Unified method for typical gear failure modeling and stiffness calculation based on the matrix equation
Fanshan MENG, Xin ZHANG, Heng XIA, Jiaxu WANG
Unified method for typical gear failure modeling and stiffness calculation based on the matrix equation
The failure types in gear systems vary, with typical ones mainly including pitting, cracking, wear, and broken teeth. Different modeling and stiffness calculation methods have been developed for various gear failure types. A unified method for typical gear failure modeling and stiffness calculation is introduced in this study by considering the deviations in the time-varying meshing stiffness (TVMS) of faulty gears resulting from the use of different methods. Specifically, a gear tooth is discretized into a large number of microelements expressed with a matrix, and unified models of typical gear failures are built by adjusting the values of the matrix microelements. The values and positions of the microelements in the tooth failure model matrix have the same physical meaning as the parameter variables in the potential energy method (PEM), so the matrix-based failure model can be perfectly matched with PEM. Afterward, a unified method for TVMS is established. Modeling of healthy and faulty gears with pitting, wear, crack, and broken tooth is performed with the matrix equation, and the corresponding TVMS values are calculated by incorporating the matrix models with PEM. On the basis of the results, the mechanism of typical fault types that affect TVMS is analyzed, and the conclusions are verified through the finite element method. The developed unified method is a promising technique for studying the dynamic response characteristics of gear systems with different failure types because of its superiority in eliminating stiffness deviations.
gears / matrix equation / failure modeling / TVMS calculation / unified method
[1] |
Gao P, Liu H, Yan P F, Xie Y K, Xiang C L, Wang C. Research on application of dynamic optimization modification for an involute spur gear in a fixed-shaft gear transmission system. Mechanical Systems and Signal Processing, 2022, 181: 109530
CrossRef
Google scholar
|
[2] |
Guan X L, Tang J Y, Hu Z H, Wang Q S, Kong X N. A new dynamic model of light-weight spur gear transmission system considering the elasticity of the shaft and gear body. Mechanism and Machine Theory, 2022, 170: 104689
CrossRef
Google scholar
|
[3] |
Ouyang T C, Mo X Y, Lu Y C, Wang J X. CFD-vibration coupled model for predicting cavitation in gear transmissions. International Journal of Mechanical Sciences, 2022, 225: 107377
CrossRef
Google scholar
|
[4] |
Al-TubiI SLong HZhangJShawB. Experimental and analytical study of gear micropitting initiation and propagation under varying loading conditions. Wear, 2015, 328–329: 8–16
|
[5] |
Huangfu Y F, Dong X J, Chen K K, Tu G W, Long X H, Peng Z K. A tribo-dynamic based pitting evolution model of planetary gear sets: a topographical updating approach. International Journal of Mechanical Sciences, 2022, 220: 107157
CrossRef
Google scholar
|
[6] |
Wang W, Liu H J, Zhu C C, Wei P T, Wu W. Micromechanical analysis of gear fatigue-ratcheting damage considering the phase state and inclusion. Tribology International, 2019, 136: 182–195
CrossRef
Google scholar
|
[7] |
Jia P, Liu H J, Zhu C C, Wu W, Lu G C. Contact fatigue life prediction of a bevel gear under spectrum loading. Frontiers of Mechanical Engineering, 2020, 15(1): 123–132
CrossRef
Google scholar
|
[8] |
Mohammed O D, Rantatalo M. Gear fault models and dynamics-based modeling for gear fault detection––a review. Engineering Failure Analysis, 2020, 117: 104798
CrossRef
Google scholar
|
[9] |
Bonaiti L, Gorla C. Estimation of gear SN curve for tooth root bending fatigue by means of maximum likelihood method and statistic of extremes. International Journal of Fatigue, 2021, 153: 106451
CrossRef
Google scholar
|
[10] |
