Abstract
Pitch error and tooth surface error are inevitable in the machining of helical gears, which will directly impact the time-varying meshing stiffness (TVMS) and transmission error (TE), thereby altering the vibration response of the gear. However, these errors are often ignored or replaced by simplified meshing errors in previous research, which cannot accurately reflect the specific effects of different errors. In this work, the distribution of various errors on the meshing surface of helical gears is fully considered, and a nonlinear contact model for helical gears with errors is established. The influence mechanisms of different errors on meshing excitation are elucidated through quasi-static meshing analysis. By incorporating the deformation coordination relationship of the meshing unit at each time sub-step, the corresponding TVMS and TE are coupled to the gear transmission in real-time, and a dynamic model influenced by tooth surface deviation is established. Finally, the time–frequency domain and dynamic load characteristics of the system under different errors are explored and the influence of mixed modification on the dynamic response of helical gears is analyzed. The findings reveal that the modification has a notable suppression effect on load fluctuation, underscoring the generality of the model for unconventional gears.
Similar content being viewed by others
Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
Artoni A, Kolivand M, Kahraman A (2010) An ease-off based optimization of the loaded transmission error of hypoid gears. J Mech Des 132(1):011010. https://doi.org/10.1115/1.4000645
Chang L, Liu G, Wu L (2015) A robust model for determining the mesh stiffness of cylindrical gears. Mech Mach Theory 87:93–114. https://doi.org/10.1016/j.mechmachtheory.2014.11.019
Chang L, Cao X, He Z et al (2018) Load-related dynamic behaviors of a helical gear pair with tooth flank errors. J Mech Sci Technol 32(4):1473–1787. https://doi.org/10.1007/s12206-018-0301-y
Chen J, Li W, Xin G et al (2019) Nonlinear dynamic characteristics analysis and chaos control of a gear transmission system in a shearer under temperature effects. Proc Inst Mech Eng Part C J Eng Mech Eng Sci 233(16):5691–5709. https://doi.org/10.1177/0954406219854112
Chen Z, Zhou Z, Zhai W et al (2020a) Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations. Mech Mach Theory 149:103838. https://doi.org/10.1016/j.mechmachtheory.2020.103838
Chen J, Li W, Sheng L et al (2020b) Study on reliability of shearer permanent magnet semi-direct drive gear transmission system. Int J Fatigue 132:105387. https://doi.org/10.1016/j.ijfatigue.2019.105387
Del Rincon AF, Viadero F, Iglesias M et al (2013) A model for the study of meshing stiffness in spur gear transmissions. Mech Mach Theory 61:30–58. https://doi.org/10.1016/j.mechmachtheory.2012.10.008
Fernández A, Iglesias M, De-Juan A et al (2014) Gear transmission dynamic: effects of tooth profile deviations and support flexibility. Appl Acoust 77:138–149. https://doi.org/10.1016/j.apacoust.2013.05.014
Fernández-del-Rincón A, Iglesias M, De-Juan A et al (2016) Gear transmission dynamics: effects of index and run out errors. Appl Acoust 108:63–83. https://doi.org/10.1016/j.apacoust.2015.11.012
Ghosh SS, Chakraborty G (2016) On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs. Mech Mach Theory 105:145–163. https://doi.org/10.1016/j.mechmachtheory.2016.06.008
Ghribi D, Bruyère J, Velex P et al (2012) A contribution to the design of robust profile modifications in spur and helical gears by combining analytical results and numerical simulations. J Mech Des 134(6):061011. https://doi.org/10.1115/1.4006740
Guo F, Fang Z (2018) Experimental and theoretical study of gear dynamical transmission characteristic considering measured manufacturing errors. Shock Vib 2018:1–20. https://doi.org/10.1155/2018/9645453
Handschuh MJ, Kahraman A, Milliren MR (2014) Impact of tooth spacing errors on the root stresses of spur gear pairs. J Mech Des 136(6):061010. https://doi.org/10.1115/1.4027337
Li Y, Yuan S, Wu W et al (2023) Dynamic analysis of the helical gear transmission system in electric vehicles with a large helix angle. Machines 11(7):696. https://doi.org/10.3390/machines11070696
Luo T, Qin X, Huang J et al (2015) Effects of helix deviation on load distributions and bending stresses of continuous engaged helical gear drives. Adv Mech Eng 7(6):1687814015588660. https://doi.org/10.1177/1687814015588660
