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- 1. 1 Technical Seminar Series - Vehicle Dynamics August 2006 ArvinMeritor Quarterly TechnicalArvinMeritor Quarterly Technical Seminar Series – Part IISeminar Series – Part II Vehicle DynamicsVehicle Dynamics Troy Tech Center July 31, 2006
- 2. 2 Technical Seminar Series - Vehicle Dynamics August 2006 ObjectivesObjectives • To introduce the basic concepts in vehicle dynamics, focusing on vehicle handling and stability • To demonstrate the use of TruckSim software in simulating in the dynamics of trucks and tractor-semi-trailer combinations • To identify the vehicle parameters that are pertinent to vehicle dynamics • Identify parameters required as inputs to TruckSim • Propose improvements to standard laboratory tests • To identify the vehicle tests and associated vehicle performance metrics used in assessing the handling performance of vehicles • Propose improvements to skid pad tests
- 3. 3 Technical Seminar Series - Vehicle Dynamics August 2006 Presentation OutlinePresentation Outline • Basic Tire Behavior • Basics of Vehicle Dynamics: Steady-State Cornering • Vehicle Tests for Handling Performance • Using TruckSim to Simulate Vehicle Dynamics • Inputs to TruckSim: Vehicle Parameters • Examples of Using Simulation Results in Generating Vehicle Handling Performance Metrics
- 4. 4 Technical Seminar Series - Vehicle Dynamics August 2006 Basic Tire BehaviorBasic Tire Behavior
- 5. 5 Technical Seminar Series - Vehicle Dynamics August 2006 SAE Tire Axis SystemSAE Tire Axis System
- 6. 6 Technical Seminar Series - Vehicle Dynamics August 2006 Definition of Slip Ratio during BrakingDefinition of Slip Ratio during Braking
- 7. 7 Technical Seminar Series - Vehicle Dynamics August 2006 Generation of Longitudinal ForceGeneration of Longitudinal Force
- 8. 8 Technical Seminar Series - Vehicle Dynamics August 2006 Longitudinal Force vs. Slip RatioLongitudinal Force vs. Slip Ratio
- 9. 9 Technical Seminar Series - Vehicle Dynamics August 2006 Effect of Road Surface on LongitudinalEffect of Road Surface on Longitudinal Force Adhesion/Friction CoefficientForce Adhesion/Friction Coefficient
- 10. 10 Technical Seminar Series - Vehicle Dynamics August 2006 Generation of Lateral Force and AligningGeneration of Lateral Force and Aligning TorqueTorque
- 11. 11 Technical Seminar Series - Vehicle Dynamics August 2006 Lateral Force and Aligning Torque vs.Lateral Force and Aligning Torque vs. Slip AngleSlip Angle
- 12. 12 Technical Seminar Series - Vehicle Dynamics August 2006 Comparing Cornering Force and CamberComparing Cornering Force and Camber ThrustThrust
- 13. 13 Technical Seminar Series - Vehicle Dynamics August 2006 Combined Slip: Friction Circle DiagramCombined Slip: Friction Circle Diagram
- 14. 14 Technical Seminar Series - Vehicle Dynamics August 2006 Combined Slip: Cornering Force andCombined Slip: Cornering Force and Aligning Torque vs. Longitudinal ForceAligning Torque vs. Longitudinal Force
- 15. 15 Technical Seminar Series - Vehicle Dynamics August 2006 Factors Affecting Tire Forces andFactors Affecting Tire Forces and MomentsMoments • Slip Ratio, Slip Angle, Inclination Angle • Normal (Vertical) Force • Road Surface • Tire Inflation Pressure • Speed of Travel • Tire Wear • Tread Pattern • Tire Construction (Bias Ply vs. Radial Ply)
- 16. 16 Technical Seminar Series - Vehicle Dynamics August 2006 Key Idea from Basic Tire Behavior:Key Idea from Basic Tire Behavior: • Control of vehicle dynamics implies controlling the following 4 variables at each wheel: • Tire Slip Ratio • Tire Slip Angle • Tire Inclination Angle • Tire Normal Force • The above variables determine the friction forces between the tire and the ground • How do we distribute the friction forces among all the wheels to get the desired vehicle behavior?
