However, severe deviations from Ackermann steering lead to tire wear becausedeviations from Ackermann lead to tire scrub.6.2.7) Aligning torque or self centering momentThe aligning torque or self-centering moment is the moment that acts against thedriver when the driver is trying to steer the vehicle or is acting with the driver (assisting)when the driver is trying to steer the vehicle. It is important that this moment acts in thedirection such that it acts against the driver when he/she is steering the vehicle. It is thismoment that will act to straighten out the tire, and this will aid in stabilizing the vehicle.It is also important that this moment is not too large so that the driver can still steer thevehicle without major difficulties. The steering angle, caster angle, kingpin angle, castertrail, and scrub radius all affect the aligning torque (Equation 26: Aligning moment).( τ ) cos( σ ) sin( σ )( r tan( σ ) rσ ) sin( δ )M = N cos+Equation 26: Aligning momentIf either the scrub radius, caster trail, caster angle, steering angle, or kingpin angle isnegative than the other parameters must be positive in a way that ensures the moment ispositive; the moment acts to straighten out the tires. In general, all of the parametersshould be kept positive to ensure the aligning torque is positive.6.2.8) Anti-dive/anti-squatThere will be weight transfer from the back to the front when the vehicle isbraking and from the front to the back when the vehicle is accelerating. The anitdive/anti-squatproperties of a suspension are similar to the roll center concept appliedearlier (5.2.2). The anti-dive/anti-squat concept applies to the longitudinal force where asthe roll center concept applies to the lateral force. A portion of the forces will passthrough the suspension components and be transferred to the frame, and this amount isdepicted by the amount of anti-dive or anti-squat present. In the study of anti-dive/antisquatthe roll center is known as the pitch center. The definition of the pitch canter is thesame as that of the roll center except it is the longitudinal force and not the lateral forcethat is applied at the pitch center. The pitch center is the location where the longitudinalforces can be applied without causing the vehicle to pitch.The location of the pitch center is found in a similar way as that of the roll centerexcept it is calculated by looking at the vehicle from the side. The following is thenecessary steps to calculate the pitch center for double A-arm type of suspension only(note to calculate the pitch center for a different type of suspension it is advised to referto a vehicle dynamics text). The first step is to locate the instant center of the front orrear suspension in the side plane of the vehicle. This is done by drawing a line thatpasses through both of the A-arms (the upper and the lower A-arm) and the interceptionof these lines represents the instant center. The next step is to draw a line which connects30

2007 Baja ProjectSuspensionthe point at the center of the contact patch of the tire to the instant center. If the previoussteps were done for the front suspension, repeat the steps for the rear suspension. Thelocation where the lines going from each of the center of the tire contact patch to theinstant center of their appropriate suspension intercept one another represents the pitchcenter. The following drawing can be used for clarification (Figure 20: The pitch center).Figure 20: The pitch centerThe pitch center can be used to indicate the amount of pitch generated. The distancebetween the height of the pitch center and the height of the center of mass of the vehiclegives an indication of the amount of pitch. The smaller this distance is the smaller theamount of pitch generated will be. However, just like with the roll center is the fact thatthe amount of jacking forces increases as the height of the pitch center is increased. Thusthere should be a compromise in the height of the pitch center; it should not be too highbecause the jacking forces will be too high and it should not be too low because there willbe too susceptible to pitch.The path of the tire in the longitudinal direction as a function of suspension travelwill determine whether the suspension is classified as anti-dive or anti-squat. If thesuspension is classified as anti-dive the point of contact of the tire will move forward(towards the front of the vehicle) as the suspension compresses and with move rearwardas the suspension extends (goes into rebound) (Figure 21: Anti-dive suspensiongeometry). If the suspension is classified as anti-squat the point of contact of the tire willmove rearward as the suspension compresses and will move forward as the suspensionextends (Figure 22: Anti-squat suspension geometry). Anti-dive designed into thesuspension system leads to harsh response over bumps; the suspension will be trying topush into the bump instead of riding over it with ease. As the suspension goes over abump it will compress, and when the anti-dive suspension compresses it moves forwardand thus tries to push into the bump. This tends to cause a harsh response, and in somecases can induce vibrations in the system which can be felt by the driver. However, antisquatdesigned into the suspension improves the performance of the suspension. Thesuspension will ride over bumps with ease. As the suspension goes over a bump itcompresses and moves rearward, thus it will follow the path of the bump with ease and31

2007 Baja ProjectSuspensiongive the indication of a smooth ride to the driver.Figure 21: Anti-dive suspension geometryIf anti-dive is designed into the suspension system it will prevent the vehicle fromdiving; the vehicle dives when it is braking. If anti-squat is designed into the suspensionsystem it will prevent the vehicle from squatting. If anti-squat is designed into thesuspension it will assist the vehicle at diving, and if anti-dive is designed into thesuspension it will assist the vehicle at squatting. Therefore, it is common proactive to usea small percentage of anti-squat in the rear and a small percentage of anti-dive in thefront.Figure 22: Anti-squat suspension geometryThe reason why anti-squat is designed in the rear is that when the vehicle is squattingweight is transferred to the rear. Therefore the effect of designing the suspension to32

2007 Baja ProjectSuspensionprevent the vehicle from squatting will be greater by designing anti-squat into the rearsuspension because the weight is being transferred to the rear. This is the same reasonwhy anti-dive is designed into the front suspension; when the vehicle is diving weight isbeing transferred to the front. However, since anti-dive leads to a harsh response overbumps which are detrimental to the suspension system, therefore a small amount of antisquatis typically designed into the suspension to optimize the performance of thesuspension. It is important that the amount of anti-squat be kept to a small percentage inboth the front and rear when they are both designed for anti-squat. This is what istypically done to suspensions today, a small amount of anti-squat is designed into boththe front and rear in order to improve the response of the suspension to changes in roadconditions.6.2.9) Motion ratio and wheel rateThe motion ratio describes the amount of shock travel for a given wheel travel.The motion ratio is simply the shock travel divided by the wheel travel. A motion ratioof 0.6 implies that the shock will compress 0.6 inches when the wheel compresses 1 inch(Figure 23: Motion ratio). As the motion ratio decreases the control arms will have to bebuilt stronger because the effective bending moment acting on them will increase. Theeffective bending moment will increase because the moment arm will increase; themoment arm is defined as (d 2 – d 1 ) from figure 23. Therefore it is more ideal to have amotion ratio as close to one as possible so that the load put on the control arms is kept toa minimum so that they can be designed as light as possible thus decreasing the unsprungmass.MR =∆L∆T≈dd12Figure 23: Motion ratio33

2007 Baja ProjectSuspensionThe amount of force transmitted to the vehicle chassis is reduced when the motionratio increases. This implies that the wheel rate will increase as the motion ratioincreases. Since the motion ratio relates both the force and displacement of the spring tothe wheel center, it must be squared to relate the wheel rate (also known as wheel centerrate) to the spring rate (if the motion ratio is reduced then the amount of spring travel andthe amount of force absorb by the spring will decrease) (Equation 27 : Wheel rate).kw =ks( MR) 2Equation 27 : Wheel rateThe wheel rate is the equivalent spring rate at the wheel. If a spring was attached at thecenterline of the wheel, then the spring rate of this spring would be equal to the wheelrate. The forces act on the tire, and thus the wheel rate is what will give an indication asto the amount of force that will be absorbed by the spring and not the spring rate.A motion ratio as close to one as possible is desired for good ride quality of thevehicle. A motion ratio of one is ideal because it reduces the amount of load into thevehicle structure (more load is absorbed by the shock), it increases shock velocity, and itreduces the unsprung mass because the suspension components do not have to absorb asbig of a load (the bending moment on the control arms decreases). However, the motionratio is typically limited because of the desired wheel travel and the chosen shock. Thisis especially true for an off-road vehicle. Off road vehicles can have wheel travelsanywhere from 8 to 12in, and suspension shocks typically do not run that big (the shocktravel will typically not be as high as 8 to 12in). It is important that the amount of shocktravel and wheel travel is chosen before the motion ratio. If a wheel travel of 10in isdesired and the shocks chosen only have a travel of 6in (in compression and in rebound)then the motion ratio is limited to 0.6 and should not exceed 0.6. The wheel travel andshock travel should be chosen as close as possible to each other so that the motion ratiocan be optimized.6.2.10) Roll stiffnessThe roll stiffness is sometimes referred to as the roll rate. The roll stiffness of thesuspension system is the amount of roll moment needed to roll the suspension by one unitof rotation (degree or radian). The roll stiffness of the suspension system is related to theride rate through the following equation (Equation 28: Roll stiffness as a function of riderate).kφ=( 12)( k )( t)Equation 28: Roll stiffness as a function of ride rateNote, the roll stiffness resulted will be in units of lb-ft/rad, the ride rate is in units of lb/inand the track is in units of feet.r2234

2007 Baja ProjectSuspension6.2.11) Vehicle ride heightThe ride height is also known as frame clearance. The ride height is the distancebetween the ground (flat ground surface) and the vehicle chassis with the driver sitting inthe vehicle. The ride height is usually measured at the lowest point on the frame.However if it is desired to measure the ride height at the front and rear of the vehicle itcan be taken as the lowest point at those portions of the vehicle.6.2.12) Understeering/Oversteering characteristics of vehicleThere are a multiple of different parameters that affect the oversteering/understeering characteristics of a vehicle. The main three parameters that affect theoversteering /understeering characteristics of a vehicle are the effective corneringstiffness of the front and rear tires and the weight distribution; the roll stiffness of thefront and rear suspensions; and the inclination of the roll axis. To determine whether thevehicle will oversteer or understeer a turn each of these parameters should be considered,however the governing effect is the effective cornering stiffness of the front and rear tiresand the weight distribution of the vehicle.Analyzing the handling dynamics of the vehicle using the bicycle model revealsthe following three criteria to determine whether the vehicle will understeer or oversteer(Equation 29: 3 cases to determine whether the vehicle will oversteer or understeer basedon the bicycle model).aC > bC the vehicle will oversteeraCaCfff< bCrr= bCrthe vehicle will understeerthe vehicle will neutral steerEquation 29: 3 cases to determine whether the vehicle will oversteer or understeer based on thebicycle modelNote, the cornering stiffness in the above three cases is the effective cornering stiffness(it includes the camber thrust effect). For further information on this effect refer tosection 5.1.2.If the roll stiffness of the front suspension is greater than the roll stiffness of therear suspension the vehicle will understeer as it turns. The vehicle will oversteer as itturns if the opposite is true. When a vehicle is cornering there will be weight transferfrom the inside tire to the outside tire, and the amount of weight transfer is depicted bytwo things. The first is the lateral load transfer due to cornering forces (2F y h r /t) and thesecond is the lateral load transfer due to vehicle roll (2k φ φ/t). The first effect isindependent on the roll moment and the roll stiffness, but it is dependent on the rollcenter height or the inclination of the roll axis; note the roll center height in this equationis the difference between the height of the center of mass and the roll center height. Asthe vertical force increases the lateral force will change as depicted by the corneringcurves of the tires (Fy/Fz verses slip angle). If the lateral force was plotted against the35

2007 Baja ProjectSuspensionvertical force for a given slip angle it can be seen that the curve is non linear (Figure 24:The lateral force verses the vertical force for a given slip angle).Figure 24: The lateral force verses the vertical force for a given slip angleThe curve is non linear in a fashion such that the change in lateral force over the changein vertical force decreases as the vertical force increases. This implies that if there is agreater amount of weight transfer in the front of the vehicle than in the rear, the net resultwill be that the overall lateral force in the front will decrease causing the vehicle toundersteer. The consider the following as an example, suppose both of the tires support avertical force of 800lb at a slip angle of 5 deg, thus each tire supports a lateral force of760lb (total is 2*760 = 1520lb). Now if the vehicle corners and there is load transfer of400lb, the inside tire will support a vertical load of 400lb and the outside a vertical loadof 1200lb. Thus the lateral load on the outside tire is 820lb and the lateral load on theinside is 460 lb and the total lateral load is 1280lb. The previous analogy shows that thelateral force will decrease as there is weight transfer for a given slip angle. If the tirewants to keep the same lateral force the slip angle will have to increase. Thus, if there ismore weight transfer in the front than in the rear, the slip angle in the front will have toincrease in order to produce the lateral forces necessary to complete the turn and the neteffect is that the front will plough out and the vehicle understeers.If the roll axis points downwards towards the front the roll center height (distancebetween the height of the center of mass and the roll center height) will be higher in thefront than in the rear and if the roll stiffness is higher in the front than in the rear theirwill be a greater amount of weight transfer in the front than in the rear thus causing thevehicle to understeer. The inclination of the roll axis affects the coupling between yawand roll. If the roll axis is inclined downward towards the front of the car then it causesthe body to yaw out (understeer) of the turn as the body rolls. Having the roll stiffnessgreater in the front than in the rear also causes the vehicle to yaw out in the turn(understeer). Therefore these three parameters (or effects) can be used to control theoversteering / understeering characteristics of the vehicle.36

2007 Baja ProjectSuspension6.3) Spring rate determinationThe spring rate is one of the components of the vehicle where the designer hascontrol of its value. It is the spring rate along with the suspension geometry (motionratio) which determines the wheel rate. The wheel rate can be assumed to be equal to theride rate because the stiffness of the tires will be much greater than the effective stiffnessof the suspension. Therefore, for good quality the Maurice Olley criteria should be usedwhen choosing the spring rates of the front and rear suspension systems (this criterion isoutlined in section 5.1.1). The front ride rate should be 30% lower than the rear ride rate.The ride frequencies of the front and rear suspensions can be calculated once the frontand rear ride rates are known (Equation 30: Ride frequency).( k )( 12)( 32. )k 1 r2ϖ = =m 2πWEquation 30: Ride frequencyNote in the equation above the weight is in lb and it is half of the weight supported by theappropriate suspension (if the ride frequency calculation is for the front than the weight ishalf of the weight supported by the front suspension). Also the ride rate is in lb/in in theabove equation and the frequency from the equation will be in hertz. Note the ridefrequency aid in determining the rear suspensions capable of catching up to the frontsuspension when the vehicle goes over a bump thus minimizing the annoying motion feltby the driver (pitch motion). Once the spring rates are known, the bounce, pitch, and rollnatural frequencies can be determined and compared to the Maurice Olley criteriaoutlined in section 5.1.1.; the necessary equations to calculate these three naturalfrequencies are also outlines in section 5.1.1 and in 5.2.9. The final step is to verify thatthe spring rates chosen for the front and rear suspensions are stiff enough to absorb theloads that they will see without bottoming out the suspension. The general rule is that if avehicle is designed to compete around a certain track than the spring rate should bechosen such that the shock bottoms out only once as it travels around the track(bottoming out is implying that the shock compresses to the point where it is just barelytouching the bump stop).With this general introduction to suspension kinematics and kinetics it will beeasier to follow the section describing the suspension kinematics and kinetics of the 2007vehicle.37

2007 Baja ProjectSuspension7) 2007 Suspension KinematicsThe independent double A-Arm suspension type was chosen for both the frontand the rear suspension systems. The double A-Arm type suspension was chosen becauseit allows for the suspension characteristics to be easily adjusted and gives more controlover the toe, camber, and scrub over the range of wheel travel. Also this type ofsuspension provides better packaging space inside the chassis and allows the wheels tomove independently and thus give the vehicle better handing over rough terrain. Thereare several parameters that need to be considered when designing the kinematicscharacteristics of the front and rear suspension systems, these parameters are:- Wheel Base, Track Width and Ride Height- Wheel Orientation- Suspension Angles- Roll center location and roll stiffness- Unsprung mass- Steering characteristics- Acceleration and BrakingThe steps taken to design the suspension kinematics for the 2007 Baja vehicle areoutlined below:7.1) Choosing the dimensions of the vehicleThe front and rear characteristics are very closely related and therefore, must bedesigned simultaneously. Before designing the suspension points, some parameters had tobe chosen based on last year’s Baja vehicle, these parameters are the Track width, Wheelbase and the Ride height as shown in Figure 25:Front TrackRear TrackRide HeightWheel BaseFigure 25: Vehicle DimensionsTrack Width: The track width of the vehicle was chosen to reduce the bending moment38

2007 Baja ProjectSuspensionacting on the control arms as well as improve the turning radius and stability of thevehicle. By increasing the track width the control arms are subject to higher stress as aresult of the bending moment induced by the shock acting on the control arms and thevertical forces acting on the tire. On the other hand, the front track width should alwaysbe wider than the rear. This allows the vehicle to handle better around corners andreduces the turning radius. The rear track width of the 2007 vehicle was designed to be1.5” shorter than the front track width. One of the main issues considered when choosingthe track width in the rear is the fact that the rear end of the frame was reduced to 4inches by introducing a more compact differential assembly, this can perhaps be seenclearer in Figure 26:Differential AssemblyFigure 26: Rear end of vehicleWheel Base: The wheel base length has a great impact on the turning radius and the pitchand bounce frequencies. However, it is mainly dictated by the length of the frame, wherethe frame has to be designed to provide enough pedal room for the driver in the front androom for the engine and drivetrain assembly in the rear. Therefore, the wheel base lengthwas reduced as much as possible while still satisfying the frame requirements.Ride Height: In a Baja vehicle it is crucial to have enough ground clearance from thebottom of the chassis to give the car the capability of going over any terrain, and thusprevent direct hits to the chassis during the competition. One of the problems that facedthe University of Windsor Baja vehicle in the past was, having to go over of logs androcks during the maneuverability event because the vehicle did not have enough groundclearance. On the other hand, designing for high ground clearance lifts the center ofgravity of the vehicle and thus increases the chances of rolling the vehicle. Therefore,there is a tradeoff between the ground clearance and the center of gravity when it comesto choosing the appropriate ride height of the vehicle. Given the fact that the compactengine transmission assembly already contributes to wards a lower center of gravity, theride height was chosen to be 1 inch higher than the previous year to reduce the possibilityof damaging the chassis or the underbody when going over rough terrain. Therefore, theinitial chosen design dimensions of the 2007 Baja vehicle can be summarized Table 1:Summary of vehicle dimensions:4”39

2007 Baja ProjectSuspensionTable 1: Summary of vehicle dimensions2006 2007Front Track Width 49” 47.5”Rear Track Width 48” 46”Wheel Base 64” 58”Ride Height 9” 10”7.2) Choosing the suspension pointsThe other suspension points depend on the selection of the wheels, tires, hubs andthe uprights. The type and size of tires and wheels are the first things selected whendesigning the suspension systems. It was decided to choose 21x7-10 tires and the 5x10ITP Douglas rims. The uprights and wheel hubs were then chosen, both the front and rearuprights are chosen from the Polaris 2006 Outlaw 500 ATVs due to their light weight andcompact geometry especially in the rear. The main advantages of the chosen front uprightis the fact that it has a smaller distance between the upper and lower ball joints. Thisfeature gives less kick back in the steering system and reduces the scrub radius of thefront suspension. The Outlaw uprights give a larger kingpin angle, however, due to theshort distance between the upper and lower ball joints, the amount of lift with steer isminimized. Once the uprights are chosen the outer suspension geometry is constrained tothe uprights connection points, however, in order to accurately determine the location ofthe outer points the uprights were sent to be CMMed and a 3-D model of the uprights wasobtained based on the CMM results. The following figure shows the 3-D model of thefront and rear uprights indicating the suspension points on each upright:UCA – Rear - Outer UCA – Front - Outer UCA - OuterBrake CaliperTie rod - OuterLCA – Rear - OuterLCA – Front - OuterLCA - OuterFigure 27: Front and Rear UprightsAfter locating the outer control arms points, the wheel center point is located byselecting the wheel hub. The Polaris 2006 Outlaw 500 wheel hub was selected for thefront since it is already compatible with the front upright. In the rear on the other hand,40

