基于打靶法的含摩擦齿轮系统运动稳定性分析

摘要

采用打靶法对含摩擦齿轮系统进行运动稳定性分析能够揭示摩擦对齿轮系统动力学行为所产生的复杂影响.建立了计及摩擦的单对齿轮非线性系统的非线性动力学模型,采用打靶法对其周期运动进行了求解,并应用Floquet乘子判断系统周期解的稳定性和分岔特点,得到了系统在不同的摩擦系数条件下周期运动的演变规律.相比于Runge-Kutta法,打靶法能得到更为全面的齿轮系统的不稳定和稳定的周期解.研究发现:摩擦能改变周期运动的性态,可在一定程度上提高系统周期运动的稳定性,同时会产生新的不稳定的周期运动,使得齿轮系统的动力学行为更为复杂.%The shooting algorithm can be used to analyze the complex influence of friction on the dynamical behavior of the gear system. The nonlinear dynamical model for the gear system with friction was established. The shooting algorithm was used to obtain its periodic motions, and Floquet multipliers were applied to estimating the stability and bifurcation property of the system periodic motions to find out the evolvement properties of the system under conditions of different frictional coefficients. The shooting algorithm can obtain more stable and unstable solutions than the Runge-Kutta method. It is found that friction can not only influence the properties of periodic motions and improve the stability of the gear system to some extent, but also create new unstable periodic motions.