- 17. 17 Technical Seminar Series - Vehicle Dynamics August 2006 Basics of Vehicle Dynamics:Basics of Vehicle Dynamics: Steady-State CorneringSteady-State Cornering
- 18. 18 Technical Seminar Series - Vehicle Dynamics August 2006 SAE Vehicle Axis SystemSAE Vehicle Axis System
- 19. 19 Technical Seminar Series - Vehicle Dynamics August 2006 Vehicle-Fixed SAE CoordinateVehicle-Fixed SAE Coordinate System:System: Symbols and DefinitionsSymbols and Definitions
- 20. 20 Technical Seminar Series - Vehicle Dynamics August 2006 Rigid Sprung Mass Equations of MotionRigid Sprung Mass Equations of Motion
- 21. 21 Technical Seminar Series - Vehicle Dynamics August 2006 Simplified Equations of MotionSimplified Equations of Motion of theof the Rigid Sprung MassRigid Sprung Mass
- 22. 22 Technical Seminar Series - Vehicle Dynamics August 2006 Bicycle Model for Lateral DynamicsBicycle Model for Lateral Dynamics
- 23. 23 Technical Seminar Series - Vehicle Dynamics August 2006 Bicycle Model for Lateral DynamicsBicycle Model for Lateral Dynamics • Assumptions • Constant forward velocity, u • No suspension, no vehicle roll or pitch • Front wheel steer angle is the average of LH and RH steer • Motions are small perturbations from an initial trim condition • All angles are small • Roadway is flat and level • Tire lateral forces are linear functions of tire slip angles • Neglect tire aligning moment • Neglect lateral load transfer • Vehicle is symmetric with respect to x-z plane • Consider only “fixed control” response, i.e., steer angle input
- 24. 24 Technical Seminar Series - Vehicle Dynamics August 2006 Bicycle Model: KinematicsBicycle Model: Kinematics • Front slip angle: • Rear slip angle: • C.G. lateral acceleration ff u rav δα − + = u rbv r − =α urvay += •
- 25. 25 Technical Seminar Series - Vehicle Dynamics August 2006 Bicycle Model Equations of MotionBicycle Model Equations of Motion • Tire force-vs-slip angle relation: • Derivation of equation of motion along the lateral direction: rryrffyf CFCF αα −=−= ; yryfyy FFFam +==∑ rrff CCurvm αα −−=+ • )( ff rfrf Cv u CC r u bCaC muvm δ= + + − ++ • )()(
- 26. 26 Technical Seminar Series - Vehicle Dynamics August 2006 Bicycle Model Equations of MotionBicycle Model Equations of Motion • Derivation of equation of motion along the yaw direction yryfzzz FbFaMrI −==∑ • rrffzz CbCarI αα +−= • ff rfrf zz Cav u CbCa r u CbCa rI δ= − + + + • )()( 22
- 27. 27 Technical Seminar Series - Vehicle Dynamics August 2006 Bicycle Model Equations of MotionBicycle Model Equations of Motion • Let the state variables be • Coupled equations of motion are: ),( rv ff rfrf Cv u CC r u bCaC muvm δ= + + − ++ • )()( ff rfrf zz Cav u CbCa r u CbCa rI δ= − + + + • )()( 22
- 28. 28 Technical Seminar Series - Vehicle Dynamics August 2006 Bicycle Model Equations of MotionBicycle Model Equations of Motion • Standard, first-order matrix form of the state equations: f zz f f zz rf zz fr frrf I Ca m C r v uI CbCa uI aCbC u um aCbC um CC r v dt d δ + +−− − −+− = )()( )()( 22
- 29. 29 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State ResponseSteady-State Response • Steady-state response determined by setting the first derivatives of the state variables to zero • Yaw rate gain • Lateral acceleration gain rf rfssf CCba ubCaCm ba ur )( )( )( 2 + − −+ = δ rf rfssf y CCba ubCaCm ba ua )( )( )( 2 2 + − −+ = δ
- 30. 30 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State ResponseSteady-State Response • If we define the understeer coefficient as • Yaw rate gain • Lateral acceleration gain g uK ba ur usssf 2 )( ++ = δ g uK ba ua usssf y 2 2 )( ++ = δ rf fr r zr f zf us CCba aCbCgm C F C F K )( )( + − =−=
- 31. 31 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State CorneringSteady-State Cornering rff u rba ααδ +− + = )( rff R L ααδ +−= ff u rav δα − + = u rbv r − =α
- 32. 32 Technical Seminar Series - Vehicle Dynamics August 2006 Equilibrium Equations duringEquilibrium Equations during Steady-State CorneringSteady-State Cornering