2007 Baja ProjectSuspensionthe Polaris 2003 Predator wheel hub was selected. This wheel hub was chosen due to itslight weight design and the fact that it makes the wheel assembly more compact. Inaddition to that, the 2003 Predator rear wheel hub is almost identical to the front wheelhub of the 2006 Outlaw with the only difference is the spline pattern in the rear hubs.Therefore, choosing these hubs was also an advantage in terms of the manufacturabilityaspects of design. Once the front and rear wheel hubs were CMMed a 3-D model of thehubs was obtained and the wheel center point was located. Figure 28 shows the 3-Dmodel of the wheel hub:Figure 28: Wheel hub7.3) Choosing the suspension geometry anglesOne of the main advantages of the Short Long Arms Independent suspension isthat it allows the orientation of the wheels to be easily adjusted by setting the suspensiongeometry. The main suspension alignment parameters are the camber angle, the toe angleas well as the caster angle. It is very important to select the static angles to optimize theperformance of the vehicle since these angles have an impact on acceleration, brakingand steering. The following describes the factors that were considered when designingthe suspension geometry angles:Camber Angle: The camber angle has a great impact on the handling characteristics ofthe vehicle. Depending on the application, the camber angle can be designed to bepositive or negative. A positive camber angle reduces the contact patch of the tire, whichmaximizes the amount of forces acting on the tire during cornering, result in anundesirable tire wear patterns and hence affects the handling of the vehicle. Therefore,the Baja vehicle was designed with a small negative camber angle in the front and rearsuspension systems to allow for better cornering characteristics and reduce the lateralload going through the control arms. In addition to that a negative camber angle incornering allows the vehicle to have an over steer characteristic which is desirable. If theinitial static camber angle is set to zero the suspension will gain positive angle as thewheel travel, thus it is important to set the static camber angle at a small negative value inorder to maintain the negative camber angle throughout the range of wheel travel.Toe Angle: The main performance areas that are affected by the toe angle are the tirewear, straight line stability, steering, acceleration and breaking. If the vehicle is designed41

2007 Baja ProjectSuspensionwith a toe out angle the wheels become at odds with each other, and thus any slight turnin front wheels will cause the inner wheel to turn at a sharper angle than the outer wheeland prompt a quick steering response. On the other hand if the vehicle is designed with atoe in angle the wheels are aligned towards each other, which gives the vehicle morestraight line stability and makes the steering less responsive. The 2007 Baja vehicle wasdesigned with a slight toe in angle in order to maintain the straight line stability of thevehicle, which plays an important role in the acceleration and hill climb events. Anotherfactor that was considered is the tire wear, in order to insure uniform tire wear patterns itis logical to think that the toe angles should be set at zero to keep the tires alignedstraight. However, due to the small compliance in the suspension system, as the vehicleaccelerates the tire will try to toe out. Therefore, the static toe in angle set up on the Bajacar will accommodate for the toe out effect as the vehicle accelerates. The toe anglealignment is perhaps not as important in the rear suspension as it is in the frontsuspension and so the rear tires were aligned to zero toe angle.Caster Angle: The caster angle has a great impact on the handling characteristics.Depending on whether the vehicle is front wheel drive or rear while drive the caster anglecan be chosen to be negative or positive. Choosing a zero angle of caster is undesirablesince it allows the external vertical forces to travel through one point of contact whichintroduces instability in the vehicle. Given the fact that the Baja vehicle is rear wheeldriven, a trailing positive caster angle is set at the front and rear wheels. The positivecaster angle provides a self centering force for the steering and makes the car easier todrive in a straight line. On the other hand, a large caster angle is not recommended sinceit will make the steering much heavier and less responsive. In the case of a Baja vehiclewhere no power steering is available, keeping the caster angle within a small range iscrucial. Thus, the caster angle should be kept between 0 degrees to 5 degrees (positivetrailing). The static suspension geometry angles for the 2007 and 2006 Baja vehicles aresummarized in the following table:Table 2: Static Suspension Angles2006 2007Front Camber -3 degrees -3 degreesRear Camber -2 degrees -2 degreesFront Toe 0 degree 1 degreeRear Toe 0 degrees 0 degreesCaster 10 degrees 4 degrees7.4) Choosing the inner suspension pointsAs mentioned earlier the outer suspension points are dictated by the vehicledimensions and the wheel hubs and uprights. Once the outer points are chosen, the innerpoints are designed to optimize the suspension performance of the vehicle. The next stepis to use ADAMS/Car to manipulate the geometry and check the suspension42

2007 Baja ProjectSuspensioncharacteristics until the optimal suspension geometry configuration is obtained. Thesuspension points are input in ADAMS as shown in Figure 29:LCA-RearUCA-Rear-UCA-RearUCA-FrontInner and outer tieroditUCA-RearLCA-RearUCA-OuterUCA-FrontLCA-Rear-Wheel CenterLCA-Front-OuterUCA-Front-OuterLCA-FrontWheel CenterLCA-OuterLCA-FrontFigure 29: ADAMS/Car suspension modelingOne constraint that dictates the inner suspension geometry is the ride height of thevehicle, since the lower inner suspension points have to be the lowest points on thechassis at a height of 10 inches from the ground. Another restraint is the steering rackposition, the steering rack points were chosen so that the rack is as low as possible, whichgives the driver more leg room in the front. Therefore, once the steering rack points andthe lower control arm points are decided, the upper control arm points are designed tooptimize the suspension performance. When choosing the inner suspension points thefollowing factors were taken into consideration:Anti Squat and Anti Dive: The main causes for the “squat” and “dive” effects are thebraking and acceleration of the vehicle. In the case of the Baja vehicle which is a rearwheel drive, as the vehicle begins to accelerate the vertical loads acting on the rearsuspension begin to increase as a result of the sprung mass distribution shifting to therear. At the same time the shift in weight distribution to the rear decreases the loadsacting on the front suspension. Therefore, as the vehicle accelerates the rear suspension isforced to jounce and the front suspension is forced to rebound, this combination of jounceand rebound results in the vehicle pitching towards the rear end. The same conceptapplies when the vehicle is braking where in this case the weight will be transferred to thefront instead resulting in a forward “dive” resulting in large moments acting on thesuspension. Therefore, in order to reduce the amount of loads acting on the suspensioncomponents during braking and acceleration, the suspension geometry has to be designedto provide anti-squat and anti-dive forces, which will also reduce the vehicle pitch.Ideally the vehicle should be designed to have both anti-squat and anti-dive, however,that requires the front and rear suspensions are oriented opposite to each other. Therefore,the Baja vehicle was designed to have anti-squat in the front and rear suspensions byorienting the suspension geometry at 5 degrees from the horizontal as shown in Figure30:43

2007 Baja ProjectSuspensionθθθ = 5 degreesFigure 30: Anti Squat AngleThis suspension geometry configuration allows the vehicle to go over bumps andrough terrain more easily by reducing the amount of loads acting on the suspensionsystem components as the tire approaches a bump. This can also be explained by the factthat the wheel travel will follow a lateral profile that is perpendicular to the road profile:Road ProfileLongitudinal WheelTravel ProfileFigure 31: Anti Squat ReactionThe longitudinal wheel travel profile of the front and rear suspension systems isplotted below versus the vertical wheel travel of the wheels using ADAMS/Car (seeFigure 32). It is clear to see from the curves that the front and rear longitudinal curvesalmost line up with each other and that implies that the front and rear wheel move in thesame longitudinal direction. It is also important to notice from the graph that for every 1inch of vertical wheel travel there is approximately 0.1 inch longitudinal wheel travel andthus the wheelbase length of the vehicle does not change much as the wheels go throughwheel travel.44

2007 Baja ProjectSuspensionFigure 32: Longitudinal wheel travelRoll Center Location: As the vehicle approaches a corner, the sprung mass distribution istransferred laterally from one side to the other resulting in higher loads on the outsideturning wheels. This transfer in the weight distribution may cause the vehicle to rolldepending on the roll moment acting on the vehicle. The roll moment depends on thelocation of the roll center and the vehicle center of gravity, where the distance betweenthe roll axis and the center of gravity represents the roll moment arm. The longitudinalposition of the roll center is not considered due to the fact that it does not have a greatimpact on the roll moment arm; the lateral location of the roll center on the other hand isgiven to be at the center line of the vehicle. Therefore, only the vertical position of theroll center is considered when designing the suspension geometry. By connecting the rollcenters in the front and rear the vehicle roll axis is formed. The orientation of the roll axishas a great impact on the oversteering and understeering characteriscs, desiging the rollaxis to be inclined towards the front of the vehicle results in understeering, whileoversteering is obtained when the roll axis is inclined towards the rear of the vehicle. Ingeneral it is desirable to design the vehicle to have a small oversteering characteristic,however, the 2007 Baja car incorporates a limited slip differential that helps whip the rearend of the car around corners which contributes to oversteering. Therefore, the front rollcenter height is designed to be lower than the rear roll center height so that the roll axis isinclined towards the front, contributing to understeering and balancing off theoversteering effect caused by the differential and the weight transfer.45

2007 Baja ProjectSuspensionVehicle CenterlineRC1RC2RC3Swing Arm Length 1Swing Arm Length 2Swing Arm Length 3Figure 33: Roll Center Height and Swing Arm LengthFigure 33 illustrates how the vertical position of the roll center is located byintersecting a line running from the center of the tire contact patch with the instant centerof the suspension. The lower suspension points are dictated by the ride height and hencethey can not be modified, however, the upper suspension points are used to adjust the rollcenter as needed. The figure above shows that as the upper control arm points are broughtcloser to the lower control arm points the roll center is increased, at the same time the“Swing Arm Length” increases resulting in less track width change. Less track widthchange with wheel travel reduces the camber gain. Thus, there is a trade off between theoptimal roll center and the optimal camber gain.Camber Gain: As mentioned earlier, a small negative camber angle is set in the rear andfront suspensions at static in order to prevent positive camber gain during cornering.However, even with the static angle set at a small negative camber, there will still besome positive camber gain as the vehicle rolls during cornering. Therefore, thesuspension geometry is designed to increase the camber gain as the wheel travels. Inother words, the camber angle is maintained negative during bump and rebound. This canbe achieved by designing the control arm points such the A-Arms are unequal in length.The following figure shows two possible configurations of the upper suspension points:Lower A-Arm LongerUpper A-Arm LongerFigure 34: Camber Gain46

2007 Baja ProjectSuspensionBump Steer: The bump steer effect is simply the change in toe angle as the wheel travels.Bump steer can be used to influence the oversteering or understeering characteristics ofthe vehicle. If the front wheels are set to toe out during bump it will make the vehicleundersteer, while on the other hand, the vehicle will tend to oversteer if the front wheelstoe in with wheel travel. It is always desirable however to minimize the bump steer inboth the front and rear suspension systems, infact ideally the rear suspension systemshould have no bump steer at all. The design criteria followed for the Baja car was tokeep bump steer as much as possible within +/-1 degree of toe.7.5) Choosing the steering tie rods lengthsAs mentioned earlier, bump steer is a very important parameter when it comes tothe suspension geometry. The length of the tie rod is basically designed to minimize thebump steer as much as possible. Given the fact that the outer steering points are alreadydecided by the upright, and the steering rack height is chosen to allow for better leg roomfor the driver, the only point that is left to be chosen is the inner tie rod point. Animportant concept that needs to be considered is the instant center (IC) of the suspensionsystem; this point represents the center of rotation of the suspension swing arm as thewheel bumps or rebounds. In order to minimize bump steer, a line connecting the innertie rod point and the outer tie rod point has to intersect the instant center of thesuspension (see figure below). By choosing the tie rod point to lie on that line, the controlarms and the steering tie rod will move together as one mechanism with the same centerof rotation, which reduces the change in the toe angle as the wheel travel.ICFigure 35: Steering tie rod lengthThe position of the inner tie rod point however is also dictated by the clearancewith the frame. The worst case scenario is when the wheel is at maximum rebound andthe steering wheel is turned 360 degrees, this case is shown in Figure 36: Tie rodclearance with control armAs can be seen the tie rod point has to be designed to accommodate for theclearance between the frame and tie rod. Therefore, choosing the tie rod points requires alot of iterations to obtain the optimal bump steer characteristic while still maintain theclearance with frame.47

2007 Baja ProjectSuspensionClearance betweentierod and frameFigure 36: Tie rod clearance with control arm7.6) Choosing the strut mounting pointsThe position of the strut mounts has a great impact on the wheel travel range ofthe suspension. Therefore, the intended maximum wheel travel range for the suspensionmust be decided first, and then the strut mounting points can be designed to obtain thedesired wheel travel range. The amount of plunge in the shock is related to the suspensionwheel travel using the motion ratio, where the motion ratio is defined as the ratio ofdisplacement in the shock to the wheel displacement:Shock _ DisplacmentMotionRatio =Wheel _ DisplacementθbaFigure 37: Motion RatioFrom the figure shown above, the motion ratio can be calculated using the followingequation:bMotionRatio =a + bKnowing the plunge displacement in the shock which is 4 inches and a desiredtotal range of wheel travel of 10 inches, the motion ratio can be calculated and theposition of the lower shock mount can be obtained from the equation above. The factorsthat were considered when designing the motion ratio are:48

2007 Baja ProjectSuspensionBending moment: When choosing the lower shock mounting point, the amount of loadsapplied by the shock on the control arms must be considered. From diagram shownabove, if the lower shock point is chosen to be very close to the wheel, the strut force hasa larger moment arm and thus inducing higher bending stress in the lower control arm.Suspension Stiffness: The orientation of the shock (angle θ) affects the overall stiffnessof the suspension. If θ is set to be close to 90 degrees, then the shock is almost verticaland the suspension has a very high stiffness (wheel rate), while on the other hand, if the θis set to be close to zero, the suspension stiffness is very low. The roll stiffness issimilarly affected by the shock mount point positions, therefore, an iteration process wasused to obtain the shock points that achieve the desired wheel travel and optimize theoverall suspension stiffness.Half Shafts: In the rear suspension the wheel travel is constrained by the anglelimitations of the Universal Joints of the half shafts. Therefore, it is important to designthe motion ratio such that at maximum bounce and rebound, the shocks are the firstcomponents that bottom out by hitting the bump stops, since the bump stop help absorbsome energy. Otherwise, if the Universal Joints bottom out first, large amounts of loadswill be applied to the half shafts and transferred to the drive train assembly.7.7) Design front and rear suspension to be consistentThe front and rear suspension systems geometry were designed by consideringeach system separately, however, it is important to make sure that the front and rearsuspension characteristics are consistent with each other in order to optimize the fullvehicle suspension performance. The following parameters were compared for the frontand rear suspension systems:Lateral Roll Center Position: The roll axis of the vehicle is formed by connecting thefront and rear roll center points. The lateral positions of the front and rear roll centershave to follow the same pattern over wheel travel, otherwise the roll axis will not beperpendicular to the centerline of the vehicle and the vehicle will be subject to yaw. Thefollowing graph compares the front and rear lateral roll centers as they vary with wheeltravel:49

2007 Baja ProjectSuspension8.3) 2007 front and rear suspension shocksThere are many different types of suspension shocks that can be used for the bajavehicle. The two most common types of shocks used are atv shocks and motocrossshocks. However, it is generally more desired to go with an atv shock for the bajavehicle. Until 2005, the University of Windsor baja team used custom Billstein shockson their baja vehicle; custom implying that the damping, shock travel and spring ratewere designed specifically for their vehicle. In 2005, the baja team decided to use a coilover shock suspension shock from Elka suspension. They decided to go with this shockbecause the damping can be adjusted in compression and rebound thus allowing thedamping characteristics to be optimized through vehicle testing and not on paper. Due tocost constraints at the beginning of suspension design, it was decided to use the samesuspension that was purchased in 2005 and to choose a set of new springs for the shocksthat will allow the ride quality of our vehicle to be optimized. It is advised that if thesesame shocks are used next year that they get re-valved. Note the type of shock alsoneeded to be determined when designing the suspension kinematics because it plays animportant role in the motion ratio designed into the suspension geometry. Since it wasdecided to go with the Elka coil over shock suspension shocks, the available main springsand the available auxiliary springs which we could purchase was supplied by themanufacturer (Appendix E).8.4) The required spring rates based on the Olley criteriaThe predict the necessary spring rates for the 2007 vehicle based on the Olleycriteria an accurate measurement of the weight and weight distribution is needed. It isimportant that this step is completed close to the end of the project so that an accuratemeasurement of the weight of the vehicle and weight distribution is known. The weightof the vehicle and the weight distribution were not measured until the majority of thecomponents were on the vehicle. The vehicle weight and weight distribution wasmeasured once about 95% of the components were complete and on the vehicle (some ofthe parts missing include: the body, the complete gas tank (the gas tank with a spill tankdesigned around it; other words just the Briggs and Stratton gas tank was used with fuelin it), and the seat cushioning) (Table 5: Weight of the vehicle and weight distribution).Note, since the shocks from 2006 were being re used they were also assembled on thevehicle at this point with the springs on them from 2006 so that an accurate measurementof the weight of the vehicle can be measured. To get an idea, the weight and weightdistribution was measured on the same night the car drove for the first time.Table 5: Weight of the vehicle and weight distributionVehicle weight with 170lb driver (lbs) 585Front weight percent (%) 47Rear weight percent (%) 53The spring rates were calculated based on the methods outlined in section 5.3 and5.1.1. The ride rate of the front suspension should be 30% lower than the ride rate of the54

2007 Baja ProjectSuspensionrear suspension based on the Olley criteria. However, there is no indication as to wherethe ride frequencies need to be in the front and in the rear in order to obtain theappropriate ride rates. So the question becomes where did we start? In 2005, thesuspension shocks were purchased from Elka Suspensions, and Elka Suspensions chosethe spring rates for the 2005 team based on the weight of the vehicle, weight distribution,and suspension geometry (motion ratio). Therefore, it was decided to use the 2005 dataand work backwards to solve for the ride frequencies of the front and rear suspension ofthe 2005 vehicle (Table 6: Ride frequencies of the 2005 vehicle).Table 6: Ride frequencies of the 2005 vehicleRide frequency (Hz)Front 1.237Rear 1.47Elka Suspensions calculates their spring rates and ride rates based on actual test data,therefore it was assumed that the ride frequencies of the 2007 vehicle should be aroundthe same values as those of 2005. The optimum way to determine the spring rated for the2007 vehicle would by experimental test. However, due to time constraints this was notfeasible, and we had to start somewhere. Thus it was assumed that the ride frequencieswould be the same in the front and in the rear as those of 2005, and the spring rates werecalculated based on this criteria (Table 7: Required spring rates for 2007 vehicle based onOlley criteria) (Appendix F).Table 7: Required spring rates for 2007 vehicle based on Olley criteriaSpring rate (lbf/in)Front 67.63Rear 68.43The results obtained are rather interesting. The front wheel rate is 37% lower than that ofthe rear wheel rate, and the front ride frequency is 16% lower than the rear ridefrequency. However, it is the ride frequency that will determine the capabilities of therear suspension to catch up to the front suspension, and in order for this to occur the ridefrequency should be 30% less in the front than in the rear to allow for the rear to catch upto the front. However, Maurice Olley did most of his analysis on suspensions onautomobiles which have close to twice as big of a wheelbase as the Baja car. Since thewheelbase is half of what Maurince Olley was using the percentage is decreased to 16%which will allow the rear to catch up to the front at a much faster pace. In other words,the rear suspension will hit the bump sooner in a Baja car than in an automobile. It isalso to be noted that while we were waiting for other parts to go on the vehicle to get thenecessary measurements to calculate the values outlined above the CarSim model wasprepared. This allowed the spring rates to be evaluated at a much faster pace to ensurethat they would be in by the time we were ready for vehicle testing.55

