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https://doi.org/10.62836/iaet.v5i1.0007
Zhang, Q., & Hou, L. (2026). Modeling and Geometric Characteristics of a Circular-Arc-Profile and Circular-Arc-Tooth-Trace Cylindrical Gear Generated by Complementary Circular-Arc Cutters. Innovations in Applied Engineering and Technology, 5(1), 0007. https://doi.org/10.62836/iaet.v5i1.0007
Volume 5, Issue 1, 2026

Modeling and Geometric Characteristics of a Circular-Arc-Profile and Circular-Arc-Tooth-Trace Cylindrical Gear Generated by Complementary Circular-Arc Cutters

To improve the limited flexibility in tooth-surface geometry control of circular-arc-tooth-trace cylindrical gears, a circular-arc-profile and circular-arc-tooth-trace cylindrical gear (C2CATT) generated by a pair of complementary, locally conjugate circular-arc cutters is proposed. Based on the machining principle of a dual-edge rotary cutter head, the cutter swept-surface equations, cutter-workpiece meshing equation, and parametric tooth-surface models are established. The effects of the main parameters on the middle-section tooth profile and tooth-trace geometric offset are then investigated. The results show that the tooth-trace geometric offset is symmetric about the mid-facewidth section, and its amplitude gradually decreases from the middle toward both ends. When the number of teeth increases from 31 to 67, the maximum offset amplitude decreases by 52.7%; when the module increases from 2 mm to 5 mm, it increases by 20.0%. Increasing the cutter-head radius effectively reduces the maximum offset amplitude. The pressure angle mainly affects the addendum, dedendum, and working tooth profile, whereas the cutter profile arc radius and root fillet coefficient primarily affect the local transition regions. The proposed model and the obtained parameter relationships provide a theoretical basis for tooth-surface design and cutter parameter selection of C2CATT gears.

circular-arc profile circular-arc-tooth-trace cylindrical gear complementary circular-arc cutter rotary cutter head tooth-surface modeling geometric characteristics

