Geometric Design, Meshing Simulation, and Stress Analysis of Pure Rolling Rack and Pinion Mechanisms

Abstract

The geometric design, meshing simulation, and stress analysis of pure rolling rack and pinion mechanisms are presented. Both the pinion and the rack are based on the active design of the meshing line to provide pure rolling for the whole cycle of meshing. The parametric equations of the contact curves on the rack and pinion tooth surfaces are determined by coordinate transformation of the meshing line equations. Three types of meshing are derived according to the motion of the generatrices along the calculated contact curves: convex-to-concave meshing, convex-to-plane meshing, and convex-to-convex meshing. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. Four different cases of design are considered to compare the meshing performance and mechanical behavior of the proposed gear mechanisms. The results include contact patterns, the unloaded function of transmission errors, and the evaluation of stresses along two cycles of meshing. The analysis of the results shows that the proposed method of design of pure rolling meshing reduces the relative sliding between tooth surfaces, whereas it decreases the contact strength of the tooth surfaces. However, if the design parameters are properly evaluated as a result of simulation and applied as proposed here, the mechanical behavior of the proposed rack and pinion mechanisms can be more favorable than that of the standard geometry of involute rack and pinion sets.