Simulation On Linear Instability And Nonlinear Bifurcation Of Light Truck Shimmy

Light truck plays an irreplaceable role in the city,urban and rural logistics transportation as well as in the municipal works,and the research of the light truck has practical significance.In the early,light truck is dominated by functional requirements,the problem of shimmy is often neglected.But the problem of shimmy will affect many performance of light truck,such as ride,handling and safety.With the raising of the demand of users,logistics and emission regulations,the light truck can not meet this requirement any more.So it is necessary to study the shimmy of light truck.At present,the study on the shimmy is mainly concentrated on passenger car which is equipped with the independent suspension,rarely on light truck which is equipped with the dependent suspension.In the past,only some research of shimmy for low speed truck which is equipped with the dependent suspension could be referenced.But there are some limitations about the research results,due to limited by basic theory of dynamics and performance of computer calculation at that time.Therefore,it is necessary to study the modeling and simulation of shimmy for light truck,on the basis of the current basic theory of dynamics and performance of computer calculation.This paper is focused on the establishment of linear and nonlinear shimmy model of light truck which equipped with dependent suspension.Subsequently performed the simulation and linear instability analysis of the linear shimmy model of light truck,and performed simulation and bifurcation characteristic analysis of the nonlinear shimmy model of light truck.According to the simulation and linear instability analysis of linear shimmy model of light truck,the speed range of linear instability was identified and the factors that affect the linear instability of linear shimmy model of light truck were recognized and determined.Furthermore,the speed range of nonlinear bifurcation was found out by means of the simulation and bifurcation characteristic analysis of nonlinear shimmy model of light truck,and naturally the factors that affect the nonlinear bifurcation of nonlinear shimmy model of light truck were recognized and determined.The research results provide a reference for the prediction and control of the shimmy in the early design stage of light truck.The main contents are as follows(1)Establishment of linear and nonlinear shimmy model of light truckThrough the analysis of the gyroscopic effect of wheel and the shimmy characteristics of tire,the gyroscopic moment of wheel and the non conservative moment of tire were calculated.By simplifying the assumptions of light truck,the mechanical model of shimmy that contained the steering wheel and the front axle was established.In addition,the mathematical model of shimmy including the steering wheel and the front axle was built on account of the Lagrangian equation.To lay the foundation for the study of shimmy of light truck,based on linear and nonlinear model of tire cornering characteristics,the linear and nonlinear shimmy model of light truck in the form of the state-space equation were established and derived.(2)Simulation of linear instability and parameter influence of linear shimmy modelBased on the linear shimmy model of light truck in the form of the state-space equation,the simulation algorithm of linear shimmy model is proposed.By performed simulation algorithm,the speed range corresponding to the linear instability of the linear shimmy model of light truck under given parameter values was determined and the factors that affect the linear instability of linear shimmy model of light truck were analyzed.(3)Simulation of nonlinear bifurcation and parameter influence of nonlinear shimmy modelBased on the nonlinear shimmy model of light truck in the form of the state-space equation combined with Magic Formula of tire,the simulation algorithm of nonlinear shimmy model was proposed.Some fundamental concepts related to bifurcation and the basic theory of bifurcation analysis are introduced in detail such as the nonlinear dynamical systems with variable parameters and the theorem of Hopf bifurcation.To simplify the bifurcation analysis process,the nonlinear shimmy model was transformed into a superposition of the linear part and nonlinear part,and the simulation algorithm of bifurcation analysis for the nonlinear shimmy model is proposed.Based on the proposed simulation algorithm of bifurcation analysis,a parameter influence simulation scheme was conducted and the factors that affect the nonlinear bifurcation of nonlinear shimmy model of light truck were analysed.The results indicated that the shimmy of light truck happened linear unstable and nonlinear bifurcation on the condition of the given parameter values.It is helpful to eliminate the linear instability and nonlinear bifurcation of shimmy of light truck with the increase of the stiffness or damping of tie cross rod,stiffness or damping of tie straight rod,kingpin equivalent damping of left or right steering wheel,lateral stiffness of left or right tire or the reduction of the caster angle of left or right kingpin,vertical stiffness of left or right tire,tire drag of left or right tire.Likewise,it is helpful to eliminate the linear instability of shimmy of light truck on the condition that the cornering stiffness of left or right tire decreased.Additionally,it is helpful to eliminate the nonlinear bifurcation of shimmy of light truck when increase relaxation length of left or right tire or reduce the half length of the contact area of left or right tire.The change of the stiffness and damping of suspension has no influence on the linear instability and nonlinear bifurcation of shimmy of light truck.