Analysis of meshing characteristics of planetary gear system considering tooth surface roughness and elastohydrodynamic lubrication

Abstract

The contact characteristics of the rough tooth surface during the meshing process are significantly affected by the lubrication state. The coupling effect of tooth surface roughness and lubrication on meshing characteristics of planetary gear is studied. An improved three-dimensional (3D) anisotropic tooth surface roughness fractal model is proposed based on the experimental parameters. Considering asperity contact and elastohydrodynamic lubrication (EHL), the contact load and flexibility deformation of the tooth surface are derived, and the deformation compatibility equation of the 3D loaded tooth contact analysis (3D-LTCA) method is improved. The asperity of the tooth surface changes the system from EHL to mixed lubrication and reduces the stiffness of the oil film. Compared with the sun-planet gear, the asperity has a greater effect on the meshing characteristics of the ring-planet gear. Compared with the proposed method, the comprehensive stiffness obtained by the traditional calculation method considering the lubrication effect is smaller, especially for the ring-planet gear. Compared with roughness, speed and viscosity, the meshing characteristics of planetary gears are most sensitive to torque.

Keywords

planetary gear / tooth surface roughness / three-dimensional loaded tooth contact analysis / elastohydrodynamic lubrication / meshing stiffness

References

[1] FengK, JiJ C, NiQ, et al.. A review of vibration-based gear wear monitoring and prediction techniques [J]. Mechanical Systems and Signal Processing, 2023, 182109605

[2] LiangX-h, ZuoM J, FengZ-peng. Dynamic modeling of gearbox faults: A review [J]. Mechanical Systems and Signal Processing, 2018, 98: 852-876

[3] MaH, FanC-z, ZhangY-c, et al.. Digital twin-inspired methods for rotating machinery intelligent fault diagnosis and remaining useful life prediction: A state-of-the-art review and future challenges [J]. Mechanical Systems and Signal Processing, 2025, 232112770

[4] LingF F. Scaling law for contoured length of engineering surfaces [J]. Journal of Applied Physics, 1987, 62(6): 2570-2572

[5] MajumdarA, TienC L. Fractal characterization and simulation of rough surfaces [J]. Wear, 1990, 136(2): 313-327

[6] MajumdarA, BhushanB. Fractal model of elastic-plastic contact between rough surfaces [J]. Journal of Tribology, 1991, 113(1): 1-11

[7] BorodichF M. Analytical studies of contact problems for fractal surfaces [J]. Tribology and Interface Engineering Series, 2005, 48: 537-545

[8] YanW, KomvopoulosK. Contact analysis of elastic-plastic fractal surfaces [J]. Journal of Applied Physics, 1998, 84(7): 3617-3624

[9] MengF-s, XiaH, ZhangX, et al.. Study on nonlinear dynamic characteristics of gear system with 3D anisotropic rough tooth surface based on fractal theory [J]. International Journal of Non-Linear Mechanics, 2023, 150104366

[10] XiaH, MengF-s, ZhangX, et al.. Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics [J]. Nonlinear Dynamics, 2023, 111(16): 14851-14877

[11] MoS, WangL, HuQ-s, et al.. Coupling failure dynamics of tooth surface morphology and wear based on fractal theory [J]. Nonlinear Dynamics, 2024, 112(1): 175-195

[12] XuX-y, ShiL, FanL-fang. A fractal prediction method for contact stiffness of helical gear considering asperity lateral contact and interaction [J]. Lubricants, 2023, 1112509

[13] ZhangQ, LiuJ-y, WuS-j, et al.. Dynamics characteristics of wind turbine gear pairs considering lubrication and tooth surface roughness [J]. Meccanica, 2024, 59(2): 255-277

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

[15] HuangK, ChengZ-b, XiongY-s, et al.. Bifurcation and chaos analysis of a spur gear pair system with fractal gear backlash [J]. Chaos, Solitons & Fractals, 2021, 142110387

