A nonlinear six degrees of freedom dynamic model of planetary roller screw mechanism

A nonlinear six degrees of freedom (DOFs) dynamic model to determine the motion and internal forces acting on the moving parts of the planetary roller screw mechanism (PRSM) is proposed in this paper. A load distribution coefficient is assumed and introduced to describe the load distribution among threads of the screw, roller and nut. The friction forces at the screw-roller, nut-roller and ring gear-carrier interfaces are calculated by using the Coulomb friction, rolling contact and Couette flow principles, respectively. Because the friction and contact forces acting on the screw, roller, nut and carrier constitute a spatial force system, the equations of motion for the PRSM, which are derived by using Newton's second law, relate the forces to the six DOFs of those parts. The transient and steady-state behaviors of the PRSM under a heavy or light external load and the sinusoid motion of the mechanism are simulated and discussed. The results show that the load conditions have great influence on the motion and internal forces of the PRSM.