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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。
The physical and geometrical parameters are established as random variables, and the dynamic equations of nonlinear vibration of the gear-rotor system with gear backlash, bearing clearance, time-varying stiffness, friction between teeth and static transmission error are considered. The Newmark-β step-by-step integration method is used to convert the nonlinear dynamic equation of the system with random parameters to the quasi-static control equation of random parameters. By using the algebraic synthesis method and the moment method for solving the numerical characteristics of random variable functions, the system Calculation formula of mean and mean square error of dynamic displacement response. The results show that the randomness of gear modulus has a great influence on the randomness of the system response. The influence of friction coefficient on the system amplitude can not be neglected. Especially when the gear gap is larger than 105m, the amplitude of the system increases.