Evaluation of Vehicle Understeer Gradient Definitions Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of the Ohio State University By Neha Ravi Dixit Graduate Program in Mechanical Engineering The Ohio State University 2009 Thesis Committee: Dr. Dennis A. Guenther, Advisor Dr. Gary J. Heydinger Copyright by Neha Ravi Dixit 2009 ABSTRACT The aim of this thesis is to study current methodologies for evaluating the understeer gradient. The SAE J266 standard gives the typical procedures to calculate the understeer gradient. The goal was to verify certain assumptions made in the formulation of the standard and to investigate differences in the J266 test methods to help predict the understeer gradient accurately. The procedures specified in this standard have been used to calculate the understeer gradients for the experimental and simulation vehicles in different situations. Field tests for understeer gradient calculations were carried out at the Transportation Research Center (TRC). The test vehicle used was Subaru Outback. As it is very important to validate the results obtained from experimental testing, vehicle dynamics software CarSim was used to simulate these tests. A vehicle model for the 2003 Ford Expedition was built in CarSim and validated using certain quasi-static and dynamic maneuvers. This model was used for simulation of understeer gradient tests in CarSim. This model was selected as the Expedition falls in the same class of vehicles as the Outback and a well validated vehicle model gives us confidence in the simulation results. The analysis was made for the standard understeer measurement methods: namely the constant radius method, constant steer method and the constant speed method. The results ii obtained through simulation were compared with the results from actual test data. The effect of steering and suspension compliances and kinematics on understeer gradient calculation has also been studied with the help of a modified Expedition model with the steering and suspension compliances and kinematics set to zero. The discussion about the theoretical calculation of understeer gradient and the importance of different contributing factors is made using the Ford Expedition as an example. The resulting trends and conclusions from this investigation are discussed in the last chapter. The future work that could be done to take this research further is also discussed. iii DEDICATION Dedicated to my parents and family, for their unconditional love and support and faith in me To my friends; for their support and guidance in all my endeavors and for making tough times easier iv ACKNOWLEDGEMENTS I would like to express my gratitude towards all those who made this thesis possible. I want to take this opportunity to thank my advisors Dr. Dennis A. Guenther and Dr. Gary J. Heydinger for their valuable guidance. They were a source of constant encouragement and support. I especially thank Denny for giving me complete freedom in choosing my classes and giving me the opportunity to explore a variety of topics. I also want to thank Dr. Kamel Salaani for his help and guidance whenever needed and Don Butler for his support. I am thankful to Dr. David Mikesell and Anmol Sidhu for giving me the opportunity of collaborating with them for the field tests. I am grateful to my colleagues Sughosh Rao and Tejas Kinjawadekar for helping and sharing the workload. Last but not the least; I thank my parents, family and friends for always supporting and understanding me. v VITA 23 January 1986………………...Born – Pune, India June 2003……………………….Fergusson College, Pune, India June 2007……………………….B.Tech.M.E. Pune University Sept. 2007 – June 2009…………Graduate Research Assistant, The Ohio State University PUBLICATIONS ‘Vehicle Dynamics Modeling and Validation with ESC of the 2003 Ford Expedition Using CarSim’ with G. Heydinger, D. Guenther, et al, SAE Conference, April 2009 FIELDS OF STUDY Major Field: Mechanical Engineering Vehicle Dynamics, Solid Mechanics vi TABLE OF CONTENTS ABSTRACT………………………………………………………………………………ii DEDICATION……………………………………………………………………………iv ACKNOWLEDGEMENTS……………………………………………………………….v VITA……………………………………………………………………………………...vi LIST OF FIGURES………………………………………………………………………ix LIST OF TABLES……………………………………………………………………….xii 1 INTRODUCTION ...................................................................................................... 1 1.1 Motivation ............................................................................................................ 1 1.2 Simulation with CarSim ....................................................................................... 2 1.3 Experimental Analysis ......................................................................................... 5 1.4 Thesis Outline ...................................................................................................... 5 2 UNDERSTEER GRADIENT THEORY .................................................................... 7 2.1 Overview .............................................................................................................. 7 2.2 Bicycle Model ...................................................................................................... 7 2.3 Very slow speed cornering ................................................................................... 8 2.4 High Speed Cornering .......................................................................................... 9 2.5 Understeer Gradient and Vehicle Stability......................................................... 13 2.6 Stability Analysis ............................................................................................... 15 2.7 Yaw Rate and Lateral Acceleration Response ................................................... 18 3 MODELING AND VALIDATION OF 2003 FORD EXPEDITION USING CARSIM ........................................................................................................................... 21 3.1 Overview ............................................................................................................ 21 3.2 Modeling ............................................................................................................ 23 3.2.1 Suspension System...................................................................................... 24 3.2.2 Steering System .......................................................................................... 26 3.2.3 Tire Model .................................................................................................. 27 3.3 Model Validation................................................................................................ 29 3.3.1 Quasi Static Tests ........................................................................................ 29 3.3.2 Dynamic Tests ............................................................................................ 38 4 SIMULATION WITH CARSIM .............................................................................. 47 4.1 Background ........................................................................................................ 47 4.1.1 Constant Radius Test .................................................................................. 47 4.1.2 Constant Steer Angle Test .......................................................................... 48 4.1.3 Constant Speed Test .................................................................................... 49 4.2 2003 Ford Expedition ......................................................................................... 50 4.2.1 Constant Radius Test .................................................................................. 50 4.2.2 Constant Steer Angle Test .......................................................................... 55 4.2.3 Constant Speed Test .................................................................................... 59 vii 4.3 Expedition Tests with Zero Compliances .......................................................... 63 4.3.1 Constant Radius Test .................................................................................. 64 4.3.2 Constant Steer Test ..................................................................................... 66 4.3.3 Constant Speed Test .................................................................................... 69 4.4 Understeer Gradient from Slowly Increasing Steer Test ................................... 72 5 EXPERIMENTAL ANALYSIS ............................................................................... 74 5.1 Background ........................................................................................................ 74 5.2 2006 Subaru Outback ......................................................................................... 75 5.2.1 Constant Radius Test .................................................................................. 75 5.2.2 Constant Steer Angle Test .......................................................................... 77 5.2.3 Constant Speed Test .................................................................................... 80 6 RESULTS AND DISCUSSION ............................................................................... 84 6.1 Background ........................................................................................................ 84 6.2 Constant Radius Test .........................................................................................