System Stability

Spring 2012 AuE-850 HOMEWORK #1 Manipulation of tire/vehicle data and Analysis of Basic directional stability (Steady-state & Transient-state behavior)

Submitted by: Arun Kumar Varadarajan

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TABLE OF CONTENTS Page Introduction……………………………………………………………………………………………………………………………. 2 Approach and Results……………..………………………………………………………………………………………………. 2 Problem 1-(a) Normal and longitudinal force…………………………………………………………….... 2 Problem 1-(b) Lateral force and Yaw moment………………..……………………………………………. 5 Problem 1-(c) Cornering Stiffness and aligning stiffness..…………………………………………….. 11 Problem 2-(A)-(a) Plot of gains for the steady state behavior……………………………………… 12 Problem 2-(A)-(b) Static Margin………………………………………………………………………………… 17 Problem 2-(B)-(a) Plot of stiffness, mass and damping coefficients….……………………..….. 18 Problem 2-(B)-(b) Locus of roots…………………………………………………………………………………. 21 Problem 2-(B)-(c) Trajectory plot………………………………………………………………………………… 22 Appendix-A Problem statement……………………………………………………………………………………………… 26 Appendix-B Matlab program…………………………..……………………………………………………………………… 28 Appendix-C Matlab output and other graphs…………………………………………………………………………. 39

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INTRODUCTION For the homework #1, the case of front wheel drive vehicle has been considered. The problem-1 discusses about determining the longitudinal and normal tire forces that are required to maintain steady speeds. Then the Lateral force F y and the Yaw moment Mz is determined using Magic Formula (Pajeka) for speeds 40-160Km/hr with intervals 40Km/hr. With same range of speed the cornering stiffness coefficient Calpha and aligning stiffness coefficient CMz for each of the car’s tire is discussed. The problem-2 discusses about the Steady state behavior and the Transient state behavior. The problem statement is given in Appendix-A. The Matlab program used to plot all the graphs is shown in Appendix-C. Approach and Results Given parameters: l2=1.596 Length of rear axle to C.G(m) l1=1.064 Length of front axle to...