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.
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References
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.
F. L. Litvin and A. Fuentes, Gear Geometry and Applied Theory, 2nd Ed., Cambridge University Press, Cambridge (2004).
S. C. Yang, Study on an internal gear with asymmetric involute teeth, Mechanism and Machine Theory, 42(8), (2007) 977–994.
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.
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.
M. S. Tunalioglu and B. Tuc, Theoretical and experimental investigation of wear in internal gears, Wear, 309(1–2), (2014) 208–215.
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.
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.
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.
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).
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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.
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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
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DOI: https://doi.org/10.1007/s12206-020-1117-0