Static Load Distribution and Axial Stiffness in a Planetary Roller Screw Mechanism

In this paper, an original approach is proposed to calculate the static load distribution and the axial stiffness of a planetary roller screw (PRS) mechanism. Assuming that the external loading is shared equally over an arbitrary number of rollers, only a sector of the system is represented to save on computing time. The approach consists in using a structure of bars, beams, and nonlinear springs to model the different components of the mechanism and their interactions. This nonlinear model describes the details of the mechanism and captures the shape of the nut as well as the bending deformation of the roller. All materials are assumed to operate in the elastic range. The load distribution and the axial stiffness are determined in three specific configurations of the system for both compressive and tensile loads. Further, the influence of the shape of the nut is studied in the case of the inverted PRS. The results obtained from this approach are also compared to those computed with a three-dimensional finite-element (3D FE) model. Finally, since the calculations appear to be very accurate, a parametric study is conducted to show the impact of the bending of the roller on the load distribution.