In this paper, we present a method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears, which includes three optimization objectives, three control parameters, and a complex-constrain genetic algorithm solving method. A new set of fundamental equations for pitch cone parameters of hypoid gear drives are established, as well as the relationships between pitch cone and curvature parameters. Based on this theory, three control parameters are selected to determine the pinion tooth surface. A hypoid gear drive is chosen for case studies. The results verify that the optimization methodology can achieve the expected optimization objectives and has good convergence. Correlations between optimization objectives and control parameters are discussed. Furthermore, a finite element model of a simplified hypoid gear drive system is established and its quasi-static meshing characteristics analyzed. The results again confirm the correctness of the optimization method. The effects of torque load on the contact pattern and transmission error are discussed. The results provide a theoretical reference for geometric calculations, quasi-static analysis, and optimal design of spiral bevel and hypoid gears.

To address the lack of comprehensive quality evaluation indicators for heat treatment after bilateral induction hardening of high-speed linear guide rails, this study draws on the concept of geometric tolerance to innovatively propose a quantitative evaluation indicator for the “symmetry” of the hardening layer depth profile, and conducts non-destructive evaluation research based on ultrasonic transverse wave backscattering technology. Aiming at the complex cross-sectional profile of the guide rail and the problem of anisotropic acoustic scattering, a multi-dimensional symmetry characterization framework driven jointly by “local pair-wise tolerance zone constraints” and a “global equivalent case depth metric” was established. This dual-driven evaluation framework effectively eliminates the evaluation loophole of “false symmetry” caused by the mutual cancellation of opposite positive and negative local deviations. By constructing an equivalent hardened layer model based on discrete feature point mapping, the interference of non-parallel complex curved surfaces on traditional continuous B-scan imaging is successfully circumvented, achieving stable characterization of the overall hardening layer coverage under specific process parameters. A 15 MHz water-immersed point-focusing ultrasonic transverse wave oblique incidence detection system was developed, paired with a self-designed spring-loaded passive conformal tracking clamping mechanism for continuous automated scanning. Experimental results demonstrate that the overall equivalent symmetry of the tested guide rail specimens remains above 98%. Verified by the metallographic Vickers hardness gradient method, the equivalent relative error between the ultrasonically measured case depth and the physical case depth is only 1.0% and 1.6%. This proves that this non-destructive evaluation method possesses excellent measurement accuracy and holds significant industrial value for online non-destructive monitoring.