Abstract A dynamic model of the planetary roller screw mechanism (PRSM) is proposed by combining Lagrange's method and Newton's second law, which can be used to determine the motion and internal forces of the PRSM efficiently. The generalized forces corresponding to the rotational angles of the screw and carrier are given with considering the forces acting on the screw, roller, nut, carrier and ring gear. Using Lagrange's method, the rotational acceleration of the carrier and the driven torque of the screw are obtained. The motion equations which include the internal forces are then derived by using Newton's second law. Furthermore, a promising algorithm of solving the derived equations is illustrated. The experiment is carried out to testify the validity of the proposed model. The simulation results obtained from the proposed model and those from the previous model are also compared. Although the simulation results are nearly the same, the CPU time of the proposed model is only about 4% of that of the previous model. Finally, the effect of structural parameters on the dynamic behaviors of the PRSM is discussed.

中文翻译：

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一种有效的行星滚柱丝杠机构动力学分析方法

摘要 结合拉格朗日方法和牛顿第二定律，提出了行星滚柱丝杠机构（PRSM）的动力学模型，可以有效地确定PRSM的运动和内力。考虑了作用在丝杠、滚子、螺母、支架和齿圈上的力，给出了对应于丝杠和支架旋转角的广义力。使用拉格朗日方法，获得了载体的旋转加速度和螺杆的驱动扭矩。然后使用牛顿第二定律推导出包含内力的运动方程。此外，还说明了求解导出方程的有前途的算法。进行实验以验证所提出模型的有效性。还比较了从所提出的模型和先前模型获得的仿真结果。尽管仿真结果几乎相同，但所提出模型的 CPU 时间仅为之前模型的 4% 左右。最后，讨论了结构参数对 PRSM 动态行为的影响。