[16] ZhaoZ-f, YangY, HanH-z, et al.. Meshing characteristics of spur gears considering three-dimensional fractal rough surface under elastohydrodynamic lubrication [J]. Machines, 2022, 108705

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

[18] YouS-y, TangJ-yuan. Thermoelastoplastic hydrodynamic lubrication contact analysis of three dimensional rough tooth surface considering micro-scale effect and thermal effect [J]. Tribology International, 2024, 191109134

[19] ShiX-j, SunW, LuX-q, et al.. Three-dimensional mixed lubrication analysis of spur gears with machined roughness [J]. Tribology International, 2019, 140105864

[20] YangX-k, Tofighi-NiakiE, ZuoM J, et al.. Analysis of spur gearbox dynamics considering tooth lubrication and tooth crack severity progression [J]. Tribology International, 2023, 178108027

[21] XiaoH-f, GaoJ-s, WuJ-zhou. Mesh stiffness model of a spur gear pair with surface roughness in mixed elastohydrodynamic lubrication [J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022, 444136

[22] ZhouC-j, XiaoZ-liang. Stiffness and damping models for the oil film in line contact elastohydrodynamic lubrication and applications in the gear drive [J]. Applied Mathematical Modelling, 2018, 61: 634-649

[23] MaH, SongR-z, PangX, et al.. Time-varying mesh stiffness calculation of cracked spur gears [J]. Engineering Failure Analysis, 2014, 44: 179-194

[24] MohammedO D, RantataloM, AidanpääJ O. Improving mesh stiffness calculation of cracked gears for the purpose of vibration-based fault analysis [J]. Engineering Failure Analysis, 2013, 34: 235-251

[25] TangX-l, ZouL, YangW, et al.. Novel mathematical modelling methods of comprehensive mesh stiffness for spur and helical gears [J]. Applied Mathematical Modelling, 2018, 64: 524-540

[26] MaH, ZengJ, FengR-j, et al.. An improved analytical method for mesh stiffness calculation of spur gears with tip relief [J]. Mechanism and Machine Theory, 2016, 98: 64-80

[27] HuangfuY-f, DongX-j, CaoY-x, et al.. A life-cycle dynamic wear degradation model of planetary gear systems [J]. Wear, 2024, 542205281

[28] LinT-j, HeZ-yin. Analytical method for coupled transmission error of helical gear system with machining errors, assembly errors and tooth modifications [J]. Mechanical Systems and Signal Processing, 2017, 91: 167-182

[29] RaghuwanshiN K, PareyA. Experimental measurement of mesh stiffness by laser displacement sensor technique [J]. Measurement, 2018, 128: 63-70

[30] KarpatF, YuceC, DoganO. Experimental measurement and numerical validation of single tooth stiffness for involute spur gears [J]. Measurement, 2020, 150107043

[31] ChangL-h, LiuG, WuL-yan. A robust model for determining the mesh stiffness of cylindrical gears [J]. Mechanism and Machine Theory, 2015, 87: 93-114

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

[33] HuangfuY-f, DongX-j, ChenK-k, et al.. A tribo-dynamic based pitting evolution model of planetary gear sets: A topographical updating approach [J]. International Journal of Mechanical Sciences, 2022, 220107157

[34] LiuZ, LiF-c, XuZ-t, et al.. Semi-analytical loaded tooth contact analysis method for spiral bevel gears [J]. International Journal of Mechanical Sciences, 2023, 253108329

[35] HanH-z, ZhaoZ-f, TianH-x, et al.. Fault feature analysis of planetary gear set influenced by cracked gear tooth and pass effect of the planet gears [J]. Engineering Failure Analysis, 2021, 121105162

[36] HanH-z, MaH, TianH-x, et al.. Sideband analysis of cracked planetary gear train considering output shaft radial assembly error [J]. Mechanical Systems and Signal Processing, 2023, 200110618