2007 Baja ProjectSuspension8.5) CarSim model for 2007 vehicleCarSim is a computer simulation of a vehicle. It is a simulation package thatallows the response of the vehicle to be determined over a wide range of road inputs. It isa program that has been proven to be accurate and is widely used in Industry for vehicledynamics testing. The only downfall with CarSim is that it is highly dependent onexperimental data and on driver inputs, ie the driver needs to be simulated. CarSim wasused to evaluate the spring rates, predict the behavior of the vehicle through differentanalyses, and to evaluate the performance of the vehicle in regards to what will be seen atcompetition (dynamic events). The following is a discussion of how the model wascreated in CarSim.CarSim has three different interfaces, two of them which need inputs in order forthe program to run (Figure 42: The three interfaces in CarSim). The first interfaceincludes the vehicle model, the controls (driver inputs) of the vehicle and theenvironment which the vehicle is going to drive on. The second interface is known as themath model interface. It is in this interface where the simulation data is specified. Thelast interface (or third interface) is known as the results interface. The last interface isused to plot data, and to view the simulation in the animator. The first and the lastinterfaces were the most used. The only parameter changed in the second interface wasthe computation stop time. Once the vehicle model was created the only parametersneeded to be changed were the vehicle environment and the vehicle controls in order tosimulate the vehicle on the appropriate path and conditions.The vehicle model is created by specifying the size of the vehicle (mass,dimensions and Inertia) and by specifying certain parameters for each of the main majorparts of the vehicle (powertrain, brakes, steering, front suspension and rear suspension)(Figure 43: Vehicle model in CarSim). The following is a brief description of the inputsfor the vehicle model which were used for the simulations on the 2007 vehicle. Note,that if an input is unclear than it is advised to go to the library reference (help, about thisscreen or push F1). The library reference was created by the staff of CarSim in order toassist its users in preparing their models. In the library reference there will be adescription about each of the inputs.The mass, dimensions and inertia of the vehicle are inputted in the model in thespring mass: rigid sprung mass screen (Figure 44: The mass, Inertia and vehicledimensions screen in CarSim). A few notes about CarSim that need to be known beforeany inputs are inputted into the model. Data can only be inputted into the model if thescreen is unlocked; the screen can be unlocked by clicking the lock on top of the screen.It is advised to create a new screen every time one of the variables on the screen needs tobe changed. This will allow the changes to be tracked and the data references not to belost. A new screen can be created by clicking on new on the top of the screen. Once thenew screen is created, the vehicle model screen (or screen which references the newscreen created) needs to be updated so that it references the screen (file) you just created.As an example, if a new screen (file) is created for the mass, dimensions and inertia ofthe vehicle than it must be changed in the vehicle model to reference the file just created.56

2007 Baja ProjectSuspensionIf this is not done, than the program will still run with reference to the previous file.Figure 42: The three interfaces in CarSimFigure 43: Vehicle model in CarSim57

2007 Baja ProjectSuspensionFigure 44: The mass, Inertia and vehicle dimensions screen in CarSimThe sprung mass of the vehicle was estimated to be an order of magnitude greaterthan the unsprung mass (this is usually the case). The inertias of the vehicle were notdetermined experimentally, thus they were left as the values estimated by CarSim. Thedimensions of the vehicle were determined by measuring the appropriate dimensions onthe vehicle.The aerodynamics model was kept the same as that estimated by CarSim. Thedrag coefficients were not tested on the 2007 vehicle, thus it was assumed that the valuespredicted by CarSim were sufficient enough for the analysis to be performed on thevehicle. The aerodynamic effects on the Baja vehicle will not be sufficient because thespeeds are not that high (aerodynamic effects depend on the square of the velocity).The powertrain model was created based on the data obtained from the powertrainteam. The first step in creating the powertrain model was to specify if the vehicle was afront drive, rear drive or all wheel drive vehicle. The 2007 Baja vehicle is a rear wheeldrive vehicle, thus this was specified in the vehicle model for powertrain. Once this wasspecified, the Rear-wheel drive: RWD model was created (Figure 45: The powertrainmodel in CarSim).58

2007 Baja ProjectSuspensionFigure 45: The powertrain model in CarSimThe torque versus RPM curve specified by Briggs and Stratton was used as the enginemodel. Since the powertrain consists of a manual transmission, the torque transfer devicewas modeled as the clutch. The transmission model is comprised of the gear ratios ofeach gear, the inertia of each gear and the upshift and downshift diagrams. Note, theupshift diagrams were modeled assuming they were independent on the vehicle throttle,however to accurately predict the upshift schedule experimental data is needed. Thedifferential was modeled as a limited slip differential indicating that there will be notorque change between the left and right sides of the differential (this is by definition ofthis type of differential). Note to get a more accurate model of the powertrain it isadvised to test the engine and obtain a fuel map for the engine. The model would bemore accurate if the fuel map of the engine would be known.The brake model was created using the information specified by the brake team.With the given information from the brake team the Brake system: 4-wheel system modelwas created (Figure 46: The brake model in CarSim). The proportional gains were allspecified to be unity because the Baja vehicle is not equipped with a proportional valve.A proportional valve is typically used on a vehicle to ensure that the front wheels lockbefore the rear wheels thus ensuring the vehicle remains stable in yaw. However, themaster cylinder size was different for the front and for the rear thus ensuring that the frontwheels will always lock before the rear wheels. The braking torques for all four wheelswas inputted in the model using the values calculated by the brake team.59

2007 Baja ProjectSuspensionFigure 46: The brake model in CarSimThe steering model was created with the assistance of the steering team for certainparameters and by using some of the data calculated in ADAMS/Car for the suspensiongeometry (kinematics) (Figure 47: The steering model in CarSim). The steering ratio wasobtained by the steering team; it is the amount the steering wheel has to turn to turn thetire by one degree. The steering kinematics was obtained from the steering team. It isthe amount the wheel will turn for a given gearbox output. The rear steering is modeledas zero, because the Baja car only has front wheel steering. It is assumed that thecompliance in the steering system is zero. The kingpin geometry was obtained fromADAMS/Car and was inputted in the model by exporting the data from ADAMS/Car intoan excel spreadsheet and copying and pasting the data into CarSim. Since the steeringratio is 2.25 to one than a moment of 1Nm of a steering moment gives 2.25Nm about thekingpin axis (this is just an approximation, to get a more of an accurate result,experimental data is needed) (this is the steering wheel torque).The suspension model includes the suspension kinematics, suspension kinetics and thetire data for both the front and rear suspensions. The suspension kinematics data for boththe front and rear suspensions was obtained by inputting the data calculated fromADAMS/Car. The suspension compliance (kinetics) was obtained from ADAMS/Car,Elka Suspensions, and from an in house Matlab program to calculate the spring rates.Since tires are highly non-linear the only thing changed in the tire model was thedimensions of the tire. The first step in creating the models is to specify in the vehiclemodel screen the type of suspension in the front and in the rear. Since the suspensions in60

2007 Baja ProjectSuspensionthe front and in the rear are both independent this type of suspension was chosen for bothtypes.Figure 47: The steering model in CarSimNote, the inputs will only be briefly described for the front suspension; they can beobtained in the rear in a similar fashion as they were obtained in the front.The front suspension kinematics was created by creating a model of frontkinematics: independent for the front suspension (Figure 48: The front suspensionkinematics model in CarSim). The unsprung mass is usually an order of magnitude lessthan the sprung mass. The track width and effective rolling radius were experimentallycalculated and then inserted into the model. It is to be noted that the curves for both theleft and right wheels are the same. The caster change was calculated by exporting thecurve of caster angle verses wheel travel into an excel file and calculating the change inthe caster angle from the static angle for all wheel travel. The longitudinal movement ofthe wheel center with suspension travel can be directly exported from ADAMS/Car (it isthe wheel_travel_base in ADAMS/Car) into an excel spreadsheet and then copied andpasted into CarSim. The camber angle versus wheel travel can be directly obtained fromADAMS/Car and exported into an excel spreadsheet and then copied and pasted intoCarSim. The toe angle is inputted in CarSim in a similar fashion. The lateral movementof the wheel center is found in a similar way as the longitudinal movement of the wheelcenter (except the curve used in ADAMS/Car is wheel_travel_track curve).61

2007 Baja ProjectSuspensionFigure 48: The front suspension kinematics model in CarSimThe suspension compliance (kinetics) was created by creating a model of frontcompliance (Figure 49: The front suspension compliance model in CarSim). Note, testswere done on the 2006 suspension springs in order to determine the progression rate ofthe springs (see section 10). These test results were used as a basis to calculate the springrates for the 2007 springs. When the CarSim model was first created the spring rateswere not known, thus the test results from the 2006 vehicle were inputted into the modelso that once the model is created it can be tested to ensure it is functional. The springdata was inputted into CarSim as a force verses displacement curve for both the extensionand compression loops. The 0 point on the x axis represents the static position of thespring, thus the static position of the shock (or installation length) needs to be known (for2007 this length was 18.375 in, so 4.375in of shock travel in compression and 1.625 in ofshock travel in extension). The test curves need to be shifted in order to take into accountthe preload initially on the shocks; the amount of compression of the springs while thevehicle is at the static position. The bump stops need to be also considered whichrepresent a sharp increase in the load once they are reached. The suspension roll stiffnesswas obtained from ADAMS/Car. Therefore once the spring rates were determined theywere inputted into ADAMS/Car to find the suspension roll stiffness and then the rollstiffness was exported into an excel spreadsheet and then copied and pasted into CarSim.The motion ratio was calculated in excel by exporting the suspension travel verses wheeltravel curve from ADAMS/Car and the slope of this curve is the motion ratio bydefinition. The shock data or damping data was obtained from Elka Suspensions andthen inputted into CarSim by copying and pasting the data into CarSim. The compliance62

2007 Baja ProjectSuspensioncoefficients were left to be equal to the values predicted by CarSim. In order to get anaccurate measurement of this, test data would be required.Figure 49: The front suspension compliance model in CarSimThe only data inputted into the tire screens was the dimensions of the tires. Thetires are one of the most important parameters to vehicle dynamics analysis. However,the tire is highly non-linear and experimental data would be required to properly modelthe tires. Thus the tire curves and stiffness predicted by CarSim was used for the analysisbecause the curves were obtained from experimental results.The controls of the model are the driver inputs. It is in this section where thereactions of the driver need to be specified in order to predict the performance of thevehicle. If the vehicle is going to brake at a certain location in the model it needs to bespecified as the driver pushing on the brake pedal at that particular location on the track.It is modeled as an increase in the master cylinder pressure. If the driver is going to steerthe car it must be specified in the steering control path. The speed of the vehicle can bespecified in the speed input section. This can be an initial vehicle speed, or a constanttarget vehicle speed. The throttle position and the gear shift schedule can also be used asinputs to the model. It is to be noted that the model will not do any of the controls unlessit is specified to. This implies that the vehicle will not shift gears unless you tell it tothrough the gear shift control input.The environment section is where the track the vehicle is to follow is specified. It63

2007 Baja ProjectSuspensionis in this section where the road friction, the shape of the track and the elevation of thetrack are all specified. This is an integral part of the analysis because it determines theroad conditions in which the vehicle is to be tested on.The results interface is where all of the results can be viewed. The animatefunction allows for the performance of the vehicle to be viewed in an animator. If certainparameters are desired from the analysis than they can be plotted by choosing whichfigures to plot (there is a total of 8 plots that can be plotted at once) and then clicking onthe plot bottom.8.6) Necessary combination of Elka Suspensions springsThe predicted or required spring rates were estimated in section 8.5. They wereestimated based on measurements of the weight and weight distribution. The availablesprings were supplied to us from the manufacturer (Elka Suspensions) (Appendix E). Itis to be noted that the spring rates of the chosen shocks are non linear; the springs getstiffer as they are compressed. The estimated spring rate will be the static spring rate; thespring rate that exist when the vehicle is at the static position. There are three auxiliarysprings and one main spring needed, and these springs are in series, thus the effectivespring rate can be calculated as follows (Equation 31: The spring rate of 4 springs inseries).k⎛⎜1=⎝ kmain1+kaux,11+kaux,21+kaux,3⎞⎟⎠−1Equation 31: The spring rate of 4 springs in seriesThe springs required to obtain the required spring rate can be calculated by varying themain and auxiliary springs until the proper spring rate is reached. One thing that can benoted is that the required spring rate in the front is more or less equivalent to the requiredspring rate in the rear (table 5). Therefore the main and auxiliary springs can be chosento be the same in the front and in the rear. A Matlab program was created in order tochose the main and auxiliary springs for the front and the rear, and the following is theresults from the analysis (Table 8: The main and auxiliary springs required to obtainedthe appropriate ride frequencies).Table 8: The main and auxiliary springs required to obtained the appropriate ride frequenciesFront RearMain spring (lbf/in) 201.6 201.6First auxiliary spring (lbf/in) 302.4 302.4Second auxiliary spring (lbf/in) 302.4 302.4Third auxiliary spring (lbf/in) 302.4 302.4Equivalent spring rate (lbf/in) 67.2 67.2Ride natural frequency (Hz) 1.2331 1.4567Wheel rate (lb/in) 19.4145 30.554564

2007 Baja ProjectSuspensionThe wheel rates (approximately equal to the ride rate) and the ride frequencies are prettyclose to the predicted values, therefore the chosen springs do meet the first part of theOlley criteria. The Matlab program also included a section which verifies that the motionratio in the front and in the rear is chosen properly; the shock will allow for the predictedwheel travel. The program also verified that a single suspension spring was capable ofabsorbing the entire weight of the vehicle. The analysis showed positive results, thusallowing the spring rates to be evaluated in CarSim in order to make sure that they will becapable of absorbing the loads from the road conditions without bottoming out more thanonce around the track it is to drive on (note the Matlab program can be found on theattached cd).8.7) Evaluation of spring rate in CarSimThe spring rates need to be evaluated in order to ensure that the suspensionsystem will be capable of absorbing the loads which are coming from the road.Therefore, the chosen spring rates were evaluated in CarSim by running the vehiclethrough 7 different analyses: acceleration, jumping performance, handling, cornering,acceleration and cornering, braking, and braking and cornering. The spring rates wereevaluated by verifying if the compression of the shocks were at reasonable amounts; theshocks were not bottoming out. The vehicle performance was also verified in order toevaluate the performance of the vehicle in all aspects. Before the analyses can becompleted in CarSim the progression of the spring rates had to be determined. However,this has to be done experimentally. Therefore, the progression of the spring rates wereestimated using the curves tested on the 2006 springs. The progression (exponentialgrowth of the load with compression) was estimated to be the same as that of the 2006springs. The spring rate of the front suspension in 2006 was 71.186 lbf/in, therefore allof the points were shifted down on the curve of the load verses displacement by3.986lbf/in (71.186 – 67.2 = 3.986lbf/in) in order to estimate the curve for the 2007springs. The curve was also shifted a bit to take into account 1in of pre load (estimated),and the load was peaked by an appropriate amount at both extremes (maximumcompression of the spring and maximum extension of the spring) to take into account thebump stops. The curve was then inputted into ADAMS/Car and a parallel wheel travelanalysis was completed on both the front and rear suspensions in order to obtain the rollstiffness of both suspensions. The roll stiffness and the spring load versus displacementcurves were then inputted into CarSim.The environment and control parts of CarSim need to be specified for each of theanalysis to be performed on the vehicle. The environment and the controls were firstcreated for each of the analysis by creating a model for each of them. A model is createdin the main window (the main window is the window where one can select run mathmodel) by clicking on new, and the models may be switched between one another byclicking on the data sets drop down menu. The environment and controls will not beexplained for every case, and if is desired to check the environment and controls for eachcase then the files can be checked which are located on the CD. As an example the65

2007 Baja ProjectSuspensionenvironment and controls will be explained for the jump performance analysis of thevehicle. The controls are as follows: no braking, no steering, an initial speed of 0km/h,the throttle position is set in such a way that the driver presses on the gas pedalimmediately and holds his/her foot on it for the whole time, and the shifting is such thatthe driver shifts from one gear to another every 1.15 seconds until he/she reaches 6 th gear.The environment is as follows: the x-y trajectory of the vehicle is a straight line; thecoefficient of friction is 0.5; the elevation is such that after the vehicle drives for 10m itstarts to climb the jump. The jump is 0.67m tall and is 2.3m long. The elevation after thejump is flat.The vehicle was tested in each of the environments created and the results are asfollows. The maximum spring compression and the maximum spring extension weredetermined (Table 9: Spring rate evaluation results).Table 9: Spring rate evaluation resultsAnalysis Maximum compression (in) Maximum extension (in)Acceleration 0.370 0.878Jumping performance 3.967 1.392Handling 0.515 0.905Cornering 0.155 0.437Acceleration and cornering 0.591 0.896Braking 0.946 1.118Braking and cornering 1.174 1.126Note, the suspension compression can be obtained by changing one of the plot options tosuspension compression and then clicking plot after the analysis is complete. Based onthe results it can be seen that the maximum extension and compression occur on the jumpperformance analysis. Thus, one can conclude that the maximum extension is safebecause the shock can still be extended by an additional amount of (0.23in), which allowssome room for play. One may also conclude that the maximum compression is safebecause the shock can still be extended by an additional 0.408in. However, the bumpstop is included in the 4.375in of compression, and it is about 1.5in thick. Therefore, theanalysis is predicting that the shock will hit the bump stop, but the force is not capable ofcompressing the shock to its full compression. The question then became is this safeenough? It is usually best to go with a softer ride for ride comfort, and the rule of thumbis that the suspension should be designed in order to let the suspension hit the bump stopsonly once as the vehicle goes around the track (or the course). After analyzing the set upfor the jump it was determined that most jumps the vehicle will see will not be this steepas the jump created, and the distance traveled by the vehicle after it hits the jump will bea lot less because the vehicle will normally land on a table top (top of a hill); thuspotential energy will not be as high as predicted in his analysis. Thus, it was decided togo with spring rates that were first chosen. Note, if this result would have been notsatisfactory than an iterative approach would be needed to determine the spring rates.The roll angle, pitch angle, yaw angle, forces at the tires, and accelerations weredetermined for each analysis and produced satisfactory results. The results will not be66

2007 Baja ProjectSuspensionpresented here, but can be check by running the analysis, see the files on the CD.However, it is to be noted that in the evaluation of the spring rates, it was more importantto determine if the springs were capable of absorbing the load than to determine theperformance of the vehicle. However, the performance of the vehicle was evaluated toensure that the vehicle did perform well in all areas, and based on the results from all ofthe analysis it was determined that this was the case. Note the animations of each of theanalysis can be seen in the attached video which can be found on the CD (Some of theresults can be found in Appendix G).8.8) Ride, bounce, pitch and wheel hop frequenciesThe ride, roll, bounce, and pitch frequencies can be calculated by following theprocedures outlined in section 6.1.1. The Matlab program based on the half car modelwas created in order to calculate the frequencies and judge the ride quality of the vehicle.It is to be noted that the suspension stiffness in this model is the wheel rate, and can becalculated knowing the spring rate and motion ratio. The damping coefficient wasobtained from Elka Suspensions; they obtained it through testing methods. The pitchinertia used in the model was the pitch inertia predicted by CarSim, the pitch inertia theyused in their models. The frequencies obtained from the Matlab analysis are as follows(Table 10: The frequencies of the vehicle). The results from the analysis are in prettygood agreement with the ride quality criteria specified by Maurice Olley. The pitchfrequency is greater than the bounce frequency and the bounce frequency is about 1.2times less than the pitch frequency (1.18 to be exact).Table 10: The frequencies of the vehicleFrequency (Hz)Bounce 1.1833Pitch 1.3985Wheel hop front 12.5511Wheel hop rear 15.0445The pitch frequency is not below 1.3 Hz as suggested by Maurice Olley, but is prettyclose to 1.3Hz. Therefore, the vehicle will perform well as vehicle ride is concerned.The amplitude ratios were also studied for two different cases. The first case is the frontof the vehicle is being excited while the rear of the vehicle is not being excited, and thesecond case is the opposite. The following amplitude ratios for a variety of frequencieswas obtained for both cases: vehicle bounce over input amplitude, vehicle pitch over theinput amplitude, motion of the unsprung mass in the front over input amplitude, motionof the unsprung mass in the rear over input amplitude (note H1 is the input in the firstcase and H2 is the input in the second) (figures 50-57).The body motion frequencies of the front and rear suspension can be calculatedfrom the motion amplitude ratio curves (these frequencies are the frequencies close to 1Hz). The wheel hop frequencies are also present in these curves (they are the secondhump). From these graphs it can be seen that it is at the low end frequencies where the67