Zhou K, Diehl E, Tang J. Deep convolutional generative adversarial network with semi-supervised learning enabled physics elucidation for extended gear fault diagnosis under data limitations. Mechanical Systems and Signal Processing, 2023, 185: 109772
CrossRef
Google scholar
|
[11] |
Karabacak Y E, Gürsel Özmen N, Gümüşel L. Intelligent worm gearbox fault diagnosis under various working conditions using vibration, sound and thermal features. Applied Acoustics, 2022, 186: 108463
CrossRef
Google scholar
|
[12] |
Chen X X, Yao Y P, Xing J Z. Meshing stiffness property and meshing status simulation of harmonic drive under transmission loading. Frontiers of Mechanical Engineering, 2022, 17(2): 18
CrossRef
Google scholar
|
[13] |
Xiang L, An C H, Zhang Y, Hu A J. Failure dynamic modeling and analysis of planetary gearbox considering gear tooth spalling. Engineering Failure Analysis, 2021, 125: 105444
CrossRef
Google scholar
|
[14] |
Meng F S, Xia H, Zhang X, Wang J X, Jin Y L. Study on nonlinear dynamic characteristics of gear system with 3D anisotropic rough tooth surface based on fractal theory. International Journal of Non-linear Mechanics, 2023, 150: 104366
CrossRef
Google scholar
|
[15] |
Meng F S, Xia H, Zhang X, Wang J X, Jin Y L. Mechanism analysis for GDTE-based fault diagnosis of planetary gears. International Journal of Mechanical Sciences, 2023, 259: 108627
CrossRef
Google scholar
|
[16] |
Yu X L, Huangfu Y, Yang Y, Du M G, He Q B, Peng Z K. Gear fault diagnosis using gear meshing stiffness identified by gearbox housing vibration signals. Frontiers of Mechanical Engineering, 2022, 17(4): 57
CrossRef
Google scholar
|
[17] |
Liang X H, Zuo M J, Feng Z P. Dynamic modeling of gearbox faults: a review. Mechanical Systems and Signal Processing, 2018, 98: 852–876
CrossRef
Google scholar
|
[18] |
Wang Q B, Chen K K, Zhao B, Ma H, Kong X G. An analytical-finite-element method for calculating mesh stiffness of spur gear pairs with complicated foundation and crack. Engineering Failure Analysis, 2018, 94: 339–353
CrossRef
Google scholar
|
[19] |
Andary F, Heinzel C, Wischmann S, Berroth J, Jacobs G. Calculation of tooth pair stiffness by finite element analysis for the multibody simulation of flexible gear pairs with helical teeth and flank modifications. Multibody System Dynamics, 2023, 59(4): 395–428
CrossRef
Google scholar
|
[20] |
Yu X, Sun Y Y, Li H G, Wu S J. An improved meshing stiffness calculation algorithm for gear pair involving fractal contact stiffness based on dynamic contact force. European Journal of Mechanics A: Solids, 2022, 94: 104595
CrossRef
Google scholar
|
[21] |
Raghuwanshi N K, Parey A. Mesh stiffness measurement of cracked spur gear by photoelasticity technique. Measurement, 2015, 73: 439–452
CrossRef
Google scholar
|
[22] |
Raghuwanshi N K, Parey A. Experimental measurement of gear mesh stiffness of cracked spur gear by strain gauge technique. Measurement, 2016, 86: 266–275
CrossRef
Google scholar
|
[23] |
Raghuwanshi N K, Parey A. Experimental measurement of mesh stiffness by laser displacement sensor technique. Measurement, 2018, 128: 63–70
CrossRef
Google scholar
|
[24] |
Verma J G, Kumar S, Kankar P K. Crack growth modeling in spur gear tooth and its effect on mesh stiffness using extended finite element method. Engineering Failure Analysis, 2018, 94: 109–120
CrossRef
Google scholar
|
[25] |
Chaari F, Fakhfakh T, Haddar M. Analytical modeling of spur gear tooth crack and influence on gearmesh stiffness. European Journal of Mechanics A: Solids, 2009, 28(3): 461–468
CrossRef
Google scholar
|
[26] |
El Yousfi B, Soualhi A, Medjaher K, Guillet F. New approach for gear mesh stiffness evaluation of spur gears with surface defects. Engineering Failure Analysis, 2020, 116: 104740
CrossRef
Google scholar
|
[27] |
Marafona J D M, Marques P M T, Martins R C, Seabra J H O. Mesh stiffness models for cylindrical gears: a detailed review. Mechanism and Machine Theory, 2021, 166: 104472
CrossRef
Google scholar
|
[28] |
