Modelling of static contact with friction of threaded surfaces in a planetary roller screw mechanism

This paper investigates the nature of the contact with friction between the threaded surfaces in a planetary roller screw mechanism (PRSM). Contact analyses are applied to both the screw/roller interface and roller/nut interface. Prior work has neglected to take a fundamental approach towards understanding the contact characteristics of threaded surfaces under the combined action of normal pressure and tangential friction forces. Accordingly, in this paper, coordinate transformations and meshing equations of threaded surfaces are used to establish the contact locations of components. The relative velocities at the screw/roller and roller/nut interfaces are derived, and it is shown that the main contact mode of the screw/roller is sliding contact due to the relative velocity in the axial direction is not equal to zero, whereas rolling contact is the main contact mode at the roller/nut interface. Then, based on the contact mechanics, after the velocities of the contact points in the contact ellipse are derived, the normal pressure and friction force distributions and the components of the displacement and stress are also derived. Lastly, a verification model is developed by finite element method (FEM) to illustrate how the developed theory may be used to perform sensitivity analyses for improved parameter designs.