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California State University, Northridge CALIFORNIA STATE UNIVERSITY, NORTHRIDGE DESIGN AND ANALYSIS OF FORMULA SAE CAR SUSPENSION MEMBERS A thesis submitted in partial fulfillment of the requirements For the degree of Master of Science in Mechanical Engineering By Evan Drew Flickinger May 2014 The thesis of Evan Drew Flickinger is approved: Dr. Robert Ryan Date Dr. Nhut Ho Date Dr. Stewart Prince, Chair Date California State University, Northridge ii DEDICATION I dedicate this thesis in loving memory of my grandfather Russell H. Hopps (November 15th, 1928 – July 19th, 2012). Mr. Hopps graduated with high honors from Illinois in 1956. He joined Lockheed- California Company in 1967 and held numerous positions with the company before being named to vice president and general manager of engineering. He was responsible for all engineering at Lockheed and supervised 3500 engineers and scientists. Mr. Hopps was directly responsible for the preliminary design of six aircraft that have gone into production and for the incorporation of advanced systems in aircraft. He was an advisor for aircraft design and aeronautics to NASA, a receipt of the UIUC Aeronautical and Astronautical Engineering Distinguished Alumnus Award, and of the San Fernando Valley Engineers Council Merit Award. iii TABLE OF CONTENTS SIGNATURE PAGE .......................................................................................................... ii DEDICATION ................................................................................................................... iii LIST OF TABLES ............................................................................................................. vi LIST OF FIGURES ......................................................................................................... viii GLOSSARY ...................................................................................................................... xi ABSTRACT ..................................................................................................................... xiv 1. CHAPTER 1 – INTRODUCTION .............................................................................. 1 1.1 Needs Statement and Problem Overview .................................................................. 1 1.2 Hypothesis and Concept for Solution........................................................................ 2 1.3 Research Objectives .................................................................................................. 2 1.4 Scope of Project ........................................................................................................ 4 2. CHAPTER 2 – PRELIMINARY CALCULATIONS ................................................. 5 2.1 Input Forces / Road Load Scenarios ......................................................................... 5 2.2 Linear Acceleration ................................................................................................... 9 2.4 Steady State Cornering ............................................................................................ 13 2.5 Linear Acceleration with Cornering ........................................................................ 15 2.6 Braking with Cornering ........................................................................................... 21 2.7 5g Bump .................................................................................................................. 22 3. CHAPTER 3 – HAND CALCULATIONS ............................................................... 23 3.1 Outline of Method ................................................................................................... 23 3.2 Assumptions and Key Methodology ....................................................................... 25 3.3 Configuration of Equations ..................................................................................... 27 3.4 Coordinate Vectors .................................................................................................. 28 3.5 Summation of Forces .............................................................................................. 30 iv 3.6 Summation of Moments .......................................................................................... 32 3.7 Formation of Matrices ............................................................................................. 37 3.8 Solving of Matrices ................................................................................................. 41 3.9 Suspension Geometry Impact.................................................................................. 43 3.10 Visual Basic Iteration Method............................................................................... 46 3.11 Member Forces versus Vertical Acceleration ....................................................... 46 3.12 Member forces versus Scrub Radius ..................................................................... 48 3.13 Member forces versus Kingpin Inclination Angle ................................................ 49 3.14 Member forces versus Caster Angle ..................................................................... 51 3.15 Member Forces versus Kingpin Inclination and Caster Angles ............................ 54 4. CHAPTER 4 – MEMBER SPECIFICATIONS ........................................................ 56 4.1 Connection Type ..................................................................................................... 56 4.2 Boundary Conditions............................................................................................... 57 4.3 Material Properties and Geometry .......................................................................... 61 CHAPTER 5 – DESIGN OF THE SUSPENSION MEMBERS ...................................... 64 5.1 Design Criteria ........................................................................................................ 64 5.2 Resultant Forces ...................................................................................................... 66 5.3 Factor of Safety ....................................................................................................... 69 5.4 Design Process ........................................................................................................ 74 REFERENCES ................................................................................................................. 77 APPENDIX A-1................................................................................................................ 78 APPENDIX A-2................................................................................................................ 82 APPENDIX A-3................................................................................................................ 85 v LIST OF TABLES Table 2.1 – Typical FSAE vehicle parameters. .................................................................. 8 Table 2.2 – Component forces based on the linear acceleration loading scenario. .......... 10 Table 2.3 – Component forces based on the brake performance loading scenario. .......... 12 Table 2.4 – Component forces based on steady state right hand cornering at a value of constant 1.0g acceleration. .......................................................................... 15 Table 2.5 – Component forces based on right hand cornering with linear acceleration. .. 20 Table 2.6 – Component forces based on right hand cornering with braking. ................... 21 Table 2.7 – Component forces based on a 5g bump condition. ........................................ 22 Table 3.1 – Suspension points for the right front corner of the FSAE vehicle. ................ 28 Table 3.2 – Vector formation and calculations for each of the front suspension members. ..................................................................................................................... 29 Table 3.3 – Wheel center points for the right front corner of the FSAE vehicle. ............. 33 Table 3.4 – Moment arm for each of the suspension members, with respect to the center of the wheel. ................................................................................................ 34 Table 3.5 – Moment arm for center tire patch forces about the wheel center .................. 38 Table 3.6 – Determination of member forces in the suspension for the braking with right- hand cornering load case ............................................................................. 41 Table 4.1 – Inboard and outboard boundary conditions for the FSAE vehicle suspension members ...................................................................................................... 59 Table 4.2 – Member geometry for the tie rod and lower control arm .............................. 62 Table 4.3 – Member geometry for the push rod and upper control arm ........................... 62 Table 4.4 – Member material properties ........................................................................... 63 vi Table 5.1 – Critical loads (lbf) determined by Euler’s buckling ....................................... 65 Table 5.2 – Maximum allowable tensile force (pound force lbf) based on yield strength 66 Table 5.3 – Member resultant forces (pound force lbf) for braking performance ............ 67 Table 5.4 – Maximum resultant compression and tension forces ..................................... 67 Table 5.5 – Resultant forces for each suspension member for the first five plots. ........... 68 Table 5.6 – Comparison of results from
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