Table Of ContentFULL VEHICLE DYNAMICS MODEL OF A
FORMULA SAE RACECAR USING ADAMS/CAR
A Thesis
by
RUSSELL LEE MUELLER
Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
August 2005
Major Subject: Mechanical Engineering
FULL VEHICLE DYNAMICS MODEL OF A
FORMULA SAE RACECAR USING ADAMS/CAR
A Thesis
by
RUSSELL LEE MUELLER
Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
Approved by:
Chair of Committee, Make McDermott
Committee Members, Arun R. Srinivasa
Glen N. Williams
Head of Department, Dennis L. O’Neal
August 2005
Major Subject: Mechanical Engineering
iii
ABSTRACT
Full Vehicle Dynamics Model of a Formula SAE
Racecar Using ADAMS/Car. (August 2005)
Russell Lee Mueller, B.S. Texas A&M University
Chair of Advisory Committee: Dr. Make McDermott
The Texas A&M University Formula SAE program currently has no rigorous method for analyzing
or predicting the overall dynamic behavior of the student-designed racecars. The objective of
this study is to fulfill this need by creating a full vehicle ADAMS/Car model incorporating an
empirical tire-road force model and validating the longitudinal performance of the model by using
vehicle responses recorded at the track. Creating the model requires measuring mass and
inertia properties for each part, measuring the locations of all the kinematic joints, testing the
Risse Racing Jupiter-5 shocks to characterize damping and stiffness, measuring engine torque,
and modeling the tire behavior. Measuring the vehicle performance requires installation of the Pi
Research DataBuddy data acquisition system and appropriate sensors. The 2002 Texas A&M
University Formula SAE racecar, the subject vehicle, was selected because it already included
some accommodations for sensors and is almost identical in layout to the available ADAMS/Car
model Formula SAE templates. The tire-road interface is described by the Pacejka ’94 handling
force model within ADAMS/Car that is based on a set of Goodyear coefficients. The majority of
the error in the model originated from the Goodyear tire model and the 2004 engine torque map.
The testing used Hoosier tires and the 2002 engine intake and exhaust configuration. The
deliverable is a full vehicle model of the 2002 racecar with a 2004 engine torque map and a tire
model correlated to longitudinal performance recorded at the track using the installed data
acquisition system. The results of the correlation process, confirmed by driver impressions and
performance of the 2004 racecar, show that the 2004 engine torque map predicts higher
performance than the measured response with the 2002 engine. The Hoosier tire on the Texas
A&M University Riverside Campus track surface produces 75±3% of peak longitudinal tire
performance predicted by the Goodyear tire model combined with a road surface friction
coefficient of 1.0. The ADAMS/Car model can now support the design process as an analysis
tool for full vehicle dynamics and with continued refinement, will be able to accurately predict
behavior throughout a complete autocross course.
iv
NOMENCLATURE
ACAR ADAMS/Car Software
ARB Anti-Roll Bar
B Pacejka '94 Handling Force Model – Stiffness Factor
BCD Pacejka '94 Handling Force Model – Stiffness
BCD or Pacejka '94 Handling Force Model – Stiffness Adjustment
LON LAT
b -b Pacejka '94 Handling Force Model – Longitudinal Tire Coefficients
0 13
BUS Bushing
C Pacejka '94 Handling Force Model – Shape Factor
CAD Computer Aided Drafting or Design
CEA Pi Research Club Expert Analysis Software
CG Center of Gravity
CNV Kinematic Joint – Constant Velocity
CYL Kinematic Joint – Cylindrical
D Pacejka '94 Handling Force Model – Peak Factor
DAQ Data Acquisition
D or Pacejka '94 Handling Force Model – Peak Factor Adjustment
LON LAT
DOF Degree(s) of Freedom
E Pacejka '94 Handling Force Model – Curvature Factor
ECU Engine Control Unit
FIX Kinematic Joint – Fixed
FSAE Formula SAE
HOK Kinematic Joint – Hooke
INL Kinematic Joint – Inline
INP Kinematic Joint – Inplane
κ Pacejka '94 Handling Force Model – Longitudinal Slip Ratio
MAP Intake Manifold (plenum) Air Pressure Sensor
MKS ADAMS/Car Units – Meters, Kilograms, Seconds
MMKS ADAMS/Car Units – Millimeters, Kilograms, Seconds
ORI Kinematic Joint – Orientation
PAX Kinematic Joint – Parallel_axes
PER Kinematic Joint – Perpendicular
PiDB Pi Research DataBuddy Logger
PLA Kinematic Joint – Planar
REV Kinematic Joint – Revolute
v
SAE Society of Automotive Engineers
S Pacejka '94 Handling Force Model – Horizontal Shift
H
SI International System of Units
SLA Short-Long Arm Suspension
SPH Kinematic Joint – Spherical
S Pacejka '94 Handling Force Model – Vertical Shift
V
TAMU Texas A&M University
TEES Texas Engineering Experiment Station
TPS Throttle Position Sensor
TRA Kinematic Joint – Translational
V6 Pi Research Version 6 Software
X Pacejka '94 Handling Force Model – Composite Slip Ratio
vi
TABLE OF CONTENTS
Page
ABSTRACT.....................................................................................................................................iii
NOMENCLATURE..........................................................................................................................iv
TABLE OF CONTENTS..................................................................................................................vi
LIST OF FIGURES.......................................................................................................................viii
LIST OF TABLES..........................................................................................................................xi
INTRODUCTION............................................................................................................................1
Objective.....................................................................................................................................1
Background.................................................................................................................................1
PROCEDURE.................................................................................................................................3
MODEL DESCRIPTION.................................................................................................................4
Model Scope...............................................................................................................................4
Coordinate Systems....................................................................................................................5
Kinematic Joints..........................................................................................................................5
Subsystems.................................................................................................................................7
Chassis Subsystem.................................................................................................................7
Front Suspension Subsystem..................................................................................................8
Rear Suspension Subsystem..................................................................................................9
Anti-Roll Bar Subsystem..........................................................................................................9
Steering Subsystem..............................................................................................................10
