Reliability assessment and identification model of time-varying tooth flank loaded contact pressure for face-hobbed spiral bevel gears

Abstract

Time-varying tooth flank loaded contact pressure provides significant access to load capability, contact strength, and fatigue life forecasting for face-hobbed spiral bevel gears. Considering the reliability and time-varying meshing characteristics, an innovative assessment and identification model is developed using the discrete convolution and fast Fourier transformation (DC-FFT)-based conjugate gradient method (CGM). The reliability assessment mainly includes the edge impact, time-varying meshing characteristics, and the maximum loaded contact pressure, in addition to conventional assessment items. Firstly, an advanced face-hobbed cutting process involving a continuous indexing method is simulated for tooth flank modeling. Subsequently, contact initialization, time-varying edge contact solution, and numerical loaded tooth contact analysis (NLTCA) approximation and operation are developed for the loaded contact pressure reliability analysis and assessment. In particular, the time-varying edge impact provides an accurate parametric computation for reliability and assessment. Moreover, a DC-FFT-based CGM is used to establish time-varying loaded flank identification considering reliability assessment. Finally, a spiral bevel gear set from a helicopter transmission system is used to verify the impact of the proposed model on the loaded flank pressure distribution.

Keywords

Loaded contact pressure / Face-hobbed spiral bevel gears / Discrete convolution and fast Fourier transform (DC-FFT) / Conjugate gradient method (CGM) / Edge impact

References

[1] Litvin FL, Fuentes A. Gear geometry and applied theory, 2004, Englewood Cliffs, PTR Prentice Hall

[2] Litvin FL, Zhang Y, Kieffer J, et al. . Identification and minimization of deviations of real gear tooth surfaces. ASME J Mech Des, 1991, 113: 55-62

[3] Alfonso FZ, Ramon RO, Ignacio GP. Numerical approach for determination of rough-cutting machine-tool settings for fixed-setting face-milling spiral bevel gears. Mech Mach Theory, 2017, 112: 22-42

[4] Ding H, Li YB, Zhang YT, et al. . High-performance tooth flank collaborative optimization model for spiral bevel and hypoid gears. Adv Eng Inform, 2023, 57 102059

[5] Artoni A, Gabiccini M, Guiggiani M, et al. . Multi-objective ease-off optimization of hypoid gears for their efficiency, noise, and durability performances. ASME J Mech Des, 2011, 133(12 121007

[6] Simon VV. Machine-tool settings to reduce the sensitivity of spiral bevel gears to tooth errors and misalignments. ASME J Mech Des, 2008, 130 082603

[7] Artoni A, Gabiccini M, Guiggiani M. Nonlinear identification of machine settings for flank form modifications in hypoid gears. ASME J Mech Des, 2008, 130 112602

[8] Chen XL, Ding H, Shao W. Adaptive data-driven collaborative optimization of both geometric and loaded contact mechanical performances of non-orthogonal duplex helical face-milling spiral bevel and hypoid gears. Mech Mach Theory, 2020, 154 104028

[9] Tang WM, Huang YK, Wu YK, et al. . Geometry design, meshing analysis and error influences of face-hobbed cycloidal bevel gears with double circular-arc profile for a nutation drive. Mech Mach theory, 2022, 176 105001

[10] Chen P, Wang SM, Li F, et al. . A direct preset method for solving ease-off surface of spiral bevel gears. Mech Mach theory, 2023, 179 105123

[11] Ding H, Huang R, Liu HM, et al. . Loaded contact fatigue-oriented carburizing surface optimization model of spiral bevel gears. Mech Mach Theory, 2022, 174 104884

[12] Han HZ, Zhang SH, Yang Y, et al. . Modulation sidebands analysis of coupled bevel gear pair and planetary gear train system. Mech Mach Theory, 2022, 176 104979

[13] Ignacio GP, Alfonso FA. Reverse engineering of spiral bevel gear drives reconstructed from point clouds. Mech Mach Theory, 2022, 170 104694

[14] Hu ZH, Ding H, Peng SD, et al. . Numerical determination to loaded tooth contact performances in consideration of misalignment for the spiral bevel gears. Int J Mech Sci, 2019, 151: 343-355

[15] Li HN, Tang JY, Chen SY, et al. . Loaded contact pressure distribution prediction for spiral bevel gear. Int J Mech Sci, 2023, 242 108027

