Tooth Contact Analysis of Cycloid Mechanism with Segmented Profile Modification Using Numerical Method

This paper presents a comprehensive analytical–numerical model for the loaded tooth contact analysis of a cycloidal drive with tooth profile modifications (TPMs). Based on the principles of contact kinetics, elastostatic contact mechanics, and differential geometry, the time-varying normal contact force, contact compression depth, relative sliding velocity, contact friction force, and loaded static transmission error (LSTE) of a cycloidal speed reducer are systematically evaluated. Furthermore, the intrinsic relationship between the transmission accuracy and contact characteristics is elucidated. Numerical parametric evaluations are conducted to identify favorable profile modification parameters by investigating the evolution of contact parameters and LSTE. To effectively reduce the peak normal contact force, a novel segmentation modification model targeting the inflection-point region with strict C1 tangential continuity is proposed along with its analytical mathematical formulation. The validity of the analytical–numerical framework is independently verified against 3D nonlinear finite element contact simulations under multiple load levels. The results indicate that the positive compound modification method is more effective in reducing the maximum normal contact force than single-parameter modifications. A comprehensive comparison reveals that excessive modification significantly increases contact force, backlash, and transmission error due to the shrinkage of active contact areas. A quantitative multi-objective trade-off index is formulated to balance peck force, backlash, and kinematic accuracy. The proposed methodology provides theoretical guidance for improving the tooth surface contact strength, optimizing clearance design, and enhancing the precision of cycloidal transmissions.