Skip to main content
SpringerLink
Log in

Mathematical model and meshing analysis of internal meshing gear transmission with curve element

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

A new internal meshing gear transmission with curve element is put forward in this paper. The mathematical principle of tooth profile generation is described based on conjugate curves theory. For a given spatial curve, the meshing equation and its conjugated spatial curve under the motion law were derived. Considering the equidistant kinematic method, general internal tooth profiles models were established by the conjugate-curve pair. Numerical example of the internal gear pair was developed according to gear parameters and gear solid models were established by MATLAB and UG software. Motion simulation result shows that the gear pair satisfies point contact condition and design requirements. Meshing analysis of tooth profiles using FEA method was carried out. Stress analysis results of tooth profiles with single point contact and two points contact were, respectively, obtained. The conclusions lay the foundation for multi-point contact generation and tooth profile design. Also, further studies on transmission characteristics and manufacturing technology of the new gear drive will be carried out.

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.

Similar content being viewed by others

References

  1. A. Singh, A. Kahraman and H. Ligata, Internal gear strains and load sharing in planetary transmissions: model and experiments, J. of Mechanical Design, 130(7), (2008) 917–928.

    Article  Google Scholar 

  2. F. L. Litvin and A. Fuentes, Gear Geometry and Applied Theory, 2nd Ed., Cambridge University Press, Cambridge (2004).

    Book  MATH  Google Scholar 

  3. S. C. Yang, Study on an internal gear with asymmetric involute teeth, Mechanism and Machine Theory, 42(8), (2007) 977–994.

    Article  MATH  Google Scholar 

  4. Y. H. Chen, G. H. Zhang, B. K. Chen and W. J. Luo, A novel enveloping worm pair via employing the conjugating planar internal gear as counterpart, Mechanism and Machine Theory, 67(9), (2013) 17–31.

    Article  Google Scholar 

  5. J. R. Cho, K. Y. Jeong, M. H. Park and D. S. Shin, Finite element structural analysis of wind turbine gearbox considering tooth contact of internal gear system, J. of Mechanical Science and Technology, 27(7), (2013) 2053–2059.

    Article  Google Scholar 

  6. M. S. Tunalioglu and B. Tuc, Theoretical and experimental investigation of wear in internal gears, Wear, 309(1–2), (2014) 208–215.

    Article  Google Scholar 

  7. T. H. Pham, L. Müller and J. Weber, Dynamically loaded the ring gear in the internal gear motor/pump: mobility method solution, J. of Mechanical Science and Technology, 32(7), (2018) 3023–3035.

    Article  Google Scholar 

  8. T. H. Pham and J. Weber, Theoretical and experimental analysis of the effect of misaligned ring gear on performance of internal gear motors/pumps, J. of Mechanical Science and Technology, 33(9), (2019) 4049–4060.

    Article  Google Scholar 

  9. Y. Y. Liu, Research on gear shaping strategy for internal helical non-circular gears and performance analyses for linkage models, J. of Mechanical Science and Technology, 28(7), (2014) 2749–2757.

    Article  Google Scholar 

  10. X. C. Gui, X. Q. Zhan, P. Ye and H. X. Li, Design and analysis of internal compound cycloid gear transmission with high contact ratio, J. of Mechanical Engineering, 53(1), (2017) 55–64 (in Chinese).

    Article  Google Scholar 

  11. Y. Yanase, M. Komori and M. Ochi, Grinding of internal gears by setting a large crossed-axes angle using a barrel-shaped grinding wheel, Precision Engineering, 52(4), (2018) 384–391.

    Article  Google Scholar 

  12. K. Uriu, T. Osafune, T. Murakami and M. Nakamura, Effects of shaft angle on cutting tool parameters in internal gear skiving, J. of Mechanical Science and Technology, 31(12), (2017) 5665–5673.

    Article  Google Scholar 

  13. J. Han and G. Z. Zhang, Investigation on formation mechanism of surface texture and modeling of surface roughness with internal gear power honing, The International J. of Advanced Manufacturing Technology, 98(9), (2018) 603–615.

    Article  Google Scholar 

  14. B. K. Chen, D. Liang and Y. E. Gao, The principle of conjugate curves for gear transmission, J. of Mechanical Engineering, 50(1), (2014) 130–136 (in Chinese).

