多级行星滚柱丝杠刚体动力学建模与分析

Rigid⁃Body Dynamic Analysis of Multi⁃Stage Planetary Roller Screw Mechanism

基于多级行星滚柱丝杠结构特点,分析了各级行星滚柱丝杠之间的运动和受力关系。采用牛顿第二定律,在不考虑加工与装配误差和零件变形情况下,推导了多级行星滚柱丝杠运动方程,并提出了求解方法。实现了计入使用工况的多级行星滚柱丝杠运动与受力计算,分析了各级行星滚柱丝杠连接处摩擦因数对该机构动力学特性的影响规律。结果表明,虽然第一级行星滚柱丝杠的丝杠直径较小,但其零件受力的初始值与稳态值均大于第二级行星滚柱丝杠;当丝杠螺旋升角较小时,多级行星滚柱丝杠的效率随着各级螺母和丝杠间摩擦因数的改变而明显变化,但受各级丝杠和丝杠间摩擦因数的影响非常小。

Based on the structural characteristics of the multi⁃stage Planetary Roller Screw Mechanism(PRSM),the motion and force among the different stages are analyzed.In terms of the Newton′s second law,the rigid⁃body motion equations of the multi⁃stage PRSM without considering the manufacturing and assembly errors are derived.Then,the method for solving the motion equations is given.The forces acting on the parts in the multi⁃stage PRSM and the motion of the mechanism can be obtained from the present rigid⁃body dynamic model.The influence of the friction coefficients among the different stages on the dynamic characteristics of the multi⁃stage PRSM is discussed.The results show that the forces acting on the first⁃stage PRSM are larger than that acting on the second⁃stage PRSM,although the nominal radius of the screw in the first⁃stage PRSM is smaller.The friction coefficient between the nut and the screw in the different stages has the great influence on the efficiency of multi⁃stages PRSM with small helix angles,while that among the screws in the different stages has the slight effect on the efficiency.