- 33. 33 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State Handling EquationSteady-State Handling Equation rff R L ααδ +−= rryrffyf CFCF αα −=−= −+= r yr f yf f C F C F R L δ rum L a Frum L b F yryf == rum C La C Lb R L rf f −+= // δ gR u C F C F R L r zr f zf f 2 −+=δ gR u K R L usf 2 +=δ g ru C F C F R L r zr f zf f −+=δ r zr f zf us C F C F K −=
- 34. 34 Technical Seminar Series - Vehicle Dynamics August 2006 Characteristic Speed and Critical SpeedCharacteristic Speed and Critical Speed • Characteristic speed (understeer vehicle) – the speed at which the steer angle required to maintain the turn radius is equal to twice the Ackermann steer angle • Critical speed (oversteer vehicle) – the speed at which the steer angle to maintain the turn radius is equal to zero us char K Lg u = us crit K Lg u − =
- 35. 35 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State Response to Steer InputsSteady-State Response to Steer Inputs • Steer angle versus speed gR u K R L usf 2 +=δ
- 36. 36 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State Response to Steer InputsSteady-State Response to Steer Inputs • Curvature response g uK L R usssf 2 1/1 + = δ
- 37. 37 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State Response to Steer InputsSteady-State Response to Steer Inputs • Yaw rate gain g uK L ur usssf 2 + = δ
- 38. 38 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State Response to Steer InputsSteady-State Response to Steer Inputs • Lateral acceleration gain g uK L ua usssf y 2 2 + = δ
- 39. 39 Technical Seminar Series - Vehicle Dynamics August 2006 Vehicle Tests for Handling PerformanceVehicle Tests for Handling Performance
- 40. 40 Technical Seminar Series - Vehicle Dynamics August 2006 Constant Radius TestConstant Radius Test )/( ga K y f us ∂ ∂ = δ g a K R L y usf +=δ
- 41. 41 Technical Seminar Series - Vehicle Dynamics August 2006 Constant Speed TestConstant Speed Test g a K g a u Lg y us y f + = 2 δ us y f K u Lg ga += ∂ ∂ 2 )/( δ us crit K Lg u − =2
- 42. 42 Technical Seminar Series - Vehicle Dynamics August 2006 Constant Speed Test: HandlingConstant Speed Test: Handling DiagramsDiagrams )/( f y us uLr g a K δ−⋅−=
- 43. 43 Technical Seminar Series - Vehicle Dynamics August 2006 Constant Steer Angle TestConstant Steer Angle Test g a L K LR yusf −= δ1 L K ga R us y −= ∂ ∂ )/( )/1(
- 44. 44 Technical Seminar Series - Vehicle Dynamics August 2006 Constant Steer Angle Test :Constant Steer Angle Test : Understeer Gradient PredictionUndersteer Gradient Prediction • Understeer gradient can be predicted by using an ADAMS or TruckSim model of the vehicle • Based on constant steer angle test • Perform 2 simulations of vehicle response to a specified step steer input, each simulation having a different initial velocity • No need to model driver steering control, no need to model vehicle speed (drive torque) control ( ) ( ) g a K R L g a K R L y us y usf 2 2 1 1 +=+=δ ( ) ( ) − − = − − = 2 1 1 2 2 2 2121 12 )/1/1( u a u a aa gL aa RR gLK yy yyyy us
- 45. 45 Technical Seminar Series - Vehicle Dynamics August 2006 Constant Steer Angle Test :Constant Steer Angle Test : Understeer Gradient PredictionUndersteer Gradient Prediction Steady-State Values: 70 kph 80 kph 90 kph 100 kph Vehicle Speed (km/hr) 69.95 79.94 89.94 99.20 Lateral Acceleration (g's) 0.26 0.29 0.31 0.33 Yaw Rate (degrees/sec) 7.63 7.28 6.95 6.66 Vehicle Roll Angle (degrees) 4.18 4.85 5.32 5.68 Vehicle Slip Angle (degrees) -0.73 -1.06 -1.38 -1.66 Percent Overshoot: 70 kph 80 kph 90 kph 100 kph Lateral Acceleration (pct.) 3.86 6.29 9.61 12.81 Yaw Rate (pct.) 15.26 21.01 25.82 30.08 Vehicle Roll Angle (pct.) 5.45 9.11 10.72 13.70 Vehicle Slip Angle (pct.) 25.31 33.34 42.99 52.48 Response Time: 70 kph 80 kph 90 kph 100 kph Lateral Acceleration (sec) 0.33 0.33 0.34 0.34 Yaw Rate (sec) 0.22 0.20 0.19 0.17 Vehicle Roll (sec) 1.15 1.12 1.09 1.07 Vehicle Slip (sec) 0.83 0.79 0.79 0.79 Handling Performance Metrics 75 kph 85 kph 95 kph Average Understeer Gradient (deg/g) 10.80 9.18 8.18 9.39 Vehicle Roll Gradient (deg/g) 27.22 21.62 20.21 23.02
