双级时变圆柱齿轮系统的扭转振动特性研究

Research on Twist Vibration Characteristcs of a Two-staged Gear System with Time-variant Meshing Stiffness

在考虑二级齿轮传动系统时变啮合刚度的情况下,建立了其动力学方程,它是一个具有周期性时变系数的线性动力学系统。将时变啮合刚度用Fourier级数展开后,用AOM推导出了系统的近似解析解。在系统的响应中,含有基频、倍频和组合频率成分,因此,AOM比谐波平衡法具有更高的精度;与其他数值方法相比,具有更快的计算速度;当响应频率等于派生系统的固有频率时,将会出现主共振、超谐共振和组合共振现象;时变啮合刚度还导致了较大的动载荷;如果忽略时变啮合刚度三次以上谐波分量,在特定的系统参数下,系统的响应无明显变化。

With a two-stage gear system with time-variant meshing stiffness taken into consideration, the paper established its dynamic equation. The equation denotes a linear dynamic system with periodic time-variant coefficients. After the time-variant meshing stiffness is expanded to the Fourier series, the A-operator method（AOM） is used to derive the approximate analytic solution of the equation. According to the numeric solution components of fundamental frequency, double frequency and combined frequency coexist in the response of the linear dynamic system. Therefore the AOM has higher precision than the harmonic balance method and faster calculation speed than other numeric methods. When the response frequency is equal to the eigen-frequency of a derived system, harmonic resonance, super-harmonic resonance and combined harmonic resonance may occur. The time-variant meshing stiff- ness also causes large dynamic load in gear pairs. If its third and more than third harmonic components are neglected, the dynamic system＇s response may not change obviously in case of some particular parameters.