斜齿行星齿轮传动系统振动模式与动载特性

Vibration mode and dynamical characteristics of helical planetary gear train

斜齿行星传动在高速重载场合中应用越来越广泛,其振动模式和动载特性研究对减振降噪设计具有重要意义.针对斜齿行星齿轮传动系统,建立了随动坐标系,推导了含陀螺效应的多自由度间隙非线性动力学方程,求解了系统的固有特性.结果表明:斜齿行星齿轮系统存在3种典型振动模式,即轴向平移-扭转耦合振动模式(重根数r=1),径向平移振动模式(重根数r=2)和行星轮振动模式(重根数r=N-3,N>3);综合考虑啮合刚度、齿侧间隙、综合误差和外载荷等激励作用,研究了啮合相位差和激励方式对动载系数的影响规律,结果表明计入啮合相位差时动载系数有所增大,当刚度波动系数ζ=1.723时,系统分岔为2周期次谐响应,随着激励参数的变化,内啮合较外啮合更快的进入混沌状态.

Helical planetary gear transmission was applied more extensively in highspeed and heavy load situations,as the vibration mode and dynamic characteristic had significant influence on vibration and noise reduction.Targeting the helical planetary gear transmission system,co-moving coordinate system was conducted,the multi-degree of freedom nonlinear dynamical equations including gyroscopic effect and backlash was derived,and the natural characteristic of the system was solved.The results show that helical planetary gear train has three typical vibration modes：axial translational-rotational coupled vibration mode（multiplicity r=1）,translational vibration mode（multiplicity r=2）and planet vibration mode（multiplicity r=N-3,N〉3）;in consideration of mesh stiffness,backlash,general errors and external load,influence laws of mesh phase difference and excitation ways to dynamical coefficient have been studied,showing that mesh phase difference makes the dynamical coefficient increase;when stiffness fluctuation coefficientζ=1.723,the system is bifurcated into 2-period sub-harmonic response,with the changes of excitation parameters,internal engagement turning into the chaotic state is earlier than external engagement.