Meshing characteristic analysis of spur gear pair with tooth surface wear fault based on improved fractal method

Abstract

The three-dimensional (3D) fractal contact model of the interaction between gear teeth is established considering the actual surface morphology of gear teeth. The time-varying meshing stiffness (TVMS) model of spur gear pair is established and verified by finite element (FE) method based on the loaded tooth contact analysis (LTCA) method and considering the influence of friction between the gear teeth. The meshing characteristics and wear depth under tooth surface wear fault condition are analyzed by incorporating the Archard’s wear model, considering the effects of tooth roughness and friction. The effects of friction and fractal parameters on TVMS and wear depth are analyzed. Friction causes the TVMS at the pitch line position to mutate. The increase in friction coefficient and decrease in fractal dimension result in the increase in wear depth and the decrease in TVMS within the region where two pairs of gear teeth engage in meshing. TVMS shows partial linearity with the change of fractal dimension. The influence of fractal dimension on TVMS and wear depth becomes increasingly prominent with the progression of wear cycles, surpassing the influence of friction coefficient.

Keywords

spur gear pair / meshing characteristics / fractal contact / friction / tooth surface wear fault

References

[1] HanY-y, ChenX-h, XiaoJ-w, et al. . An improved coupled dynamic modeling for exploring gearbox vibrations considering local defects. Journal of Dynamics, Monitoring and Diagnostics, 2023, 2(4): 262-274[J]

[2] HuangR-y, XiaJ-y, ZhangB, et al. . Compound fault diagnosis for rotating machinery: State-of-the-art, challenges, and opportunities. Journal of Dynamics, Monitoring and Diagnostics, 2023, 2(1): 13-29[J]

[3] ChenK-k, HuangfuY-f, MaH, et al. . Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths. Mechanical Systems and Signal Processing, 2019, 130: 273-292 J]

[4] PatilV, ChouhanV, PandyaY. Geometrical complexity and crack trajectory based fatigue life prediction for a spur gear having tooth root crack. Engineering Failure Analysis, 2019, 105: 444-465 J]

[5] RezaeiM, PoursinaM, JaziS H, et al. . Multi crack detection in helical gear teeth using transmission error ratio. Journal of Mechanical Science and Technology, 2019, 33(3): 1115-1121 J]

[6] ShenZ-x, QiaoB-j, YangL-h, et al. . Evaluating the influence of tooth surface wear on TVMS of planetary gear set. Mechanism and Machine Theory, 2019, 136: 206-223 J]

[7] ShenZ-x, QiaoB-j, YangL-h, et al. . Fault mechanism and dynamic modeling of planetary gear with gear wear. Mechanism and Machine Theory, 2021, 155: 104098 J]

[8] HuangfuY-f, ZhaoZ-f, MaH, et al. . Effects of tooth modifications on the dynamic characteristics of thin-rimmed gears under surface wear. Mechanism and Machine Theory, 2020, 150103870 J]

[9] WangH-b, ZhouC-j, WangH-h, et al. . A novel contact model for rough surfaces using piecewise linear interpolation and its application in gear wear. Wear, 2021, 476203685 J]

[10] OsmanT, VelexP. Static and dynamic simulations of mild abrasive wear in wide-faced solid spur and helical gears. Mechanism and Machine Theory, 2010, 45(6): 911-924 J]

[11] BajpaiP, KahramanA, AndersonN E. A surface wear prediction methodology for parallel-axis gear pairs. Journal of Tribology, 2004, 126(3): 597-605 J]

[12] LiuX-z, YangY-h, ZhangJun. Investigation on coupling effects between surface wear and dynamics in a spur gear system. Tribology International, 2016, 101383-394 J]

[13] FengK, BorghesaniP, SmithW A, et al. . Vibration-based updating of wear prediction for spur gears. Wear, 2019, 426–427: 1410-1415 J]

[14] ZhouC-j, XingM-c, HuB, et al. . A modified wear model considering contact temperature for spur gears in mixed elastohydrodynamic lubrication. Tribology Letters, 2020, 68(4): 110 J]

[15] WangH-b, TangL-w, ZhouC-j, et al. . Wear life prediction method of crowned double helical gear drive in point contact mixed elastohydrodynamic lubrication. Wear, 2021, 484–485: 204041 J]

[16] TianH-x, HanH-z, ZhaoZ-f, et al. . Wear prediction and meshing characteristics for the planetary gear set considering angular misalignment and rotating carrier. Engineering Failure Analysis, 2022, 140106583 J]

[17] DrozdovY N, GavrikovY A. Friction and scoring under the conditions of simultaneous rolling and sliding of bodies. Wear, 1968, 114291-302 J]

[18] BenedictG H, KelleyB W. Instantaneous coefficients of gear tooth friction. ASLE Transactions, 1961, 4(1): 59-70 J]

[19] XuH, KahramanA. Prediction of friction-related power losses of hypoid gear pairs. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 2007, 221(3): 387-400[J]