Shen Z X, Yang L H, Qiao B J, Luo W, Chen X F, Yan R Q. Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear. Frontiers of Mechanical Engineering, 2022, 17(1): 9
CrossRef
Google scholar
|
[29] |
Chaari F, Baccar W, Abbes M S, Haddar M. Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission. European Journal of Mechanics A: Solids, 2008, 27(4): 691–705
CrossRef
Google scholar
|
[30] |
Meng F S, Xia H, Zhang X, Wang J X. A new tooth pitting modeling method based on matrix equation for evaluating time-varying mesh stiffness. Engineering Failure Analysis, 2022, 142: 106799
CrossRef
Google scholar
|
[31] |
Ma H, Zeng J, Feng R J, Pang X, Wen B C. An improved analytical method for mesh stiffness calculation of spur gears with tip relief. Mechanism and Machine Theory, 2016, 98: 64–80
CrossRef
Google scholar
|
[32] |
Xie C Y, Hua L, Han X H, Lan J, Wan X J, Xiong X S. Analytical formulas for gear body-induced tooth deflections of spur gears considering structure coupling effect. International Journal of Mechanical Sciences, 2018, 148: 174–190
CrossRef
Google scholar
|
[33] |
Feng M J, Ma H, Li Z W, Wang Q B, Wen B C. An improved analytical method for calculating time-varying mesh stiffness of helical gears. Meccanica, 2018, 53(4–5): 1131–1145
CrossRef
Google scholar
|
[34] |
Huang W K, Ma H, Zhao Z F, Wang P F, Peng Z K, Zhang X X, Zhao S T. An iterative model for mesh stiffness of spur gears considering slice coupling under elastohydrodynamic lubrication. Journal of Central South University, 2023, 30(10): 3414–3434
CrossRef
Google scholar
|
[35] |
Zhao W Q, Liu J, Zhao W H, Zheng Y. An investigation on vibration features of a gear-bearing system involved pitting faults considering effect of eccentricity and friction. Engineering Failure Analysis, 2022, 131: 105837
CrossRef
Google scholar
|
[36] |
Thirumurugan R, Gnanasekar N. Influence of finite element model, load-sharing and load distribution on crack propagation path in spur gear drive. Engineering Failure Analysis, 2020, 110: 104383
CrossRef
Google scholar
|
[37] |
Brethee K F, Zhen D, Gu F S, Ball A D. Helical gear wear monitoring: modeling and experimental validation. Mechanism and Machine Theory, 2017, 117: 210–229
CrossRef
Google scholar
|
[38] |
Huangfu Y F, Zhao Z F, Ma H, Han H Z, Chen K K. Effects of tooth modifications on the dynamic characteristics of thin-rimmed gears under surface wear. Mechanism and Machine Theory, 2020, 150: 103870
CrossRef
Google scholar
|
[39] |
Huangfu Y F, Chen K K, Ma H, Li X, Han H Z, Zhao Z F. Meshing and dynamic characteristics analysis of spalled gear systems: a theoretical and experimental study. Mechanical Systems and Signal Processing, 2020, 139: 106640
CrossRef
Google scholar
|
[40] |
Liu Z M, Shang E L, Huangfu Y F, Ma H, Zhu J Z, Zhao S T, Long X H, Li Z W. Vibration characteristics analysis of flexible helical gear system with multi-tooth spalling fault: simulation and experimental study. Mechanical Systems and Signal Processing, 2023, 201: 110687
CrossRef
Google scholar
|
[41] |
Chen K K, Huangfu Y F, Ma H, Xu Z T, Li X, Wen B C. Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths. Mechanical Systems and Signal Processing, 2019, 130: 273–292
CrossRef
Google scholar
|
[42] |
Chen K K, Huangfu Y F, Zhao Z F, Ma H, Dong X J. Dynamic modeling of the gear-rotor systems with spatial propagation crack and complicated foundation structure. Mechanism and Machine Theory, 2022, 172: 104827
CrossRef
Google scholar
|
[43] |
Liu Z M, Chang C, Hu H D, Ma H, Yuan K G, Li X, Zhao X J, Peng Z K. Dynamic characteristics of spur gear system with tooth root crack considering gearbox flexibility. Mechanical Systems and Signal Processing, 2024, 208: 110966
CrossRef
Google scholar
|
[44] |
Pedersen N L, Jørgensen M F. On gear tooth stiffness evaluation. Computers & Structures, 2014, 135: 109–117
CrossRef
Google scholar
|
[45] |
Munro R G, Palmer D, Morrish L. An experimental method to measure gear tooth stiffness throughout and beyond the path of contact. Proceedings of the Institution of Mechanical Engineers Part C, Journal of Mechanical Engineering Science, 2001, 215: 793–803
