A multi-roller static model of the planetary roller screw mechanism based on energy method

A multi-roller static model for planetary roller screw mechanisms (PRSMs) is proposed using an energy method to obtain contact load sharing and distribution. The relative positions of meshing points within one pitch are considered to calculate structural potential energy by discretization. By combining force balance constraints with the principle of minimum potential energy, an optimization problem is formulated to derive the static characteristics. The model is validated through finite element simulations and existing experimental results, demonstrating that it meets engineering accuracy requirements. The model is more concise and comprehensible, enabling it to account for more complete structural deformations, thus making it more comprehensive. Furthermore, it provides a new perspective for the calculation of static load sharing and distribution. The model is used to analyze the influence of pitch, roller threads number and thread dedendum on static characteristics of PRSMs. Analysis reveals that load distribution non-uniformity increases with pitch and roller threads number. When the thread dedendum increases within a certain range, the load distribution non-uniformity decreases.