| Steering wheel shimmy is a common phenomenon in our daily life. It seriously affects the handing stability, comfort and driving safety of vehicle. It is important to study the shimmy for significance and practical value.In this paper, a mathematical model of steering wheel shimmy with non-independent suspension is established. It contains two nonlinear factors. The Magic Formula Tire Model is used to describe the tire nonlinear lateral characteristics. And dynamic model of two-state clearance bring the nonlinear impact force. Firstly, according to theories of nonlinear dynamics bifurcation and ordinary differential equation, the bifurcation characteristics of steering wheel self-excited shimmy is studied. Numerical simulations are carried out with MATLAB software, and the influences of initial incentive and different parameters to the self-excited shimmy are analyzed. Then the process of the Lagrange equations method used to establish steering wheel shimmy model with clearance of steering knuckle kingpin is described in details. The influence of kingpin’s clearance is also analyzed. Finally, in a particular combination of parameters numerical simulation, the sensitivity to initial conditions, phase trajectory, Poincare section and power spectrum of shimmy system with clearance are studied.There is a summary of the work in the last part. It is considered that the steering wheel self-excited shimmy is the Hopf bifurcation. The system bifurcation point is the speed of shimmy vehicle. And the limit cycle formed after the Hopf bifurcation is corresponding to the phenomenon of steering wheel. The amplitude of shimmy system with kingpin clearance is increased observably, and the scope of shimmy speed enlarges. The existence of clearance may make self-excited shimmy change into non-periodic vibration. The conclusion is the nonlinear contact-impact force plays an important role on the vehicle shimmy to generate chaotic vibration phenomenon. |
PDF Full Text Request