2007 Baja ProjectSuspensionloads coming from the road are transferred to the vehicle body on both bounce and pitchmodes.Figure 50: Motion amplitude ratio for front excitationFigure 51: Pitch/Excitation amplitude ratio for front excitation68

2007 Baja ProjectSuspensionFigure 52: Motion of the rear unsprung mass/excitation amplitude for front excitationFigure 53: Motion of the front unsprung mass/excitation amplitude for front excitation69

2007 Baja ProjectSuspensionFigure 54: Motion amplitude ratio for rear excitationFigure 55: Pitch/Excitation amplitude ratio for rear excitation70

2007 Baja ProjectSuspensionFigure 56: Motion of the front unsprung mass/excitation amplitude for rear excitationFigure 57: Motion of the rear unsprung mass/excitation amplitude for rear excitation71

2007 Baja ProjectSuspensionRight at body motion frequencies the excitation amplitudes is amplified and the driverwill feel the most disturbances at this frequency. Thus, performing an analysis on thevehicle ride comfort or vertical dynamics allowed the ride quality of the vehicle to bepredicted (for further details refer to the program on the CD).8.9) Prediction of vehicle performance in regards to the dynamiceventsThe performance of the vehicle was once again evaluated by analyzing how thevehicle will perform at the dynamic events at the competition. The purpose of this was topredict the performance of the vehicle and to compare the results obtained from CarSimwith actual test results. Therefore, four new models were created to simulate each of thedynamic events at the competition (acceleration, hill climb, suspension and traction, andmaneuverability). Each of the models consists of an environment and a control filecreated in order to simulate the performance of the vehicle at each of these events.However, it will not be discussed how these were created, and if someone is interestedthe files are attached with the CD.Since one of the goals of this exercise was to compare the results to actual testdata, the acceleration and maneuverability tracks were created in CarSim to simulate thetracks the actual vehicle was tested on. The vehicle was tested at a local track(Powerband), and a portion of the course was mapped out to simulate the maneuverabilitytrack, and this same track was created in CarSim. The acceleration times were calculatedfor 100ft and 150ft distances, thus they were also calculated for the same distances inCarSim. The hill climb event was not tested, because there was not a hill sufficientlylarge enough to test the vehicle on. Therefore, a hill was created in CarSim and it wasverified if the vehicle could make it up the hill without any struggles. The gear shiftschedule was varied until the optimum (best time) was obtained in CarSim and this wasused as an indication for the driver (Figure 58: The hill created to simulate the hill climb).Figure 58: The hill created to simulate the hill climb72

2007 Baja ProjectSuspensionThere was also no data for the suspension and traction course because it was unclear whatthe course at the competition was going to be comprised of. Therefore a course whichconsisted of a lot of bumps and a handling section was created in CarSim in order topredict the performance of the vehicle as it travels along this course. The course wascreated in CarSim anticipating the course to be like the one predicted (Figure 59:Suspension and traction course).By analyzing the performance of the vehicle and by predicting its behaviorallowed for a better in sight as to how to better prepare the vehicle for each of the eventsat the competition. CarSim was also used to assist the driver in acceleration and inmaneuverability while testing the vehicle. This allowed the driver to get a better insightof what path to follow for the maneuverability event and what gear to start in and o shiftup to for the acceleration event. The direct comparisons between CarSim simulations andthe testing can be found on a video which can be found on the attached CD.Figure 59: Suspension and traction courseOne of the areas needed for improvement as suspension kinetics is concerned isthe preparation before competition. The bounce and pitch frequencies of the vehiclebody were not known at the competition, and on e judge in particular was looking forthese values. Therefore it is advised that a spreadsheet be prepared ahead of time andbrought to competition to show the judges all of the relevant data as suspension kineticsand kinematics is concerned.73

2007 Baja ProjectSuspension9) Suspension Component Design9.1) Choice of MaterialsTubing materials: The suspension control arms are constructed of circular steel tubing.Factors such as strength, weight and cost were considered when choosing the control armtubing materials. Table 11: Summary of material properties compares the differentaspects of some of the materials considered:MaterialSteel 4130(Annealed)Steel 1020CDSteel 1018CDCarbonContent(%)Table 11: Summary of material propertiesYieldStrength(Mpa)TensileStrength(Mpa)ElasticModulus(Gpa)Density(×1000kg/m 3 )30 % 436 670 190-210 7.7-8.0320 % 390 470 190-210 7.7-8.0318 % 370 440 190-210 7.7-8.03There is not weight difference between any of these materials since they all havethe same density. Steel 4130 has higher carbon content than the other two alloys,therefore, it has better mechanical properties. The only disadvantage with steel 4130 iscost, however, since all steel tubing was donated, chormoly tubing was chosen for thecontrol arms.Tabs materials: Steel 4130 was again chosen for the tabs materials due to its superiorproperties. It was decided to use a minimum thickness of 0.08 inches steel plate for all thetabs in the suspension systems. Laser and water jet cutting was then used to fabricate thesheet metal into the required shapes and geometry for the suspension pick points tabs.Bushing materials: Past Baja vehicles have always used Delran Nylon for all thesuspension bushings due to its durability and ease of machining. In the past it has beenproven that Delran Nylon can withstand wear and provide very smooth connections.However, this year it was decided to try a different cheaper material which is HDPE(High Density Polyethylene). After several test runs wit the Baja vehicle it was noticedthat the bushings were starting to wear resulting in compliance in the suspensionmechanism connections. Therefore, it was decided to replace all the suspension bushingswith a different material. In order to avoid any risks, Bronze “oil impregnated” was usedto make the bushings, this material has a much higher wear resistance yet at the sametime it is much heavier.74

2007 Baja ProjectSuspension9.2) Front Suspension System9.2.1) Control ArmsOnce the suspension points were designed in ADAMS/Car they were input intoCATIA in order to design the control arms structure. Each one of the designedsuspension points represents the center of a joint between two tubes. First CATIA wasused to form a wire frame model of the control arm by joining the suspension points. Thenext step was to choose the appropriate tubing profile for each member of the control armstructure. A circular profile was chosen for the tubing, due to its ease ofmanufacturability and better aesthetics aspects. Given the fact that the strut is mounted tothe lower control arm, it is exposed to large loads during the suspension bounce andrebound. Circular tubing of an outer diameter of 1 inch and a thickness of 0.065 incheswas used for the front lower control arm. The control arm members were drawnseparately as shown in Figure 60 below in order to obtain the exact dimensions and notchsizes for all the members:Room forFigure 60: Front lower control armSimilar procedure was followed when designing the upper control arm structure.The loads traveled through the upper control arm are not as critical as the lower controlarm. A combination of two tube sizes was used for the upper control arm, where the maincontrol arm structure was made of 0.75 inches OD by 0.049 inches Thickness, while theback tube that forms he pivot of the control arm with the frame is 1 inch OD by 0.049thick inch. Despite the fact that the loads transferred through the upper control arm aresmall, the back tube was added to support the structural rigidity of the control arm. Figure61 below shows the structure of the upper control arm (Appendix H)The clearance between the control arms, shocks and steering tie rods at full wheeltravel and steering was taken into consideration as well. An iterative design process wasused, where the control arms design was checked for clearance in ADAMS/Car thenmodified accordingly in CATIA until a design that is easy to manufacture and at the same75

2007 Baja ProjectSuspensiontime provides the required clearance was obtained.Figure 61: Front upper control arm9.2.2) Finite Element AnalysisIn order to accurately model the effects of lateral, normal and strut loads, anassembly finite element model should be used. Furthermore, an FEA assembly model canbe used to examine the stresses acting on each of the suspension components. However,in the case of the front suspension system it is very difficult to model the ball jointbetween the control arms and the upright. Therefore, FEA analysis was done separatelyon each of the front suspension components with special emphasis on critical parts. Thepart that is most likely to experience the largest loads is the lower control arm. Theboundary conditions for the control arm were modeled as shown in below, where the balljoint, the spring and the pivots where taken into consideration and modeled as restraints.The load is applied at the lower strut mount as shown in Figure 62, the direction of theforce was chosen be acting along the strut line.Spring ElementLoadsBall Joint RestraintPivot RestraintFigure 62: Front lower control arm FEA76

2007 Baja ProjectSuspensionThe magnitude of the load was calculated based on the maximum vertical force acting onthe tire using the following equation:( Normal _ Tire Force) ⋅ ( MotionRatio)Strut _ Force = _Where, the motion ratio was used to convert the normal tire force into the force actingthrough the shock. A finite element analysis on the front suspension upright was alsodone. The upright was modeled with the upper and lower ball joints boundary conditionsand the normal tire force acting on the spindle of the upright. Figure 63 further explainshow the upright was modeled and the FEA results:Upper Ball Joint RestraintSteering Tie RodBall JointMaximum StressNormal Tire ForceLower Ball Joint RestraintFigure 63: Front upright FEAPerforming finite element analysis on the front suspension as one mechanism isdifficult due to the fact that it is not possible to model the ball joint connect between twomembers, and thus the degrees of freedom of the system will not be accurately modeled.However, if the ball joints are modeled as solid part that are fastened to the control armsand the upright, then the results from the finite element analysis will simulate the worstcase scenario of the ball joint reaching their maximum rotation angle and the frontsuspension bottoming out. Despite the fact that this model does not give an accuratemeasure of the amount of stress through each member, it allows for simulating the effectof the normal tire force as well as the strut force simultaneously. The full frontsuspension FEA model is shown in Figure 64: Front suspension assembly FEA.77

2007 Baja ProjectSuspensionFigure 64: Front suspension assembly FEA9.2.3) JointsPivot Joints: The tabs and used to form pivot joints between the control arms and theframe which allows the control arms to rotate as the wheel travel. The control arms areconnected to the frame by attaching them to steel tabs that are welded to the frame. Thetabs were made from a 0.080 inches thick steel 4130 sheet metal. Being subjected to largebending and tensional stress, the tabs are considered the weakest link in the suspensionassembly and thus the strength of the suspension system is only as strong as the tabs. Inorder to give the tabs more resistance to bending stress and increase the weld area, bendswere incorporated to the tabs structure as shown in Figure 65:Figure 65: Laser cut tabsThe tabs were manufactured using water jet cutting, where the desired profile wascut and then a bending machine was used to obtain the correct bends. Designing thepivots and connection points to be as smooth as possible contributes to the overallsuspension stiffness. Any small resistance in the pivots or connections degrees offreedom will add up to slow the movement of the suspension system as it rotates about itsinstant center. Therefore, the suspension joints were designed with the appropriate78

2007 Baja ProjectSuspensionbushings and lubrications to reduce friction and improve the suspension response. Thefront suspension system incorporates two joints on each control arm, connecting it to theframe and the wheel upright. The basic construction of a pivot joint is shown in Figure66:BushingTubeInsert TubingGapTabBoltFigure 66: Pivot joint constructionAs shown in the diagram, bronze bushings are used to prevent direct metal onmetal contact and allow the joint to move smoother. A small steel tube is used to runthrough the joint assembly so that the joint pivots about that tube, it is also used as aprotection to the bolt that fastens the whole joint together. It can be seen from thediagram above that the insert tubing that runs through the joint assembly was madeslightly longer than the length of the tube and the bushings, which leaves a small gabbetween the bushing and the tab. This was done intentionally to prevent the tabs fromcrushing on the bushings as the bolt is tighten to fasten the whole assembly and thusallowing the joint to pivot freely. The bushings were also used in the front suspensionsystem to give more control over the caster angle orientation. The caster angle can bechanged by adjusting the bushing sizes on each side of the upper control pivot joint. Thiscaster adjustment method can be better understood from the following simplified diagram(Figure 67: Caster adjustment mechanism).Ball Joints: The control arm is connected to the upright using a ball joint which allowsfor the front suspension to control the vertical travel and the steering angle of the wheel.A Ricky Stator ball joint that allows 30 degrees rotation range is used in the frontsuspension. The ball joint is attached to the control arm using a threaded steel insert thathas a hex head lip (see Figure 68).The ball joint is fastened to the steel insert using the two nuts as shown in thefigure. If the nuts are unfastened and the steel insert is rotated it will result in moving theball joint out towards the wheel or in towards the frame. Thus, given the fact that thismechanism is used for both the upper and lower control arms, it can be used to adjust thecamber angle orientation of the wheel without having to disassemble the suspension79

2007 Baja ProjectSuspensionsystem. This camber adjustment mechanism is very handy when it comes to finalizing thesuspension geometry before driving the car as it is very convenient to test differentcamber angles.Bushing Control Arm BushingFigure 67: Caster adjustment mechanismNutsBall JointInsert Control Arm UprightFigure 68: Camber adjustment mechanism9.2.4) Steering tie rod and bump stopThe tie rods are linkages connecting the steering rack to the wheel upright, wherethe tie rod is connected to the steering rack through a left handed hiem joint and to thewheel upright though a right handed ball joint. The steering tie rods are considered one ofthe weakest links in the front suspension assembly. The tie rods take some of the loadstransferred from the wheel through the upright, breaking the steering tie rods afterlanding from a jump was the main issue for past Baja vehicle. It was also noticed in thepast that the tie rod material itself can withstand high loads, however, it was at the jointsbetween the tie rod and the steering rack and the wheel upright is where the tie rod will80

2007 Baja ProjectSuspensionmost likely to break. Therefore, it was decided to use hiem and ball joints with strongermaterial and bigger diameter, also steel 4130 with an OD of 0.75 inches and a thicknessof 0.065 inches was used to make the tie rods. A left hand and right hand threaded insertsare welded to each end of the tie rods. The combination of left and right hand threadsallows the length of the tie rods to be easily adjusted to change the toe angle of the frontwheels.Ball Joint Tie rod Hiem JointFigure 69: Steering tie rodThe steering system also incorporates a steering stop that dictates the maximumand minimum angle of steering. The main purpose of the steering stop is to prevent thewheel upright from hitting the control arm as the wheel reaches maximum steering angleand maximum wheel travel. A rubber sleeve was attached to the steering stop to absorbsome of the impact energy. For the convenience of packaging, the steering stop wasmounted on the upright where the tie rod attaches to the wheel upright. Figure 70 showsthe steering stop and how it was installed:Steering StopFigure 70: Steering stop81

2007 Baja ProjectSuspension9.3) Rear Suspension System9.3.1) Control ArmsSimilar procedure was applied when designing the rear suspension control armsas the front control arms, where the suspension points were input into CATIA fromADAMS/Car. Two main factors had to be considered when designing the rear controlarms; the first factor is the introduction of the differential uprights and the reduction inthe width of the rear end of the frame. This design change resulted in the control armsbeing much longer than previous years, which increased the bending moment of the strutforce acting on the lower control arm. Another factor that had to be considered was theclearance with other components of the suspension system. In order to save weight in theunsprung mass of the vehicle, the small outlaw 500 uprights were used, however, thatresulted in the uprights being packaged very close to the center of the wheel and hence,creating very small clearance room for the control arm joints. Also, there was a clearanceissue between the shock and the drive shaft, it was necessary to make sure that the controlarm is designed such that there is enough clearance room between the chock and thedrive shafts. These constraints are shown in Figure 71:Rim ProfileLower Strut MountUprightLower Control ArmBendingArmsMomentFigure 71: Schematic of rear lower control armThe above diagram shows that due to the clearance constraints, the control armstructure was designed such that the width of the control arm near the wheel is muchsmaller than the width near the frame. This resulted in the shock mount point beingconcentrated on one member rather than distributed equally on the entire control armstructure. Thus, the strut force acting on the control arm has two main bending momentarms, which is a weak point in the design; however, it was accounted for by using biggertubing for the control arm member that is subjected to highest bending stress. A circulartubing of 1.25 inches OD and 0.065 thickness was used for the tube member which takesmost of the load from the strut. The rest of the control arm members were made out of 1inch OD and 0.065 thickness circular tubing. The upper control arm design is not ascritical as the lower control arm, since most of the load is transferred though the lowercontrol arm. The main function of the upper control arm is to maintain the orientation ofthe wheel and give better control over the suspension geometry. Clearance however, is82

2007 Baja ProjectSuspensionstill a factor when designing the upper control arm, where the clearance with rim and theshock being the main factors dictating the geometry of the upper control arm. 0.75 ODcircular tubing with 0.049 thickness was used for the structure of the upper control arm.The ease of manufacturing was again taken into consideration when designing the rearcontrol arms, most of the members were designed to be straight and bends were reducedwhere possible, however, it was necessary to add bends still due to the compactpackaging in the rear suspension assembly. Figure 72 shows the design model of theupper and lower control arms, with each member of the structure being drawn separatelyin order to obtain an accurate measure of the member lengths and notch sizes(AppendixH):Lower Control ArmUpper Control ArmFigure 72: Rear control armsGiven the fact that the upper control arms are not subjected to as high loads as the lowercontrol arms, the option making the upper control arms out of aluminum was considered.Figure 73 shows a picture of the constructed aluminum upper control arm:Figure 73: Aluminum rear upper control arm83

2007 Baja ProjectSuspension9.3.2) Finite Element AnalysisIn order to obtain a better estimate of the stress in each component of the rearsuspension system, an assembly finite element analysis was done by modeling the jointsbetween each member. The rear suspension system is easier to model than the frontsuspension due to the fact that all the joints in the rear are pivot joints with one degree offreedom as appose to the ball joint in the front suspension. The normal loads of the tireand the stiffness of the shock were modeled by applying vertical force at the wheelupright and introducing a spring element at the lower shock mount on the control arm asshown below:Spring ElementPivotJointsContact Connection(UCA-Upright)ContactMaximum StressFigure 74: Rear suspension assmebly FEA9.3.3) JointsHiem Joints: similar to the front suspension system, the control arms are connected tothe frame using sheet metal tabs that are welded to the frame. However, in order to gainmore control over the rear suspension camber and toe angles, hiem joints were fastenedto the ends of the control arms and then attached to the tabs on the frame. By threadingthe hiem joints in and out of the control arms ends, the length of each side of the controlarms is adjusted separately and hence given control over the wheel orientation. The jointbetween the control arm and the tab is shown in details in Figure 75:In order to give the joint more structural rigidity, small spacers were insertedbetween the hiem joint and the tab walls; this will prevent the tab walls from crushing thejoint as the bolt is tightened.84

2007 Baja ProjectSuspensionSpacersHiem JointTabsBoltFigure 75: Hiem jointPivot Joint (A-Arms to Upright): The joint connection between the control arms and theuprights were constructed in similar manner to that of the front control arm pivotconnection with the frame, where a combination of bushings and steel insert were used tomake the joint less stiff. The length of the steel insert was made longer than the bushingsin order to make sure that the bolt fastening the joint together is not crushing thebushings. The upright-control arm connection is shown in Figure 76:BushingsGap9.4) InstallationFigure 76: Upright to control arm pivotThe installation of the suspension system on the frame was done by firstassembling each component of the suspension system which includes the upright, controlarms, bushings, pivot joints, hiem joints as well as ball joints. The suspension system85