Wheel and Tire Subsystem...................................................................................................11
Brake Subsystem..................................................................................................................11
Powertrain Subsystem...........................................................................................................11
Sub-Models...............................................................................................................................12
Shocks...................................................................................................................................13
Differential.............................................................................................................................14
Powertrain..............................................................................................................................14
Tires.......................................................................................................................................15
Driver, Road, and Straight-Line Acceleration Event Setup....................................................17
SUB-MODEL AND SUBSYSTEM DATA COLLECTION..............................................................19
Kinematic Joints........................................................................................................................19
Vehicle CG................................................................................................................................21
Mass and Inertia........................................................................................................................23
Engine Torque Map...................................................................................................................23
Shock Damping and Stiffness Testing......................................................................................25
VEHICLE RESPONSE..................................................................................................................28
Data Acquisition System...........................................................................................................28
Logger...................................................................................................................................28
Wheel Speed.........................................................................................................................29
Suspension Travel.................................................................................................................30
Steering Wheel Angle............................................................................................................31
Beacon and Lap Layout.........................................................................................................31
Engine Speed........................................................................................................................31
vii
Page
Throttle Position.....................................................................................................................32
Sampling Rate.......................................................................................................................32
Miscellaneous DAQ System Suggestions.............................................................................32
Vehicle Response Testing........................................................................................................33
System Configurations..........................................................................................................33
Procedure..............................................................................................................................34
Post-Processing....................................................................................................................36
MODEL CORRELATION..............................................................................................................38
Comparison of Simulated and Measured Responses...............................................................38
Configuration 1......................................................................................................................39
Configuration 2......................................................................................................................39
Configuration 3......................................................................................................................39
Configuration 4......................................................................................................................39
Overall Observations.............................................................................................................40
Conclusions...............................................................................................................................41
RECOMMENDED NEXT STEPS.................................................................................................42
SUMMARY....................................................................................................................................43
REFERENCES.............................................................................................................................44
APPENDIX A FIGURES.............................................................................................................45
APPENDIX B TABLES................................................................................................................94
VITA............................................................................................................................................113
viii
LIST OF FIGURES
Page
Figure 1: Coordinate System Orientation.....................................................................................46
Figure 2: Front Suspension Subsystem.......................................................................................47
Figure 3: Rear Suspension Subsystem........................................................................................48
Figure 4: Front Suspension Subsystem Parts.............................................................................49
Figure 5: Rear Suspension Subsystem Parts..............................................................................49
Figure 6: Anti-Roll Bar Subsystem Parts.....................................................................................50
Figure 7: Steering Subsystem Parts............................................................................................50
Figure 8: Coil-Over Shock Sub-Model.........................................................................................51
Figure 9: Suspension Springs......................................................................................................51
Figure 10: Suspension Dampers.................................................................................................52
Figure 11: Viscous Differential.....................................................................................................52
Figure 12: Normal Load Effects on Normalized Longitudinal Tire Force.....................................53
