Generic placeholder image

Recent Advances in Electrical & Electronic Engineering

Editor-in-Chief

ISSN (Print): 2352-0965
ISSN (Online): 2352-0973

Review Article

Research Progress on Gear Transmission System Dynamics

Author(s): Bingwei Gao*, Yongkang Wang and Guangbin Yu

Volume 17, Issue 4, 2024

Published on: 25 August, 2023

Page: [327 - 344] Pages: 18

DOI: 10.2174/2352096516666230714141145

Price: $65

Abstract

Background: The dynamics research of gear transmission systems mainly revolves around "excitation-model-response". The increasing number of dynamic incentive factors considered in the study has brought new problems to selecting modeling and solution methods and analyzing dynamic characteristics.

Objective: This study aims to sort out the main research content of gear transmission system dynamics. Moepver, the commonly used analysis models, modeling, and solution methods are compared, and references for method selection and in-depth research are provided.

Methods: This paper reviews the representative papers and patents related to the dynamic analysis of the gear system. The main contents of the dynamic excitation, dynamic model and dynamic characteristic analysis of the gear system are discussed, and suggestions for future development directions are given.

Results: The dynamic excitations mainly considered in the current research are internal excitations and external excitations; random excitations are rarely considered. This paper analyzes and summarizes the commonly used modeling methods, model classification, solution methods, and dynamic characteristics research content. The advantages and disadvantages of several commonly used analysis models, modeling, and solution methods and their applicable occasions are summarized for the reference of researchers.

Conclusion: The dynamics study of the gear system is a systematic work. It requires comprehensively considering the influence of dynamic excitations and selecting appropriate methods to establish and solve the model to obtain the dynamic characteristics that can better reflect the actual working conditions of the gear system. It is of great significance to improve the performance of the gear system.

