Bifurcation analysis of wheel shimmy with non-smooth effects and time delay in the tyre–ground contact
Bifurcation analysis of wheel shimmy with non-smooth effects and time delay in the tyre–ground contact
复制标题
具有非光滑效应和轮胎与地面接触时滞的车轮摆振分叉分析
作者：
S. Beregi;D. Takács;G. Stépán
本文用刷式轮胎模型分析了拖轮的非线性动力学。同时考虑了轮胎与地面接触的时滞和由接触摩擦引起的系统的非光滑性。首先，对无限维系统进行中心流形约化，将控制方程转化为包含线性和分段光滑二阶项的规范形式。然后，这个规范形式被用来建立系统的非双曲平衡点的稳定性，并给出在线性稳定边界出现的极限环的估计。通过这种方式，证明了非光滑延迟系统中的亚临界Hopf分岔如何产生标准轮胎模型无法检测到的非线性参数范围。
The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre–ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, the centre manifold reduction is performed on the infinite-dimensional system transforming the governing equations into a normal form containing linear and piecewise-smooth second-order terms. Then, this normal form is used to establish the stability of the non-hyperbolic equilibria of the system and to give an estimation of the limit cycles emerging at the linear stability boundary. This way, it is demonstrated how subcritical Hopf bifurcations in the non-smooth delayed system generate bistable parameter ranges, which are left undetected by standard tyre models.