直齿行星传动罚函数修形优化及动力学分析

Penalty function modification optimization and dynamics analysis of spur planetary gear transmission

针对直齿行星传动齿轮修形问题,提出了减小齿轮副承载传动误差波动幅度的直齿行星轮系罚函数修形优化方法.研究了内外啮合直齿轮承载接触分析(LTCA)方法,并与Romax软件计算结果进行对比验证;基于承载接触分析方法计算承载传动误差,提出了直齿行星轮系内外啮合齿轮副的罚函数修形优化方法,进行了行星轮系内外啮合齿轮副修形优化设计.为了验证修形减振效果,将承载传动误差转换为啮合刚度,建立了直齿行星传动系统动力学模型,分析了内外修形优化对轴承支撑处振动加速度的影响.动力学分析表明:外啮合优化修形可以显著减小太阳轮支撑处振动加速度,内啮合修形优化可以减小内齿圈支撑处振动加速度,而且外啮合修形减振效果更好.

To solve tooth modification problem of spur planetary gear trains,a penalty function modification optimization method was proposed to reduce the fluctuation amplitude of the loaded transmission error of gear pair.The loaded tooth contact analysis(LTCA)method of internal and external spur gear pair was studied,and the method was verified by means of comparing with the calculation results from Romax software.Based on the LTCA method,the loaded transmission error was calculated,and the penalty function modification optimization method of internal and external spur gear pair was proposed,and the corresponding modification optimization designs were carried out.To verify the vibration absorption effect of the optimized modification spur planetary gear system,the loaded transmission error was shifted to meshing stiffness,and dynamics model was established to analyze the influence of internal and external optimized modification on vibration acceleration of bearing support positions.Dynamics analysis results show that the optimized modification of external spur gear pair can reduce the vibration acceleration on the support positions of the sun gear significantly,and the optimized modification of internal spur gear pair can effectively reduce the maximum vibration acceleration on the support positions of the ring gear.From the view of vibration absorption,the modification of external spur gear pair is better than that of internal gear pair.