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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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2191-0294
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Volume 18, Issue 7-8

Issues

Influence of the Random System Parameters on the Nonlinear Dynamic Characteristics of Gear Transmission System

Jingyue Wang
  • Corresponding author
  • The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China
  • School of Automobile and Transportation, Shenyang Ligong University, Shenyang 110159, China
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Haotian Wang / Huan Wang / Lixin Guo
Published Online: 2017-10-27 | DOI: https://doi.org/10.1515/ijnsns-2016-0119

Abstract

In order to analyze the influence of the random parameters of the system on the nonlinear dynamic characteristics of the gear transmission system, considering the random perturbation of damping ratio, gear backlash, meshing frequency, meshing stiffness and the low frequency excitation caused by torque fluctuation, the random vibration equations of three-degree-of-freedom gear transmission system are established according to the Newton’s law. The motion differential equations are solved by the Runge–Kutta method. The effects of different random parameters such as load ratio, tooth frequency ratio, damping ratio, gear backlash and meshing stiffness on the dynamic response of the gear transmission system are analyzed in light and heavy loads and low and high speeds.

Keywords: gear transmission system; random perturbation; nonlinear dynamic characteristic; Runge-Kutta method; stability; bifurcation; chaos

References

  • [1]

    A. Kahraman and R. Singh, Non-linear dynamics of a spur gear pair, J. Sound Vib. 142(1) (1990), 49–75.CrossrefGoogle Scholar

  • [2]

    A. Kahraman and R. Singh, Nonlinear dynamics of a geared rotor-bearing system with multiple clearances, J. Sound Vib. 144(3) (1991), 469–506.CrossrefGoogle Scholar

  • [3]

    A. Kahraman and R. Singh, Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system, J. Sound Vib. 146(1) (1991), 135–156.CrossrefGoogle Scholar

  • [4]

    J. Wang, T.C. Lim and M.F. Li, Dynamics of a hypoid gear pare considering the effects of time-varying mesh parameters and backlash nonlinearity, J. Sound Vib. 308(1-2) (2007), 302–329.CrossrefGoogle Scholar

  • [5]

    C.W. Chang-Jian, Bifurcation and chaos analysis of the porous squeeze film damper mounted gear-bearing system, Comput. Math. Appl. 64(5) (2012), 798–812.CrossrefWeb of ScienceGoogle Scholar

  • [6]

    M. Byrtus and V. Zeman, On modeling and vibration of gear drives influenced by nonlinear couplings, Mech. Mach. Theory. 46(3) (2011), 375–397.Web of ScienceCrossrefGoogle Scholar

  • [7]

    T. Tobe and K. Sato, Statistical analysis of dynamic loads on spur gear teeth, Trans. Jpn. Soc. Mech. Eng. 20(146) (1976), 3652–3661.Google Scholar

  • [8]

    T. Tobe, K. Sato and N. Takatsu, Statistical analysis of dynamic loads on spur gear teeth: Experimental study, Trans. Jpn. Soc. Mech. Eng. 20(148) (1977), 746–752.Google Scholar

  • [9]

    A.S. Kumar, M.O.M. Osman and T.S. Sankar, On statistical analysis of gear dynamic loads, J. Vibr. Acoust. Stress, Reliab. Des. 108 (1986), 362–368.CrossrefGoogle Scholar

  • [10]

    S.V. Neriva, R.B. Bhat and T.S. Sankar, On the dynamic response of a helical geared system subjected to a static transmission error in the form of deterministic and filtered white noise inputs, J. Vibr. Acoust. Stress, Reliab. Des. 110(4) (1988), 501–506.CrossrefGoogle Scholar

  • [11]

    Y. Wang and W.J. Zhang, Stochastic vibration model of gear transmission systems considering speed-dependent random errors, Nonlinear Dyn. 17(2) (1998), 187–203.CrossrefGoogle Scholar

  • [12]

    G. Matej, J. Đani, B. Pavle, et al., Model-based prognostics of gear health using stochastic dynamical models, Mech. Syst. Signal Process. 25(2) (2011), 537–548.CrossrefGoogle Scholar

  • [13]

    Y. Wang and W. Zhang, Modelling of gear stochastic vibration considering non-white noise errors, Chin. Sci. Bull. 44(4) (1999), 375–378.CrossrefGoogle Scholar

  • [14]

    Z.G. Chen, Y.M. Shao and T.C. Lim, Non-linear dynamic simulation of gear response under the idling condition, Int. J. Automot. Technol. 13(4) (2012), 541–552.CrossrefWeb of ScienceGoogle Scholar

  • [15]

    C.W. Chang-Jian and H.C. Hsu, Chaotic responses on gear pair system equipped with journal bearings under turbulent flow, Appl. Math. Model. 36(6) (2012), 2600–2613.CrossrefWeb of ScienceGoogle Scholar

  • [16]

    K. Sato, S. Yamamoto and T. Kawakami, Bifurcation sets and chaotic states of a gear system subjected to harmonic excitation, Comput. Mech. 7(3) (1991), 173–182.CrossrefGoogle Scholar

  • [17]

    C. Padmanabhan and R. Singh, Analysis of periodically forced nonlinear Hill’s oscillator with application to a geared system, J. Acoust. Soc. America. 99(1) (1996), 324–334.CrossrefGoogle Scholar

  • [18]

    J.M. Yang, Vibration analysis on multi-mesh gear-trains under combined deterministic and random excitations, Mech. Mach. Theory. 59 (2013), 20–33.CrossrefWeb of ScienceGoogle Scholar

  • [19]

    J.Y. 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. 67(2) (2012), 1053–1065.Web of ScienceCrossrefGoogle Scholar

  • [20]

    H. Moradi and H. Salarieh, Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity, Mech. Mach. Theory. 51 (2012), 14–31.Web of ScienceCrossrefGoogle Scholar

  • [21]

    L. Walha, T. Fakhfakh and M. Haddar, Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash, Mech. Mach. Theo. 44(5) (2009), 1058–1069.CrossrefGoogle Scholar

  • [22]

    J. Wang, H. Wang and L. Guo, Analysis of Effect of Random Perturbation on Dynamic Response of Gear Transmission System, Chaos, Solitons Fractals. 68 (2014), 78–88.CrossrefWeb of ScienceGoogle Scholar

  • [23]

    J. Wang, H. Wang and L. Guo, Analysis of stochastic nonlinear dynamics in the gear transmission system with backlash, Int. J. Nonlinear Sci. Numer. Simul. 16(2) (2015), 111–121.Web of ScienceGoogle Scholar

About the article

Received: 2016-08-18

Accepted: 2017-10-16

Published Online: 2017-10-27

Published in Print: 2017-12-20


The authors gratefully acknowledge the support of programs for the State Key Laboratory of Mechanical Transmissions (SKLMT-KFKT-201605), the Natural Science Foundation of Liaoning Province of China (20170540786), the China Postdoctoral Science Foundation (2017M610497), the Open Foundation of Key Discipline of Mechanical Design and Theory of Shenyang Ligong University (4771004kfx08) and the National Natural Science Foundation of China (51275082).


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 18, Issue 7-8, Pages 619–630, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0119.

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