Hopf bifurcation character of an interactive vehicle–road shimmy system under bisectional road conditions

Abstract

The adhesion coefficients of a bisectional road have significant coupled influences on the shimmy characteristics of the front wheels of a vehicle. A four-degree-of-freedom model for a representative sport utility vehicle was established. This model considered the adhesion coefficients of a bisectional road and the friction of the steering system of the suspension. The existence and stability of the system’s limit cycles were qualitatively determined using the Hopf bifurcation theorem and the centre manifold theory based on the model. The influences of the adhesion coefficients on the Hopf bifurcation characteristics of the system were calculated using a numerical method. The results showed that the road adhesion coefficient μ1 of the left front wheel and the road coefficient μ2 of the right front wheel significantly affected the vehicle shimmy and coupling relationship when different. Keeping μ1 at a certain value, the swing angles and the angular velocities of the two front wheels consistently decreased when μ2 decreased. The phenomenon repeatedly occurred when the difference Δ μ between the adhesion coefficients increased. Moreover, the discrepancy between the amplitude of the left front wheel and the amplitude of the right front wheel is much more apparent when both the adhesion coefficients are larger. Good agreement between the shimmy characteristics of the two wheels was also found when comparing the results using the centre manifold reduced-dimensions method with the numerical method. Furthermore, a higher reduced order caused the reduced system to be closer to the original system.

Active Shimmy Control Method for Driverless Electric Vehicle Considering Unknown Sensor Measurement Error via Sampled-Data Output Feedback

“…Bian et al built a 5-DOF model to analyze the suspension damping characteristics influence on the wheel shimmy of four wheel-independent-drive electric vehicles [13]. Wei et al analyzed shimmy bifurcation characteristics based on a 4-DOF model in [14] and established a 7-DOF dynamic model of whole vehicle self-excited vibration induced by the shimmy of front wheels which considering the nonlinear factor of tire lateral force and dry friction force in suspension and steering system in [15]. By the way, some researchers also studied the shimmy phenomenon of the aircraft land wheel widely [16,17].…”

Numerical continuation applied to internal combustion engine models

“…14 The methods are also shown to be useful in the analysis of wheels, tyres and suspension dynamics, with the damping force shown to dramatically affect the behaviour of the suspension 15 and the slip angle and vehicle speed shown to play major roles in the development of vibration. 14 Shimmy behaviour has also been studied, with limit cycles being observed under bisectional road conditions 16 and bistable parameter ranges were found for towed wheels. 17 Furthermore, the approach was used in determining the stability of permanent synchronous motors 18 and regions of dynamic behaviour in braking dynamics.…”