[20] KarC, MohantyA R. An algorithm for determination of time-varying frictional force and torque in a helical gear system. Mechanism and Machine Theory, 2007, 42(4): 482-496 J]

[21] Fernandez Del RinconA, ViaderoF, IglesiasM, et al. . A model for the study of meshing stiffness in spur gear transmissions. Mechanism and Machine Theory, 2013, 6130-58 J]

[22] FekI N, HammamiM, KsentiniO, et al. . Frictional dynamic model predictions of FZG-A10 spur gear pairs considering profile errors. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2021, 235(7): 1390-1404 J]

[23] MengF-s, XiaH, ZhangX, et al. . 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, 150104366 J]

[24] LiG, WangZ H, ZhuW D. Prediction of surface wear of involute gears based on a modified fractal method. Journal of Tribology, 2019, 141(3): 031603 J]

[25] YuX, SunY-y, ZhaoD, et al. . A revised contact stiffness model of rough curved surfaces based on the length scale. Tribology International, 2021, 164107206 J]

[26] YuX, SunY-y, LiH-g, et al. . Nonlinear characteristics of gear pair considering fractal surface dynamic contact as internal excitation. International Journal of Non-Linear Mechanics, 2022, 143104027 J]

[27] PanW-j, LingL-y, QuH-y, et al. . Early wear fault dynamics analysis method of gear coupled rotor system based on dynamic fractal backlash. Journal of Computational and Nonlinear Dynamics, 2022, 171011003 J]

[28] YuX, SunY-y, LiH-g, et al. . An improved meshing stiffness calculation algorithm for gear pair involving fractal contact stiffness based on dynamic contact force. European Journal of Mechanics – A, 2022, 94104595 J]

[29] LiX-p, XuJ-c, YangZ-m, et al. . The influence of tooth surface wear on dynamic characteristics of gear-bearing system based on fractal theory. Journal of Computational and Nonlinear Dynamics, 2020, 154041004 J]

[30] LiuZ-f, ZhangT, WangY-d, et al. . Experimental studies on torsional stiffness of cycloid gear based on machining parameters of tooth surfaces. International Journal of Precision Engineering and Manufacturing, 2019, 2061017-1025 J]

[31] ChenQ, WangY-d, TianW-f, et al. . An improved nonlinear dynamic model of gear pair with tooth surface microscopic features. Nonlinear Dynamics, 2019, 96(2): 1615-1634 J]

[32] MAO Han-cheng, SUN Yong-guo, XU Tian-tian, et al. Numerical calculation method of meshing stiffness for the beveloid gear considering the effect of surface topography [J]. Mathematical Problems in Engineering, 2021: 8886792. DOI: https://doi.org/10.1155/2021/8886792.

[33] YuG-b, MaoH-c, JiangL-d, et al. . Fractal contact mechanics model for the rough surface of a beveloid gear with elliptical asperities. Applied Sciences, 2022, 12(8): 4071 J]

[34] ZhaoZ-f, HanH-z, WangP-f, et al. . An improved model for meshing characteristics analysis of spur gears considering fractal surface contact and friction. Mechanism and Machine Theory, 2021, 158104219 J]

[35] ShiX-j, LuX-q, HeT, et al. . Predictions of friction and flash temperature in marine gears based on a 3D line contact mixed lubrication model considering measured surface roughness. Journal of Central South University, 2021, 2851570-1583 J]

[36] HuangfuY-f, ChenK-k, MaH, et al. . Meshing and dynamic characteristics analysis of spalled gear systems: A theoretical and experimental study. Mechanical Systems and Signal Processing, 2020, 139106640 J]

[37] WangP-f, XuH-y, MaH, et al. . Effects of three types of bearing misalignments on dynamic characteristics of planetary gear set-rotor system. Mechanical Systems and Signal Processing, 2022, 169108736 J]

[38] LiuZ-m, ChangC, HuH-d, et al. . Dynamic characteristics of spur gear system with tooth root crack considering gearbox flexibility. Mechanical Systems and Signal Processing, 2024, 208110966 J]

[39] LiuZ-m, ShangE-l, HuangfuY-f, et al. . Vibration characteristics analysis of flexible helical gear system with multi-tooth spalling fault: Simulation and experimental study. Mechanical Systems and Signal Processing, 2023, 201110687 J]

[40] HuangW-k, MaH, ZhaoZ-f, et al. . 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 J]

[41] BuckinghamEAnalytical mechanics of gears, 1949, New York, McGraw-Hill Book Co.[M]

[42] Mahovic PoljacekS, RisovicD, FuriC K, et al. . Comparison of fractal and profilometric methods for surface topography characterization. Applied Surface Science, 2008, 254(11): 3449-3458 J]

[43] ShenF, LiY-h, KeL-liang. On the size distribution of truncation areas for fractal surfaces. International Journal of Mechanical Sciences, 2023, 237107789 J]