Next »
Graphical Abstract

[1]
X.F. Tan, G.W. Zhang, L.Y. Xie, and X.H. He, "Summary and outlook on gear system’s kinetic study", Journal of Mechanical & Electrical Engineering, vol. 31, no. 5, pp. 559-562, 2014.
[2]
X. Yang, Z.X. Li, Z.J. Zhang, S.H. Shi, and K.L. Zhu, "Prospects for research on non-linear dynamics of gears", Shandong Industrial Technology, no. 20, p. 1, 2018.
[3]
M. Li, T. Sun, and H.Y. Hu, "Review on dynamics of geared rotor-bearing systems", J Vibrat Eng, vol. 15, no. 3, pp. 383-411, 2002.
[4]
W.A. Tuplin, and E.L. Broghamer, "Gear Load Capacity", J. Appl. Mech., vol. 30, no. 3, pp. 479-480, 1963.
[http://dx.doi.org/10.1115/1.3636605]
[5]
A. Kahraman, and R. Singh, "Non-linear dynamics of a spur gear pair", J. Sound Vibrat., vol. 142, no. 1, pp. 49-75, 1990.
[http://dx.doi.org/10.1016/0022-460X(90)90582-K]
[6]
A. Kahraman, and R. Singh, "Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system", J. Sound Vibrat., vol. 146, no. 1, pp. 135-156, 1991.
[http://dx.doi.org/10.1016/0022-460X(91)90527-Q]
[7]
L. Fan, S.P. Wang, and H.B. Duan, "Non-linear dynamic modeling method for gear tooth damage failure of internal meshing gear shaft reducer", C.N. Patent 107092750.
[8]
Y. Zhang, M.M. Wang, Z.Y. Tang, and S.W. Li, "Method for solving dynamic characteristics of involute straight gear transmission system", C.N. Patent 110162909.
[9]
F. Bruzzone, and C. Rosso, "Sources of Excitation and Models for Cylindrical Gear Dynamics: A Review", Machines, vol. 8, no. 3, p. 37, 2020.
[http://dx.doi.org/10.3390/machines8030037]
[10]
J.J. Wang, and R.F. Li, "The theoretical system of the gear vibration theory", Zhongguo Jixie Gongcheng, vol. 9, no. 12, pp. 55-58, 1998.
[11]
R.F. Li, and J.J. Wang, Gear System Dynamics: Vibration, Impact, Noise., Science Press, 1997.
[12]
J.J. Wang, T. Hong, R.Z. Wu, and R.F. Li, "Researches on parametric vibration of gear transmission systems-a review", J Vibrat Shock, vol. 16, no. 4, pp. 69-73, 1997.
[13]
Y.F. Huangfu, X.L. Yu, X.J. Dong, X.H. Long, and Z.K. Peng, "Dynamic modelling of two-stage gear systems with localized wear defects", J. Phys. Conf. Ser., vol. 2184, no. 1, p. 012011, 2022.
[http://dx.doi.org/10.1088/1742-6596/2184/1/012011]
[14]
F. Chaari, T. Fakhfakh, and M. Haddar, "Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness", Eur. J. Mech. A, Solids, vol. 28, no. 3, pp. 461-468, 2009.
[http://dx.doi.org/10.1016/j.euromechsol.2008.07.007]
[15]
Z.G. Chen, Z.W. Zhou, and Y.Q. Liu, "Method and device for calculating time-varying meshing stiffness of straight-tooth cylindrical gear pair", C.N. Patent 111027149, 2019.
[16]
Y. Cai, "Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (a new stiffness function of helical involute tooth pair)", J. Mech. Des., vol. 117, no. 3, pp. 460-469, 1995.
[http://dx.doi.org/10.1115/1.2826701]
[17]
Q. Wang, H. Ma, X. Kong, and Y. Zhang, "A distributed dynamic mesh model of a helical gear pair with tooth profile errors", J. Cent. South Univ., vol. 25, no. 2, pp. 287-303, 2018.
[http://dx.doi.org/10.1007/s11771-018-3737-4]
[18]
L. Liu, G. Liu, H.W. Wang, L.Y. Wu, F. Gao, and L. Yang, "Gear pair meshing stiffness calculation method considering geometric eccentric errors", C.N. Patent 110427718, 2019.
[19]
S. Li, "Effects of misalignment error, tooth modifications and transmitted torque on tooth engagements of a pair of spur gears", Mechanism Mach. Theory, vol. 83, pp. 125-136, 2015.
[http://dx.doi.org/10.1016/j.mechmachtheory.2014.09.011]
[20]
