Skip to main content
SpringerLink
Log in

An analytical prediction methodology of the correlation between transmission error and tooth pitch error for face-hobbed hypoid gears

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

Transmission error (TE) as an important indicator in high performance gear pairs and accurate prediction of the TE is an important scientific issue. On this research, the relationship and connections between TE and tooth pitch error (TPE) for face-hobbed hypoid gears (FH-HG) are researched. Firstly, the kinematics of FH-HG based on the cutter-plate, machine and gear blanks are elucidated and the mathematical tooth surface of considering PE and the finite element model (FEM) are established. After, the effect of PE on the TE is explored and the relationship between PE and TE is analyzed by comparison the curves of the TPE, TPE and coincidence (TPE-C) with the calculating TE. Then, the curve segment idea of TE of pinion and gear is adopted to calculate the TPE of gear pair, respectively. The analytical prediction formulas of TE and TPE is proposed. Finally, an experiment example verifies the efficient of this method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Liang C, Song C, Zhu C et al (2023) Modelling method, simulation and experimental verification of hypoid gear involved tooth surface deviation under manufacturing process. Mech Mach Theory 182:105248

    Article  Google Scholar 

  2. Wildhaber E (1945) Basic relationship of hypoid gears. Am Mach 90(20):24–30

    Google Scholar 

  3. Wildhaber E (1946) Basic relationship of hypoid gears-II. Am Mach 90(3):108–111

    Google Scholar 

  4. Wildhaber E (1946) Basic relationship of hypoid gears-III. Am Mach 90(5):131–134

    Google Scholar 

  5. Stadtfeld H (1991) Duplex method of manufacturing a generated spiral-toothed bevel gear of a bevel-gear or hypoid-gear drive. U.S. Patent 5000632

  6. Vijayakar S (1991) A combined surface integral and finite contact problem element solution for a three-dimensional. Int J Numer Meth Eng 31:525–545

    Article  Google Scholar 

  7. Fan Q (2006) Computerized model and simulation of spiral bevel and hypoid gears manufactured gleason face hobbing process. J Mech Des 128(6):1315–1327

    Article  Google Scholar 

  8. Fan Q (2007) Enhanced algorithms of contact simulation for hypoid gear drives produced by face-milling and face-hobbed process. J Mech Des 129(1):31–37

    Article  Google Scholar 

  9. Fong ZH (2000) Mathematical model of universal hypoid generator with supplemental kinematic flank correction motions. J Mech Des 122(1):136–142

    Article  Google Scholar 

  10. Shih YP, Fong ZH, Lin CY (2007) Mathematical model for a universal face hobbing hypoid gear generator. J Mech Des 129(1):38–47

    Article  Google Scholar 

  11. Gonzalez-Perez I, Fuentes A, Ruiz-Orzaez R (2015) An approach for determination of basic machine-tool settings from blank data in face-hobbed and face-milled hypoid gears. J Mech Des 137(9):093303

    Article  Google Scholar 

  12. Gonzalez-Perez I, Fuentes A (2017) Analytical determination of basic machine-tool settings for generation of spiral bevel gears and compensation of errors of alignment in the cyclo-palloid system. Int J Mech Sci 120:91–104

    Article  Google Scholar 

  13. Han D, Tang J (2018) Six sigma robust multi-objective optimization modification of machine-tool settings for hypoid gears by considering both geometric and physical performances. Appl Soft Comput 70:550–561

    Article  Google Scholar 

  14. Han D et al (2017) Nonlinearity analysis based algorithm for identifying machine settings in the tooth flank topography correction for hypoid gears. Mech Mach Theory 113:1–21

    Article  Google Scholar 

  15. Chen Z, Zhou Z, Zhai W, Wang K (2020) Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations. Mech Mach Theory 149:103838

    Article  Google Scholar 

  16. Xiong C, Chen S (2020) Experimental study of the effect of assembly error on the lightly loaded TE of spur gear with crown modification. J Low Freq Noise Vib Active Control 39(4):1039–1051

    Article  Google Scholar 

  17. Huang D, Wang Z, Kubo A (2020) Hypoid gear integrated wear model and experimental verification design and test. Int J Mech Sci 166:105228

    Article  Google Scholar 

  18. Hu Q, Chen X, Xu Z, Mai Q, Zhu C (2020) Study on kinematic characteristics of planetary multistage face gears transmission. Proc Inst Mech Eng Part D J Automob Eng 234(2–3):572–585

    Article  Google Scholar 

  19. Liang C, Song C, Zhu C et al (2020) Investigation of the effects with linear, circular and polynomial blades on contact characteristics for face-hobbed hypoid gears. Mech Mach Theory 146:1–14

    Article  Google Scholar 

  20. Liu S, Song C, Zhu C et al (2019) Investigation on the influence of work holding equipment errors on contact characteristics of face-hobbed hypoid gear. Mech Mach Theory 138:95–111

    Article  Google Scholar 

  21. Liang C, Song C, Zhu C et al (2020) Investigation of tool errors and their influences on tooth surface topography for face-hobbed hypoid gears. J Mech Des 142:1–11

    Article  Google Scholar 

  22. Liang C, Song C, Zhu C et al (2020) Effects of machine-tool parameters on geometry and contact pattern for face hobbed hypoid gears. Meccanica 57:1429–1442

    Article  MathSciNet  Google Scholar 

Download references

Funding

This study was funded the National Natural Science Foundation of China (52175040, 52205051) and Project No. 2022CDJKYJH050 supported by the Fundamental Research Funds for the Central Universities.

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400030, China

    Cheng Xue, Chengcheng Liang, Chaosheng Song, Xinzi Li & Siyuan Liu

Authors
  1. Cheng Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chengcheng Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chaosheng Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xinzi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Siyuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chengcheng Liang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xue, C., Liang, C., Song, C. et al. An analytical prediction methodology of the correlation between transmission error and tooth pitch error for face-hobbed hypoid gears. Meccanica 59, 217–233 (2024). https://doi.org/10.1007/s11012-023-01749-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-023-01749-z

Keywords

Search

Navigation