Multi-Error Collaborative Tooth Surface Modification of High Reduction Ratio Hypoid Gears Considering Cutter and Machine Tool Errors

In the machining process of high reduction ratio hypoid gears (HRHGs), cutter tool geometry errors (CGE) and machine tool setting parameters errors (MSE) significantly affect tooth surface accuracy. Existing studies mainly focus on analyzing the effects of MSE alone or investigate CGE and MSE under conventional reduction ratios, while comprehensive research on the coupled effects of tooth top error (TTE), tooth root error (TRE), and root mean square deviation (RMS) is limited. To address this gap, this paper proposes a tooth surface correction method based on the integration of Sobol’ sensitivity analysis and NSGA-II optimization algorithms. A multidimensional mapping model was established between CGE, MSE parameters, and tooth surface accuracy indices (TTE, TRE, and RMS) to achieve coordinated error optimization. Sobol’ global sensitivity analysis (GSA) was conducted to identify the key influencing parameters of cutter geometry and machine settings. A multi-objective optimization model was developed using the NSGA-II algorithm, targeting TTE, TRE, and RMS. The fast non-dominated sorting mechanism effectively identified the Pareto-optimal solutions, enabling inverse compensation of critical error factors and significantly improving the machining accuracy of hypoid gears. The results revealed that, on the concave flank, the deviations of tooth top, tooth root, and tooth mean square decreased by a minimum improvement of 75.4%, 70.1%, and 73.3%. Furthermore, on the convex flank, the corresponding deviations decreased by a minimum improvement of 78.1%, 75.0%, and 73.1%. These results verify the high accuracy of the proposed algorithm in correcting the tooth flanks of HRHGs.