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Meccanica
Published in:

18-12-2024 | Research

Multi-state meshing characteristics and global nonlinear dynamics of a spur gear system considering local tooth breakage

Authors: Qing-Zhong Gong, Jian-Fei Shi, Wen-Hu Nan, Gang Zhao, Peng-Fei Qi

Published in: Meccanica | Issue 1/2025

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Abstract

The article investigates the complex dynamics of spur gear systems subject to local tooth breakage, a common fault in gear operations. It introduces a multi-state meshing dynamic model to analyze the impact of tooth damage on meshing vibration mechanisms and global nonlinear dynamics. The study highlights the transformation of double-tooth meshing into single-tooth meshing due to tooth breakage, affecting the contact ratio and load distribution. The research also reveals the evolution of dynamic meshing forces and uncovers a new bifurcation phenomenon, 'incomplete bifurcation,' under multi-initial values. This work offers crucial insights into the intricate behavior of gear systems under fault conditions, contributing to the development of more robust and reliable gear designs.
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Literature
1.
Goswami P, Rai RN (2023) A systematic review on failure modes and proposed methodology to artificially seed faults for promoting PHM studies in laboratory environment for an industrial gearbox. Eng Fail Anal 146:107076
2.
Feng K, Ji JC, Ni Q et al (2023) A review of vibration-based gear wear monitoring and prediction techniques. Mech Syst Signal Process 182:109605MATH
3.
Shi J, Gou X, Zhu L (2018) Bifurcation and erosion of safe basin for a spur gear system. Int J Bifurc Chaos 28:1830048MathSciNetMATH
4.
Dixit Y, Kulkarni MS (2023) Multi-objective optimization with solution ranking for design of spur gear pair considering multiple failure modes. Tribol Int 180:108284MATH
5.
Litak G, Friswell MI (2005) Dynamics of a gear system with faults in meshing stiffness. Nonlinear Dyn 41(4):415–421MATH
6.
Luo Y, Cui L, Zhang J et al (2021) Vibration mechanism and improved phenomenological model of planetary gearbox with broken sun gear fault. Measurement 178:109356MATH
7.
Karpat F, Dirik AE, Kalay OC et al (2021) Fault diagnosis with deep learning for standard and asymmetric involute spur gears. ASME Int Mech Eng Congr Expos Am Soc Mech Eng 85697:V013T14A029MATH
8.
Tian X, Zuo MJ, Fyfe KR (2004) Analysis of the vibration response of a gearbox with gear tooth faults. ASME Int Mech Eng Congr Expos 47063:785–793MATH
9.
Han H, Yuan K, Ma H et al (2023) Mesh characteristic analysis and dynamic simulation of spur gear pair considering corner contact and tooth broken fault. Eng Fail Anal 143:106883MATH
10.
Yang W, Jiang D, Han T (2017) Effects of tooth breakage size and rotational speed on the vibration response of a planetary Gearbox. Appl Sci 7(7):678MATH
11.
Zhang X, Niu H, Hou C et al (2021) Tooth faults detection of planetary gearboxes based on tooth root strain signal of ring gear. Measurement 170:108685
12.
Hou J, Yang S, Li Q, Wang J (2021) Mesh stiffness calculation and vibration analysis of the spur gear pair with tooth crack, considering the misalignment between the base and root circles. Int J Mech Syst Dyn 1:143–156MATH
13.
Dadon I, Koren N, Klein R et al (2019) A step toward fault type and severity characterization in spur gears. J Mech Des 141(8):1–22
14.
Han L, Qi HJ (2017) Influences of tooth spalling or local breakage on time-varying mesh stiffness of helical gears. Eng Fail Anal 79:75–88MATH
15.
Shen ZX, Qiao BJ, Yang LH et al (2021) Fault mechanism and dynamic modeling of planetary gear with gear wear. Mech Mach Theory 155:104098MATH
16.
Karray M, Chaari F, Viadero F, et al (2013) Dynamic response of single stage bevel gear transmission in presence of local damage. In: New trends in mechanism and machine science, theory and applications in engineering, pp 337–345
17.
Chen W, Lei Y, Fu Y et al (2021) A study of effects of tooth surface wear on time-varying mesh stiffness of external spur gear considering wear evolution process. Mech Mach Theory 155:104055MATH
18.
Huangfu Y, Zhao Z, Ma H et al (2020) Effects of tooth modifications on the dynamic characteristics of thin-rimmed gears under surface wear. Mech Mach Theory 150:103870MATH
19.
