汽车盘式制动系统的稳定性分析

Stability Analysis of Automotive Disc Brake System

针对汽车盘式制动器制动时摩擦引起的低频振动问题,建立了Sprag-Slip非线性数学模型。以摩擦系数作为分岔参数,运用常微分方程稳定性理论分析了系统的稳定性,并用数值分析方法得出系统在平衡点发生Hopf分岔的结论。进一步地,取其他参数组合计算得到了系统稳定性区域图。结果表明:摩擦系数过大,系统失稳并发生Hopf分岔,从而引起系统自激振动;摩擦系数及钳盘夹角相比于质量、刚度以及阻尼等系统参数对制动系统稳定性影响更显著。

For the problem of low frequency vibration in the disc brake caused by friction during the automotive braking,a Sprag-Slip nonlinear mathematical model was established.With the friction coeffi?cient as the bifurcation parameter,the stability of the system was studied by the stability theory of ordinary differential equations.It is concluded that the system Hopf bifurcation occurs at the equilibriumpoint by the numerical analysis method.Furthermore,the other parameters of the system were calculat?ed and the stability range of the system was obtained.The analysis results show that when the friction coefficient becomes too large,the system loses its stability and Hopf bifurcation occurs which leads to self-excited vibration in this system;compared with other parameters such as mass,stiffness and damping,the friction coefficient and caliper angle have a significant effect on the stability of the brake system.