2007 Baja ProjectSuspensiongeometry points were designed to an accuracy of 0.01 inch, however, when it comes toinstalling the suspension system on the frame, it is very difficult to maintain thesuspension points as desired in the design. In order to some what install the suspensionsystem close to the actual designed points, the tabs were not welded on the framedirectly, instead the tabs were attached to the control arms joints and then welded to theframe.The first step in locating the suspension points on the frame was setting the frameon a flat table and the planar coordinates of the points were inscribed on the table. Thevertical location of the points was determined by using a threaded rod that is mounted ona square block. The height can be located in the threaded rod by threading a nut on therod and then adjusting the height of the nut to match that of the desired suspension point.Once the height is located using the nut, the threaded rod can now be moved on the flattable where the planar coordinates of the suspension points are scribed. It is veryimportant to keep in mind that the suspension points obtained from ADAMS/Carrepresent the center of the joints between the frame and the control arm and hence thusclearance distance between the frame and the control arms had to be taken intoconsideration. The approximate location of the suspension points is then marked on theframe.The installation of the front suspension system was done by first tack welding thetabs for the lower control arm to the frame. The tabs for the upper control arms were tackwelded by first using a fixture as shown in the figure below to maintain the suspensionpoint geometry. The fixture shown in the figure consists of two magnetic base poles thatwere used to attach a shaft to act as the upper control arm pivot point.Figure 77: Front control assemblyThe rear suspension system was assembled differently than the front suspension.The control arms, upright, bushings, hiem joints and tabs were all assembled togetherbefore attaching the rear suspension to the frame. The suspension points were thenlocated on the frame using a similar procedure to that used in the front. Small spacers andthe magnetic base poles where used to fix the entire suspension assembly to the framewhile it was being welded. The figure below shows the rear suspension assembly being86

2007 Baja ProjectSuspensionwelded to the frame:Figure 78: Rear control assembly87

2007 Baja ProjectSuspension10) Shocks (Dampers & Springs)10.1) Chosen shocksThe suspension shocks are one of the first things that need to be determinedbecause the suspension geometry is dependent on them. The motion ratio needs to bedetermined such that the desired wheel travel will not bottom out the shocks. So if thetotal designed wheel travel is 10in and the maximum shock travel is 6in, than the motionratio is limited to 0.6 (this was the case for when the suspension was designed in 2007).Therefore, it is important that the suspension shocks are chosen early so that the correctmotion ratio is designed into the suspension system.It was decided to use the suspension shocks (Elka Suspensions coil over shocksuspension shock) which were purchased in 2005 on our vehicle because of moneyconstraints at the beginning of the project (Figure 79: Elka Suspensions coil over shock).Figure 79: Elka Suspensions coil over shockThese shocks were chosen because they have adjustable damping in both rebound andcompression; they have a progressive spring rate; and they have adjustable pre load. It isto be noted that if it was not for cost constraints the same Elka Suspension shocks wouldhave been chosen, but they have been chosen with the reservoirs directly connected to theshock and not with remote reservoirs and with a greater amount of shock travel. Agreater amount of shock travel would have been more desired because it would haveallowed the shock to be moved closer to the wheel in the rear and in the front thusallowing the bending moment to decrease on the control arms, thus improving theirstrength. It was also desired to have a greater shock travel because then the motion ratiocan increase which permits less amount of force to be transferred to the vehicle body thuspermitting a better ride. The Elka Suspensions coil over shock will also permit thesprings to be changed which allowed us to choose the appropriate springs to give us adesired spring rate.It is to be noted that in the past (before 2005) the University of Windsor Bajateams used Billstein suspension shocks. These suspension shocks are designed for theparticular vehicle; the damping coefficient of the shocks is chosen based on thedimensions of the suspension system and vehicle, it is not adjustable. It was more88

2007 Baja ProjectSuspensiondesired to go with the Elka Suspensions coil over shock suspension shocks becausetheses shocks have adjustable damping which allows the damping of the suspensionsystem to be tuned through vehicle testing which is the more desired route to take. Thesprings on the Elka Suspension coil over shocks suspension shocks are much narrower indiameter (about half the diameter) which is more desired for clearance problems betweenthe upper control arm and the shock. It will be easier to design the upper control armaround a narrower shock.10.2) Adjustable DampingThe Elka Suspensions coil over shock suspension shocks have adjustable dampingin both rebound and compression. This is a desired feature because it allows the dampingof the suspension system to be tuned for optimum performance through vehicle testing.The compression damping is adjusted by turning the knob on the remote reservoir, andthe rebound damping is adjusted by turning the knob at the bottom of the shock (Figure80: Rebound and compression damping adjustment).CompressiondampingRebound dampingadjustmentFigure 80: Rebound and compression damping adjustmentThe compression knob is used to adjust the hydraulic resistance of the shock to highspeed impacts. The compression knob can be set to full hard or full soft or dome wherein between; there are 30 clicks of adjustment between full soft or full hard. A full hardcompression setting will provide a better resistance to impacts, but the ride will be stiffer.A full soft setting will provide a smooth ride, but there will be less resistance to impacts.The rebound knob can be set to full fast or full slow. The rebound adjustment is whatdetermines the speed at which the shock will return to its initial state after it is beingcompressed from an impact; it determines the kickback of the suspension system. Acorrect rebound adjustment would imply that the rear wheels will keep the maximumtraction of the vehicle by keeping the wheels on the ground without inducing anykickback to the vehicle; without launching the driver from the vehicle. There are 50clicks of rebound adjustment between full soft and full hard. With a full fast position theshock will return to its initial position very fast, and the effect is that the rear of the89

2007 Baja ProjectSuspensionvehicle will kick and move from side to side after hitting a series of bumps. In thissituation the driver will as if he/she is being launched from the car. With a full slowposition the shock will return to its initial position very slow, and the effect is that thesuspension shock will not have time to return to its initial position when a series ofbumps is encountered. In this case the shock will run out of suspension travel and maybottom out. It is not recommended that the rebound position be set to full soft or fullhard.The compression and rebound settings that best suit the vehicle need to bedetermined through vehicle testing. There are 30 clicks of compression adjustment and50 clicks of rebound adjustment, so where did we start; what values were they set at thebeginning of testing? The initial values of the compression and rebound settings were setto be equal to the values used by the 2006 team. The settings were then changed in orderto optimize the performance of the vehicle by testing the vehicle through a variousamount of tests. The compression and rebound settings were first adjusted as theacceleration and braking of the vehicle were tested. The reason for this was because thevehicle needs to be tested in gradual steps. If the settings are not properly set or therewas a mistake in the calculations for the appropriate spring rates then the vehicle shouldnot jump over jumps because this is where major damage can occur. Thus, the vehiclewas first tested in braking and acceleration and the jounce and rebound of the suspensionwere verified. If the spring rates were not chosen properly the pitch of the vehicle will benoticeable as the vehicle is accelerating or braking. The estimated pitch of the vehiclewas determined from the analysis performed on the vehicle in CarSim, and this value wasused to verify if the suspension compression or extension was too much while the vehiclewas accelerating or braking. The compression and rebound settings were also adjustedwhile testing the acceleration and braking performance of the vehicle. The performanceof the vehicle was then evaluated as the vehicle drove over a series of bumps, and thecompression and extension of the shocks were verified. The rebound setting was alsochanged in order to eliminate the kickback of the vehicle and to eliminate the shock frombottoming out. The final test performed on the vehicle in order to tune the suspensionwas a jump performance of the vehicle, and the compression damping was adjusted inorder to ensure that the suspension shocks had enough impact resistance set into them.Once the compression damping was set, the rebound damping was set in order to ensurethat the vehicle did not kickback after hitting the jump.10.3) Progressive spring ratesThe Elka coil over shock suspension shocks have a progressive spring rate. Thisimplies that more the springs are compressed the stiffer they become. A progressivespring rate is obtained by stacking several springs in series. With the Elka suspensioncoil over shocks there are three auxiliary springs and one main spring. The main springis at the bottom and the auxiliary springs are stacked on top it. The main spring will notstart to compress until the auxiliary springs are compressed. There is a crossoverbetween each of the springs when they are assembled on the suspension shock (Figure81: Suspension springs with the crossovers). Each crossover has a longer side and a90

2007 Baja ProjectSuspensionsofter side, and the manner in which they are placed in the shock play a role in depictingthe spring progression. If all of the crossovers are placed in the shock in a manner thatthe larger portion (longer sides) of the crossover is facing up (as depicted in the figure),then the effect is to increase the spring progression. The crossovers are what determineshow much the auxiliary springs will compress, thus the effect of putting the longer sidesfacing up is to cancel out the active stroke of the auxiliary springs sooner when the shockis in compression. If all the crossovers are placed in the shock in a manner where theshorter sides face up than the effect is to reduce the progression of the springs, and therate decreases.Figure 81: Suspension springs with the crossoversThis leads to a softer ride, but the suspension will be more susceptible to bottoming out.The positions of the crossovers were changed while testing the vehicle and the optimumposition was found through vehicle testing. The positions of the crossovers were chosento allow for a soft ride, but to ensure that the suspension shocks do not bottom out morethan once around the track.The 2006 shocks were tested on a test rig to determine the progression of thesprings and to determine the effect of the position of the crossovers. The following is theresults for when the longer side of the crossovers are all facing up and for when theshorter side of the crossovers are all facing up for the front suspension of the 2006vehicle (Figure 82: Load versus displacement of Elka Suspension with longer sides ofcollars facing up) (Figure 83: Load versus displacement of Elka Suspension with shortersides of collars facing up). It can be seen from the results that the springs are indeedprogressive springs and that by placing the crossovers in the shock with the longer sidefacing up does indeed lead to a higher spring rate. These curves were used to predict theload verses displacement curve of the 2007 shocks which were inputted into the CarSimmodel and ADAMS/Car models.It is recommended that a new set of suspension shocks with a greater shock travelbe chosen for next year if there are funds to do so. If there are money constraints as therewas in 2007, and the Elka Suspension coil over shock suspension shocks are re used on91

2007 Baja ProjectSuspensionthe vehicle than it is advised that the shocks get sent back to Elka Suspension to get revalved. Further information regarding the suspension shocks can be found in AppendixL.Load vs. Position30002500Load (N)2000150010005000-50 0 50 100 150 200Position (mm)Figure 82: Load versus displacement of Elka Suspension with longer sides of collars facing upLoad vs. Position30002500Load (N)20001500100050000 50 100 150 200Position (mm)Figure 83: Load versus displacement of Elka Suspension with shorter sides of collars facing up92

2007 Baja ProjectSuspension11) Hubs & Uprights11.1) Background & ResearchFront uprights were selected for their robust structure, lightweight design andoptimal outer suspension points. The design utilized is that of the 2006 Polaris Outlaw500 ATV. Stock OEM front and rear hubs were selected from Polaris’s 2006 Outlaw 500and Predator ATV models respectively.The rear suspension uprights were designed with goals of reducing size andweight, increasing strength and ease of manufacturing. Polaris’s 2006 Outlaw 500 ATVsetup was modified to accommodate the rear control arms while maintaining consistentsuspension points to promote interchangeability. A casting method was investigated butturned down mainly due to material availability and strength. After thoroughinvestigation, a CNC process was implemented.11.2) Concepts & BrainstormingAside from the rear uprights, OEM Polaris parts were used. With that said, thetopic of discussion will be primarily centered on the rear upright design. The machiningmethod used was selected from a number of possible options listed below:1. Machine from a piece of stock billet Aluminum (It may be expensive to domanually as a production part, but if this part were to be put into production a CNCprogram would be written and it would be much less expensive) This process would bestronger than the OEM Polaris part – which is the case for the following 3 processoptions, since the original part is die cast Aluminum.2. Green Sand mold (Aluminum Sand casting) - A process by which we use thepart and have to literally pound "green sand" around each half of the part for Aluminumto be poured into. Only final machining is required which results in minimal wastedmaterial.3. Monoshell Casting (recommended) - This is where we would roughly replicatethe part by carving a shape with wax. The oversized shape is then dipped into plaster ofParis then sand about 3 times. Once the layers are hard, the wax is melted out (through asmall hole drilled into it) then immediately, Aluminum is poured. This process implies aself-tempering process as well. The shell is then broken off and final machining isemployed.4. Machined from steel - Producing it with steel would not be smart since it is tooheavy for our purpose. If steel were to be used, the stock piece of steel and machiningwould cost nearly the same as Aluminum, but a harder machining process and heavierresult. If the uprights were constructed using separate steel parts, bolts should not be93

2007 Baja ProjectSuspensionused as a fastening method, welding would be optimal. For such a thick part, major edgepreparation and groove cutting would be required. In addition, TIG welding must beused (skilled trade). Basically, making it out of sections and welding would cost as muchas machining it, since there is so much time spent manually prepping edges and TIGwelding. To the added cost you must add weight, so now what you have is a part thatwould cost nearly the same as machining the block of Aluminum, but heavier.Monoshell casting was seriously considered at Nemak but was rejected for thefollowing reasons:• The rear upright is made from A356 Al with a T6 temper. An A356 alloy hassuperior properties when compared to A319 (the alloy used to produce the engineblocks). The A319 should not be used for suspension components without again,significantly altering the part.• A hand poured casting is a very risky process, especially when being performedby an inexperienced pourer. This is a risk that could jeopardize the team’sperformance in the endurance race (the most heavily weighted portion of thiscompetition).• If testing (destructive and non-destructive) is to be performed on the finished part,there will not be sufficient time to arrange this once we finally have a finishedpart. Fixturing must be made as well as arrangements and machine time at thetesting facility.• Through speaking to a member of the 2006 U of W casting team, it was explainedthat this process took 2 years to perfect one part. Seeing as a dissimilar part is tobe produced, time becomes a major issueSeveral design iterations were considered before finalizing the current structure.This evolution is shown in Appendix I11.3) CATIA ModelingCatia V5 was used extensively to arrive at the final design of the rear upright.After a specific design was developed it was then validated using Catia’s FEA package.Not only was the part simulated as an individual piece, but also it was thoroughly testedas an assembly with the remaining rear suspension parts. A final model is shown belowin (Figure 84: Final Catia model).Figure 84: Final Catia model94

2007 Baja ProjectSuspension11.4) FEAThe rear upright’s structure exhibits several important design considerations thatwere used to help strengthen the part, add minimal weight and best accommodate thecontrol arms. Such features include re-enforced webbing to support both upper and lowerrear control arms; added underlying surface structure that proved to increase strengthwith an insignificant addition of weight; a slightly decreased overall width to fit thecontrol arm assembly. The finalized design geometry was kept very simplistic as tominimize CNC machining time.An assembly FEA of the rear suspension assembly is shown below in (Figure 85: RearAssembly FEA).Figure 85: Rear Assembly FEA11.5) Materials & Manufacturing Procedure UsedA more robust structure was possible using a CNC process and 6061-T6Aluminum for its high strength to weight ratio and high modulus of toughness. Althougha greater cost of manufacturing resulted, the advantage of increased strength and weightreduction highly outweighed this downfall. This design offered a 25% reduction inweight when compared to the lightest used in previous years.The finalized design geometry was kept very simplistic as to minimize CNCmachining time. This was accomplished by limiting complexity which results inreducing the number of required tooling changes. This in turn reduced overall time forpart production and thus cost.11.6) Finished Product11.6.1) TestingTesting of the OEM parts was not performed since they were approved forproduction at Polaris Industries. We felt this was enough proof that the parts will hold upfor Baja SAE since ATVs are designed for much more rigorous activities.95

2007 Baja ProjectSuspensionSince the rear upright is a rather robust part, testing was implemented using onlyFEA. It was determined that parts like tabs for instance would fail long before this part.Considering the process used to manufacture this part, the structure is far stronger thanthe part this one is based upon (cast OEM Polaris).Other testing methods that were considered and recommended includetensile/compressive and fatigue. Tensile/compression tests can easily be performed usingan Instron machine with the appropriate fixturing. This type of set-up was planned butomitted due to timing and priority (Figure 86: Proposed test setup).Figure 86: Proposed test setupIt was recommended by Polaris to do fatigue testing as an assembly. This is howthey test the parts at their facility. A fixture that tests the fatigue properties of theassembly supports a full quarter of the vehicle’s suspension. This also gives a good ideaof how the part functions as an assembly with all the appropriate bearings and accessoriesfitted and to provide the most realistic test of the part.11.7) Recommendations for ImprovementsThe front hubs, uprights and rear hubs were merely selected and therefore noactual design was required of these parts. The rear uprights although required extensiveanalysis and were developed from scratch.It is suggested that a more cost effective method is used to produce these parts, asCNC is a very expensive route. Especially when considering this project as havingpotential for mass production, a casting method or one of similar cost should beimplemented.96

2007 Baja ProjectSuspension12) Tires and Rims12.1) Background and ResearchThe tires and rims were researched to give the best combination of tread patternand low unsprung mass for competing purposes. Rims needed to be lightweight andductile to resist cracking if disturbed during the competition. Tires needed to be selectedto give the best off-road endurance possible. Inexpensive tires and rims would assist withour cost report.Table 12: 2003 Testing DataWheel/Tire CalculationsTiresizeupr/btm tireheightCenterline XfactorYfactorwheelwidthOFFSET(from center)18 8.3 4 12.3 2.794 1.517 5 1.51719 8.3 4.5 12.8 2.908 1.403 5 1.40320 8.3 5 13.3 3.022 1.289 5 1.28921 8.3 5.5 13.8 3.135 1.176 5 1.17622 8.3 6 14.3 3.249 1.062 5 1.06223 8.3 6.5 14.8 3.362 0.949 5 0.949Fast Trekker tires were selected based on this test data (completed in 2004). Justprior to the competition, we were interested in Dunlop tires based on the tread patternobserved from one tire we obtained. So, three more tires were ordered to give the vehiclea full set and the vehicle was tested with these four tires. The Dunlop tires prove to givebetter cornering performance, a more responsive ride and gave a faster vehicle speed.Therefore it was decided to use these tires at competition.12.2) Concepts and BrainstormingThe tire provides three main functions:1. It supports the weight of the vehicle, while cushioning against shocks/bumps inthe road.2. It develops longitudinal forces for acceleration and braking.3. It develops lateral forces for braking.The design of a tire is very complex and non-linear, difficult to model. Tread pattern forthe best support of off-road driving was desired, so we chose radial-ply style tires. Thetread pattern is shown below (Figure 87: Tire internal cord scenarios)Specifications of the 2007 tires are P21-7-10. The manufacturer is Dunlop and the max.Pressure is 36 psi.97

2007 Baja ProjectSuspensionFigure 87: Tire internal cord scenariosUnder acceleration and braking, there is more slippage than normal because of therubber deforming to overcome changing friction forces, due to the changing distributionof the normal forces.Figure 88 Tire contact patch reactionsUpon cornering, the tires experience shear forces acting on the contact patch incontact with the ground. The distribution of the forces is asymmetric, so the tire patch incontact with the terrain is under elastic deformation while cornering due to the lateralforces. The net lateral force induces a self-aligning moment about the tire vertical axis sothat the moment applied by the steering rack on the tire is balanced.98

2007 Baja ProjectSuspensionFigure 89 Contact patch aligning momentTire stiffness is modeled as a series of springs. They are located at the surface ofthe tires that are in contact with the ground. Smaller slip angles induce smaller lateralforces during cornering, so understeering is desired whenever possible.Tires are essentially modeled as pressure vessels, with the internal forces causedby the air pressure inside the tire tubes.Figure 90 Internal Pressure ModelAs the tire provides traction force by gripping the road, it must slip relative to theroad. Behavior is evident by the following graph (Figure 91 Lateral force, traction forceaffect on slip %).Figure 91 Lateral force, traction force affect on slip %99