References

  1. Wu Y-C, Chen KY, Tsay C-B, et al. Contact Characteristics of Circular-Arc Curvilinear Tooth Gear Drives. Journal of Mechanical Design 2009; 131: 081003. https://doi.org/10.1115/1.3151805.
  2. Peng Y, Song A, Shen Y, et al. A Novel Arc-Tooth-Trace Cycloid Cylindrical Gear. Mechanism and Machine Theory 2017; 118: 180–193. https://doi.org/10.1016/j.mechmachtheory.2017.08.009.
  3. Zhang Q, Hou L, Tang R, et al. Method of Processing and an Analysis of Meshing and Contact of Circular Arc Tooth Trace Cylindrical Gears. Transactions of FAMENA 2016; 40: 11–24. https://doi.org/10.21278/TOF.40402.
  4. Liang S, Luo P, Hou L, et al. Research on Processing Error of Special Machine Tool for VH-CATT Cylindrical Gear. Machines 2022; 10: 679. https://doi.org/10.3390/machines10080679.
  5. Liang S, Hou L, Zhang H, et al. Bifurcation and Chaos Analysis of Cutter Head-Spindle System of VH-CATT Gear Machine Tool Considering Time-Varying Stiffness. The International Journal of Advanced Manufacturing Technology 2023; 124: 3995–4008. https://doi.org/10.1007/s00170-021-08360-0.
  6. Liang S, Wu Y, Hou L, et al. Research on Influence Mechanism of Geometric Error Sources on Tooth Surface Error of VH-CATT Gear Special Machine Tool. The International Journal of Advanced Manufacturing Technology 2023; 128: 5529–5546. https://doi.org/10.1007/s00170-023-12001-z.
  7. Wang S, Hou L, Dong L, et al. Manufacturing-Oriented Modeling and Strength Analysis of an Arc-Tooth Cylindrical Gear. Journal of Sichuan University (Engineering Science Edition) 2012; 44: 210–215. https://doi.org/10.15961/j.jsuese.2012.02.029. (in Chinese)
  8. Zhao F, Hou L, Duan Y, et al. Forming Theory and Digital Modeling of a Circular-Arc Gear Generated by a Rotary Cutter. Journal of Sichuan University (Engineering Science Edition) 2016; 48: 119–125. https://doi.org/10.15961/j.jsuese.2016.06.017. (in Chinese)
  9. Zhao F, Hou L, Chen Y, et al. Complete Tooth-Surface Mathematical Model and Analysis of Cutting Conditions for Circular-Arc-Tooth-Trace Cylindrical Gears. Journal of Jilin University (Engineering and Technology Edition) 2020; 50: 875–885. https://doi.org/10.13229/j.cnki.jdxbgxb20190058. (in Chinese)
  10. Chen B, Gao Y, Liang D. Construction of Tooth Surfaces for Conjugate-Curve Gears. Journal of Mechanical Engineering 2014; 50: 18–24. https://doi.org/10.3901/JME.2014.03.018. (in Chinese)
  11. Luo L, Hou L, Zhao F, et al. Geometric Characteristics of Variable-Hyperbolic Circular-Arc-Tooth-Trace Cylindrical Gear Transmission. Advanced Engineering Sciences 2018; 50: 171–179. https://doi.org/10.15961/j.jsuese.201700511. (in Chinese)
  12. Ma D, Ye Z, Yang H. Tooth Surface Reconstruction and Tooth Profile Geometric Analysis of Circular Arc Tooth Trace Cylindrical Gears. Transactions of FAMENA 2019; 43: 29–44. https://doi.org/10.21278/TOF.43103.
  13. Jiang B, Ren Z, Duan J, et al. Modeling and Load-Carrying Capacity Analysis of a Circular-Arc-Profile and Circular-Arc-Tooth-Trace Cylindrical Gear. Journal of Mechanical Strength 2022; 44: 742–746. https://doi.org/10.16579/j.issn.1001.9669.2022.03.033. (in Chinese)
  14. Wu Y, Hou L, Luo L, et al. Research on the Effect Law of Machine Tool Errors on Tooth Surface Errors of Curvilinear Gear. Journal of Mechanical Engineering 2020; 56: 100–109. https://doi.org/10.3901/JME.2020.21.100. (in Chinese)
  15. Wei Y, Li Z, Liu Y, et al. Geometric Contact Characteristics and Sensitivity Analysis of a Variable-Hyperbolic circular-Arc-Tooth-Trace Cylindrical Gear Considering Errors. Journal of Northwestern Polytechnical University 2022; 40: 679–689. https://doi.org/10.1051/jnwpu/20224030679. (in Chinese)
  16. Wei Y, Wang Y, Li Z, et al. Geometric Contact Characteristics of Variable Hyperbolic Circular-Arc-Tooth-Trace Cylindrical Gear under Different Machine Tool Errors and Sensitivity Analysis for Impact Factors. The Journal of Strain Analysis for Engineering Design 2024; 59: 269–280. https://doi.org/10.1177/03093247241232865.
  17. Ma D, Jiang B, Bao L, et al. Study on the Contact Performance of the Variable Hyperbolic Circular Arc Tooth Trace Cylindrical Gear with Installation Errors. Mechanical Sciences 2024; 15: 353–366. https://doi.org/10.5194/ms-15-353-2024.
  18. Guo R, Wei Y, Liu Y, et al. Analytical Solution to Contact Characteristics for a Variable Hyperbolic Circular-Arc-Tooth-Trace Cylindrical Gear. Mechanical Sciences 2021; 12: 923–932. https://doi.org/10.5194/ms-12-923-2021.
  19. Ma D, Liu Y, Ye Z, et al. Analysis of the Tooth Surface Contact Area of a Circular-Arc-Tooth-Trace Cylindrical Gear Under Load. Transactions of FAMENA 2021; 45: 79–94. https://doi.org/10.21278/TOF.451018220.
  20. Ma D, Liu Y, Ye Z, et al. Modification Design and Loaded Tooth Contact Analysis of Variable-Hyperbolic Circular-Arc-Tooth-Trace Cylindrical Gears. Journal of Vibration and Shock 2023; 42: 170–179. (in Chinese).
  21. Zhang Q, Chen Z, Wu Y, et al. Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel. Computer Modeling in Engineering Sciences 2024; 140: 593–619. https://doi.org/10.32604/cmes.2023.046319.
  22. Ma D, Ye Z. Nonlinear Dynamic Characteristics of Modified Variable Hyperbolic Circular Arc Tooth Trace Cylindrical Gears. Scientific Reports 2025; 15: 15108. https://doi.org/10.1038/s41598-025-97254-2.
  23. Ma D, Long J, Zhu Z. Meshing Characteristics of Variable Hyperbolic Circular-Arc Tooth Trace Cylindrical Gears with Cutter Errors. Mechanical Sciences 2025; 16: 475–491. https://doi.org/10.5194/ms-16-475-2025.

Supporting Agencies

  1. Funding: This work was supported by the Sichuan Science and Technology Program (Project No. 2023ZYD0139), the Natural Science Foundation of Sichuan Province (Project No. 2022NSFSC0454, 2022NSFSC1975).