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

Xin Li,Geng Liu,Chunyu Song,Shangjun Ma,Qi Wan,Xiaojun Fu

doi:10.1051/jnwpu/20203851001

Abstract

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.

Highlights

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 results show that the forces acting on the first⁃stage PRSM are larger than that acting on the second⁃stage PRSM, 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

Summary

Introduction

示。图 2 中,局部坐标系 oPk⁃xPkyPkzPk 的原点 oPk 位于第 k 级丝杠的轴承支撑处,zPk 轴与丝杠轴线重合, xPk 轴与任一滚柱轴线相交且随着第 k 级保持架旋转,θPk 为第 k 级保持架的转角,MSk 和 FNk 分别为第 k 级丝杠的驱动力矩和螺母负载;fSk 为第 k 级丝杠内花键所受到的摩擦力;MNk 为第k级螺母在与第k + 1 级丝杠连接处所受到的摩擦力矩。 MNk = μNS | FNk | rNSk sign( θ S ) 式中: sign( θ S) 的定义与(6) 式相同。在图 2 中, θ Sk ,θ Pk 和 θ Rk 分别为第 k 级丝杠、保持架和滚柱的转速;vSk,vNk 和 vRk 分别为第 k 级丝杠、螺母和滚柱的移动速度。 Éê - rSRk( θ S - θ Pk ) sinφSRk - nSk θ Pk rRSk sinφRSk ùú vP RSk

Results

Conclusion