Figure 13: Scaling Effects on Normalized Longitudinal Tire Force..............................................53
Figure 14: Simulation Setup – Full-Vehicle Analysis Straight-Line Acceleration.........................54
Figure 15: Kinematic Joint Locations – First Laser Level Orientation (y direction)......................55
Figure 16: Kinematic Joint Locations – Second Laser Level Orientation (x direction)................56
Figure 17: Hardpoint Measurement Using a Laser Level............................................................56
Figure 18: SolidWorks Model for Estimating Inertia....................................................................57
Figure 19: Powertrain Subsystem Engine Torque Map...............................................................58
Figure 20: Risse Racing Jupiter-5 Shock #1 – Total Force, All 5 Tested Settings......................59
Figure 21: Risse Racing Jupiter-5 Shock #1 – Damping, MID Bump + MID Rebound................60
Figure 22: Risse Racing Jupiter-5 Shock #1 – Damping, MID Bump + HI Rebound...................60
Figure 23: Risse Racing Jupiter-5 Shock #1 – Damping, MID Bump + LOW Rebound..............61
Figure 24: Risse Racing Jupiter-5 Shock #1 – Damping, HI Bump + MID Rebound...................61
Figure 25: Risse Racing Jupiter-5 Shock #1 – Damping, LOW Bump + MID Rebound..............62
Figure 26: Risse Racing Jupiter-5 Shock #1 – Stiffness (Speed = 0.13 mm/s)...........................62
Figure 27: Risse Racing Jupiter-5 Shock #2 – Total Force, All 5 Tested Settings......................63
Figure 28: Risse Racing Jupiter-5 Shock #2 – Damping, MID Bump + MID Rebound................64
Figure 29: Risse Racing Jupiter-5 Shock #2 – Damping, MID Bump + HI Rebound...................64
Figure 30: Risse Racing Jupiter-5 Shock #2 – Damping, MID Bump + LOW Rebound..............65
Figure 31: Risse Racing Jupiter-5 Shock #2 – Damping, HI Bump + MID Rebound...................65
Figure 32: Risse Racing Jupiter-5 Shock #2 – Damping, LOW Bump + MID Rebound..............66
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Page
Figure 33: Risse Racing Jupiter-5 Shock #2 – Stiffness (Speed = 0.13 mm/s)...........................66
Figure 34: Risse Racing Jupiter-5 Shock #4 – Total Force, All 5 Tested Settings......................67
Figure 35: Risse Racing Jupiter-5 Shock #4 – Damping, MID Bump + MID Rebound................68
Figure 36: Risse Racing Jupiter-5 Shock #4 – Damping, MID Bump + HI Rebound...................68
Figure 37: Risse Racing Jupiter-5 Shock #4 – Damping, MID Bump + LOW Rebound..............69
Figure 38: Risse Racing Jupiter-5 Shock #4 – Damping, HI Bump + MID Rebound...................69
Figure 39: Risse Racing Jupiter-5 Shock #4 – Damping, LOW Bump + MID Rebound..............70
Figure 40: Risse Racing Jupiter-5 Shock #4 – Stiffness (Speed = 0.13 mm/s)...........................70
Figure 41: DAQ Installation – Pi DataBuddy Logger....................................................................71
Figure 42: DAQ Installation – Front Wheel Speed Sensor..........................................................72
Figure 43: DAQ Installation – Rear Wheel Speed Sensor...........................................................73
Figure 44: DAQ Installation – Front Suspension Travel..............................................................74
Figure 45: DAQ Installation – Rear Suspension Travel...............................................................75
Figure 46: DAQ Installation – Steering Wheel Angle...................................................................76
Figure 47: DAQ Installation – Beacon Receiver..........................................................................76
Figure 48: Configuration 1 – Filtered Rear Wheel Speed and Longitudinal Slip Ratio................77
Figure 49: Configuration 1 – Longitudinal Chassis Acceleration.................................................78
Figure 50: Configuration 1 – Engine Speed.................................................................................78
Figure 51: Configuration 1 – Longitudinal Chassis Speed...........................................................79
Figure 52: Configuration 1 – Longitudinal Slip Ratio....................................................................79
Figure 53: Configuration 1 – Normalized Tire Force vs. Longitudinal Slip Ratio.........................80
Figure 54: Configuration 1 – Throttle Position.............................................................................80
Figure 55: Configuration 1 – Damper Travel...............................................................................81
Figure 56: Configuration 2 – Longitudinal Chassis Acceleration.................................................82
Figure 57: Configuration 2 – Engine Speed.................................................................................82
Figure 58: Configuration 2 – Longitudinal Chassis Speed...........................................................83
Figure 59: Configuration 2 – Longitudinal Slip Ratio....................................................................83
Figure 60: Configuration 2 – Normalized Tire Force vs. Longitudinal Slip Ratio.........................84
Figure 61: Configuration 2 – Throttle Position.............................................................................84
Figure 62: Configuration 2 – Damper Travel...............................................................................85
Figure 63: Configuration 3 – Longitudinal Chassis Acceleration.................................................86
Figure 64: Configuration 3 – Engine Speed.................................................................................86
Figure 65: Configuration 3 – Longitudinal Chassis Speed...........................................................87
Figure 66: Configuration 3 – Longitudinal Slip Ratio....................................................................87
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Page
Figure 67: Configuration 3 – Normalized Tire Force vs. Longitudinal Slip Ratio.........................88
Figure 68: Configuration 3 – Throttle Position.............................................................................88
Figure 69: Configuration 3 – Damper Travel...............................................................................89
Figure 70: Configuration 4 – Longitudinal Chassis Acceleration.................................................90
Figure 71: Configuration 4 – Engine Speed.................................................................................90
Figure 72: Configuration 4 – Longitudinal Chassis Speed...........................................................91
Figure 73: Configuration 4 – Longitudinal Slip Ratio....................................................................91
Figure 74: Configuration 4 – Normalized Tire Force vs. Longitudinal Slip Ratio.........................92
Figure 75: Configuration 4 – Throttle Position.............................................................................92
Figure 76: Configuration 4 – Damper Travel...............................................................................93
Description:C. Pacejka '94 Handling Force Model – Shape Factor. CAD. Computer Aided Drafting or Design. CEA. Pi Research Club Expert Analysis Software. CG.
