摘要
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。
Considering backlash of gcar pairs and radial clearance of bearings, time-varying mesh stiffness and time-varying bearing stiffness were derived. Mass, stiffness and damping matrices of a system were obtained by using the finite element method, then they are assembled with the integrating method. Nonlinear dynamic model of a geared flexible rotor-bedring system was established under complex loads. Using the modified FPA method to determine the solution period, using Runge-Kutta method and Newton-Raphson method to solve nonlinear dynamic equations, then the largest Lyapunov index was obtained to determine the dynamical behavior of the system. The dynamic equations were simalated numerically and the effects of rotational speed, backlash, shaft stiffness, bearing radial clearance on the nonlinear dynamic behavior of the system were studied. The results showed that tooth off and bilateral impact phenomenon occur with increase in backlash, and the quasi-periodic motion changes into a chaotic motion around the critical speed; with decrease in shaft stiffness, the bending-torsion coupled vibration critical speed decreases, the gear teeth off and the vibration amplitude also decrease ; when the radial clearance increases, the effects of nonlinear vibration of bearing on the system increase and the excitation amplitude of bearing varying stiffness increases.
出处
《振动与冲击》
EI
CSCD
北大核心
2013年第8期171-178,198,共9页
Journal of Vibration and Shock
基金
中央高校基本科研业务费专项资金资助
国家自然科学基金(50905061)
中国博士后科学基金资助(2011M500554)