X.L. Zhang, P. Zhao, W.H. Han, X. Si, D. Ling, and H.B. Zhang, "Helical gear time-varying mesh stiffness calculating method based on finite element analysis", C.N. Patent 107763173, 2017.
[21]
N.K. Raghuwanshi, and A. Parey, "Experimental measurement of mesh stiffness by laser displacement sensor technique", Measurement, vol. 128, pp. 63-70, 2018.
[http://dx.doi.org/10.1016/j.measurement.2018.06.035]
[22]
F.H. Liu, "Gear dynamic transmission error determination", U.S. Patent 10274399, 2016.
[23]
H.K. Lee, "Apparatus for measuring gear transmission error", U.S. Patent 2016349146, 2015.
[24]
Z.Y. Shi, Z.H. Shu, and R. Li, "Gear dynamic transmission error measurement method and gear dynamic transmission error measurement device", C.N. Patent 106813922.
[25]
P. Velex, and M. Maatar, "A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behavior", J. Sound Vibrat., vol. 191, no. 5, pp. 629-660, 1996.
[http://dx.doi.org/10.1006/jsvi.1996.0148]
[26]
H.N. Özgüven, and D.R. Houser, "Dynamic analysis of high speed gears by using loaded static transmission error", J. Sound Vibrat., vol. 125, no. 1, pp. 71-83, 1988.
[http://dx.doi.org/10.1016/0022-460X(88)90416-6]
[27]
R.G. Parker, S.M. Vijayakar, and T. Imajo, "Non-linear dynamic response of a spur gear pair: Modelling and experimental comparisons", J. Sound Vibrat., vol. 237, no. 3, pp. 435-455, 2000.
[http://dx.doi.org/10.1006/jsvi.2000.3067]
[28]
L. Ryali, and D. Talbot, "Dynamic load distribution of planetary gear sets subject to both internal and external excitations", Forsch. Ingwes., vol. 86, no. 3, pp. 283-294, 2022.
[http://dx.doi.org/10.1007/s10010-021-00506-6]
[29]
G. Tian, Z. Gao, P. Liu, and Y. Bian, "Dynamic modeling and stability analysis for a spur gear system considering gear backlash and bearing clearance", Machines, vol. 10, no. 6, p. 439, 2022.
[http://dx.doi.org/10.3390/machines10060439]
[30]
S. Wei, Q.K. Han, and F.L. Chu, "Review on research of uncertain dynamics for gear system", Jixie Gongcheng Xuebao, vol. 52, no. 1, p. 1, 2016.
[http://dx.doi.org/10.3901/JME.2016.01.001]
[31]
H. Liu, P.F. Yan, C. Zhang, and X. Zhang, "Helical gear pair stochastic dynamics modeling method based on uncertainty", C.N. Patent 111488681.
[32]
Q. Chen, Y. Ma, S. Huang, and H. Zhai, "Research on gears’ dynamic performance influenced by gear backlash based on fractal theory", Appl. Surf. Sci., vol. 313, pp. 325-332, 2014.
[http://dx.doi.org/10.1016/j.apsusc.2014.05.210]
[33]
W.Y. Liu, Y.G. Sun, G.B. Yu, and V. Tupolev, Journal of Mechanical Transmission, vol. 46, no. 4, pp. 55-62, 2022.
[34]
W.A. Tuplin, "Gear‐tooth stresses at high speed", Proc.- Inst. Mech. Eng., vol. 163, no. 1, pp. 162-175, 1950.
[http://dx.doi.org/10.1243/PIME_PROC_1950_163_020_02]
[35]
H.W. Wang, G. Liu, L. Liu, X.F. Li, L.Y. Wu, and J.Y. Gong, "Dynamics modeling method for multi-input and multi-output gear transmission system", C.N. Patent 110516384, 2019.
[36]
S. Wang, R. Zhu, and Jin Feng, "Study on load sharing behavior of coupling gear-rotor-bearing system of GTF aero-engine based on multi-support of rotors", Mechanism Mach. Theory, vol. 147, p. 103764, 2020.
[http://dx.doi.org/10.1016/j.mechmachtheory.2019.103764]
[37]
M.B. Lin, and M.H. Lin, "Analysis of gear system dynamic characteristics with tooth surface friction", J Liaoning Univ Technol, vol. 40, no. 4, pp. 225-229, 2020.
[38]
Z. Bacem, B. Imen, A. Kamel, W. Lassaad, and H. Mohamed, "Study of dynamic behavior of a bevel gear used in vertical axis wind turbine", Zhongguo Jixie Gongcheng Xuekan, vol. 43, no. 6, pp. 569-577, 2022.
[39]