[37] CooleyC G, LiuC-g, DaiX, et al.. Gear tooth mesh stiffness: A comparison of calculation approaches [J]. Mechanism and Machine Theory, 2016, 105: 540-553

[38] MarafonaJ D M, MarquesP M T, MartinsR C, et al.. Mesh stiffness models for cylindrical gears: A detailed review [J]. Mechanism and Machine Theory, 2021, 166104472

[39] HuangW-k, MaH, ZhaoZ-f, et al.. An iterative model for mesh stiffness of spur gears considering slice coupling under elastohydrodynamic lubrication [J]. Journal of Central South University, 2023, 30(10): 3414-3434

[40] LiuZ-m, ChangC, HuH-d, et al.. Meshing characteristic analysis of spur gear pair with tooth surface wear fault based on improved fractal method [J]. Journal of Central South University, 2024, 31(5): 1619-1636

[41] ZhengM, HanY, HouS-w, et al.. Anisotropic 3D rough surface reconstruction model based on fractal method and its application in contact characteristics [J]. Meccanica, 2024, 59(2): 235-254

[42] Dwyer-JoyceR S, ReddyhoffT, ZhuJ. Ultrasonic measurement for film thickness and solid contact in elastohydrodynamic lubrication [J]. Journal of Tribology, 2011, 1333031501

[43] LiuN, MaH, ZhaoZ-f, et al.. Dynamic characteristics of gear-rotor system with gear eccentricity and wear fault [J]. Nonlinear Dynamics, 2024, 112(18): 16003-16035

[44] HaddadC DThe elastic analysis of load distribution in wide-faced helical gears [D], 1991, Newcastle. Newcastle University.

[45] CooperD H. Hertzian contact-stress deformation coefficients [J]. Journal of Applied Mechanics, 1969, 362296

[46] TianH-x, ZhaoX-j, HuangW-k, et al.. A stiffness model for EHL contact on smooth/rough surfaces and its application in mesh stiffness calculation of the planetary gear set [J]. Tribology International, 2024, 196109720

[47] ChangW R, EtsionI, BogyD B. Static friction coefficient model for metallic rough surfaces [J]. Journal of Tribology, 1988, 110(1): 57-63

[48] YanW, KomvopoulosK. Contact analysis of elastic-plastic fractal surfaces [J]. Journal of Applied Physics, 1998, 84(7): 3617-3624

[49] LiX-p, YueB, ZhaoG-h, et al.. Fractal prediction model for normal contact damping of joint surfaces considering friction factors and its simulation [J]. Advances in Mechanical Engineering, 2014, 6378518

[50] YangX-k, Tofighi-NiakiE, ZuoM J, et al.. Analysis of spur gearbox dynamics considering tooth lubrication and tooth crack severity progression [J]. Tribology International, 2023, 178108027

[51] RaghuwanshiN K, PareyA. Experimental measurement of spur gear mesh stiffness using digital image correlation technique [J]. Measurement, 2017, 111: 93-104

[52] XiaoH-f, GaoJ-s, WuJ-zhou. Mesh stiffness model of a spur gear pair with surface roughness in mixed elastohydrodynamic lubrication [J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022, 444136

[53] ZhouC-j, XiaoZ-l, ChenS-y, et al.. Normal and tangential oil film stiffness of modified spur gear with non-Newtonian elastohydrodynamic lubrication [J]. Tribology International, 2017, 109: 319-327

[54] RamaT, GnanasekarN. Investigation of the effect of load distribution along the face width and load sharing between the pairs in contact on the fracture parameters of the spur gear tooth with root crack [J]. Engineering Failure Analysis, 2019, 97: 518-533

[55] PedreroJ I, PleguezuelosM, ArtésM, et al.. Load distribution model along the line of contact for involute external gears [J]. Mechanism and Machine Theory, 2010, 45(5): 780-794

RIGHTS & PERMISSIONS

Central South University