[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
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

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

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

Fax: +1 618 650 2555 Email: aluo@siue.edu

Spectral Density Prediction for Response of Nonlinear Gear Pairs under Random Excitation

Journal of Applied Nonlinear Dynamics 3(3) (2014) 283--294 | DOI:10.5890/JAND.2014.09.007

Jianming Yang$^{1}$; Ping Yang$^{2}$

$^{1}$ Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St John’s, NL, Canada

$^{2}$ School of Mechanical Engineering, Jiangsu University, Zhenjiang, Jiangsu, P.R. China

Download Full Text PDF

 

Abstract

This paper investigates the dynamic response of a gear pair under random excitation from the view point of spectral density. Two methods are used to calculate the response spectral density function (SDF). The first method uses the statistical linearization (SL) technique to find an equivalent linear system to the original nonlinear one, then the response SDF is calculated with the equivalent linear system. While the second method regards the natural frequency of the system as a function of the response amplitude which is a random variable and its probability density function (PDF) is computed through stochastic averaging (SA). Then the response SDF is computed as a probabilistic averaging over the whole range of amplitude. Simulation result shows that both methods can predictthe resonant frequency very well and consistently in the case of weaknonlinearity. But with increasing of nonlinearity, the SDF predicted from the SL technique tends to be narrower than that from method II.

Acknowledgments

This work is supported financially by the IgniteR&D from Research & Development Corporation, Newfoundland and Labrador, Canada.

References

  1. [1]  Ozguven, H.N.L. and Houser, D.R. (1988), Mathematical models used in gear dynamics-A review, Journal of Sound and Vibration, 121 (3), 383-411.
  2. [2]  Wang,J.,Li, R., and Peng, X. (2003), Survey of nonlinear vibration of gear transmission systems, ASME Applied Mechanics Review, 56 (3), 309-330.
  3. [3]  Tobe, T. and Sato, K. (1977), Statistical analysis of dynamic loads on spur gear teeth, Bulletin of JSME, 20(145), 882-889.
  4. [4]  Tobe, T., Sato, K., and Takatsu, N. (1977), Statistical analysis of dynamic loads on spur gear teeth:Experimental study, Bulletin of JSME, 20(148), 1315-1320.
  5. [5]  Kumar, A.S., Osman, M., and Sanker, T.S. (1986), On statistical analysis of gear dynamic loads, ASME:Journal of Vibration, Acoustics, Stress, and Reliability in Design, 108(3), 362-368.
  6. [6]  Pfeiffer, F. and Kunert, A. (1990), Rattling models from deterministic to stochastic processes, Nonlinear Dynamics, 1(1), 63-74.
  7. [7]  Wang, Y. and Zhang, W.J. (1998), Stochastic vibration model of gear transmission systems considering speed-dependent random errors, Nonlinear Dynamics, 17(2), 187-203.
  8. [8]  Naess, A., Kolnes, F.E., and Mo, E. (2007), Stochastic spur gear dynamics by numerical path integration, Journal of Sound and Vibration, 302(4-5), 936-950.
  9. [9]  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(3), 034501- (1-4).
  10. [10]  Yang, J. and Yang, P. (2012), Random gear dynamics based on path integration method -IMECE2012-85944, in: Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, Houston, TA, USA, November 9-15.
  11. [11]  Yang, J. (2013), Vibration analysis on multi-mesh gear-trains under combined deterministic and random excitations, Mechanism and Machine Theory, 59(1), 20-33.
  12. [12]  Theodossiades, S. and Natsiavas, S. (2000), Non-linear dynamics of gear-pair systems with periodic stiffness and backlash, Journal of Sound and vibration, 229(2), 287-310.
  13. [13]  Roberts, J.B. and Spanos, P.D. (1999), Random Vibration and Statistical Linearization, John Wiley & Sons, New York.
  14. [14]  Miles, R.N. (1993), Spectral response of a bilinear oscillator, Journal of Sound and Vibration, 163(2), 319- 326.
  15. [15]  Bouc, R. (1994), The power spectral density of response for a strongly nonlinear random oscillator, Journal of Sound and Vibration, 175(3), 317-331.
  16. [16]  Rudinger, F. and Krenk, S. (2003), Spectral density of oscillator with bilinear stiffness and white noise excitation, Probabilistic Engineering Mechanics, 18(3), 215-222.
  17. [17]  Spanos, P.D., Kougioumtzoglou, I.A.,and Soize, C.(2011), On the determination of the power spectrum of random excited oscillators via stochastic averaging: An alternative perspective, Probabilistic Engineering Mechanics, 26(1), 10-15.
  18. [18]  Lutes, L. and Sarkani, S.(2003), Random Vibrations: Analysis of Structural and Mechanical Systems, Elsevier Science.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates