多级行星齿轮系统耦合动力学分析与试验研究

Multi-stage Planetary Gears Dynamic Coupling Analysis and Experimental Investigation

基于齿轮啮合理论和Lagrange方程,考虑各级齿圈扭转支撑刚度,提出运用集中参数法建立多级行星齿轮—箱体耦合扭转动力学模型。在分析多级行星齿轮啮合相位关系的基础上,确定各齿轮对时变啮合刚度,并运用有限元法获取各齿圈扭转支撑刚度。行星齿轮传动误差表示为轴频和齿频叠加的谐波函数,分析多级行星齿轮传动的主要激励特征。针对盾构机三级行星减速器某施工地段的运行条件,求解行星齿轮系统的动态响应,并分析其时频特性。采用背靠背能量回馈试验台架测试方案,测量盾构机行星减速器的振动加速度,采用数值积分计算振动速度和位移,并分析其振动特性。研究表明盾构机行星减速器振动试验数据与计算结果具有良好的一致性,验证多级行星齿轮系统耦合动力学模型的准确性。

Based on gearing theory and Lagrange equation, considering the torsional support stiffnesses of each ring gears, the coupling torsional dynamic model for multi-stages planetary gears train （PGT）-housing is developed by lumped-parameter method. The mesh stiffnesses are defined based on analysis of mesh phasing relations among planetary gears, and then the torsional support stiffnesses are obtained by FE method. The harmonic waves composite with shaft frequencies and mesh frequencies are presented to describe the transmission errors of the planetary gears, and the main inner excitations of 3-stages planetary gears are analyzed. According to the operating condition for 3-stages planetary gearbox of shield machine less than one working district, the dynamic responses of the planetary gears are simulated, and its time-frequency properties are analyzed. The acceleration data retested by using the scheme of back-to-back power circulation set-up, which lead the vibration displacements and velocities are calculated by numerical integral method, and the vibration properties are also analyzed. Research indicated that the calculation agreed with the test data well, which validated the accuracy of coupling dynamic model for multi-stages planetary gears.