- 46. 46 Technical Seminar Series - Vehicle Dynamics August 2006 Take-Away: Steady-State CorneringTake-Away: Steady-State Cornering • Understeer gradient: • Steady-state handling equation: • A critical speed exists when a vehicle is oversteer • Characteristic speed is a measure of understeer • Steady-state characteristics are important performance metrics of vehicle handling capabilities • Understeer gradient determines steady-state response • Standard tests are available for measuring understeer gradient r zr f zf us C F C F K −= gR u K R L usf 2 +=δ
- 47. 47 Technical Seminar Series - Vehicle Dynamics August 2006 Other Factors Affecting UndersteerOther Factors Affecting Understeer
- 48. 48 Technical Seminar Series - Vehicle Dynamics August 2006 Other Factors Affecting UndersteerOther Factors Affecting Understeer • Lateral load transfer / roll moment distribution • Tire camber (may be induced by vehicle roll) • Roll steer • Lateral force compliance (steer and camber) • Aligning torque compliance (steer and camber) • Aligning torque • Tractive force (FWD vs. RWD) • Steering system compliance
- 49. 49 Technical Seminar Series - Vehicle Dynamics August 2006 Other Factors Affecting UndersteerOther Factors Affecting Understeer
- 50. 50 Technical Seminar Series - Vehicle Dynamics August 2006 Other Factors Affecting UndersteerOther Factors Affecting Understeer
- 51. 51 Technical Seminar Series - Vehicle Dynamics August 2006 Other Factors Affecting UndersteerOther Factors Affecting Understeer
- 52. 52 Technical Seminar Series - Vehicle Dynamics August 2006 Understeer Budget: Example 1Understeer Budget: Example 1 • Prof. Barak’s example (SAE Seminar) • Tire cornering stiffness and weight distribution contributes 50% to vehicle understeer • Aligning torque compliance steer contributes 23% to vehicle understeer Factor Front (deg/g) Rear (deg/g) Front – Rear (deg/g) Tire Cornering Stiffness 3.24 1.86 1.38 Aligning Torque 0.065 -0.088 0.153 Aligning Torque Compliance 0.665 0.038 0.627 Lateral Force Compliance 0.20 0.11 0.09 Roll Camber (with aligning torque) 0.86 0.46 0.40 Roll Steer 0.35 0.23 0.12 Understeer Gradient 5.38 2.61 2.77
- 53. 53 Technical Seminar Series - Vehicle Dynamics August 2006 Understeer Budget: Example 2Understeer Budget: Example 2 • J. C. Dixon, Tires, Suspension and Handling (SAE Publication, 1996): • Tire cornering stiffness and weight distribution contributes 14% to vehicle understeer • Aligning torque compliance steer contributes 29% to vehicle understeer Factor Front (deg/g) Rear (deg/g) Front – Rear (deg/g) Tire Cornering Stiffness 7.2 6.6 0.6 Aligning Torque 0.1 -0.1 0.2 Aligning Torque Compliance 1.3 0.1 1.2 Lateral Force Compliance 0.2 0.2 0.0 Roll Camber 1.2 0.0 1.2 Roll Steer 0.5 -0.5 1.0 Understeer Gradient 10.5 6.3 4.2
- 54. 54 Technical Seminar Series - Vehicle Dynamics August 2006 Take-Away: Factors Affecting UndersteerTake-Away: Factors Affecting Understeer • Understeer is not determined by the ratio of axle load to tire cornering stiffness alone • Suspension design can have a big impact on vehicle understeer/oversteer characteristics • The steady-state handling equation derived from the linear bicycle model can still be used as long as we account for other effects that contribute to the understeer gradient
- 55. 55 Technical Seminar Series - Vehicle Dynamics August 2006 Limit Handling Performance due toLimit Handling Performance due to Nonlinear Tire CharacteristicsNonlinear Tire Characteristics
- 56. 56 Technical Seminar Series - Vehicle Dynamics August 2006 Limit Handling due to Tire NonlinearitiesLimit Handling due to Tire Nonlinearities • Motivation: load sensitivity of rear axle tire lateral force • Normal force increases due to lateral load transfer • Increase in normal force results in increase in required slip angle to maintain the same level of required lateral force • Increase in slip angle results in decrease in cornering force • Change in cornering compliance may result in oversteer
