Tooth surface error correction method of hypoid gear based on Morris–LM (Levenberg–Marquard) fusion algorithm

• Published in: International journal of advanced manufacturing technology Vol. 139; no. 3; pp. 1291 - 1310
• Main Authors: Li, Jun, Wang, Zhonghou, Chen, Mingzhi, Yuan, Chongyue, Gou, Zhenglong, Wu, Yunlong
• Format: Journal Article
• Language: English
• Published: London Springer London 01.07.2025; Springer Nature B.V
• Subjects: Accuracy; Algorithms; CAE) and Design; Computer-Aided Engineering (CAD; Deviation; Efficiency; Engineering; Error correction; Error correction & detection; Flanks; Gear teeth; Hypoid gears; Industrial and Production Engineering; Machine tools; Machining; Mechanical Engineering; Media Management; Mutual coupling; Normal distribution; Original Article; Parameter identification; Parameter sensitivity; Process parameters; Sensitivity analysis; Morris–LM fusion algorithm; Measurement experiments; Hypoid gear; Tooth surface error correction
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-025-15821-3

The accuracy of the tooth flank can be affected by incorrectly adjusting the machine tool parameters during the processing of hypoid gears. Notably, the complex mutual coupling and nonlinear relationship between the parameters make any attempt to improve processing accuracy on the tooth flank challenging. Hence, this paper introduces a method for correcting tooth flank errors in gears using the Morris–LM (Levenberg-Marquard) fusion algorithm. The Morris algorithm is utilized for global sensitivity analysis of the processing parameters, allowing for an intuitive comparison of effects caused by errors. Additionally, a random disturbance amount, obeying a normal distribution, is introduced into the global system to accurately reflect the key processing parameters that significantly impact tooth flank errors in the actual processing. The complex nonlinear model established with the correction of tooth flank errors contains multiple key processing parameters. The flank accuracy is evaluated by integrating deviations containing tooth-top, tooth-root, and tooth-mean-square. Then, key machining parameters are adjusted using the LM algorithm with a trust-region strategy to enhance the efficiency of tooth flank correction. After correcting the processing parameters, multiple measurements on different tooth flanks were conducted. The results revealed that viewed from the concave flank, the deviations of tooth-top, tooth-root, and tooth-mean-square decreased by a minimum of 80.34, 74.23, and 81.24%. Furthermore, viewed from the convex flank, the corresponding deviations decreased by a minimum of 83.99, 80.33, and 82.35%. These results verify the high accuracy of the proposed algorithm in correcting the tooth flanks of hypoid gears.