H.R. Cao, Y.C. Sun, C.H. Wei, J.H. Shi, and X.F. Chen, "Method and system for representing fault signal strength and transmission characteristics of gear transmission system", C.N. Patent 114414236, 2022.
[40]
B. Han, X.H. Yang, G. Liu, H.W. Wang, and L.Y. Wu, "Gear transmission system three-dimensional modeling method", C.N. Patent 110263445, 2019.
[41]
R.G. Parker, V. Agashe, and S.M. Vijayakar, "Dynamic response of a planetary gear system using a finite element/contact mechanics model", J. Mech. Des., vol. 122, no. 3, pp. 304-310, 2000.
[http://dx.doi.org/10.1115/1.1286189]
[42]
M.R. Kang, "Development of dynamic model to predict three-dimensional vibrations of helical gear pair", Transact Korean Society Noise Vibrat Eng, vol. 31, no. 2, pp. 215-225, 2021.
[http://dx.doi.org/10.5050/KSNVE.2021.31.2.215]
[43]
C.Z. Liu, J.Y. Zheng, D.T. Qin, S.X. Chen, T. Zhang, and D. Gao, "Slicing coupling dynamics modeling method for high-speed thin-wall gear transmission system", C.N. Patent 115618688.
[44]
C.J. Zhou, Z.Z. Qiao, and H.H. Liu, "Dynamic response analysis method for multi-stage gear transmission system under different types of cracks", C.N. Patent 114997000, 2022.
[45]
T. Iwatsubo, S. Arii, and R. Kawai, "Coupled lateral-torsional vibration of rotor system trained by gears: Part 1. Analysis by transfer matrix method", Bull. JSME, vol. 27, no. 224, pp. 271-277, 1984.
[http://dx.doi.org/10.1299/jsme1958.27.271]
[46]
H. Lee, and H.S. Yoon, "Torsional vibration analysis of a planetary gear type antiresonant vibration isolator using transfer matrix method, Part I: System modeling", J. Mech. Sci. Technol., vol. 34, no. 3, pp. 1005-1012, 2020.
[http://dx.doi.org/10.1007/s12206-020-0203-7]
[47]
L. Liu, H.W. Wang, G. Liu, L.Y. Wu, J.Y. Gong, and D. Ma, "Full-coupling dynamics modeling method for gear transmission system", C.N. Patent 110222471.
[48]
L. Eris, "Coupling system", E. P. Patent 4151876, 2021.
[49]
D.T. Qin, R.B. Chen, C.Z. Liu, L.X. Hui, Z.B. Yang, and X.S. Yin, "Model modeling method for kinetic model of rigid-flexible electromechanical coupling fan gear generator", C.N. Patent 112287485.
[50]
A. Tatar, C.W. Schwingshackl, and M.I. Friswell, "Dynamic behaviour of three-dimensional planetary geared rotor systems", Mechanism Mach. Theory, vol. 134, pp. 39-56, 2019.
[http://dx.doi.org/10.1016/j.mechmachtheory.2018.12.023]
[51]
A. Farshidianfar, and A. Saghafi, "Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems", Nonlinear Dyn., vol. 75, no. 4, pp. 783-806, 2014.
[http://dx.doi.org/10.1007/s11071-013-1104-4]
[52]
S.P. Wang, and L. Fan, "Modeling method of planet carrier crack fault kinetic model of helicopter main reducing gear", C.N. Patent 105069209, 2015.
[53]
S.D. Yavuz, Z.B. Saribay, and E. Cigeroglu, "Nonlinear dynamic analysis of a drivetrain composed of spur, helical and spiral bevel gears", Nonlinear Dyn., vol. 100, no. 4, pp. 3145-3170, 2020.
[http://dx.doi.org/10.1007/s11071-020-05666-8]
[54]
Z. Cao, Z. Chen, and H. Jiang, "Nonlinear dynamics of a spur gear pair with force-dependent mesh stiffness", Nonlinear Dyn., vol. 99, no. 2, pp. 1227-1241, 2020.
[http://dx.doi.org/10.1007/s11071-019-05348-0]
[55]
X.P. Qin, and S.Z. Dong, "Six-degree-of-freedom kinetic model modeling method for internal meshing gear pair", C.N. Patent 112395711.
[56]
A. Kahraman, "Natural modes of planetary gear trains", J. Sound Vibrat., vol. 173, no. 1, pp. 125-130, 1994.
[http://dx.doi.org/10.1006/jsvi.1994.1222]
[57]