- 57. 57 Technical Seminar Series - Vehicle Dynamics August 2006 Limit Handling due to Tire NonlinearitiesLimit Handling due to Tire Nonlinearities • Basic kinematic relation between steer angle and tire slip angles still applies • Four possible cases, as lateral acceleration increases: • Initial oversteer, becomes more oversteer (vehicle spins) • Initial understeer, becomes more understeer (vehicle plows) • Initial understeer, becomes oversteer (vehicle spins) • Initial oversteer, becomes understeer (vehicle plows) rff R L ααδ +−= 21 ααδ −+= R L f
- 58. 58 Technical Seminar Series - Vehicle Dynamics August 2006 Limit Handling due to Tire NonlinearitiesLimit Handling due to Tire Nonlinearities Case 1: OS Case 2: US
- 59. 59 Technical Seminar Series - Vehicle Dynamics August 2006 Limit Handling due to Tire NonlinearitiesLimit Handling due to Tire Nonlinearities Case 3: US OS Case 4: OS US
- 60. 60 Technical Seminar Series - Vehicle Dynamics August 2006 Limit Handling due to Tire NonlinearitiesLimit Handling due to Tire Nonlinearities Ideal US
- 61. 61 Technical Seminar Series - Vehicle Dynamics August 2006 Take-Away: Limit HandlingTake-Away: Limit Handling • Vehicle US/OS characteristics are not constant due to nonlinearities in the tire force-deflection relations • Other factors such as body roll will change the US/OS characteristics of the vehicle during operations • Commercial vehicles, due to their high C.G. locations, are more susceptible to changes in US/OS • Consider understeer gradient as the slope of (α1 – α2) vs. (Ay/g) curve
- 62. 62 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State Handling of Tractor-Semi-TrailerSteady-State Handling of Tractor-Semi-Trailer CombinationsCombinations
- 63. 63 Technical Seminar Series - Vehicle Dynamics August 2006 Steady-State Handling Model of Tractor-Semi-Steady-State Handling Model of Tractor-Semi- Trailer CombinationTrailer Combination
- 64. 64 Technical Seminar Series - Vehicle Dynamics August 2006 Handling Equation for the TractorHandling Equation for the Tractor gR u K R L tus t f 2 ,+=δ gR u C W C W R L r r f ft f 2 −+= αα δ
- 65. 65 Technical Seminar Series - Vehicle Dynamics August 2006 Handling Equation for the Semi-TrailerHandling Equation for the Semi-Trailer gR u K R L sus s 2 ,+=Γ gR u C W C W R L s s r rs 2 −+=Γ αα
- 66. 66 Technical Seminar Series - Vehicle Dynamics August 2006 Trailer Articulation Angle GainTrailer Articulation Angle Gain • 2 Modes of Instability Possible • Tractor Jackknife • Trailer Swing • Note: stability analysis results are first-order approximations from linear model ( ) ( ) ( ) ( )gRuKRL gRuKRL tust suss f 2 , 2 , + + = Γ δ
- 67. 67 Technical Seminar Series - Vehicle Dynamics August 2006 Tractor JackknifeTractor Jackknife • 2 Cases Possible • Case 1: and • Case 2: and and • Critical Speed tus t crit K Lg u ,− = 0, <tusK 0, >susK 0, <tusK 0, <susK ( ) ( )tstussus LLKK <,,
- 68. 68 Technical Seminar Series - Vehicle Dynamics August 2006 Tractor SwingTractor Swing • and and • Critical Speed tus t crit K Lg u ,− = 0, <tusK 0, <susK ( ) ( )tstussus LLKK >,,
- 69. 69 Technical Seminar Series - Vehicle Dynamics August 2006 Using TruckSim to Simulate Vehicle DynamicsUsing TruckSim to Simulate Vehicle Dynamics
- 70. 70 Technical Seminar Series - Vehicle Dynamics August 2006 Vehicle Test or Computer Simulation?Vehicle Test or Computer Simulation? • Vehicle tests are more appropriate when: • Test vehicle for a specific product is available • Objective is to identify potential problems in normal operation of a specific vehicle • A subjective evaluation is required from a driver or passenger • Problem requires high fidelity modeling such that modeling and simulation requires too much time • Operator safety (e.g., crash or rollover events) is not an issue • Etc.
