Study on the Bifurcation Characteristics of Front Wheel Self-excited Shimmy

According to theories of nonlinear dynamics and ordinary differential equation, the bifurcation characteristics of front wheel self-excited shimmy of some motor vehicle with non-independent suspension are studied. The Magic Formula Tire Model is used to describe the tire nonlinear lateral characteristics. Various bifurcation diagrams indicating the relationship between angle amplitudes of right tire and vehicle speed are presented, Computer analyses were carried out to calculate the range of shimmy speed of the motor vehicle with MATLAB when Hopf bifurcation takes place. And the tire angle amplitudes of different parameters to the self-excited shimmy are analyzed. The numerical simulation results indicate that structural parameters of steering mechanism and tire parameters both have influence on the self-excited shimmy. Self-excited shimmy may disappear under the conditions of certain parameters combination. With the change of some parameters, the vehicle speed relating to tire maximum angle amplitude of the self-excited shimmy change correspondingly. Furthermore, steering stiffness, tire cornering stiffness and pneumatic trail show greater impact on the amplitude of vehicle front wheel self-excited shimmy.