时变位姿下行星齿轮传动系统动应力计算模型及其参数影响研究

Dynamic Stress Calculation Model of Planetary Gear Transmission System under Time-varying Posture and its Parameter Influence Research

考虑行星轮系内部非惯性和机体时变位姿外部非惯性的综合影响,推导了任意时变位姿下带有机匣的行星轮系构件运动方程,计入时变啮合刚度、啮合误差、侧隙和啮入冲击,建立了时变位姿下行星齿轮传动系统级动力学模型,并采用精细积分时程法(Precision integration method,PIM)求解得到了动态啮合力序列。根据齿间载荷分配关系进一步得到单齿啮合力序列。最后结合修正Heywood公式与Hertz公式构建了时变位姿下行星齿轮传动系统齿根弯曲动应力和接触动应力计算模型,并研究了机体平飞、滚转和筋斗位姿参数对接触动应力、弯曲动应力的影响规律。结果表明:不同时变位姿参数对弯曲、接触动应力影响显著,且对不同齿轮副影响不同,即加剧了齿轮副间承载不均;筋斗运动角速度对动应力影响比平飞加速度、滚转角速度以及筋斗回转半径对其影响复杂;机匣对动应力影响随加速度增大而增加。研究成果为时变位姿下行星齿轮传动动应力计算与高可靠性设计提供了理论依据。

Considering the comprehensive influence of the internal non-inertia of the planetary gear train and the external non-inertial of the body’s time-varying posture,the motion equations of the planetary gear train components with casing in any time-varying posture of the body are derived.Taking into account the time-varying meshing stiffness,meshing error,clearance and meshing impact,the planetary gear transmission system-level dynamics model under time-varying posture is established,and the dynamic meshing force sequence is obtained by the precision integration method(PIM).According to the load distribution relationship between teeth,and the single-tooth meshing force sequence is further obtained.Finally,combining the modified Heywood formula and Hertz formula,a calculation model for the tooth root bending dynamic stress and contact dynamic stress of the planetary gear transmission system with time-varying posture is constructed,and the influence laws of the body’s level flight,roll and somersault pose parameters on contact dynamic stress and bending dynamic stress are studied.The results indicate that:different time-varying pose parameters have a significant effect on dynamic bending and contact stress,and have different effects on different gear pairs,that is,aggravating the uneven load between gear pairs.The angular velocity of somersault motion has a more complicated effect on dynamic stress than that of horizontal acceleration,roll angular velocity and gyration radius.The effect of casing on dynamic stress increases with the acceleration.The research provides a theoretical basis for dynamic stress calculation and high-reliability design of planetary gears under time-varying postures.