- 71. 71 Technical Seminar Series - Vehicle Dynamics August 2006 Vehicle Test or Computer Simulation?Vehicle Test or Computer Simulation? • Modeling and simulation are more appropriate when: • Test vehicle for a specific product is not available • Objective is to identify the cause of performance problems • A sensitivity study on one or more design variables is desired • Design synthesis: evaluate candidate designs and answer many “what if” questions • Problem of concern requires low or moderate fidelity models such that modeling and simulation can be accomplished in a reasonable amount of time • Repeatable tests of rollover or crash events are desired • Accident reconstruction • Etc.
- 72. 72 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSimTruckSim • Simulate dynamic behavior of trucks, buses, and tractor- semi-trailer combinations • Simulate response of vehicle to driver inputs such as steering, braking, and acceleration • Simulate response of vehicle to environment such as rough roads, wind • Includes provisions for interfacing with Matlab/Simulink to simulate the response of the vehicles with active controls (e.g., active suspension or steering)
- 73. 73 Technical Seminar Series - Vehicle Dynamics August 2006 Why Use TruckSim?Why Use TruckSim? • Pre-defined vehicle models – no need to create a model from scratch; requires user to input vehicle parameters • Fast runtime – vehicle models are represented by ordinary differential equations (ODE’s) using a minimum number of independent variables • Easy to use interface –interfaces are intuitive, and can be navigated like a web browser • What If Analysis – vehicle design parameters can be changed quickly, hence, design decisions regarding vehicle dynamics can be made quicker • Mature product – developed by UMTRI in 1980’s
- 74. 74 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim ModelsTruckSim Models • Single-unit truck or bus • 1 or 2 steer axles • Single or tandem drive axles • Front: solid axle or independent suspension • Rear: solid axle suspension • Frame twist feature available with custom license • Tractor-semi-trailer combination • Tractor: 2 or 3 axles, all solid axle suspensions • Semi-trailer: 1, 2, or 3 axles, all solid axle suspensions • A-train doubles • Double trailers with single trailer axles • Special configurations possible with custom license
- 75. 75 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Typical ScenariosTruckSim: Typical Scenarios • Constant Radius Test • Step Steer Test • Double Lane Change • Straight-line braking (constant-µ or split-µ) • Braking while turning • Acceleration • Rollover: fish-hook maneuver
- 76. 76 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Run Control ScreenTruckSim: Run Control Screen
- 77. 77 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Vehicle Configuration ScreenTruckSim: Vehicle Configuration Screen
- 78. 78 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Tractor Screen (3 axles)TruckSim: Tractor Screen (3 axles)
- 79. 79 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Trailer Screen (3 axles)TruckSim: Trailer Screen (3 axles)
- 80. 80 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Trailer Payload ScreenTruckSim: Trailer Payload Screen
- 81. 81 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Tractor Screen (2 axles)TruckSim: Tractor Screen (2 axles)
- 82. 82 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Tractor Sprung Mass ScreenTruckSim: Tractor Sprung Mass Screen
- 83. 83 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Solid Axle Kinematics ScreenTruckSim: Solid Axle Kinematics Screen
- 84. 84 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Axle Lateral .vs. Roll MotionTruckSim: Axle Lateral .vs. Roll Motion
- 85. 85 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Suspension ScreenTruckSim: Suspension Screen