2007 Baja ProjectSuspensionSlip angle is defined according to the following behavior for different slip angles.Theoretically it is the angle during cornering between the tire’s direction of heading andthe tire’s direction of travel.Figure 92 Aligning moment for vertical loads and slip anglesAt low slip angles, lateral force is linearly related to the slip angle.F y = C α* α, C α is the cornering stiffnessThe magnitude of the cornering stiffness is dependant on a list of parameters:1. Tire size, type2. Number of cords in tire3. Cord angles (radial, bias-ply type dependant)4. Wheel width5. Tread6. Load inflation pressureVehicle cornering speed is irrelevant. Larger tires have greater corneringstiffnesses for a specified loading. They also have higher load capacity than smaller tires.For tires with the same diameters but greater widths than normal tires carcass stiffnesses(in the interior cords of the tire) will be higher than normal, so cornering stiffness willalso be higher.Aligning moment is dependant on the size of the contact patch and the growth ofthe slip region. Shear stress and torque responsible for aligning moment are dependanton the distance from the centerline of the contact patch and the tire centre. So, the meancontributors to the aligning moment are the tread elements edge of the contact patch. Atgreater slip angles, the aligning moment decreases.100

2007 Baja ProjectSuspensionFigure 93 Lateral forces for brake forces at different slip anglesThis plot shows the general effect on lateral force when braking is applied fordifferent slip angles. As the driver hits the brake pedal, the net lateral force decreases dueto the increase in the tire, induced by the braking demand. Knowing that the friction limitfor a tire is defined by the dynamic coefficient of friction multiplied by the load, it isevident that the friction can be increased for a lateral force, a braking force or acombination of both. However, the vector sum of the two must not exceed the frictionlimit defined by the plot. Therefore, the limit is defined as a friction circle in the plane oflongitudinal and lateral forces.Figure 94 Lateral forces and aligning moments for different traction forcesUsing zero traction force as a reference, it is clear that when lateral forces areapplied the aligning moment decreases. So, applying a braking force tends to stiffen thetires with respect to the mechanism that generates lateral force. The reduction of aligningmoment implies a reduction in the net lateral force acting on the contact patch, because of101

2007 Baja ProjectSuspensionthe decrease in shear stresses at the contact patch. High sensitivity to the vertical load isevident in the plots. The sensitivity is due to the moment’s influence by the size of thecontact patch. Doubling the load doubles the size of the contact patch, where aligningmoment is most affected (at extremities of the contact patch). So, the aligning momentincreases gradually as shown in the graph with increasing vertical load (traction forceincrease induces vertical load increase).When the vehicle is operated under combined braking and cornering, thelongitudinal and lateral forces change from their independent behaviours drastically.Longitudinal slip generally decreases the lateral force for a given slip angle. An increasein slip angle reduces the longitudinal force developed for a certain braking condition.As traction forces are applied towards their maximum value, lateral forcedecreases because the friction approaches its limits. As well, the aligning momentdecreases to the point where it may even be negative towards the braking limit. Negativealigning moment tends to steer the wheels to a greater slip angle, as well as affect thestability in braking through the steering system.For a positive normal traction force the lateral force decreases slightly and thealigning moment increases drastically. Near the maximum braking force, both lateralforce and aligning moment decrease. However, the aligning moment never becomesnegative for the maximum driving force.In regards to vehicle performance, braking during a steady turn causes the tires toslip and the lateral forces to decrease. This alters the path of the vehicle while braking.Also, when steering is applied during braking, the vehicle will have lower steering andbraking performance compared to the results when applied independently. The minimumdecrease in braking performance occurs while cornering with a lateral acceleration of0.3g. As the maximum braking force is approached, the vehicle response can bedegraded to the point of total loss of control. The description of the control loss dependson the order in which the front and rear tires approach the wheel-lock condition. Frontwheellockup will make the vehicle unsteerable while rear-wheel lockup will induce spinoutmotion.For ideal tires, lateral force is zero for zero slip angle. In reality, this is not thecase. At small slip angles, real tires show the above behavior for forward and reversegear selections. The lateral force behaves differently for forward and reverse drives, andusually has a nonzero value at α = 0. This is the result of the cords in the radial-ply tiresfor the BAJA vehicle, due to the angles of these cords in the belt layers. To avoid thisimbalance in forces, belts are made with alternating belt layers at opposite angles.However, perfectly balancing the cords is impossible. So, a free-rolling tire will nottravel in a straight line, but will travel in a skewed line with respect to its center plane.As well, when rolling forward, if the tire experiences a force to the right, it willexperience a force to the right when it rolls in the opposite direction due to the cords.Thus, when tire lateral force is measured with zero slip angle, the result is the forceaveraged from both directions of travel. Ply-steer is dependant on the vertical reaction of102

2007 Baja ProjectSuspensionthe tire.Figure 95 Vertical and longitudinal reactions for tire roll over a bumpReactions plotted above show that as the tire collides with the leading edge of thebump, the vertical force starts to rise due to the vertical displacement of the tire. Theforce continues to rise until the tire completely rolls out of the depression. A longitudinalforce is also generated due to the suspension control arms providing the pulling forcerequired for the tire to rise up onto the bump. Thus, the tire will have a reaction. Onceon the bump, the vertical force increases so the rolling resistance increases. Thelongitudinal force decreases and will not return to its original value but will rise againwhen the control arms balance to adjust to a new height to balance the vertical forces.During vehicle operation, the tire also acts as a vibration absorber, smoothing outthe roughness in the terrain. This influences the vertical motion of the body and wheels.So, vibration analysis needed to be considered. The tire has a natural frequency in whichit will resonate, affecting the transmission of vibrations to the vehicle frame. This mayalso cause vehicle frame resonance. A large amount of tire mass is concentrated at thetreads. These treads connect to the tires by sidewalls which are compatible with treads.This compatibility allows the treads to resonate when excited by road inputs. Vibrationmodes and corresponding tire behaviors are shown here.Figure 96 Tire natural frequency vibration modes103

2007 Baja ProjectSuspensionThe first mode involves a simple vertical disturbance without distortions. It iseasily excited with vertical forces in the contact patch at a certain frequency. The motionis vertical, so it is transmitted to the wheel and suspension control arms.The second mode shows an elliptical vibration such that the oscillation issymmetrical about the horizontal and vertical axes. The top and bottom of the tire arealways moving out of phase such that there is no disturbance to the wheel. Vertical loadsat the control patch are generally absorbed by the tire avoiding their transmission to thewheel and suspension control arms. Similarly, the third and higher modes are effective inavoiding transmission of vibrations to the wheel and control arms, and have similarelliptical vibrations except with more axes of symmetry. In-between these modalresonant frequencies the tire does not resonate. There are no axes of symmetry forvibration isolation. This asymmetry results in net forces that are imposed around thecircumference of the wheel, with the net force affecting the motion of the wheel. Thecontact patch is stationary, so the tire is a very stiff element for all vertical forces actingon it at these frequencies. The natural frequencies of the tires and the frame respectivelywere ω = 10 Hz for wheel hop, ω = 1 Hz for body motion. Damping in the tire was verysmall relative to the damping in the suspension (shocks), so tire cornering stiffness wasusually negligible for vibration frequency calculations. For the entire suspension system,compression damping was usually less than rebound damping. So, there is littledifference between damped and undamped natural frequencies.Rolling loss factor determines how much of the wheel radius is subtracted fromthe original to obtain the effective radius. This is the slope of the angular speed and thespeed of the vehicle relationship. V = ω*ReFigure 97 Rolling loss factor graphAn appropriate rim offset for the tires was needed for proper track width. Forexample, if a 5” rim had its centreface 1” from one outer surface, 4” from the innersurface, the track width (distance between centerlines of tires) would be greater for theouter surface pointing away from the vehicle, and vice-versa. The track width affects the104

scrub (distance the tire displaces when the vertical load is placed on the frame.2007 Baja ProjectSuspensionTires needed to have the best tread pattern possible for off-road driving. Materialselected was required to be low weight for rotation support purposes. Specifically,centrifugal forces are applied to the rims more than the actual tire when the tires arerolling. Stresses would result from these forces, so the material would also need to betough enough to tolerate this while still being low weight. Tire tubes were used for thepurpose of preventing leaks if the rims were disturbed during the competition.The rim width was selected for compatibility with our 7” tires, so we selected 5”thick rims to give a 1” offset from the face of each tire. The surface where our hubs werebolted to inside the rim is 1” from one outer surface and 4” from the other surface. So,the track width is adjustable depending on which side of the rim you want to face awayfrom the vehicle. The rims that we found at the shop in the CARE centre that we utilizedare made of aluminum. Rim type is TIP.12.3) CATIA ModelingRims were modeled in CATIA for comparison purposes.12.4) Additional AnalysisFigure 98 CATIA Model of RimFull assemblies of rims, hubs, uprights, and control arms were made for the rearsuspension.105

2007 Baja ProjectSuspensionFigure 99 CATIA Model of Rear Suspension Assembly12.5) Materials and Manufacturing Procedures UsedMaterial selected for the rims was aluminum, for lightweight and ductilitypurposes. If our rims were disturbed during the competition, the aluminum would justdent, where a brittle material would crack. This crack would propagate across the rimface and the vehicle would no longer be operable. Tire material was the natural materialof all tires i.e. rubber.12.6) Finished Product12.6.1) Product Assembly and MaintenanceRims and tires were put together by first deflating the tire if necessary and slidingthe rims into the tire using a lever tool to ply the tire side surfaces up to provide enoughclearance for the rim to enter the tire body. This was taken care of by Bruce Durfy,technician at the CARE Centre at the University of Windsor. Tubes were inserted intothe tire for the purpose of easier filling and to prevent leakage during the competition.12.6.2) TestingTires and rims were tested many times prior to competition by driving the vehicleon the CARE Centre parking lot, the once open-dirt field across the street from the CARECentre, Dylan Langlois’s off-road course in Kingsville. Cornering stiffnesses werecalculated for each tire for turning the vehicle around a corner at a certain slip angle.Scrub was measured by weight being applied to the rear and front parts of the vehicle.This is the distance the tires displace laterally when the frame is loaded enough (eg. whenthe vehicle land from a high jump). Tire pressures were adjusted for each of the dynamicevents at the competition for optimal vehicle performance. The following table illustrates106

2007 Baja ProjectSuspensionour optimal pressure readings for each event.Table 13: Tire PressureEvent Name Front Tire Pressure [psi] Rear Tire Pressure [psi]Suspension & Traction 15 5Maneuverability 8 4Hill Climb 16 4Acceleration 8 4Endurance 8 4The logic behind our tire pressures is behind the off-road conditions of eachevent. For Suspension and Traction, the front tire pressure is set at 15psi giving adifferential of 10 psi with the rear tire pressure to give maximum traction in the front forsteep hill climbs while not dragging the vehicle down in the rear. For maneuverability,the same effect is desired without as steep hills. Likewise, Hill Climb requires the mosttraction with a front pressure of 16psi and a differential of 11 psi with the rear.Acceleration pressures were set at 8psi for the front, 4psi in the rear for stability uponachieving high vehicle acceleration. Endurance was a four hour race with many steephills, so the tires needed to last with good uphill climb capabilities, so a front tire pressureof 8psi with a rear tire pressure of 4psi was selected. As well, at low tire pressures theshock should be adjusted so that minimum threads are showing to give minimum preload.This is to minimize the already large contact patch causing traction with the road, givingthe shocks some control over the ride quality. So, powertrain has the most influence overthe tires rather than the suspension system. Likewise, at high tire pressures the shockshould be adjusted so that the maximum number of threads are showing for maximumpreload. This is to maximize the tire contact patch with the ground, to give the tires anadequate amount of control of the ride quality since they are such a high pressure thatthey are basically solid, having little control over the traction with the terrain. So,without this preload the powertrain system has all the control over the tire ride, so there isnot as much shock absorption by the shock and strut systems as compared with lowpressures.12.7) Recommendations for ImprovementDuring the second trial of the suspension and traction event, the tires hit a rockand the vehicle was pulled from the event. An alternate tread pattern is a possibility forimproving the tire durability in these situations. Rims were adequate in resisting fatiguefailure for the four hour endurance race. They resisted fracture for the four otherdynamic events as well.107

2007 Baja ProjectSuspension13) Suspension tuning and testing13.1) Suspension kinematics adjustment and measurementSuspension tuning and testing is extremely important and is a key to optimizationof the vehicle performance in all aspects. The first step in tuning the suspension of the2007 vehicle was to adjust the suspension geometry to the designed conditions. It ismerely impossible to fabricate and assemble the suspension to the exact designed staticsuspension kinematic parameters (toe, camber, and caster static angles). Thus, there wasadjustability designed into the suspension system in order to adjust the static kinematicparameters to the designed values. The front suspension has the option of adjusting thetoe, caster and camber angles, and the rear suspension has the option adjusting the toeand camber angles. The following is a discussion of how these angles were measured onthe vehicle.The caster angle was measured only in the front because it can only be adjusted inthe front and because it is one of the most important parameters in the front suspension.The reason for this is it effects the aligning moment, and it is absolutely necessary thatthe aligning moment is positive. The caster angle was measured with just the uprightconnected to the control arms. The frame was positioned at the proper ride height (theride height that would be obtained if the driver was in the vehicle). A belt was used tocompress the shock on the measurement side of the vehicle so that the shock compressesto its static amount. The upright was rotated about the kingpin axis, so that the ball jointscan be assessed. A square was positioned on the ground and close to the ball joints. Astring was positioned in the middle of the ball joint on the upper control arm and wastightened to the ball joint of the lower control arm. Two longitudinal distances weremeasured between the square and the string (distances were measured between the twoball joints) (L 1 and L 2 ) and the length in the vertical direction between the longitudinalmeasurements was measured (L 3 ). These distances can be used to measure the casterangle (Equation 32: Caster angle from measurements) (Figure 100: Caster anglemeasurement).τ = tan−1⎛ L⎜⎝2− LLEquation 32: Caster angle from measurementsIf the caster angle is measured and is not equal to or close to the desired value, than thebushing size of the upper control arms needs to be changed in order to change the casterangle, and the measurement process needs to be repeated.The toe angle was measured in the front and in the rear of one side of the vehiclesimultaneously (with one setup). The toe angle measurement should be performed whenthe vehicle is at its static position; therefore the static ride height of the vehicle was set.31⎞⎟⎠108

2007 Baja ProjectSuspensionFigure 100: Caster angle measurementThe angle was measured using two jack stands, a rope, and a measuring device (tapemeasure or vernier caliper). The rope was wrapped around one jack stand and thenpulled tight and wrapped around the second jack stand. The two jack stands with therope tight between them was pushed close to the vehicle and the distance between therope and the centerline of the vehicle was measured at the front and rear of the vehicle.The position of the two jacks with the rope tight between them was moved until the twodistances were equal to each other. The locations on the tire where measurements weregoing to be taken were marked on the tire with a marker. The measurements were takenat the middle of the tire (middle of the tire when looking at the side view of the vehicle;the middle distance between the top and bottom of the tire) and the distance between thecenter and the front and the center and the rear of the tire was marked as the same. Thedistance between the rope and the marked location on the tire was measured at the frontand at the rear marked locations on the tire (L 1 and L 2 ), and the distance between the twomeasurements was taken (L 3 ). These measurements were taken for both the front andrear tires which allowed for the toe angle to be measured at the front and at the rear(Equation 33: Toe angle measurement) (Figure 101: Toe angle measurement).109

2007 Baja ProjectSuspensiontoe angle= tan−1⎛ L1− L⎜⎝ L32⎞⎟⎠Equation 33: Toe angle measurementFigure 101: Toe angle measurementThe toe angle in the front suspension was adjusted by changing the length of the tie rodand it was adjusted by changing the heim joints in the rear. The toe angles weremeasured on both sides of the vehicle. If the measured toe angle is not equal to or closeto the desired value than the static toe angle needs to be changes and the measurementprocess needs to be repeated.The camber angle was measured using a camber angle measurement tool (notethis tool belongs to Formula SAE). A flat piece of metal was placed on the tire in the110

2007 Baja ProjectSuspensionmiddle of the tire when looking at the vehicle from the side view. The camber anglemeasurement tool was placed on this piece of metal and the measurement was read fromthe tool (Figure 102: Camber angle measurement).Figure 102: Camber angle measurementThe camber angle for each tire was measured independently, and if the values were notequal to or close to the desired static values than they need to be adjusted to the desiredvalues. The camber angle is adjusted in the front by rotating the camber adjustmentinsert and is adjusted in the rear by changing the heim joints. If the measured valueswere not close to the desired values than the camber angle needs to be changed and themeasurement process needs to be repeated.The wheelbase and track width of the vehicle were measured using a tapemeasure. The track width was measured by taking the distance between the inside of theleft tire and the outside of the rear tire; the opposite can also be done (Figure 103: Trackwith measurement). The wheelbase was measured in a similar way as the track width.The distance was taken by measuring the distance between the front of the front tire andthe front of the rear tire at the centerline of the vehicle. The wheelbase can also bemeasured by taking the distance between the front and rear spindles.13.2) Dynamic tuning of the suspensionThe Elka Suspension coil over shock suspension shocks have adjustable dampingin rebound and compression, have an adjustable progressive spring rate, and haveadjustable pre-load. All of these parameters were adjusted in order to optimize theperformance of the vehicle in all aspects. These parameters were adjusted by performingvarious dynamic tests on the vehicle. These parameters were adjusted by runningthrough three different dynamic tests. The first test was to test the acceleration andbraking performance of the vehicle. The second test the vehicle was driven on a coursethat consisted of a series of bumps and some sharp corners. The third test the jumpperformance of the vehicle was evaluated. The performance of the vehicle was evaluated111

2007 Baja ProjectSuspensionfor each of the tests and the shocks adjustments were changed in order to optimize theperformance of the vehicle.Figure 103: Track with measurementThe compression damping is used to adjust the shocks resistance to impact and tomeasure the quality of the ride. The rebound adjustment is used to determine how fastthe shock returns to its original position after it is being compressed. The rebounddamping is used to adjust the kickback of the suspension. The pre load and the positionof the crossovers will determine the effective spring rate of the shocks (the progression ofthe shocks). A greater pre load and placing the crossovers such that the longer end isfacing up both lead to a greater spring rate, and thus increase the resistance of the shockto impacts. A higher spring rate also leads to a stiffer ride (for more details about theshocks refer to section 10). A spreadsheet was created in order to keep track of thechanges in the suspension system (Appendix J). It is a good idea to keep track of thechanges made in the suspension system because this will allow for the information to bestored which will allow the optimum performance of the vehicle to be assessed after allthree of the tests are complete.13.3) Problems during testingThere were a few suspension issues which arose while the vehicle was beingtested. The first issue that came about was the front portion of the rear lower control armbent. The exact cause of the bend was not known, however it was determined that it wascaused by impacting something, possibly a rock in the ground. It was decided to put aprotection layer on the front of the front and rear control arms in order to protect themfrom impacts. The protection layer consists of a layer of PVC tubing which is covered bya layer of rubber tubing and finally held together using shrink wrap. The rubber layer isused to absorb some of the impact energy while the PVC tubing is used to take some ofthe load and to reinforce the control arm (Figure 104: The protection layer on the controlarms). It is recommended that the protection layer be used on the lower control arms atthe front and the rear because it was an idea that was recommended by the judges. It isalso recommended that a bumper be added to the rear of the vehicle in order to protectthe rear assembly of the vehicle. The upper control arm got dented in during competitionbecause another car rear ended our car.112

