Advertisement

Journal of Mechanical Science and Technology

, Volume 32, Issue 10, pp 4829–4838 | Cite as

Investigation on the semi-conjugate tooth model and disc milling process of logarithmic spiral bevel gears of pure-rolling contact

  • Rulong Tan
  • Changyan Peng
  • Bingkui ChenEmail author
Article
  • 40 Downloads

Abstract

Conventional logarithmic spiral bevel gears (LSBGs) introduce full-conjugate surfaces (line contact) to generate teeth of the pinion and the gear. However, in general, these full-conjugate surfaces are constructed by spherical involute curves and it is difficult to manufacture these surfaces. Therefore, this article tries to use semi-conjugate surfaces (point contact) as the tooth profiles to make they can be manufactured by the disc milling process and of pure-rolling contact. The design method, manufacture kinematics and stress distribution situations of the LSBGs with semi-conjugate surfaces are investigated. Conjugate surface theory and spatial conjugate curve meshing theory are both introduced to complete the analytical arguments. Finite element analysis (FEA) is introduced to evaluate the contact mechanical characteristics of the LSBGs under loads. From the analytical and simulated results, it is concluded that, through the disc milling process, the LSBGs of continuous pure-rolling contact can be manufactured and mesh correctly. Besides, the manufactured LSBGs maintain pure-rolling contact approximately when they are under loads.

Keywords

Logarithmic spiral bevel gears Manufacture kinematics Contact mechanics Point contact Pure-rolling contact 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. Wildhaber, Surface curvature, Product Engineering, 27 (5) (1956) 184–191.Google Scholar
  2. [2]
    M. L. Baxter, Second-order surface generation, Industrial Mathematics, 23 (2) (1973) 85–106.MathSciNetGoogle Scholar
  3. [3]
    Y. C. Tsai and P. C. Chin, Surface geometry of straight and spiral bevel gears, Journal of Mechanical Design, 109 (4) (1987) 443–449.Google Scholar
  4. [4]
    Q. Fan, Computerized modeling and simulation of spiral bevel and hypoid gears manufactured by gleason face hobbing process, Journal of Mechanical Design, 128 (6) (2005) 1315–1327.CrossRefGoogle Scholar
  5. [5]
    I. Gonzalez-Perez and A. Fuentes-Aznar, Analytical determination of basic machine-tool settings for generation of spiral bevel gears and compensation of errors of alignment in the cyclo-palloid system, International Journal of Mechanical Sciences, 120 (2017) 91–104.CrossRefGoogle Scholar
  6. [6]
    V. Simon, Design of face-hobbed spiral bevel gears with reduced maximum tooth contact pressure and transmission errors, Chinese Journal of Aeronautics, 26 (3) (2013) 777–790.CrossRefGoogle Scholar
  7. [7]
    V. V. Simon, Manufacture of optimized face-hobbed spiral bevel gears on computer numerical control hypoid generator, Journal of Manufacturing Science and Engineering, 136 (3) (2014) 031008.CrossRefGoogle Scholar
  8. [8]
    Y. Michlin and V. Myunster, Determination of power losses in gear transmissions with rolling and sliding friction incorporated, Mechanism and Machine Theory, 37 (2) (2002) 167–174.CrossRefzbMATHGoogle Scholar
  9. [9]
    P. J. L. Fernandes and C. McDuling, Surface contact fatigue failures in gears, Engineering Failure Analysis, 4 (2) (1997) 99–107.CrossRefGoogle Scholar
  10. [10]
    M. Ristivojevic, T. Lazovic and A. Vencl, Studying the load carrying capacity of spur gear tooth flanks, Mechanism and Machine Theory, 59 (0) (2013) 125–137.CrossRefGoogle Scholar
  11. [11]
    M. J. Wagner, W. F. Ng and S. G. Dhande, Profile synthesis and kinematic analysis of pure rolling contact gears, Journal of Mechanical Design, 114 (2) (1992) 326–333.CrossRefGoogle Scholar
  12. [12]
    C.-H. Chen, A formula for determining limit noninterference curvature in pure rolling conjugation gears by using geometro-kinematical concepts, Journal of Mechanical Design, 117 (1) (1995) 180–184.CrossRefGoogle Scholar
  13. [13]
    Y. Song, Q. Liao, S. Wei, L. Guo, H. Song and L. Zhou, Modelling, simulation and experiment of a novel pure rolling cycloid reducer with involute teeth, International Journal of Modelling, Identification and Control, 21 (2) (2014) 184–192.Google Scholar
  14. [14]
    R. Tan, B. Chen and C. Peng, General mathematical model of spiral bevel gears of continuous pure-rolling contact, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229 (15) (2015) 2810–2826.Google Scholar
  15. [15]
    R. L. Huston and J. J. Coy, Surface geometry of circular cut spiral bevel gears, Journal of Mechanical Design, 104 (4) (1982) 743–748.CrossRefGoogle Scholar
  16. [16]
    R. L. Huston and J. J. Coy, Ideal spiral bevel gears—A new approach to surface geometry, Journal of Mechanical Design, 103 (1) (1981) 127–132.CrossRefGoogle Scholar
  17. [17]
    T. Xiang, L. Gu and J. Xu, The meshing angular velocity and tangential contact force simulation for logarithmic spiral bevel gear based on Hertz elastic contact theory, Journal of Mechanical Science and Technology, 30 (8) (2016) 3441–3452.CrossRefGoogle Scholar
  18. [18]
    Z. Duan, H. Chen, Z. Ju and J. Liu, Mathematical model and manufacture programming of loxodromic-type normal circular-arc spiral bevel gear, Frontiers of Mechanical Engineering, 7 (3) (2012) 312–321.CrossRefGoogle Scholar
  19. [19]
    J. T. Alves, M. Guingand and J.-P. de Vaujany, Designing and manufacturing spiral bevel gears using 5-axis computer numerical control (CNC) milling machines, Journal of Mechanical Design, 135 (2) (2013) 024502.CrossRefGoogle Scholar
  20. [20]
    T. Xiang, L. Gu and L. Xiao, Accurate modeling of logarithmic spiral bevel gear based on the tooth flank formation and Boolean addition operation, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 230 (9) (2016) 1650–1658.CrossRefGoogle Scholar
  21. [21]
    D. B. Dooner, Kinematic geometry of gearing, 2nd Edition, John Wiley & Sons Inc., New York, USA (2012).CrossRefGoogle Scholar
  22. [22]
    B. Chen, D. Liang and Z. Li, A study on geometry design of spiral bevel gears based on conjugate curves, International Journal of Precision Engineering and Manufacturing, 15 (3) (2014) 477–482.CrossRefGoogle Scholar
  23. [23]
    B. Chen, D. Liang and Y. Gao, Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228 (17) (2014) 3200–3208.Google Scholar
  24. [24]
    R. Tan, B. Chen, C. Peng and X. Li, Study on spatial curve meshing and its application for logarithmic spiral bevel gears, Mechanism and Machine Theory, 86 (2015) 172–190.CrossRefGoogle Scholar
  25. [25]
    F. L. Litvin and A. Fuentes, Gear geometry and applied theory, Cambridge University Press, New Jersey, USA (2004).CrossRefzbMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanical TransmissionChongqing UniversityChongqingChina
  2. 2.College of Electrical EngineeringChongqing UniversityChongqingChina

Personalised recommendations