Analytical prediction of the geometry of contact ellipses and kinematics in a roller screw versus experimental results

This paper brings together the geometry of threaded contact areas and roller screw kinematics in order to shine some light on the local phenomena which dissipate power in the mechanism. The subject has received little attention in current literature, often because only the global kinematics is studied. Moreover, principal directions of curvature are usually assumed from the start. In this paper, differential geometry is used to calculate the result, which proves to be different from published research. Next, the classic Hertzian theory is adapted for slightly conforming contacts, which can be encountered in common roller screw designs. The generalized equations are used to deduce the shape, size and orientation of the contact ellipses for both the roller-screw and the roller-nut contacts. The two appear to be very different in terms of local kinematics. A new stationary model is introduced, which can calculate the sliding velocity field at any point within the contact area. The model has only one degree of freedom in the form of a slip ratio, which depends on lubricant properties and dynamics. An experimental setup was designed to measure this ratio and thus allow comparison with analytical models available in the literature.