2007 Baja ProjectSuspensionFigure 104: The protection layer on the control armsThe second issue that came about was the bending of the rear control arm. Thevehicle was tested by running it over a big jump at the testing grounds for the Bajavehicle (Powerband). The impacts of the jump caused the rear control to bend directlyunderneath where the shock connects to the control arm (Figure 105: The bend in thecontrol arm).Figure 105: The bend in the control armThe control was bent back and a new one was created with a greater diameter and wallthickness. The control ended up bending a second type, thus a third one was built and itwas reinforced by putting angle iron underneath the control arm (Figure 106: Angle ironto reinforce the rear control arms). It is to be noted that it was expected that the controlarm was bending because the shock would lock up before coming close to bottoming out.The control arm kept bending on the same side, so the expected reason is that somethingis wrong with the shock that it is causing it to lock up sooner than it should. Thus, ifthese shocks are re used next year than they need to be re-valved.The third issue that occurred while testing the vehicle was the wear in thebushings. After putting many hours on the vehicle, the bushings wore down to a pointwhere there was too much play in the suspension system (Figure 107: The wear in thebushings).113

2007 Baja ProjectSuspensionFigure 106: Angle iron to reinforce the rear control armsFigure 107: The wear in the bushingsThis issue was resolved by changing the bushings to oil impregnated bronze. Thismaterial is more resistance to wear and has an oil impregnated into it which allowslubrication to be present even after the material starts to wear. The lower controlbushings in the font and all of the bushings in the rear were changed to the oilimpregnated bronze bushings.The fourth issue that arose was an outside bearing on the front suspensionexploded. The front suspension was originally assembled with the original Polarisbearings. These bearings are cheaply made and are not strong enough to support theloads seen by the vehicle. One of the outside bearings was disassembled and there was aminimum amount of balls in the bearing which is not good. Therefore, it was decided togo with Timken tapered needle roller bearings for the inside and outside front suspensionbearings (Figure 108: Timken tapered needle roller bearings). These bearings wereassembled into the wheel hub and were tested through several tests and at competitionand proved themselves as they did not break or explode. Thus, it is highly recommendedthat these bearings be used on next year’s vehicle.114

2007 Baja ProjectSuspensionFigure 108: Timken tapered needle roller bearingsThe final suspension issue that arose during testing was that a heim joint seized.This caused an additional load on the suspension system and could lead to failures. Thiscould also be one of the reasons why the rear control arm bent. This issue was overcomeby greasing the heim joints before each test. Thus it is recommended that all of the heimjoints equipped on the vehicle are equipped with a grease nipple, thus permitting them tobe greased on a per test basis.It is very important to have time to test the car. There are five major issues thatoccurred to the suspension system while the vehicle was being tested and they wouldhave not been spotted if it wasn’t for vehicle testing and poor results could have arosefrom this. Thus, it is recommended that the vehicle should be done 2 months beforecompetition permitting time for vehicle testing.115

2007 Baja ProjectSuspension14) Strain gage testing14.1) Background & ResearchIt was decided to complete strain gauge testing on the car since the control armsshowed significant damage after testing the completed vehicle. Also, during the designportion of the competition, judges placed a lot of emphasis on strain gauge testing thevehicle; the judges were very impressed by teams who completed this task. Before thetesting commenced, research was completed to make sure that the project couldaccurately be accomplished. Rob Rieveley provided excellent insight on strain gaugingand had many comments and suggestions regarding the topic. After numerous meetingswith Rob, it was decided to strain gauge one quarter of the car (symmetry may beapplied) but a lot of background work had to be completed before actually applyinggauges to the car.Many documents were read prior to physically completing the task regarding howto apply gauges, different types of circuits, temperature compensations and so on tobecome familiar with the concept of strain gauging. A lot of useful information can befound in Theory and Design for Mechanical Measurements 4 th edition byFigliola/Beasley as well as on the internet. Please refer to on the Baja drive for relevantinformation regarding strain gauging.An earlier test was carried out by performing static tests using a control arm fromthe 2004 Baja car which yielded less than satisfactory results. The objective was tocorrelate between actual and theoretical results using Catia’s FEA package. Muchknowledge was gained by working alongside Pat Seguin, Engineering Technologist andLucian Pop, Civil Engineering Technician. It was then realized that a much simpler testhad to be performed to better understand the strain gauging concept.14.2) Concepts & BrainstormingA fixture was constructed from 4130 steel to support the 2004 control arm duringthe static test. The orientation of this test setup is further elaborated in the FEAsubsection below.Testing on a steel specimen was completed prior to testing on the actual car. Thiswas completed to learn how to apply gauges and to learn all the necessary concepts andprocedures needed to fully understand basic strain gauging operations. The steelspecimen was constructed out of the same material as the control arms and had a box tubeattached to one end as shown below in Figure 109: Strain gauge testing specimen.116

2007 Baja ProjectSuspensionFigure 109: Strain gauge testing specimenBefore the strain gauges were mounted to the specimen, it was cleaned andpolished using a fine sand paper. Pat Seguin was contacted for help in applying thegauges. He went through the necessary steps and procedures needed to successfullyapply a strain gauge. Gauges were mounted on the top and bottom of the specimen. Twogauges were needed to account for temperature change in the specimen during testing andalso, in this set up, the gauges could detect tension and compression.The box tube was used to securely attach the specimen to the fixtures used fortesting. Axial and bending tests were completed on the specimen. For the bending test,the specimen was clamped horizontally to the side of a metal fixture and weights wereattached to the end of the specimen as illustrated in Figure 110: Bending of test specimen.For the axial test, the specimen was clamped vertically to the top of a truss and weightswere attached to the end of the specimen as illustrated in Figure 111: Axial test onspecimen. The tests were conducted in the Structures Lab in Essex Hall under thesupervision of Pat Seguin. The data obtained from the tests were compared to the dataobtained from the Catia model to quantify the results. Fully understanding the dataacquired from the strain gauge experiment is the key to being successful whenimplementing strain gauges on the Baja car.Figure 110: Bending of test specimen117

2007 Baja ProjectSuspension14.3) CATIA ModelingFigure 111: Axial test on specimenThe specimen was modeled in Catia with the correct dimensions and materialproperties applied. The Catia model of the test specimen is illustrated inFigure 112:Specimen modeled in Catia, while the control arm Catia model is illustrated in Figure113 : 2004 lower control arm model.Figure 112: Specimen modeled in CatiaFigure 113 : 2004 lower control arm model118

2007 Baja ProjectSuspension14.4) FEAData acquired from the static strain gauge test was used to calculate the VonMises stresses. This was used for comparison with the stresses calculated using CatiaFEA technology. The FEA for a 500 lb loading is shown in Figure 114 - 2004 lowercontrol arm FEA for 500 lb loading. The maximum stress was found at the bottom of thecontrol arm just above the clamped cylinders, which are shown in the figure. Percentageerrors were calculated with Microsoft Excel 2003 formula option.Figure 114 - 2004 lower control arm FEA for 500 lb loadingAn FEA analysis was completed using Catia to simulate the testing performed in theStructures Lab. The results from the FEA quantified the results obtained from the statictesting with a reasonable 6.8% error that may have been a result of several factors. Theseinclude exact material properties, gauge mounting (adhesive), precise dimensions andequipment inaccuracy. Two separate analyses were conducted as described below.1) Cantilever FEA simulation of the specimen.Figure 115 - Cantilever FEA simulationThe above image illustrates the Von Misses stresses (left) and displacement (right) of thespecimen in the cantilever set up. It was found that the highest Von Misses stressesoccurred where the shaft attached to the box beam and the largest deflection occurred at119

2007 Baja ProjectSuspensionthe end of the shaft. These results were very similar to the actual results found from thestrain gauge test conducted in the Structures Lab.2) Axial FEA simulation of the specimenFigure 116 - Axial FEA simulationFigure 116 illustrates the Von Misses Stress (left) and the displacement (right) of the specimen in theaxial set up. Similar to the bending simulation, the highest Von Misses stress was found to be wherethe shaft attaches to the box beam and the largest deflection was found to be at the end of the shaft.Once again, these results were found to be comparable to the results found during the physical axialtest of the specimen.14.5) Additional AnalysisStrain gauge testing was also completed on the Baja car. Strain gauges weremounted on the control arms to detect the maximum bending and axial strain. Thegauges were strategically mounted in locations of peak stress as indicated by Catia. Thisis illustrated in the figure below. Additional gauges are mounted opposite to the ones inview. This was tested to quantify the results obtained from the complete vehicleassembly FEA. Obtaining these stresses could provide better input for the analysiscompleted using the simulation programs.Gauge 1 2 3 4 5Figure 117 - 2007 control arm gauging locations120

2007 Baja ProjectSuspensionLoads were applied to the vehicle with the instrumentation installed. This wascarried out at the Structures lab in Essex Hall to obtain actual strain values that can becompared to the FEA.14.6) Materials & Manufacturing Procedure UsedMaterials used can be found on the Baja drive in the 2007 and 2004 folders.14.7) Recommendations for ImprovementsObtain a wireless data acquisition system with enough inputs to analyze eachpoint of concern on a full quarter of the car (symmetry may be applied). With a wirelesssystem, strains obtained from a realistic dynamic testing environment can be achieved.121

2007 Baja ProjectSuspension15) Suspension Prototype15.1) Background & ResearchPrototype design goal is to find an ideal rear suspension which includesmaintaining traction at all times, minimizing bump steer, and providing enough travel toabsorb the impacts from the rough terrain. Various independent suspension systems wereanalyzed by ADAMS and CATIA software. The analysis concentrated on system’sperformance, including camber angle, toe angle, roll centre height, anti squat and wheeltravel track. Three possible options were considered, the trailing arm, semi trailing armand the new semi trailing arm.15.2) Concepts & BrainstormingThe rear suspension system is important to a vehicle’s overall ride and handing,which include live-axle, semi-independent, and independent. Independent rearsuspensions are mainly found on some RWD cars and 4WD vehicles. Independentsuspensions have a centrally mounted final driver with axles extending from it. In anindependent rear suspension system, each rear wheel can move independently of theopposite rear wheel. There are double wishbone suspension, McPherson strutssuspension, trailing link suspension and semi-trailing link suspension. Combined withdouble A arm and semi trailing arm, we try to develop a new semi trailing arm. Due tothe complexity and feasibility for Mini Baja, we only take the following suspensions tocompare and analyze: trailing arm, semi trailing arm and new semi trailing arm.Figure 118: Tailing arm and Semi trailing arm122

2007 Baja ProjectSuspension15.3) ADAMS ModelingDesign goals for the rear suspension include maintaining a certain ride height androll center height, minimizing toe angle during the wheel travel, and achieving a certainrange of camber angle and anti squat during whole wheel travel. Based on above factorsand issues, three possible options were considered, the trailing arm, the semi trailing arm,and new semi trailing arm.1. Semi-trailing armFigure 119: Semi trailing arm2. Trailing armFigure 120: Tailing arm123

2007 Baja ProjectSuspension3. New semi-trailing armFigure 121: New semi trailing armFigure 122: Camber angle comparison124

2007 Baja ProjectSuspensionFigure 123: Roll centre comparisonFigure 124: Toe angle comparison125

2007 Baja ProjectSuspensionFigure 125: Anti Squat comparisonFigure 126: Wheel travel track comparisonThe difference between the trailing arm and semi-trailing arm is that the axis ofthe trailing arm is at right angles to the vehicle centerline whereas the semi-trailing armaxis angle inboard and toward the rear.The trailing arm is relatively simple and is popular on FWD vehicles. It offers theadvantage that the car body floor pan can be smooth and more free space can be obtainedfor power train between the suspension control arms. If the pivot axes lie parallel to the126

2007 Baja ProjectSuspensionfloor, the compressing and rebounding wheels undergo no track width, camber or toe-inchange, and the wheel base simply shortens slightly. If torsion springs are applied, thelength of the control arm can be used to influence the progressivity of the springing toachieve better vibration behavior under load. The low body roll centre at floor level is adisadvantage as is the fact that the wheels incline more with the body when corneringthan with other independent wheel suspensions.The semi trailing arm is a special type of half trailing and half transverse, which isfitted mainly in RWD and four-wheel drive cars. We can analyze it by splitting it intotwo vectors, one is the trailing component and another is the transverse component. Thetrailing component leads to understeer. On the other hand, the transverse component isactually equals to a swing axle suspension, which always introduce oversteer due to bodyroll. As a result, the two components cancel each other and result in near neutral steeringresponse. Semi-trailing has a disadvantage - when the wheel moves up and down, camberangle changes, unlike double A arm.No matter semi-trailing arm or trailing arm suspensions, since they are rigidlyattached to the wheels, inevitably more shock and noise could be transferred to the carbody. The new semi trailing arm is a combination type of double A arm and semitraining arm. It is simpler than double A arm, which will reduce the unsprung weight.However, it will keep the advantage of double A arm, such as characteristic of no mutualwheel influence. Moreover, it will overcome some of the disadvantages of semi-trailingarm, especially under hard cornering or running on bumpy roads.15.4) Additional AnalysisThe double a-arm offers good wheel control and large wheel travel abilities. Thetrailing arm suspension allows even more control over wheel angles; however this systemis more considered on front-wheel drive vehicles, and more exposed to harsh conditions.Instead of using just 4 rod ends on the double A arm, the trailing arm and semi trailingarm uses more complex components. This dramatically increases the overall cost for thesystem, and is not worth the added adjustability. The new semi trailing arm is not chosendue to the uncertain performance. The added simplicity of the system and bettermaneuverability are outweighed by the better performing double a-arm in this scenario.Combined with the large travel, wheel angle control and better performance the double a-arm was selected.15.5) CATIA & FEAThe rough design of the prototype rear suspension has been modeled in Catia v5in an assembly drawing. The design was based on ADAMS/CAR simulation. Since this isa prototype design, the default property of steel in Catia was applied.127

2007 Baja ProjectSuspensionFigure 127: Prototype Suspension Assembly 1Figure 128: Prototype Suspension Assembly 2We separated the upper and lower control arm for the Finite Element Analysis.For the upper control arm the resultant force was applied on the end connecting to theupright. And also the force applied by the shock mounted on the lower control arm wasconsidered. For the lower control arm, the resultant force is only applied on the outerpoint while the inner ends are assumed to be clamped in the analysis.128

2007 Baja ProjectSuspensionFigure 129: Rear Lower Control Arm FEAFigure 130: Rear Upper Control Arm FEA15.6) Materials & Manufacturing Procedure UsedBased on feasibility and cost factors, prototype team only built one suspensionprototype, new semi trailing arm. The material is the remaining PVC pipes which wereused for frame team’s mockup. Prototype team drew the part draft in paper according toADAMS and CATIA data, then cut PVC pipes into required parts, then glued together.129

2007 Baja ProjectSuspensionActually, these parts can not assembly together when we attempted to attach them toframe mockup. Therefore, the sizes of the final prototype are modified to fit the framemockup. The size adjustment for lower control arms was not too much, but the uppercontrol arm was extent 1.5 inch.15.7) Finished Product15.7.1) Product Assembly & MaintenanceThe following pictures show the different views of the prototype:Figure 131: Prototype front viewFigure 132: Prototype back view130

2007 Baja ProjectSuspensionFigure 133: Prototype top viewFigure 134: prototype side view131

2007 Baja ProjectSuspensionFigure 135: Joint and axis control15.7.2) TestingAfter the prototype was built, the wheel travel distance, camber angle, toe angle,caster angle and force distribution were checked. Therefore, the following characteristicswere got for this new semi trailing arm:1. Large wheel travel distance, larger than 12”;2. Small camber and toe angle change;3. Large caster angle change.Figure 136: Camber checking 1132

2007 Baja ProjectSuspensionFigure 137: Camber checking 215.8) Recommendations for ImprovementsBased on 2007 Min Baja competition experience and past Windsor competitionrecords, Hill climbing is the choke point of Windsor team. The original reason of thischoke point is too heavy during hill climbing when the engine power is limited.Therefore, how to effectively reduce vehicle weight will be the most critical issue for thefuture Windsor Mini Baja team. As suspension team, how to reduce the weight ofsuspension but keep a good performance is the most important thing. Prototype teamspent more time to pay attention to various rear suspensions during 2007 competition.There are varieties of suspensions which are pretty simple but achieved niceperformances. Semi trailing arms were pretty popular in 2007 completion; even thoughthe majority of vehicles were equipped with double A arm. Dramatically, the championteam from Brazil was equipped with non-independent suspension, some kind of live-axlesuspension. There are also some pretty simple independent suspensions, which onlyconnected one arm with the spring strut and drive shift. The trend of future rearsuspension will be multiform, simple and light weight.The following pictures were come from 2007 Mini Baja competition teams.133

2007 Baja ProjectSuspension1. Semi-trailing armFigure 138: Semi trailing arm 1Figure 139: Semi trailing arm 2134

2007 Baja ProjectSuspension2. Trailing armFigure 140: Tailing arm 1Figure 141: Tailing arm 2135

2007 Baja ProjectSuspension3. New semi-trailing armFigure 142: New Semi trailing arm 1Figure 143: New Semi trailing arm 2136

2007 Baja ProjectSuspension4. Other suspensionsFigure 144: Other suspension 1Figure 145: Other suspension 2137

2007 Baja ProjectSuspensionFigure 146: Other suspension 3138

2007 Baja ProjectSuspension16) References and contacts16.1) Contacts-CarSim training and license:Damon A. BeckerMechanical Simulation912 North Main Street, Suite 210Ann Arbor, MI 48104 USAPhone: (734) 668-2930Fax: (734) 668-2877Email: dbecker@carsim.com- Custom Rear Upright CNC:Omni Tool Ltd.Rino S. Marinelli5495 Outer DriveWindsor, ON N9A 6J3Phone: (519)-737-7147Fax: 1(519)-737-7448Email: Rino.marinelli@omni-tool.com- Aluminum Casting:Robert Mackay, Ph.D.Metallurgical Engineering SpecialistNemak Engineering Centre4655 G.N. Booth DriveWindsor, ON N9C 4G5Phone: 1-519-972-2005Fax: 1-519-972-1133E-mail: rmackay7@nemak.com- Fabrication of control arms:Dino FavaroValco Fabricating & MachiningDivision of Valiant Machine & Tool Inc1235 St Luke Road,Windsor, ONN8Y 4W7Phone: 519-971-9666139

2007 Baja ProjectSuspension- Water Jet cut tabs:Dan PominvilleCenterline (Windsor) Limited415 Moton Drive, Windsor, OntarioN9J 3T8Phone: (519) 734-8464- Power coating control arms:Robert BrantSES Power Coating786 Howard AveR.R.#1 McGregor, OntarioPhone: (519) 726-4658- OEM Polaris parts:Pat McArdlePolaris Industries7290 East Viking BoulevardWyoming, MN 55092Email: pat.mcardle@polarisind.com.16.2) Websites1. Picture of camber angle. Retrieved July 2007, fromhttp://www.redranger.com.au/images/Faqs/Camber%20angle.JPG2. Vehicle suspension system, (2006). Retrieved January 2007, fromhttp://www.twbbs.net.tw/1297490.html3. Automobile Ride, Handling, and Suspension Design, (2006). Retrieved January2006, From http://www.rqriley.com/suspensn.htm4. SAE Mini Baja, (2007). Retrieved January 2007, fromhttp://www.egr.msu.edu/baja5. Independent Suspension, (2000). Retrieved January 2000, fromhttp://www.autozine.org/technical_school/suspension/tech_suspension21.htm6. Suspension geometry, (1999). Retrieved January 2006, fromhttp://www.rqriley.com/suspensn.htm140