L. Xiang, N. Gao, L. Tang, and P.F. Guo, "Non-linear dynamic features of wind turbine’s gear systems subjected to internal and external excitations", J. Vib. Shock, vol. 37, no. 5, pp. 126-132, 2018.
[58]
L. Xiang, Z. Deng, and A. Hu, "Dynamical analysis of planetary gear transmission system under support stiffness effects", Int. J. Bifurcat. Chaos, vol. 30, no. 6, p. 2050080, 2020.
[http://dx.doi.org/10.1142/S0218127420500807]
[59]
D. Fu, S. Gao, and H. Liu, "Study on dynamics of a two-stage gear transmission system with and without tooth breakage", Processes (Basel), vol. 9, no. 12, p. 2141, 2021.
[http://dx.doi.org/10.3390/pr9122141]
[60]
H. Nevzat Özgüven, and D.R. Houser, "Mathematical models used in gear dynamics—A review", J. Sound Vibrat., vol. 121, no. 3, pp. 383-411, 1988.
[http://dx.doi.org/10.1016/S0022-460X(88)80365-1]
[61]
W. Bartelmus, "Mathematical modelling and computer simulations as an aid to gearbox diagnostics", Mech. Syst. Signal Process., vol. 15, no. 5, pp. 855-871, 2001.
[http://dx.doi.org/10.1006/mssp.2001.1411]
[62]
C.F. Li, S.H. Zhou, W.M. Liu, Z.H. Ren, and B.C. Wen, "Vibration of bending-torsion coupling gear-rotor-rolling bearing transmission system", J Aerospace Power, vol. 29, no. 7, pp. 1543-1555, 2014.
[63]
G. Wesley Blankenship, and R. Singh, "A new gear mesh interface dynamic model to predict multi-dimensional force coupling and excitation", Mechanism Mach. Theory, vol. 30, no. 1, pp. 43-57, 1995.
[http://dx.doi.org/10.1016/0094-114X(94)00018-G]
[64]
T. Eritenel, and R.G. Parker, "Modal properties of three-dimensional helical planetary gears", J. Sound Vibrat., vol. 325, no. 1-2, pp. 397-420, 2009.
[http://dx.doi.org/10.1016/j.jsv.2009.03.002]
[65]
B.Q. Kang, and G.X. Feng, "Modeling and dynamics characteristic analysis of helical gear system with considering tooth surface friction", J Mech Transmission, vol. 39, no. 7, pp. 136-140, 2015.
[66]
Z. Ren, J.X. Xie, and S.H. Zhou, "Vibration characteristic analysis of helical gear-rotor-bearing system with coupled lateral-torsional-axial", Jixie Gongcheng Xuebao, vol. 51, no. 15, pp. 75-89, 2015.
[http://dx.doi.org/10.3901/JME.2015.15.075]
[67]
A. Kahraman, "Planetary gear train dynamics", J. Mech. Des., vol. 116, no. 3, pp. 713-720, 1994.
[http://dx.doi.org/10.1115/1.2919441]
[68]
B. Jin, Y. Bian, X. Liu, and Z. Gao, "Dynamic modeling and nonlinear analysis of a spur gear system considering a nonuniformly distributed meshing force", Appl. Sci. (Basel), vol. 12, no. 23, p. 12270, 2022.
[http://dx.doi.org/10.3390/app122312270]
[69]
A. Kahraman, "Load sharing characteristics of planetary transmissions", Mechanism Mach. Theory, vol. 29, no. 8, pp. 1151-1165, 1994.
[http://dx.doi.org/10.1016/0094-114X(94)90006-X]
[70]
A. Saada, and P. Velex, "An extended model for the analysis of the dynamic behavior of planetary trains", J. Mech. Des., vol. 117, no. 2A, pp. 241-247, 1995.
[http://dx.doi.org/10.1115/1.2826129]
[71]
P. Sondkar, and A. Kahraman, "A dynamic model of a double-helical planetary gear set", Mechanism Mach. Theory, vol. 70, no. 6, pp. 157-174, 2013.
[http://dx.doi.org/10.1016/j.mechmachtheory.2013.07.005]
[72]
H.Q. Zhang, H. Dong, L.B. Wang, and X.L. Zhao, "Effect of tooth surface friction on bending torsional axial pendular coupling non-linear amplitude frequency characteristic of marine herringbone gear", J Mech Transmission, vol. 46, no. 5, pp. 9-16, 2022.
[73]
K. Nakamura, "Tooth separations and abnormal noise on power-transmission gears", Bull. JSME, vol. 10, no. 41, pp. 846-854, 1967.
[http://dx.doi.org/10.1299/jsme1958.10.846]
[74]
