Influence of spur-gear tooth-profile geometry on mesh efficiency and transmission error: A common-benchmark multi-objective comparison

Abstract

Reducing gear-mesh loss without compromising STE, DTE and load capacity is central to high-performance transmission design. Non-involute tooth-flank geometries can redistribute sliding, contact conformity and mesh compliance, but published comparisons often confound geometry with benchmark and modelling assumptions. This study compares standard and pressure-angle-optimized involutes, Cubic-CP, S-gear, an involute–cycloid composite and a circular-contact-path construction on an invariant 19/49 steel-gear benchmark. A common event-resolved conjugate-contact framework evaluates curvature, rolling and sliding, unilateral multi-pair load sharing, tooth compliance, thermal partial-EHL loss, STE and DTE. Identity-preserving contact-force histories feed the tribological and transmission-error solvers, while nonlinear phase-load torque surfaces interface with the torsional model. Constrained multi-fidelity optimization and qualification are supplemented by continuum-FE strength assessment. No profile is uniformly superior. Among the joint Pareto-knee selections, the S-gear defines the efficiency–strength extreme, delivering the largest mesh-loss reduction (57.1%) and the most favourable FE strength indicators; relative to the standard involute, root stress and peak surface pressure decrease by 18.9% and 52.6%, while STE and DTE peak-to-peak decrease by 19.5% and 14.8%. The selected Cubic-CP joint design gives a more gradual compromise, reducing mesh loss, STE and DTE peak-to-peak by 37.3%, 17.8% and 27.9%. Composite and circular-path designs occupy intermediate regions governed by tribological gain, curvature regularity and load-transfer timing. Similar STE values need not produce similar DTE or resonance exposure; preferred geometry is therefore objective and application dependent.