A Novel Arc-Cycloid Conjugate Pair for Spiral Bevel Gears: Design, Meshing Analysis, and Experimental Validation

This paper introduces a novel arc-cycloid conjugate pairing for spiral bevel gears comprising a single-start arc spiroid pinion and cycloidal bevel gear, overcoming inherent limitations of conventional involute designs including undercutting vulnerability and discontinuous contact patterns. Mathematical derivation employing coordinate transformations and envelope theory establishes continuous contact lines spanning entire tooth flanks on both members, with analytical determination of key meshing characteristics such as induced normal curvature distributions and theoretical contact trajectories ensuring kinematic stability. Loaded tooth contact analysis predicts interfacial stress behavior under operational loads, validated through finite element simulations demonstrating reduced stress concentration. Experimental characterization of a functional prototype verifies enhanced dynamic performance through systematic quantification of instantaneous transmission ratio stability across speed ranges and maintained high transmission efficiency under varying loads, while loaded contact pattern inspections corroborate full tooth width engagement and validate theoretical predictions. The proposed geometry significantly improves load distribution capabilities while ensuring manufacturing feasibility through modern production techniques, offering substantial potential for high-load applications in intersecting-axis transmissions.