C.C. Wang, "Rotational vibration with backlash—part 1", J. Mech. Des., vol. 100, no. 2, pp. 363-373, 1978.
[http://dx.doi.org/10.1115/1.3453923]
[75]
A. Kahraman, and G.W. Blankenship, "Interactions between commensurate parametric and forcing excitations in a system with clearance", J. Sound Vibrat., vol. 194, no. 3, pp. 317-336, 1996.
[http://dx.doi.org/10.1006/jsvi.1996.0361]
[76]
S.L. Lau, and Y.K. Cheung, "Amplitude incremental variational principle for non-linear vibration of elastic systems", J. Appl. Mech., vol. 48, no. 4, pp. 959-964, 1981.
[http://dx.doi.org/10.1115/1.3157762]
[77]
J. Yang, T. Peng, and T.C. Lim, "An enhanced multi-term harmonic balance solution for nonlinear period-one dynamic motions in right-angle gear pairs", Nonlinear Dyn., vol. 67, no. 2, pp. 1053-1065, 2012.
[http://dx.doi.org/10.1007/s11071-011-0048-9]
[78]
G. Liu, and R.G. Parker, "Nonlinear, parametrically excited dynamics of two-stage spur gear trains with mesh stiffness fluctuation", Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci., vol. 226, no. 8, pp. 1939-1957, 2012.
[http://dx.doi.org/10.1177/0954406212447509]
[79]
J.F. Nie, M.L. Zheng, G.B. Yu, J.M. Wen, and B. Dai, "The method of multiple scales in solving non-linear dynamic differential equations of gear systems", Appl. Mech. Mater., vol. 274, pp. 324-327, 2013.
[http://dx.doi.org/10.4028/www.scientific.net/AMM.274.324]
[80]
Z. Rao, C.Y. Zhou, Z.H. Deng, and M.Y. Fu, "Nonlinear torsional instabilities in two-stage gear systems with flexible shafts", Int. J. Mech. Sci., vol. 82, pp. 60-66, 2014.
[http://dx.doi.org/10.1016/j.ijmecsci.2014.02.021]
[81]
E. Pipitone, C.M. Firrone, and S. Zucca, "Application of multiple-scales method for the dynamic modelling of a gear coupling", Appl. Sci. (Basel), vol. 9, no. 6, p. 1225, 2019.
[http://dx.doi.org/10.3390/app9061225]
[82]
Y.J. Zhang, Z. Meng, and Y.Z. Sun, "Dynamic modeling and chaotic analysis of gear transmission system in a braiding machine with or without random perturbation., vol. Vol. 2016", Shock and Vibration, 2016.
[83]
H. Fukuma, T. Furukawa, and T. Aida, "Fundamental research on gear noise and vibration: (6th report, generation mechanism of radial and axial vibration of spur gears)", Bull. JSME, vol. 16, no. 97, pp. 1094-1107, 1973.
[http://dx.doi.org/10.1299/jsme1958.16.1094]
[84]
L. Xiang, N. Gao, and A. Hu, "Dynamic analysis of a planetary gear system with multiple nonlinear parameters", J. Comput. Appl. Math., vol. 327, pp. 325-340, 2018.
[http://dx.doi.org/10.1016/j.cam.2017.06.021]
[85]
X. Li, X. Liu, X. Li, W. He, and H. Guo, "Improved method for analysing the dynamic response of gear transmission systems", Eng. Comput., vol. 39, no. 9, pp. 3232-3254, 2022.
[http://dx.doi.org/10.1108/EC-08-2021-0500]
[86]
P.H. Lou, "Analysis method for dynamic characteristics of multi-stage planetary gear structure", W.O. Patent 2023000376.
[87]
F. Djemal, A. Ghorbel, O. Graja, M. Abdennadher, L. Walha, and M. Haddar, "Vibration analysis of nonlinear powertrain model with randomly cracked teeth under acyclism operation", J. Braz. Soc. Mech. Sci. Eng., vol. 43, no. 9, p. 433, 2021.
[http://dx.doi.org/10.1007/s40430-021-03151-w]
[88]
S. Li, Q. Wu, and Z. Zhang, "Bifurcation and chaos analysis of multistage planetary gear train", Nonlinear Dyn., vol. 75, no. 1-2, pp. 217-233, 2014.
[http://dx.doi.org/10.1007/s11071-013-1060-z]
[89]
L. Xiang, S.X. Liu, and J.H. Zhang, "Non-linear dynamic characteristics of two-stage planetary gear transmission system in wind turbine gearbox", J Vibrat Shock, vol. 39, no. 15, pp. 193-199, 2020.