    Article  Google Scholar 

  15. R. L. Tan, B. K. Chen, C. Y. Peng and X. Li, Study on spatial curve meshing and its application for logarithmic spiral bevel gears, Mechanism and Machine Theory, 86(4), (2015) 172–190.

    Article  Google Scholar 

  16. D. Liang, B. K. Chen and Y. E. Gao, Theoretical and experimental investigations on parallel-axis gear transmission with tubular meshing surfaces, International J. of Precision Engineering and Manufacturing, 16(10), (2015) 2147–2157.

    Article  Google Scholar 

  17. Y. E. Gao, B. K. Chen and D. Liang, Mathematical models of hobs for conjugate-curve gears having three contact points, Proceedings of the Institution of Mechanical Engineers, Part C: J. of Mechanical Engineering Science, 229(13), (2015) 2402–2411.

    Google Scholar 

  18. B. K. Chen, D. Liang and Z. Y. Li, A study on geometry design of spiral bevel gears based on conjugate curves, International J. of Precision Engineering and Manufacturing, 15(3), (2014) 477–482.

    Article  Google Scholar 

  19. D. Liang, B. K. Chen and Y. E. Gao, Hobbing manufacturing of new type of involute-helix gears for wind turbine gearbox, International J. of Precision Engineering and Manufacturing — Green Technology, 6(1), (2019) 305–313.

    Article  Google Scholar 

  20. S. Feng, L. H. Chang and Z. X. He, A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs, J. of Mechanical Science and Technology, 34(59), (2020) 2477–2485.

    Article  Google Scholar 

  21. A. Fuentes, R. Ruiz-Orzaez and I. Gonzalez-Perez, Computerized design, simulation of meshing, and finite element analysis of two types of geometry of curvilinear cylindrical gears, Computer Methods in Applied Mechanics and Engineering, 272(4), (2014) 321–339.

    Article  MATH  Google Scholar 

  22. S. Y. Liu, C. S. Song, C. C. Zhu, C. C. Liang and X. Y. Yang, Investigation on the influence of work holding equipment errors on contact characteristics of face-hobbed hypoid gear, Mechanism and Machine Theory, 138(8), (2019) 95–111.

    Article  Google Scholar 

  23. C. C. Liang, C. S. Song, C. C. Zhu, Y. W. Wang, S. Y. Liu and R. H. Sun, Investigation of tool errors and their influences on tooth surface topography for face-hobbed hypoid gears, J. of Mechanical Design, 142(4), (2020) 1–11.

    Article  Google Scholar 

Download references

Acknowledgments

The research is supported by National Key Research and Development Program of China (Grant No. 2018YFB2001300), National Natural Science Foundation of China (Grant No. 51975078), Fundamental and Frontier Research Project of Chongqing (Grant No. cstc2018jcyjAX0029), Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201900736) and Chongqing Key Laboratory of Urban Rail Transit System Integration and Control Open Fund (Grant No. CKLURTSIC-KFKT-202005). The financial support is gratefully acknowledged. The authors would like to thank the editor and reviewers for review of this manuscript.

Author information

Authors and Affiliations

  1. School of Mechanotronics & Vehicle Engineering, Chongqing Jiaotong University, Chongqing, 400074, China

    Dong Liang

  2. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400030, China

    Dong Liang, Weibin Li & Bingkui Chen

Authors
  1. Dong Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weibin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bingkui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong Liang.

Additional information

Dong Liang received his Ph.D. in Mechanical Design and Theory from Chongqing University, China. He also spent two years as a postdoctoral researcher at Chongqing University, China. He currently works in School of Mechanotronics & Vehicle Engineering at Chongqing Jiaotong University, China. His research areas of interest include gear design, optimization and manufacturing.

Weibin Li received his M.S. in Mechanical Design and Theory from Chongqing University, China. His research areas of interest include gear design and manufacturing.

Bingkui Chen is currently a Professor for the State Key Lab of Mechanical Transmissions at Chongqing University, China. He is also a Vice Director of the CMES Gear Technical Committee. Prof. Chen has conducted pioneering research related to gear geometry, kinematics, dynamics and manufacturing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liang, D., Li, W. & Chen, B. Mathematical model and meshing analysis of internal meshing gear transmission with curve element. J Mech Sci Technol 34, 5155–5166 (2020). https://doi.org/10.1007/s12206-020-1117-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-1117-0

Keywords

Search

Navigation