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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Investigation on Rattle of Gears under Random Loading

Journal of Applied Nonlinear Dynamics 5(2) (2016) 221--230 | DOI:10.5890/JAND.2016.06.008

Yubing Wen; Jianming Yang

Department of Mechanical Engineering, Memorial University, St John’s, A1B 3X5, Canada

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This paper investigates the random rattle motion of a single stage spur gear pair subjected to deterministic and random excitation. The motion is treated separately as free flight between the boundaries and the instant impact at the two boundaries. Numerical path integration method is applied to obtain the probability density of the response during free flight. Monte Carlo simulation is also conducted to verify the efficiency and accuracy of path integration in solving this strongly nonlinear dynamic problem. Comparison between results from path integration and Monte Carlo simulation is made and good agreement is achieved.


  1. [1]  Pfeiffer, F. and Kunert, A. (1990), Rattling models from deterministic to stochastic processes, Nonlinear Dynamics, 1 (1), 63-74.
  2. [2]  Kahraman, A. and Singh, R. (1991), Interactions between time-varying mesh stiffness and clearance nonlinearities in a geared system, Journal of Sound and Vibration, 146 (1), 135-156.
  3. [3]  Theodossiades, S. and Natsisvas, S. (2000), Non-linear dynamics of gear-pair systems with periodic stiffness and backlash, Journal of Sound and Vibration, 229, 287-310.
  4. [4]  Yang, J. and Yang, P. (2012), Random gear dynamics based on path integration method, Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition Vol. 4, Houston, Texas, USA pp. 879-888.
  5. [5]  Yang, J. (2013), Vibration analysis on multi-mesh gear-trains under combined deterministic and random excitations, Mechanism and Machine Theory, 59, 20-33.
  6. [6]  Kunert, A. and Pfeiffer, F. (1990), Stochastic model for rattling in gear-boxes, Nonlinear Dynamics in Engineering Systems, 173-180.
  7. [7]  Feng, Q. and Pfeiffer, F. (1998), Stochastic model on a rattling system, Journal of Sound and Vibration, 215 (3), 439-453.
  8. [8]  Wang, M.Y., Zhao, W., and Manoj, R. (2002), Numerical modelling and analysis of automotive transmission rattle, Journal of Vibration and Control, 8(7), 921-943.
  9. [9]  Luo, A. and O'Connor, D. (2009), Periodic motions and chaos with impacting chatter and stick in a gear transmission system, International Journal of Bifurcation and Chaos 19 (06), 1975-1994.
  10. [10]  Luo, A. and O'Connor, D. (2009), Impacting chatter and stick in a transmission system with two oscillators, Proceedings of the Institution of Mechanical Engineers, Part K, Journal of Multi-body Dynamics, 223 (3), 159-188.
  11. [11]  Luo, A. and O'Connor, D. (2009), Periodic motions with impacting chatter and stick in a gear transmission system, Journal of Vibration and Acoustics, 131 (4), 041013.
  12. [12]  Wen, J.M. and Feng, Q. (2004), Two-stage stochastic model on rattling vibration with amplitude modulation, Shock and Vibration, 11 (5), 693-702.
  13. [13]  Dimentberg, M. and Iourtchenko, D.(2004), Random vibrations with impacts: a review, Nonlinear Dynamics, 36 (2-4), 229-254.
  14. [14]  Sun, J.Q. and Hsu, C.S.(1990), The generalized cell mapping method in nonlinear random vibration based upon short-time gaussian approximation, ASME:Journal of Applied Mechanics, 57, 1018-1025.
  15. [15]  Yu, J.S., Cai, G.Q., and Lin, Y.K. (1997), A new path integration procedure based on gauss-legendre scheme, International Journal of Non-Linear Mechanics, 32, 759-768.
  16. [16]  Naess, A., Kolnes, F.E., and Mo, E. (2007), Stochastic spur gear dynamics by numerical path integration, Journal of Sound and Vibration, 302, 936-950.
  17. [17]  Mo, E. and Naess, A. (2009), Nonsmooth dynamics by path integration: An example of stochastic and chaotic response of a meshing gear pair, ASME: Journal of Computational and Nonlinear Dynamics, 4, 034501.