[90]
G.B. Yu, J.M. Wen, G.X. Li, and X. Cao, "GEAR method for solving dynamics differential equations of gear systems China", Instrument and Control Technology Exchange Conference, 2007.
[91]
A. Hammami, A. Fernandez Del Rincon, F. Chaari, M.I. Santamaria, F. Viadero Rueda, and M. Haddar, "Effects of variable loading conditions on the dynamic behaviour of planetary gear with power recirculation", Measurement, vol. 94, pp. 306-315, 2016.
[http://dx.doi.org/10.1016/j.measurement.2016.07.083]
[92]
L.H. Chang, Z.X. He, J.Z. Su, and F.Q.L. Zhang, "Non-linear dynamics calculation method for gear pair", C.N. Patent 108052760.
[93]
Z.W. Han, Y. Lv, R.F. Ma, S.C. Niu, and L.Q. Ren, "Dynamic performance of gear surface with bionic micro-morphology", J Beijing Univ Technol, vol. 37, no. 6, pp. 806-810, 2011.
[94]
A.N. Sova, G.S. Mazlumyan, A.A. Kotrovskij, R.V. Yushchuk, and S.A. Eruslankin, "Test bench for gears testing", R.U. Patent 2716175, 2019.
[95]
H.K. Sung, H.K. Jeoung, H.H. Kyung, S.P. Byung, and T.Y. Young, "An apparatus for investigating a vibration property of a reduction gear box", K. R. Patent 20210066772.
[96]
M. Abruzzo, M. Beghni, C. Santus, and S. Manconi, Dynamic behavior of a power re-circulating gear test rig including periodic variation of mesh stiffness and static transmission error.vol. Vol. 159. Mech Machine Theory, 2020.
[97]
R.B. Neriya, "Coupled torsional flexural vibration of a geared shaft system using finite element method", Shock Vibrat Bull, vol. 3, pp. 13-25, 1985.
[98]
Z.J. Fan, C. Zhou, C. Tian, Q. Wang, L.J. Gui, and W.Q. Ding, "Calculation method for driving axle gear dynamic characteristics considering main speed reducer housing", C.N. Patent 103971006.
[99]
J.X. Zhou, W.L. Sun, and L. Cao, "Natural characteristics of the herringbone gear transmission system", IOP Conf. Ser.: Mater. Sci. Eng, vol. 324, p. 012066, 2018.
[http://dx.doi.org/10.1088/1757-899X/324/1/012066]
[100]
H. Ma, "Method for estimating inherent characteristics and pitch diameter vibration of thin-rim gear system", C.N. Patent 111783258, 2020.
[101]
H.W. Wang, "Herringbone gear system dynamic response calculation method under basic swing condition", C.N. Patent 110598338.
[102]
W. Li, J. Sun, and J. Yu, "Analysis of dynamic characteristics of a multi-stage gear transmission system", J. Vib. Control, vol. 25, no. 10, pp. 1653-1662, 2019.
[http://dx.doi.org/10.1177/1077546319830810]
[103]
Z.M. Xiao, F. Chen, and K.L. Zhang, "Analysis of dynamic characteristics of the multi-stage planetary gear transmission system with friction force", Hindawi Limited, vol. 2021, pp. 1-10, 2021.
[104]
B.R. Eric, "Condition monitoring for components of a gearbox", U.S. Patent 11486483, 2020.
[105]
F. Kucukay, "Dynamic behaviour of high speed gears", In: Rotating Machinery, Institution of Mechanical Engineers, 1984, pp. 81-90.
[106]
S. Theodossiades, and S. Natsiavas, "Non-linear dynamics of gear-pair systems with periodic stiffness and backlash", J. Sound Vibrat., vol. 229, no. 2, pp. 287-310, 2000.
[http://dx.doi.org/10.1006/jsvi.1999.2490]
[107]
X. Wang, M.H. Zhu, W.L. Zhang, and C. Zhao, "Gear transmission system non-linear stability-based fault diagnosis method", C.N. Patent 108694302.
[108]
Y.S. Bian, X.H. Liu, D.B. Tian, B.H. Jin, and J.L. Peng, "Optimization design method for heavy-load and unbalance-load gear transmission system based on motion stability", C.N. Patent 113010974.

Rights & Permissions Print Cite
© 2024 Bentham Science Publishers | Privacy Policy