An Analytical Equation to Compute the Maximum Contact Stress of the Incomplete Spur Gear in the Planetary Roller Screw Mechanism

Planetary roller screw mechanism (PRSM) is a precision mechanical transmission device that converts rotary motion into linear motion through thread engagement. Thoroughly studying the radial engagement and contact characteristics of the incomplete gear pair in the planetary roller screw mechanism reduces the difficulty of calibrating the contact strength of the incomplete gear pair. It also has positive implications for the design selection and engineering applications of planetary roller screw mechanism. Therefore, this paper will focus on the radial engagement and contact characteristics of the incomplete gear pair in the planetary roller screw mechanism, and the paper work completed are as follows: Firstly, the engagement equations of the tooth surfaces between the roller straight tooth and the internal gear are derived. Secondly, the finite element model of the incomplete spur gear pair is developed. And an analytical model to calculate the positions and lengths of contact lines of the incomplete spur gear pair are proposed. The results obtained from the analytical model and those from the finite element model are compared. Lastly, combing the results of the two models, a formula to compute the maximum contact stress of the incomplete spur gear is derived.