CrossRef
Google scholar
|
[46] |
Pimsarn M, Kazerounian K. Efficient evaluation of spur gear tooth mesh load using pseudo-interference stiffness estimation method. Mechanism and Machine Theory, 2002, 37(8): 769–786
CrossRef
Google scholar
|
[47] |
Cooley C G, Liu C G, Dai X, Parker R G. Gear tooth mesh stiffness: a comparison of calculation approaches. Mechanism and Machine Theory, 2016, 105: 540–553
CrossRef
Google scholar
|
[48] |
Ma H, Song R Z, Pang X, Wen B C. Time-varying mesh stiffness calculation of cracked spur gears. Engineering Failure Analysis, 2014, 44: 179–194
CrossRef
Google scholar
|
[49] |
Düzcükoğlu H, İmrek H. A new method for preventing premature pitting formation on spur gears. Engineering Fracture Mechanics, 2008, 75(15): 4431–4438
CrossRef
Google scholar
|
[50] |
Xu X Y, Lai J B, Lohmann C, Tenberge P, Weibring M, Dong P. A model to predict initiation and propagation of micro-pitting on tooth flanks of spur gears. International Journal of Fatigue, 2019, 122: 106–115
CrossRef
Google scholar
|
[51] |
Tan C K, Irving P, Mba D. A comparative experimental study on the diagnostic and prognostic capabilities of acoustics emission, vibration and spectrometric oil analysis for spur gears. Mechanical Systems and Signal Processing, 2007, 21(1): 208–233
CrossRef
Google scholar
|
[52] |
Aslantaş K, Tasgetiren S. A study of spur gear pitting formation and life prediction. Wear, 2004, 257(11): 1167–1175
CrossRef
Google scholar
|
[53] |
Lei Y G, Liu Z Y, Wang D L, Yang X, Liu H, Lin J. A probability distribution model of tooth pits for evaluating time-varying mesh stiffness of pitting gears. Mechanical Systems and Signal Processing, 2018, 106: 355–366
CrossRef
Google scholar
|
[54] |
Mao K, Chetwynd D G, Millson M. A new method for testing polymer gear wear rate and performance. Polymer Testing, 2020, 82: 106323
CrossRef
Google scholar
|
[55] |
Shen Z X, Qiao B J, Yang L H, Luo W, Yang Z B, Chen X F. Fault mechanism and dynamic modeling of planetary gear with gear wear. Mechanism and Machine Theory, 2021, 155: 104098
CrossRef
Google scholar
|
[56] |
Flodin A, Andersson S. Simulation of mild wear in helical gears. Wear, 2000, 241(2): 123–128
CrossRef
Google scholar
|
[57] |
Wan Z G, Cao H R, Zi Y Y, He W P, He Z J. An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack. Engineering Failure Analysis, 2014, 42: 157–177
CrossRef
Google scholar
|
[58] |
Wang S Y, Zhu R P. An improved mesh stiffness calculation model for cracked helical gear pair with spatial crack propagation path. Mechanical Systems and Signal Processing, 2022, 172: 108989
CrossRef
Google scholar
|
[59] |
Jedliński Ł, Syta A, Gajewski J, Jonak J. Nonlinear analysis of cylindrical gear dynamics under varying tooth breakage. Measurement, 2022, 190: 110721
CrossRef
Google scholar
|
[60] |
Yang W G, Jiang D X, Han T. Effects of tooth breakage size and rotational speed on the vibration response of a planetary gearbox. Applied Sciences, 2017, 7(7): 678
CrossRef
Google scholar
|
[61] |
Jiang H J, Liu F H. Dynamic features of three-dimensional helical gears under sliding friction with tooth breakage. Engineering Failure Analysis, 2016, 70: 305–322
CrossRef
Google scholar
|
[62] |
Li Z W, Ma H, Feng M J, Zhu Y P, Wen B C. Meshing characteristics of spur gear pair under different crack types. Engineering Failure Analysis, 2017, 80: 123–140
CrossRef
Google scholar
|
[63] |
Han H Z, Ma H, Tian H X, Peng Z K, Zhu J Z, Li Z W. Sideband analysis of cracked planetary gear train considering output shaft radial assembly error. Mechanical Systems and Signal Processing, 2023, 200: 110618
CrossRef
Google scholar
|
[64] |
Pandya Y, Parey A. Experimental investigation of spur gear tooth mesh stiffness in the presence of crack using photoelasticity technique. Engineering Failure Analysis, 2013, 34: 488–500
CrossRef
Google scholar
|
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〈 | 〉 |