[16] Sheveleva GI, Volkov AE, Medvedev VI. Algorithms for analysis of meshing and contact of spiral bevel gears. Mech Mach Theory, 2007, 422): 198-215

[17] Peng SD, Ding H, Tang JY. Accurate numerical computation of loaded tooth surface contact pressure and stress distributions for spiral bevel gears by considering time-varying meshing characteristics. Adv Eng Softw, 2019, 135 102683

[18] Kolivand M, Kahraman A. A load distribution model for hypoid gears using ease-off topography and shell theory. Mech Mach Theory, 2009, 44: 1848-1865

[19] Ding H, Tang JY, Shao W, et al. . An innovative determination approach to tooth compliance for spiral bevel and hypoid gears by using double-curved shell model and Rayleigh-Ritz approach. Mech Mach Theory, 2018, 130: 27-46

[20] Qu W, Ding H, Tang JY. An innovative semi-analytical determination approach to numerical loaded tooth contact analysis (NLTCA) for spiral bevel and hypoid gears. Adv Eng Softw, 2020, 149 102892

[21] Vivet M, Tamarozzi T, Desmet W, et al. . On the modeling of gear alignment errors in the tooth contact analysis of spiral bevel gears. Mech Mach Theory, 2021, 155 104065

[22] Gabiccini M, Bracci A, Guiggiani M. Robust optimization of the load contact pattern in hypoid gears with uncertain misalignments. ASME J Mech Des, 2010, 132 041010

[23] Lu SF, Ding H, Rong KB, et al. . Composite mechanical deformation based semi-analytical prediction model for dynamic loaded contact pressure of thin-walled aerospace spiral bevel gears. Thin-Walled Struct, 2022, 171 108794

[24] Bracci A, Gabiccini A, Artoni A, et al. . Geometric contact pattern estimation for gear drives. Comput Methods Appl Mech Eng, 2009, 198: 1563-1571

[25] Huangfu YF, Dong XJ, Chen KK, et al. . Coupling mechanism between systematic elastic deformation and gear surface damage. Int J Mech Sci, 2023, 238 107850

[26] Ding H, Li HP, Shao W, et al. . Prediction and control for local bearing contact-based collaborative grinding of non-orthogonal aerospace spiral bevel gears. Mech Syst Signal Process, 2021, 160 107841

[27] Huang DQ, Wang ZH, Kubo A. Hypoid gear integrated wear model and experimental verification design and test. Int J Mech Sci, 2020, 166 105228

[28] Liu ZR, Wei HB, Wei J, et al. . Parametric modelling of vibration response for high-speed gear transmission system. Int J Mech Sci, 2023, 249 108273

[29] Ding H, Tang JY, Zhong J, et al. . A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears. J Manuf Syst, 2016, 41: 228-238

[30] Ding H, Zhang YT, Li HP, et al. . Bending fatigue life oriented tooth flank dry-grinding tool modification for cleaner manufacturing of spiral bevel gear product. J Clean Prod, 2021, 328 129566

[31] Simon VV. Design and manufacture of spiral bevel gears with reduced transmission errors. ASME J Mech Des, 2009, 131(4 041007

[32] Ding H, Rong SF, Rong KB, et al. . Semi-FEM dynamic meshing impact forecasting model for spiral bevel and hypoid gear transmission. Appl Math Model, 2022, 104: 279-305

[33] Fan Q, DaFoe RS, Swanger JW. Higher-order tooth flank form error correction for face-milled spiral bevel and hypoid gears. ASME J Mech Des, 2008, 130 072601

[34] He D, Ding H, Tang JY. A new analytical identification approach to the tooth contact points considering misalignments for spiral bevel or hypoid gears. Mech Mach Theory, 2018, 121: 785-803

[35] Shi JF, Gou XF, Zhu LY. 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, 2022, 112: 47-77

[36] Ding H, Li HP, Huang R, et al. . Adaptive data-driven prediction and optimization of tooth flank heat treatment deformation for aerospace spiral bevel gears by considering carburizing-meshing coupling effect. Int J Heat Mass Transf, 2021, 174 121301

[37] Litvin FL, Vecchiato D, Fuentes A, et al. . Automatic determination of guess values for simulation of meshing of gear drives. Comput Methods Appl Mech Eng, 2004, 193: 3745-3758

[38] Rong KB, Ding H, Chen SY, et al. . Top-rem grinding tool modification considering loaded edge contact for spiral bevel gears. Adv Eng Inform, 2022, 53 101697