Wang H, Tang L, Zhou C et al (2021) Wear life prediction method of crowned double helical gear drive in point contact mixed elastohydrodynamic lubrication. Wear 484:204041
20.
Amarnath M, Lee SK (2015) Assessment of surface contact fatigue failure in a spur geared system based on the tribological and vibration parameter analysis. Measurement 76:32–44MATH
21.
Feng K, Smith WA, Borghesani P et al (2021) Use of cyclostationary properties of vibration signals to identify gear wear mechanisms and track wear evolution. Mech Syst Signal Process 150:107258
22.
Chen K, Huangfu Y, Ma H et al (2019) Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths. Mech Syst Signal Process 130:273–292MATH
23.
Wang S, Zhu R (2022) An improved mesh stiffness calculation model for cracked helical gear pair with spatial crack propagation path. Mech Syst Signal Process 172:108989MATH
24.
Thirumurugan R, Gnanasekar N (2020) Influence of finite element model, load-sharing and load distribution on crack propagation path in spur gear drive. Eng Fail Anal 110:104383MATH
25.
Thirumurugan R (2020) Study on the quality and tooth root load carrying capacity of the high contact ratio asymmetrical gear tooth machined using WCEDM process. Mater Manuf Processes 35:1352–1361MATH
26.
Yang L, Wang L, Yu W et al (2021) Investigation of tooth crack opening state on time varying meshing stiffness and dynamic response of spur gear pair. Eng Fail Anal 121:105181MATH
27.
Yang L, Wang L, Shao Y et al (2023) A double-layer iterative analytical model for mesh stiffness and load distribution of early-stage cracked gear based on the slicing method. Mech Syst Signal Process 198:110456
28.
Yu W, Mechefske CK, Timusk M (2018) A new dynamic model of a cylindrical gear pair with localized spalling defects. Nonlinear Dyn 91:2077–2095MATH
29.
Guilbault R, Lalonde S, Thomas M (2015) Modeling and monitoring of tooth fillet crack growth in dynamic simulation of spur gear set. J Sound Vib 343:144–165MATH
30.
Hu J, Hu NQ, Yang Y et al (2022) Nonlinear dynamic modeling and analysis of a helicopter planetary gear set for tooth crack diagnosis. Measurement 198:111347MATH
31.
Hu AJ, Liu SX, Xiang L et al (2022) Dynamic modeling and analysis of multistage planetary gear system considering tooth crack fault. Eng Fail Anal 137:106408MATH
32.
Chen KK, Huangfu YF, Zhao ZF et al (2022) Dynamic modeling of the gear-rotor systems with spatial propagation crack and complicated foundation structure. Mech Mach Theory 172:104827MATH
33.
Abdallah O, Sassi S (2024) Contribution of friction-induced vibration to the realistic failure analysis of spur gear cracked teeth. Eng Fail Anal 158:107956MATH
34.
Zhao J, Hou L, Li Z et al (2022) Prediction of tribological and dynamical behaviors of spur gear pair considering tooth root crack. Eng Fail Anal 135:106145MATH
35.
Chen Z, Shao Y (2011) Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth. Eng Fail Anal 18(8):2149–2164MATH
36.
Ghorbel A, Zghal B, Abdennadher M et al (2018) Effect of the gear local damage and profile error of the gear on the drivetrain dynamic response. J Theor Appl Mech 56(3):765–779MATH
37.
Cooley C, Wang Y, Hood A (2022) Damage-induced dynamic tooth contact forces in spur gears with root cracks. SAE Int J Adv Curr Prac Mobil 5:57–66
38.
Luo Y, Baddour N, Liang M (2019) Dynamical modeling and experimental validation for tooth pitting and spalling in spur gears. Mech Syst Signal Process 119:155–181MATH
39.
Huangfu YF, Chen KK, Ma H et al (2020) Meshing and dynamic characteristics analysis of spalled gear systems: a theoretical and experimental study. Mech Syst Signal Process 139:106640MATH
40.
Cheng ZB, Huang K, Xiong YS et al (2022) An improved model for dynamic characteristics analysis of high-contact-ratio spur gears considering localised tooth spall defect. Eng Fail Anal 140:106600MATH
41.
Shi LJ, Wen J, Pan BS et al (2020) Dynamic characteristics of a gear system with double-teeth spalling fault and its fault feature analysis. Appl Sci 10:7058MATH
42.
Jedliński Ł, Syta A, Gajewski J et al (2022) Nonlinear analysis of cylindrical gear dynamics under varying tooth breakage. Measurement 190:110721
43.
Jiang HJ, Shao YM, Mechefske CK (2014) Dynamic characteristics of helical gears under sliding friction with spalling defect. Eng Fail Anal 39:92–107MATH
44.
Jiang HJ, Liu FH (2016) Dynamic features of three-dimensional helical gears under sliding friction with tooth breakage. Eng Fail Anal 70:305–322MATH
45.
