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<p>In the process of machining hypoid gears using the double-helix method, machine tool setting parameters errors (MSE) have a significant impact on tooth surface accuracy. Existing studies mainly focus on the single-helix method or independently analyze the effects of MSE on tooth surface deviations, lacking research on the coupled effects of root mean square deviation (RMS) and midpoint pitch error (MPE). To address this issue, this paper proposes a tooth surface correction method based on the Sobol'-LM hybrid algorithm. By constructing a multidimensional mapping model between MSE and tooth surface accuracy indices (RMS and MPE), coordinated error optimization is achieved. Taking the Oerlikon S17 machine tool as the research object, local sensitivity analysis (LSA) and global sensitivity analysis (GSA) of machine tool parameters are performed using the Sobol' algorithm. Based on the Levenberg-Marquardt (LM) algorithm, a nonlinear least squares optimization model is developed, using RMS and MPE as the joint objective function. Through an adaptive damping factor adjustment mechanism, key error terms are inversely solved and compensated, thereby improving the machining accuracy of hypoid gears. Multiple measurement experiments demonstrate that after optimization and compensation, the RMS of the concave and convex tooth surfaces decreased by 78.5 and 79.4% at least, respectively, while the MPE decreased by 89.1% at least, which verified the effectiveness and robustness of the proposed method in the tooth surface modification of hypoid gears.</p>

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Research on Multi-Error Collaborative Tooth Surface Modification Method for Hypoid Gears Based on Sobol'-LM Fusion Algorithm

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Jun Li,
  • Zhonghou Wang,
  • Mingzhi Chen,
  • Zhenglong Gou,
  • Chongyue Yuan,
  • Changfeng He,
  • Yongming Yang,
  • Li Ding

摘要

In the process of machining hypoid gears using the double-helix method, machine tool setting parameters errors (MSE) have a significant impact on tooth surface accuracy. Existing studies mainly focus on the single-helix method or independently analyze the effects of MSE on tooth surface deviations, lacking research on the coupled effects of root mean square deviation (RMS) and midpoint pitch error (MPE). To address this issue, this paper proposes a tooth surface correction method based on the Sobol'-LM hybrid algorithm. By constructing a multidimensional mapping model between MSE and tooth surface accuracy indices (RMS and MPE), coordinated error optimization is achieved. Taking the Oerlikon S17 machine tool as the research object, local sensitivity analysis (LSA) and global sensitivity analysis (GSA) of machine tool parameters are performed using the Sobol' algorithm. Based on the Levenberg-Marquardt (LM) algorithm, a nonlinear least squares optimization model is developed, using RMS and MPE as the joint objective function. Through an adaptive damping factor adjustment mechanism, key error terms are inversely solved and compensated, thereby improving the machining accuracy of hypoid gears. Multiple measurement experiments demonstrate that after optimization and compensation, the RMS of the concave and convex tooth surfaces decreased by 78.5 and 79.4% at least, respectively, while the MPE decreased by 89.1% at least, which verified the effectiveness and robustness of the proposed method in the tooth surface modification of hypoid gears.