基于啮合相位分析的盾构机减速器多级行星齿轮传动动力学特性

Dynamic Characteristics of Multi-stage Planetary Gears of Shield Tunnelling Machine Based on Planet Mesh Phasing Analysis

基于齿轮啮合理论和Lagrange方程,运用集中参数法建立多级行星齿轮系统的扭转动力学模型。采用梯形波表示啮合刚度的时变特性,分析行星齿轮啮合过程中的相位关系,计算盾构机减速器三级行星齿轮不同啮合位置的扭转振动结构频率。针对齿轮啮合误差特点,采用轴频和齿频叠加的谐波函数表示行星齿轮传动误差,考虑受啮合相位关系影响的行星齿轮系统时变刚度,系统分析多级行星齿轮传动的内部激励特征。基于某施工标段的统计负载,考虑内外激励,求解三级行星齿轮系统的动态响应,并对齿轮振动频谱特性进行分析。通过计算减速器不同转速下的系统构件动态响应,研究齿轮振动与盾构机减速器输入转速的关系,为盾构机驱动系统运行工况的选择提供了依据。

Based on gearing theory and Lagrange equation,the torsional dynamic model for multi-stages planetary gears train is developed by lumped-parameter method.Trapezoid waves are used to express the time-varying mesh stiffness,and the mesh phasing relations among planetary gears are analyzed.For the 3-stages planetary gears of shield tunnelling machine,the torsional vibration frequencies are calculated at the different mesh position of sun and planet gears.According to the characteristics of the gears mesh errors,the harmonic waves composited with shaft frequencies and mesh frequencies are presented to describe the transmission errors of the planetary gears.Considering the time-varying mesh stiffness with different mesh phases of planet gears,the inner excitations of 3-stages planetary gears are analyzed systematically.The dynamic responses of the 3-stages planetary gears are simulated under the inner and external excitation got from a statistical load,and the spectrum properties of gears vibration are also analyzed.The dynamic response of system components are calculated under different speeds for the reducer,and the relationship between gears vibration and the rotational speed of the reducer is studied,which provides the base for choosing the suitable operating condition of driving system of the shield tunnelling machine.