Makam S (2010) An experimental study on the influence of misalignments on the static transmission error of hypoid gear pairs. The Ohio State University, Columbus, OH
Mohamad EN, Komori M, Murakami H et al (2009) Analysis of general characteristics of transmission error of gears with convex modification of tooth flank form considering elastic deformation under load. J Mech Des 131(6):2751–2764. https://doi.org/10.1115/1.3116261
Mohamad EN, Komori M, Murakami H et al (2010) Effect of convex tooth flank form deviation on the characteristics of transmission error of gears considering elastic deformation. J Mech Des 132(10):101005. https://doi.org/10.1115/1.4002458
Mucchi E, Dalpiaz G, Rivola A (2010) Elastodynamic analysis of a gear pump. Part ii: meshing phenomena and simulation results. Mech Syst Signal Proc 24(7):2180–2197. https://doi.org/10.1016/j.ymssp.2010.02.004
Sainsot P, Velex P, Duverger O (2004) Contribution of gear body to tooth deflections—a new bidimensional analytical formula. J Mech Des 126(4):748–752. https://doi.org/10.1115/1.1758252
Tian H, Huang W, Liu Z et al (2023) Analysis of dynamic mesh stiffness and dynamic response of helical gear based on sparse polynomial chaos expansion. Machines 11(7):736. https://doi.org/10.3390/machines11070736
Wan Z, Cao H, Zi Y et al (2015) Mesh stiffness calculation using an accumulated integral potential energy method and dynamic analysis of helical gears. Mech Mach Theory 92:447–463. https://doi.org/10.1016/j.mechmachtheory.2015.06.011
Wang Q, Zhang Y (2017) A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors. J Vib Control 23(2):272–289. https://doi.org/10.1177/1077546315576828
Wei J, Sun W, Wang L (2011) Effects of flank deviation on load distributions for helical gear. J Mech Sci Technol 25(7):1781–1789. https://doi.org/10.1007/s12206-011-0416-x
Xie C, Hua L, Lan J et al (2018) Improved analytical models for mesh stiffness and load sharing ratio of spur gears considering structure coupling effect. Mech Syst Signal Proc 111:331–347. https://doi.org/10.1016/j.ymssp.2018.03.037
Xun C, Long X, Hua H (2018) Effects of random tooth profile errors on the dynamic behaviors of planetary gears. J Sound Vib 415:91–110. https://doi.org/10.1016/j.jsv.2017.11.022
Yang DCH, Lin JY (1987) Hertzian damping, tooth friction and bending elasticity in gear impact dynamics. J Mech Des 109(2):189–196. https://doi.org/10.1115/1.3267437
Yang Y, Wang J, Zhou Q et al (2018) Mesh stiffness modeling considering actual tooth profile geometry for a spur gear pair. Mech Ind 19(3):306. https://doi.org/10.1051/meca/2018026
Yang Y, Xu M, Du Y et al (2019) Dynamic analysis of nonlinear time-varying spur gear system subjected to multi-frequency excitation. J Vib Control 25(6):1210–1226. https://doi.org/10.1177/1077546318814951
Yoon M, Lee J, Seo C et al (2017) Helical gear geometry modification for reduction of transmission error by tooth deflection. In: Proceedings of the 3rd international conference on mechatronics and robotics engineering, pp 106–112. https://doi.org/10.1145/3068796.3068807
Yuan B, Chang S, Liu G et al (2018) Quasi-static and dynamic behaviors of helical gear system with manufacturing errors. Chin J Mech Eng 31(1):1–9. https://doi.org/10.1186/s10033-018-0238-1
Yuan B, Liu G, Liu L (2020) Quasi-static characteristics and vibration responses analysis of helical geared rotor system with random cumulative pitch deviations. Appl Sci 10(12):4403. https://doi.org/10.3390/app10124403
Yuan B, Liu G, Yue Y et al (2021) A novel tooth surface modification methodology for wide-faced double-helical gear pairs. Mech Mach Theory 160:104299. https://doi.org/10.1016/j.mechmachtheory.2021.104299
Zhang T, Wang J, Wu Y et al (2015) Effect of machining errors on the gear engagement using contact finite element method. In: ASME turbo expo 2015: turbine technical conference and exposition. American Society of Mechanical Engineers. https://doi.org/10.1115/GT2015-42779
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 52275061).
Funding
National Natural Science Foundation of China (no. 52275061).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this paper.
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.
About this article
Cite this article
Chen, J., Zhu, R., Chen, W. et al. General Meshing Modeling and Dynamic Characteristics Analysis of Helical Gear Pair with Tooth Surface Deviation. Iran J Sci Technol Trans Mech Eng (2024). https://doi.org/10.1007/s40997-024-00751-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40997-024-00751-4