Yang Y, Hu N, Tang J et al (2021) Dynamic analysis for a spur geared rotor system with tooth tip chipping based on an improved time-varying mesh stiffness model. Mech Mach Theory 165:104435
46.
Shi J, Gou X, Zhu L (2019) Modeling and analysis of a spur gear pair considering multi-state mesh with time-varying parameters and backlash. Mech Mach Theory 134:582–603MATH
47.
Shi J, Gou X, Jin W et al (2023) Multi-meshing-state and disengaging-proportion analyses of a gear-bearing system considering deterministic-random excitation based on nonlinear dynamics. J Sound Vib 544:117360MATH
48.
Shi JF, Gou XF, Zhu LY (2020) Bifurcation of multi-stable behaviors in a two-parameter plane for a non-smooth nonlinear system with time-varying parameters. Nonlinear Dyn 100:3347–3365MATH
49.
Zhu LY, Li ZF, Gou XF et al (2021) Analysis of safety characteristics by nonlinear dynamics and safety basin methods for the spur gear pair in the established teeth contact safety domain. Mech Syst Signal Process 158:107718MATH
50.
Li ZF, Zhu LY, Chen SQ et al (2022) Study on safety characteristics of the spur gear pair considering time-varying backlash in the established multi-level safety domains. Nonlinear Dyn 109(3):1297–1324MATH
51.
Zhu LY, Li ZF, Gou XF et al (2021) Evolutionary mechanism of safety performance for spur gear pair based on meshing safety domain. Nonlinear Dyn 104(1):215–239MATH
52.
Liu P, Zhu L, Gou X et al (2021) Neighboring periodic motion in spur gear pair and its identification methods. Nonlinear Dyn 106(4):2991–3023MATH
53.
Mo S, Zhang Y, Luo B et al (2022) The global behavior evolution of non-orthogonal face gear-bearing transmission system. Mech Mach Theory 175:104969MATH
54.
Bai XZ, Qiu HZ, Shi JF et al (2023) Nonlinear dynamic modeling and global instability analyses of planetary gear trains considering multi-state engagement and tooth-contact temperature effects. Nonlinear Dyn 111(22):20843–20868
55.
Gou XF, Zhu LY, Chen DL (2015) Bifurcation and chaos analysis of spur gear pair in two-parameter plane. Nonlinear Dyn 79:2225–2235MATH
56.
Ma H, Song R, Pang X et al (2014) Time-varying mesh stiffness calculation of cracked spur gears. Eng Fail Anal 44:179–194MATH
57.
Yang Y, Tang J, Hu N et al (2023) Research on the time-varying mesh stiffness method and dynamic analysis of cracked spur gear system considering the crack position. J Sound Vib 548:117505MATH
58.
Saxena A, Parey A, Chouksey M (2016) Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects. Eng Fail Anal 70:200–211
59.
Liu H, Yan P, Gao P (2020) Effects of temperature on the time-varying mesh stiffness, vibration response, and support force of a multi-stage planetary gear. J Vib Acoust 142:051110MATH
60.
Sun Z, Chen S, Hu Z et al (2022) Analytical models for thermal deformation and mesh stiffness of spur gears under steady temperature field. Eng Fail Anal 133:105972MATH
61.
Gou X, Zhu L, Qi C (2017) Nonlinear dynamic model of a gear-rotor-bearing system considering the flash temperature. J Sound Vib 410:187–208MATH
62.
Zhang X, Zhong J, Li W et al (2022) Nonlinear dynamic analysis of high-speed gear pair with wear fault and tooth contact temperature for a wind turbine gearbox. Mech Mach Theory 173:104840
63.
Shi JF, Gou XF, Zhu LY (2022) Five-state engaging model and dynamics of gear-rotor-bearing system based on time-varying contact analysis considering gear temperature and lubrication. Appl Math Model 112:47–77MathSciNetMATH
64.
Pan W, Li X, Wang L et al (2019) Nonlinear response analysis of gear-shaft-bearing system considering tooth contact temperature and random excitations. Appl Math Model 68:113–136MathSciNetMATH
65.
Pedrero JI, Pleguezuelos M, Sánchez MB (2023) Analytical model for meshing stiffness, load sharing, and transmission error for helical gears with profile modification. Mech Mach Theory 185:105340MATH
66.
Sánchez MB, Pleguezuelos M, Pedrero JI (2017) Approximate equations for the meshing stiffness and the load sharing ratio of spur gears including hertzian effects. Mech Mach Theory 109:231–249MATH
Metadata
Title
Multi-state meshing characteristics and global nonlinear dynamics of a spur gear system considering local tooth breakage
Authors
Qing-Zhong Gong
Jian-Fei Shi
Wen-Hu Nan
Gang Zhao
Peng-Fei Qi
Publication date
18-12-2024
Publisher
Springer Netherlands
Published in
Meccanica / Issue 1/2025
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-024-01924-w

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