随机参数齿轮系统的非线性动力响应分析

建立了物理参数和几何参数均为随机变量，并考虑具有齿轮侧隙、轴承间隙、时变刚度、齿间摩擦力和静态传递误差的齿轮-转子系统非线性振动的动力学方程。利用Newmark-β逐步积分法将此随机参数时变刚度系统的非线性动力学方程转换为随机参数的拟静力学控制方程，利用求解随机变量函数数字特征的代数综合法和矩法，导出了系统动态位移响应的均值和均方差计算公式。算例结果表明：齿轮模数的随机性对系统响应的随机性影响较大，摩擦系数对系统振幅的影响不可忽视，特别当齿轮的间隙大于10?5m时，系统的振幅受其影响增大。关键词：随机参数；齿轮-转子系统；非线性动力学；Newmark-β法；时变刚度

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE OF GEAR-ROTOR WITH RANDOM PARAMETERS

The nonlinear dynamic model of gear-rotor with random physical and geometrical parameters was established,and many factors were considered,i.e.,the gear backlash,the bearing slackness,the time-varying stiffness,the friction between teeth and the static transmission error.In what follows,the nonlinear dynamic equations were transformed into quasi-static governing equations by using the method of Newmark-β step-by-step integration.The mean value and the variance of dynamic displacement response were obtained by exploiting both the algebra synthesis and moment methods which are used for solving the numerical characteristics of random variables.The numerical examples show that the analogical-digital randomness has a rather large effectiveness on the system response,and the impact of the friction coefficient on the vibration amplitude cannot be ignored,especially when the bearing slackness is larger than 10 5m.