- 86. 86 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Suspension ComplianceTruckSim: Suspension Compliance
- 87. 87 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Suspension DampingTruckSim: Suspension Damping
- 88. 88 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Auxiliary Roll StiffnessTruckSim: Auxiliary Roll Stiffness
- 89. 89 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: TiresTruckSim: Tires
- 90. 90 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Tire Data - Longitudinal ForcesTruckSim: Tire Data - Longitudinal Forces
- 91. 91 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Tire Data - Lateral ForcesTruckSim: Tire Data - Lateral Forces
- 92. 92 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Tire Data - Aligning MomentTruckSim: Tire Data - Aligning Moment
- 93. 93 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Tire Model – Pacejka CoefficientsTruckSim: Tire Model – Pacejka Coefficients
- 94. 94 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Steering SystemTruckSim: Steering System
- 95. 95 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Steered Wheel KinematicsTruckSim: Steered Wheel Kinematics
- 96. 96 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Brake SystemTruckSim: Brake System
- 97. 97 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Brake Torque Data from DynoTruckSim: Brake Torque Data from Dyno
- 98. 98 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Truck with PowertrainTruckSim: Truck with Powertrain
- 99. 99 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: 4WD PowertrainTruckSim: 4WD Powertrain
- 100. 100 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Engine Torque MapTruckSim: Engine Torque Map
- 101. 101 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Transmission Gear RatiosTruckSim: Transmission Gear Ratios
- 102. 102 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Transmission Shift ScheduleTruckSim: Transmission Shift Schedule
- 103. 103 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Viscous DifferentialTruckSim: Viscous Differential
- 104. 104 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: X-Y Plots (Post-Processing)TruckSim: X-Y Plots (Post-Processing)
- 105. 105 Technical Seminar Series - Vehicle Dynamics August 2006 Embedding a TruckSim Model inEmbedding a TruckSim Model in Matlab/SimulinkMatlab/Simulink
- 106. 106 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim: Animation (Post-Processing)TruckSim: Animation (Post-Processing)
- 107. 107 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim Results: Constant Radius TestTruckSim Results: Constant Radius Test
- 108. 108 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim Results: Constant Speed TestTruckSim Results: Constant Speed Test
- 109. 109 Technical Seminar Series - Vehicle Dynamics August 2006 TruckSim Results: Constant Steer Angle TestTruckSim Results: Constant Steer Angle Test Lateral Acceleration Yaw Rate
- 110. 110 Technical Seminar Series - Vehicle Dynamics August 2006 Summary of Suspension CharacterizationSummary of Suspension Characterization Inputs Required in TruckSimInputs Required in TruckSim • Suspension kinematics • Axle steer vs. axle roll • Axle dive vs. wheel travel • Wheel recession vs. jounce • Lateral motion vs. jounce • Lateral motion vs. axle roll • Toe and camber settings • Axle steer vs. axle wrap • Axle steer vs. wheel travel • Left wheel vs. right wheel steer angle (Ackerman) • Spring and shock motion ratios • Suspension compliance • Spring force vs. displacement • Shock force vs. velocity • Auxiliary roll stiffness • Axle lateral stiffness • Axle fore-aft stiffness • Toe angle vs. Fx • Steer angle vs. Fy • Steer angle vs. Mz • Camber angle vs. Fx • Camber angle vs. Fy • Camber angle vs. Mz
- 111. 111 Technical Seminar Series - Vehicle Dynamics August 2006 Questions?Questions?

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