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Development of Vehicle Dynamics Tools for Motorsports

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Development of Vehicle Dynamics Tools for Motorsports AN ABSTRACT OF THE DISSERTATION OF Chris Patton for the degree of Doctor of Philosophy in Mechanical Engineering presented on February 7, 2013. Title: Development of Vehicle Dynamics Tools for Motorsports. Abstract approved: ______________________________________________________________________________ Robert K. Paasch In this dissertation, a group of vehicle dynamics simulation tools is developed with two primary goals: to accurately represent vehicle behavior and to provide insight that improves the understanding of vehicle performance. Three tools are developed that focus on tire modeling, vehicle modeling and lap time simulation. Tire modeling is based on Nondimensional Tire Theory, which is extended to provide a flexible model structure that allows arbitrary inputs to be included. For example, rim width is incorporated as a continuous variable in addition to vertical load, inclination angle and inflation pressure. Model order is determined statistically and only significant effects are included. The fitting process is shown to provide satisfactory fits while fit parameters clearly demonstrate characteristic behavior of the tire. To represent the behavior of a complete vehicle, a Nondimensional Tire Model is used, along with a three degree of freedom vehicle model, to create Milliken Moment Diagrams (MMD) at different speeds, longitudinal accelerations, and under various yaw rate conditions. In addition to the normal utility of MMDs for understanding vehicle performance, they are used to develop Limit Acceleration Surfaces that represent the longitudinal, lateral and yaw acceleration limits of the vehicle. Quasi-transient lap time simulation is developed that simulates the performance of a vehicle on a predetermined path based on the Limit Acceleration Surfaces described above. The method improves on the quasi-static simulation method by representing yaw dynamics and indicating the vehicle’s stability and controllability over the lap. These improvements are accomplished while maintaining the simplicity and computational efficiency of the two degree of freedom method. ©Copyright by Chris Patton February 7, 2013 All Rights Reserved Development of Vehicle Dynamics Tools for Motorsports by Chris Patton A DISSERTATION submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Presented February 7, 2013 Commencement June 2013 Doctor of Philosophy dissertation of Chris Patton presented on February 7, 2013. APPROVED: ______________________________________________________________________________ Major Professor, representing Mechanical Engineering ______________________________________________________________________________ Head of the School of Mechanical, Industrial and Manufacturing Engineering ______________________________________________________________________________ Dean of the Graduate School I understand that my dissertation will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my dissertation to any reader upon request. ______________________________________________________________________________ Chris Patton, Author ACKNOWLEDGEMENTS This dissertation represents the final stage of my formal education and in the nearly quarter century that I have been a student, there have been countless teachers, instructors, and professors that have guided me to this point. This is in addition to my friends and family that have supported, encouraged, and often worked alongside me. To you all, I offer my thanks. The following are several acknowledgements directly related to my dissertation. I would like to thank my adviser Dr. Robert Paasch for providing personal guidance as well as inspiration and guidance for the Global Formula Racing Team (GFR). This team has provided an amazing environment of collaborative education, which would not have come to be without Dr. Paasch’s guidance and support. Thank you to all the members of GFR that have developed the team to its current state, including members of the Beaver Racing Team at Oregon State University and the BA Racing Team at the Duale Hochschule Baden-Württemberg in Ravensburg Germany, that laid the groundwork that would become GFR. Through the development of our vehicles, countless team members have contributed to my understanding of vehicle dynamics. Without this extraordinary group of people that I have been privileged to work with, creating this dissertation would not have been possible. I am grateful to the many people and institutions that have made Formula SAE and Formula Student possible, including the volunteers and organizers that work tirelessly to provide students with the venues to practice and demonstrate the fruits of our education. In particular, I would like to thank the design judges who shared their knowledge and experience, and consistently challenged me to expand my own. These events would not be possible without the support of SAE, VDI and IMechE. I would like to acknowledge the Formula SAE Tire Testing Consortium and Calspan for providing access to the tire data used in this dissertation. Finally, I would like to thank my family. While I attribute much of my educational achievement to the happy, loving and encouraging environment provided by my family, I would like thank them in particular for managing to bring up and engineer that is only mildly socially awkward. TABLE OF CONTENTS Page 1. Dissertation Introduction ......................................................................................................... 2 2. Tire Modeling: A Fitting Process for a Non-Dimensional Tire Model with Arbitrary Inputs .... 4 2.1. Introduction ..................................................................................................................... 5 2.2. Background ...................................................................................................................... 5 2.2.1. Pacejka – Delft Tire .................................................................................................. 5 2.2.2. Nondimensional Tire Theory .................................................................................... 6 2.3. Pure Slip Model Structure ................................................................................................ 8 2.3.1. Nondimensional Transform ..................................................................................... 8 2.3.2. Simplified Magic Formula ...................................................................................... 10 2.3.3. Model Parameter Response Surfaces .................................................................... 11 2.4. Fitting Pure Slip Model Parameters ............................................................................... 12 2.4.1. Description of Test Data......................................................................................... 12 2.4.2. Identifying Normalization and Shift Parameters ................................................... 12 2.4.3. Identifying Magic Formula Parameters.................................................................. 15 2.4.4. Fitting Response Surfaces ...................................................................................... 16 2.4.5. Determining Model Order ..................................................................................... 18 2.5. Combined Slip Model ..................................................................................................... 20 2.5.1. Interaction Response Surface Definition ............................................................... 20 2.5.2. Fitting Interaction Response Surfaces ................................................................... 22 2.6. Error Evaluation ............................................................................................................. 26 2.6.1. Pure Slip ................................................................................................................. 27 2.6.2. Combined Slip ........................................................................................................ 29 2.6.3. Rim Width .............................................................................................................. 29 2.7. Future Work ................................................................................................................... 31 TABLE OF CONTENTS (Continued) Page 2.8. Conclusion ...................................................................................................................... 31 3. Vehicle Modeling: Creating Milliken Moment Diagrams under general Yaw and Longitudinal Acceleration Conditions ................................................................................................................. 32 3.1. Introduction ................................................................................................................... 33 3.2. Background .................................................................................................................... 34 3.2.1. - Diagrams ................................................................................................... 34 3.2.2. - Diagrams .................................................................................................... 38 3.2.3. Applications ............................................................................................................ 40 3.3. Creating Acceleration Moment Diagrams ....................................................................
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