Principal Curvature Calculation and Contact Characteristics Analysis of the Planetary Roller Screw Mechanism

The generalized contour equation and spiral surface equation of the screw, roller and nut are developed, based on their structural characteristics. By defining the origin of raceway section on the central axis of the corresponding part, the tedious coordinate transformation caused by defining the origin of raceway section on the contour center of the thread tooth in the existing model is avoided. Besides, the principal curvatures at the corresponding contact positions on the screw-roller contact interface and the nut-roller contact interface are deduced using the principle of differential geometry, and then compared with the traditional method based on the equivalent ball model. The main curvature difference, contact ellipse area and maximum contact stress are solved by using Hertzian contact theory, and the influence of the structural parameters on the contact characteristics are discussed. The results show that the main curvatures of the screw/nut raceway in a principal plane are not zero, which means the equivalent ball model when calculating the principal curvature would bring a large error. Increasing the pitch of planetary roller screw mechanism increases the main curvature difference on the two contact interfaces of the roller, but hardly affects the contact ellipse area and the maximum contact stress. Increasing the normal flank angle of thread causes the main curvature difference and the contact area to decrease simultaneously, but a big normal flank angle of thread leads to an increased contact stress and thus friction. © 2020 Journal of Mechanical Engineering.