Kinematic modeling of a planetary roller screw mechanism considering runout errors and elastic deformation

With the increasing applications of the planetary roller screw mechanism (PRSM) in mechanical systems particularly machine tools, a comprehensive mathematical model is required to define the kinematic characteristics and relations of the PRSM, such that its performances can be predicted for reliability analysis and design of machine tools. In this paper, the influences of machining and assembly errors on the motion characteristics of the PRSM are analyzed, and the kinematic model of the PRSM is established considering runout errors and elastic deformation. The planetary roller screw mechanism can be considered as a spring-mass system for analysis of the elastic deformation of the ball screw's thread under inertial force. For the spring-mass system, adjacency matrix is introduced to define the relationships between the elastic displacements of the joints and the deformations of the elements. Then, by considering the balance of force and the coordination of deformation, the nonlinear motion model of the double-nut roller screw is established. The effectiveness of the proposed model is verified by comparing the analytical results with the experimental data.