2007 Baja ProjectSuspension7. Suspension geometry. Retrieved March 2005, fromhttp://home.scarlet.be/~be067749/58/c1/index.htm (Note this website isrecommended as a reference)8. Tire curve, Retrieved April 2006, fromhttp://code.eng.buffalo.edu/dat/sites/tire/img54.gif9. Camber angle, Retrieved April 2006, fromhttp://www.crcc.org.uk/images/image004.jpg10. Toe angle, Retrieved March 2006, fromhttp://www.bastiantire.com/images/toe_in.gif11. Kingpin axis, Retrieved May 2006,http://www.desertrides.com/reference/images/terms/sai-scrub.gif12. Tire slip angle, Retrieved April 2006,http://www.donpalmer.co.uk/cchandbook/images/tyrebasics.gif16.3) Books and professional papers1. Dixon, John C., (1996) Tires, Suspension and Handling, Warrendale, PA: Societyof Automotive Engineers2. Milliken ,William F., Milliken, Douglas L., (1995) Race Car Vehicle Dynamics,Warrendale, PA: Society of Automotive Engineers (Note this is a recommendedbook to buy)3. Genta, Giancarlo (1997) Motor Vehicle Dynamics, Singapore: World ScientificPublishing Co. Pte. Ltd4. Hewson, P., (2005) Method for estimation tyre cornering stiffness from basic tyreinformation, UK, School of Computing and Engineering, University ofHuddersfield5. Gillespie, T. D. (Thomas D.) (1992) Fundamentals of vehicle dynamics,Warrendale, PA : Society of Automotive Engineers (Note this is a recommendedbook to buy)6. Rajamani, Rajesh. (2005) Vehicle dynamics and control, New York : Springer7. Wong, J. Y. (Jo Yung) (2001) Theory of ground vehicles, New York : John Wiley8. Erjavec, Jack (2006) Automotive suspension and steering, Clifton Park, NY :141

2007 Baja ProjectSuspensionThomson Delmar Learning9. Reimpell, Jörnsen. & Stoll, Helmut (1996) The automotive chassis: engineeringprinciples, Warrendale, PA : Society of Automotive Engineers10. Matschinsky, Wolfgang (2000) Road vehicle suspensions, London, UK:Professional Engineering Pub11. BOSCH, (2004) Automotive Handbook 6 th Edition, Warrendale, PA: Society ofAutomotive Engineers142

2007 Baja ProjectSuspension17) Appendixes17.1) Appendix AThe derivation of the half car modelFBD’s: Sprung mass:( Zs+ aθ − Zf) kfZ s ( Zs− bθ− Zr) kr( Z &s + a & θ − Z&f ) Cf( Z &s − b & θ − Z&r) Crθm sThe unsprung mass at the front of the vehicle( Zs+ aθ− Zf) kf( Z &s + a & θ − Z&f ) Cfm ufZ f( Z f ) ktfF = ( ktf )( hf )The unsprung mass at the front of the vehicle:( Zs− bθ− Zr) kr( Z &s − b & θ − Z&r) Crm urZ r( Z r) ktrF = ( ktr)( hr)From the first FBD (free body diagram)143

2007 Baja ProjectSuspension∑ FZs= msZ&&s− ( Zs+ aθ− Zf) kf− ( Zs− bθ− Zr) kr− ( Z&s + a & θ − Z&f ) Cf− ( Z&s − b & θ − Z&r)Cr= msZ&&smsZ&&s + ( Z&s + a & θ − Z&f ) Cf+ ( Z&s − b & θ − Z&r) Cr+ ( Zs+ aθ− Zf) kf+ ( Zs− bθ− Zr)kr= 0∑ Mpitch axes = I && θ− a[ ( Z&s + a & θ − Z&f ) Cf+ ( Zs+ aθ− Zf) kf] + b[ ( Z&s − b & θ − Z&r) Cr+ ( Zs− bθ− Zr)kr]= I && θI && θ + ( Z&s + a & θ − Z&f ) aCf− ( Z&s − b & θ − Z&r) bCr+ ( Zs+ aθ− Zf) akf− ( Zs− bθ− Zr) bkr= 0From the second FBD:From the third FBD:∑ FZf= mufZ&&f( Zs+ aθ− Zf) kf+ ( Z&s + a & θ − Z&f ) Cf− ( Zf) ktf+ ( hf) kmufZ&&f + ( Z&f − ( Z&s + a & θ) Cf+ Zf− ( Zs+ aθ) kf+ Zf( ) ( ) ktf= ( hf) ktftf= mufZ&&f∑ FZr= murZ&&r( Zs− bθ− Zr) kr+ ( Z&s − b & θ − Z&r) Cr− ( Zr) ktr+ ( hr)ktr= murZ&&rmurZ&&r + ( Zr− ( Zs− bθ)) kr+ ( Z&r − ( Z&s − b & θ) Cr+ ( Zr) ktr= ( hr) ktrCombining all of the equations into matrix form yields the equations of the half carmodel:⎡m⎢⎢0⎢ 0⎢⎣ 0s⎡⎢+ ⎢⎢⎢⎣0I00( kf+ kr) ( akf− bkr)2 2( akf− bkr) ( a kf+ b kr)− kf− km0r00uf0 ⎤⎧Z&&s⎫⎡⎪ ⎪0⎥ ⎢&&⎥θ⎨ ⎬ + ⎢0 ⎥⎪Z&&f⎪⎢⎥⎪ ⎪⎢mur⎦⎩Z&&r⎭⎣− akfbkr( Cf+ Cr) ( aCf− bCr)2 2( aCf− bCr) ( a Cf+ b Cr)− Cf− Cr− kf− akf( kf+ ktf)0− Cf− Cr⎤⎧Z&s⎫⎪ ⎪− aC⎥f bCr&⎥θ⎨ ⎬− aCfCf0 ⎥⎪Z&f⎪⎥bCr0 Cr⎦⎪⎩Z&r⎪⎭− kr⎤⎧Zs⎫⎧ 0 ⎫bk⎥⎪⎪ ⎪ ⎪r⎥θ0⎨ ⎬ = ⎨( )( )( )( )⎪ ⎪ ⎬0 ⎥ ff tf⎪Z⎪ ⎪ h k⎥⎦⎪⎩Zr⎪⎭⎪⎩ hrktr⎭( kr+ ktr)144

2007 Baja ProjectSuspension17.2) Appendix BThe derivation of the bicycle modelFBD:Defining body slip angle and the steering angle:From the FBD (free body diagram)∑Fy = maFf+ Fr= m v∑MG= Ir&lat(&+ ru)aFf− bFr= Ir&(2)(1)It is possible to further simplify the equations by assuming that the lateral force is linearlyrelated to the tire slip angle through the cornering stiffness. This is usually acceptable for145

2007 Baja ProjectSuspensiona laterally acceleration of up to 0.4 to 0.5g’s.Ff= −CFr= −CBy considering the front and the rear tires separately, it is possible to find expressions forthe tire slip angles (α) using kinematics.fαfrαrvuuvtftfrtfltr= v + ra= u= utrrtrl= v − rb= u − r= u + r( tw)2( tw)Further assume that the vehicles forward velocity (u) is much greater than the width ofthe vehicle (u >> r(t/2)), thereforeu = utantantfr( αf+ δ )( αr)= u=tfl= u=2( v + ra)( v − rb)utrru= utrlAlso, assume small angles, thustanαfαr( θ ) ≈ θ( v + ra)==u( v − rb)u− δSo equation 1 becomes146

2007 Baja ProjectSuspension⎡mv&= −⎢⎣⎡ +mv&+⎢⎣ u( v + ra) ( v − rb)u⎤− δ Cf⎥ −⎦( CfCr) ( aCf− bCr)⎤ ⎡⎥v +⎦⎢⎣⎡⎢⎣uu⎤Cr⎥ − mru⎦⎤+ mu r = Cf⎥ δ⎦Equation 2 becomes⎡Ir&= −⎢⎣⎡Ir&+⎢⎣( v + ra) ( v − rb)u⎤ ⎡− δ aCf⎥+⎢⎦ ⎣2 2( aCf− bCr) ⎤ ⎡ ( a Cf+ b Cr) ⎤r aCfδu⎥v +⎦⎢⎣uu⎤⎥bC⎦⎥⎦r=Combining equation 1, and 2 into matrix form leads to the linear bicycle model⎡m⎢⎣ 0⎡0⎤⎧v&⎫ ⎢⎨ ⎬ + ⎢I⎥⎦⎩r&⎭ ⎢⎣( Cf+ Cr) ( aCf− bCr)u2 2( aCf− bCr) ( a Cf+ b Cr)uuu⎤+ mu⎥⎧v⎫⎧ Cf⎫⎥⎨⎬ = ⎨ ⎬δ⎥⎩r⎭⎩aCf⎭⎦147

2007 Baja ProjectSuspension17.3) Appendix C148

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2007 Baja ProjectSuspension17.4) Appendix DCritical speed calculations of 2006 vehicleThe cornering stiffness of the front and rear tires were calculated using equation 24.6E = 27x10N2 (belt compression modulus)ms = 0.15 (sidewall vertical deflection)b = 0.015m(belt thickness)⎛ 0.0254m⎞w = ( 7in)⎜ ⎟ = 0.1778m(width of the tire)⎝ in ⎠⎛ OD − ID ⎞ ( 21in−10in)⎜ ⎟=⎝ 2a⎠=2= 0.785714 (aspect ratio)w7inID ⎛10in⎞⎛0.0254m⎞r = = ⎜ ⎟⎜⎟ = 0.127m(inner radius)2 ⎝ 2 ⎠⎝in ⎠C =C =2[( rt+ wat)]⎡ ⎡ ⎛⎢sin⎢arccos⎜1−⎢⎣⎣ ⎝2swa3Ebtwt⎞⎤⎤⎛⎡⎜⎛⎟⎥⎥π − sin⎢arccos⎜1−swa⎞⎤⎞⎟⎥( r ) ⎜( ) ⎟ t + wat⎠⎦⎥⎦⎝ ⎣ ⎝ rt+ wat⎠⎦⎠63( 2)( 27 × 10 )( 0.015)( 0.1778)⎡2 ⎡−1⎛[( (( )( )))]( 0.15)( 0.1778)( 0.785714)0.127 + 0.1771 0.785714 ⎢sin⎢cos⎜1−( 0.127 + (( 0.1771)( 0.785714)))⎡ ⎡−1⎛⎢π− sin⎢cos⎜1−⎢⎣⎣ ⎝C = 59419.5 Nrad⎢⎣( 0.15)( 0.1778)( 0.785714)( 0.127 + (( 0.1771)( 0.785714)))⎣⎝⎞⎤⎤⎟⎥⎥⎠⎦⎥⎦t⎞⎤⎤⎟⎥⎥×⎠⎦⎥⎦Since the same type of tire is used in the front and in the rear the cornering stiffness willbe the same in the front and rear. The following is the calculation of the critical speed.154

⎛ 0.4535924kg ⎞m = 600lb⎜⎟ = 272.155kg⎝ lb ⎠⎛ 336lb⎞a = ⎜ ⎟1.6256m= 0.910336m⎝ 600lb⎠b = 1.6256m - 0.910336m = 0.715264ml = a + b = 1.6256muucriticalcritical==272.155kg5915.27NkgmN2007 Baja ProjectSuspension2( 2×59419.5 N )( 2×59419.5 N )( 1.6256m)radrad( 0.910336m)( 2×59419.5 N ) − ( 0.715264m)( 2×59419.5 N)22m ⎛ mkg⎜2⎝ Ns⎞⎟⎠=5915.27m2s2rad⎛= 77.1811 ms⎝km( )⎜3.6h= 277.852 km⎜ ⎟⎟h1ms⎞⎠rad155

2007 Baja ProjectSuspension17.5) Appendix E156

2007 Baja ProjectSuspension17.6) Appendix FPredicted spring ratesThe following shows the analysis used to determine the predicted spring rates. Thewheel rates can be predicted from the ride frequencies.2 ⎛ wfront ⎞krf= ( fn,front)( 2π))⎜2g⎟⎝ ⎠⎛ ⎛ 585lb⎞ ⎞2 ⎜ ( 0.47)⎜ ⎟ ⎟⎛ 1.237cycles2 rad ⎞ 1.1 ftk ⎜⎛ ⎞⎛π ⎞ ⎜⎛ ⎞⎟rf=⎟ ⎝ ⎠⎜ ⎟⎜⎟s cycle⎜⎜ ⎟2 32.2ft ⎝12in⎠⎟⎝⎝⎠⎝⎠⎠⎜ ⎜⎛2 ⎟⎞s ⎟⎝⎝ ⎠⎠lbfkrf= 19.5386inSimilarly,lbfk rr= 31. 1148inThe spring rates can be calculated from the wheel rates and the motion ratios of the frontand rear suspensions.krfkf=2MRSimilarly,kkff( )lbf19.5386=in( 0.5375)lbf= 67.6295inlbfk r= 68. 4321inf2157

2007 Baja ProjectSuspension17.7) Appendix GAcceleration Plots158

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2007 Baja ProjectSuspensionAcceleration and Cornering160

2007 Baja ProjectSuspensionBraking161

2007 Baja ProjectSuspensionBraking and Cornering162

2007 Baja ProjectSuspensionS Shaped Plots163

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2007 Baja ProjectSuspension2007 Jump Performance165

2007 Baja ProjectSuspensionCornering166

2007 Baja ProjectSuspension17.8) Appendix H167

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2007 Baja ProjectSuspensionPictureMaximumStress(Pa) Asthetics ClearanceEase ofManufacturing Weight TotalLowercontrolArm 15 3 1 1 1 11LowercontrolArm 22 2 1 2 4 11LowercontrolArm 34 4 1 3 2 14LowercontrolArm 41 FAILS 5 3 0LowercontrolArm 53 5 1 4 5 18179

2007 Baja ProjectSuspension17.9) Appendix I180

2007 Baja ProjectSuspensionWeight saving methods were investigated but were not significant enough to jeopardizestrengthArrived at final product192

2007 Baja ProjectSuspension17.10) Appendix JSpreadsheets to record the data during testing193

2007 Baja ProjectSuspensionTestNumberN/A1234567TestDateVehicleWeight(lb)VehicleWeight withDriver (lb)DriverFrontleftWeight per Tire (lb)FrontrightRearleftRearrightFrontleftShock Preload (in)FrontrightRearleftRearrightRideHeight(1in)2006Vehicle 465 635 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/AMay14/07 419 590 Herman 140 140 155 155 2.307 2.345 2.254 2.252 10.125May15/07May15/07May15/07May15/07May19/07 406 Kamil 135 129 151 152 2.182 2.22 2.004 2.0028 2.017 2.016May9 28/07 2.185 2.216 2.503 2.51011121314151617181920212223194 194

2007 Baja ProjectSuspensionTestNumberFrontleftCamber Angle (degree)FrontrightRearleftRearrightFrontleftToe Angle (degree)FrontrightRearleftRearrightRebound Adjustment (clicks from fullfast position)FrontleftFrontrightRearleftRearrightCompression Adjustment (clicks fromfull soft position)N/A N/A N/A N/A N/A N/A N/A N/A N/A 30 24 40 26 12 7 0 31 -3 -3 -2.1 -1.8 0.37 0.25 0 0.37 24 24 26 26 7 7 3 323 19 19 21 214 19 19 21 21 4 4 0 05 15 15 17 17 4 4 0 06789 -2 -2 0.3 0.3 22 22 10 1010 32 32 15 1511 20 20 20 2012 5 513 10 1014 15 1515 10 1016 5 517 3 318 5 519 15 15 20 20 20 2020 10 10 10 1021 3 322 5 5 5 523 -1.5 0.3 0.3 0.3 0.25FrontleftFrontrightRearleftRearright195 195

2007 Baja ProjectSuspensionTestNumberN/A1FrontleftTire Pressure (psi)FrontrightRearleftRearright2 7 6.2 6 63LefttopTurnbuckle position (in)LeftbottomRighttopRightbottomSpacing betweenrotors and frame (in)LeftsideRight side4 Control arm rear dented5 6.25 6.25 6.5 6.56 0.352 0.425 0.317 0.333 0.132 0.3277891011121314151617181920212223Notes196 196

2007 Baja ProjectSuspension17.11) Appendix K17.11.1) Rear suspension assembly Bill of Material:PicturePartDescription# ofpartsMaterial Specifications Supplier ManufacturerTire 2 RubberKT851B - 9 lbs21x7-10Tires UnlimitedDunlopRim 2 AluminumT-9 Pro Series10x5ITPWheel Hub 2 Aluminum Predetator Polaris PolarisUpright 2 Aluminum Outlaw 500 Polaris Polaris197 197

2007 Baja ProjectSuspensionBearing 22- Race RollerBearingPolarisPolraisBushings 24Bronze (Oilimpregnated)Canadian bearingMachined in theshopUpper inserttubing2 Steel 41300.5" x 0.049thick x 4 incheslengthEMJ tubingMachined inshopLower Inserttubing2 Steel 41300.5" x 0.049thick x 7 incheslengthEMJ tubingMachined inshopUpper DrillRod4High GradeSteelM10 x 6 inchesandM10 x 8 inchesEssex Metal198 198

2007 Baja ProjectSuspensionLower ControlArm2 Steel 4130 EMJ tubingFabricated atValientUpper ControlArm2 Steel 4130 EMJ tubingFabricated atValientLarge HiemJoints2 ChormonelyASM-ASB Rodends RightHand 5/8"- 18Aurora BearingAurora BearingSmall HiemJoints6 Mild SteelAM-AB Rodends RightHand M10-1.5Aurora BearingAurora Bearing199 199

2007 Baja ProjectSuspensionTabs 18 Steel 4130ShoulderBolts2High GradeSteel1/2" ShoulderBolt (length of1.25")FastenalFastenalShoulderBolts8High GradeSteelM10 Shoulderbolt (length of30mm )FastenalFastenalLock Nuts 8High GradeSteelM8 Nylock Nuts Fastenal FastenalLock Nuts 2High GradeSteel3/8 Nylock Nuts Fastenal Fastenal200 200

2007 Baja ProjectSuspension17.11.2) Front suspension assembly Bill of MaterialPicturePartDescription# ofpartsMaterial Specifications Supplier ManufacturerTire 2 RubberKT851B - 9 lbs21x7-10Tires Unlimited(www.tiresunlimited.com)DunlopRim 2 AluminumT-9 Pro Series10x5ITPWheel Hub 2 Aluminum Outlaw 500 Polaris PolarisUpright 2 Aluminum Outlaw 500 Polaris Polaris201 201

2007 Baja ProjectSuspensionBearing 4tapered needleroller bearingsTimkenTimkenBushings 12Bronze (Oilimpregnated)Canadian bearingMachined inthe shopUpper inserttubing2 Steel 41300.5" x 0.049thick x 12inches lengthEMJ tubingMachined inshopLower Inserttubing4 Steel 41300.5" x 0.049thick x 3inches lengthEMJ tubingMachined inshopUpper DrillRod2High GradeSteelM10 x 12inchesEssex MetalLower DrillRod2High GradeSteelM10 x 8 inches Essex Metal202 202

2007 Baja ProjectSuspensionLowerControl Arm2 Steel 4130 EMJ tubingFabricated atValientUpperControl Arm2 Steel 4130 EMJ tubingFabricated atValientBall Joint 4 Mild Steel M16 x 1.75 RH Ricky Stator YAMAHASteeringHiem Joint2 Mild Steel M12 x 1.5 RH Polaris PolarisSteeringHiem Joint2 Mild SteelAB M10 x1.5Left handedAurora BearingAuroraBearing203 203

2007 Baja ProjectSuspensionTabs 14 Steel 4130ShoulderBoltsHigh GradeSteelM10 Shoulderbolt (length of50mm )FastenalFAstenalLock Nuts 4High GradeSteelM8 NylockNutsFastenalFastenal204 204

2007 Baja ProjectSuspension17.12) Appendix LOther Relevant information205

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