[39] Kolivand M, Kahraman A. An ease-off based method for loaded tooth contact analysis of hypoid gears having local and global surface deviations. ASME J Mech Des, 2010, 132 071004

[40] Kong XN, Ding H, Huang R, et al. . Adaptive data-driven modeling, prediction and optimal control for loaded transmission error of helicopter zerol spiral bevel gear transmission system. Mech Mach Theory, 2021, 165 104417

[41] Gabiccini M, Bracci A, Guiggiani M. Robust optimization of the loaded contact pattern in hypoid gears with uncertain misalignments. ASME J Mech Des, 2010, 132 041010

[42] Shao W, Ding H, Tang JY, et al. . A data-driven optimization model to collaborative manufacturing system considering geometric and physical performances for hypoid gear product. Robot Comput Integr Manuf, 2018, 54: 1-16

[43] Liu JP, Shu XB, Kanazawa H, et al. . A model order reduction method for the simulation of gear contacts based on arbitrary Lagrangian Eulerian formulation. Comput Methods Appl Mech Eng, 2018, 338: 68-96

[44] Ding H, Rong SF, Rong KB, et al. . Life cycle assessment-driven collaborative optimization model of power dry cutting for face-hobbing hypoid gear production. J Clean Prod, 2023, 385 135710

[45] Artoni A, Kolivand M, Kahraman A. An ease-off based optimization of the loaded transmission error of hypoid gears. ASME J Mech Des, 2010, 132 011010

[46] Lei DC, Rong KB, Song BY, et al. . Digital twin modeling for tooth surface grinding considering low-risk transmission performance of non-orthogonal aviation spiral bevel gears. ISA Trans, 2022, 128: 646-663

[47] Rong KB, Ding H, Kong XN, et al. . Digital twin modeling for loaded contact pattern-based grinding of spiral bevel gears. Adv Eng Inform, 2021, 49 101305

[48] Ding H, Zhang YT, Kong XN, et al. . Data-driven bending fatigue life forecasting and optimization via grinding top-rem tool parameters for spiral bevel gears. Adv Eng Inform, 2022, 53 101724

[49] Polonsky IA, Keer LM. A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques. Wear, 1999, 231: 206-219

[50] Liu SB, Wang Q, Liu G. A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses. Wear, 2000, 243: 101-111

[51] Ding H, Tang JY. Six sigma robust multi-objective optimization modification of machine-tool settings for hypoid gears by considering both geometric and physical performances. Appl Soft Comput, 2018, 70: 550-561

[52] Simon VV. Load distribution in spiral bevel gears. ASME J Mech Des, 2007, 1292): 201-209

[53] ANSI/AGMA (2005) Design manual for bevel gears. ANSI/AGMA; ANSI/AGMA 2005-D03

[54] Fuentes A, Iserte JL, Ignacio GP, et al. . Computerized design of advanced straight and skew bevel gears produced by precision forging. Comput Methods Appl Mech Eng, 2011, 200: 2363-2377

[55] Chen X, Wang ZL, Xu J, et al. . Sustainable production of micro gears combining micro reciprocated wire electrical discharge machining and precision forging. J Clean Prod, 2018, 188: 1-11

[56] Ding H, Li YB, Zhao QY, et al. . On micro flank geometric topography design for spiral bevel and hypoid gears. Mech Mach Theory, 2023, 183 105236

[57] Hu ZH, Ding H, Peng SD, et al. . A novel collaborative manufacturing model requiring both geometric and physical evaluations of spiral bevel gears by design for six sigma. Mech Mach Theory, 2019, 133: 625-645

[58] Hibbit, Karlsson & Sirensen, Inc (1998) ABAQUS/standard user’s manual. 1800 Main Street, Pantucket, RI 20860-4847

Funding

National Natural Science Foundation of China(52205507)

National Key Research and Development Plan Project(2024FYB4708703)

Army Equipment Department Pre-research Project(KY-1044-2023-0442)

AVIC Hunan Power Mechanical Research Institute Industry-University-Research Cooperation fund(KY-1044-2024-0149)

National Key Lab Fund Project of Helicopter Dynamics(2024-CXPT-GF-JJ-093-09)

Taihang National Laboratory Technology Research and Development Project(HFZC20250275)

RIGHTS & PERMISSIONS

Shanghai University and Periodicals Agency of Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature

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