考虑多间隙的齿轮柔性转子耦合系统非线性动力学分析

考虑齿侧间隙、轴承径向间隙，推导时变啮合刚度和时变轴承刚度，使用有限元法建立质量、刚度、阻尼矩阵并使用整体法组装，建立能够适用于复杂载荷的齿轮滚动轴承柔性转子系统非线性动力学模型。使用FPA修正法确定求解周期，采用Runge-Kutta法、Newton-Raphson法对非线性动力学方程组求解，求解最大Lyapunov指数判断系统的动力学行为。对动力学方程进行数值仿真，研究转速、齿侧间隙、转轴刚度、轴承径向间隙等参数对非线性动力学行为的影响。研究结果表明，随着齿侧间隙增大，齿轮系统会出现脱齿和挤齿现象，临界转速附近由拟周期运动进入混沌运动。随着转轴刚度降低，弯扭耦合振动临界转速减小，脱齿、挤齿和冲击现象逐渐减轻。随着径向间隙增大，轴承的非线性振动对系统的影响逐渐增大，轴承变刚度激励的幅值增大。

Nonlinear Dynamics Analysis of Gear Flexible Rotor System Considering Multi-Clearances

Considering backlash and radial clearance of bearing, time-varying mesh stiffness and time-varying bearing stiffness are conducted. Mass, stiffness and damping matrix are obtained by using finite element method, then they are assembled by the integrated method. Nonlinear dynamic model of gear bearing flexible rotor system is established which can be applied to complex load. Using modified FPA method to determine the period of solution, using the Runge-Kutta method, Newton-Raphson method for solving nonlinear dynamic equations, and the largest Lyapunov index to determine the dynamical behavior of the system. Nµmerical simulations of the dynamic equations and the affection of the rotational speed, backlash, shaft stiffness, the bearing radial clearance to the nonlinear dynamic behavior are studied. The results shows that tooth off, bilateral impact phenomenon are occurred as the increase of backlash, and quasi-periodic motion changes into chaotic motion around the coupling critical speed of bending and torsion. With the decrease of shaft stiffness, bending-torsional vibration critical speed decreases, the gear teeth off state and amplitude is also changed. As the radial clearance increases, the affections of nonlinear dynamics of bearing to system increase and amplitude of bearing increases.