Full Content is available to subscribers

Subscribe/Learn More  >

Random Gear Dynamics Based on Path Integration Method

[+] Author Affiliations
Jianming Yang

Memorial University of Newfoundland, St John’s, NL, Canada

Ping Yang

Jiangsu University, Zhenjiang, Jiangsu, China

Paper No. IMECE2012-85944, pp. 879-887; 9 pages
  • ASME 2012 International Mechanical Engineering Congress and Exposition
  • Volume 4: Dynamics, Control and Uncertainty, Parts A and B
  • Houston, Texas, USA, November 9–15, 2012
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4520-2
  • Copyright © 2012 by ASME


Gears exhibit vibrations during operation which contain apparently random components. Due to time-varying stiffness and backlash nonlinearity, it is very hard, if not impossible, to get a closed form response of gears under combination of deterministic and random loads. This paper employs a numerical method termed as path integration to obtain the probability density of the response at discrete time instants. The random excitation is assumed to be White noise. The response of the gear is a Markovian processes under the random excitation. In order to capture the probability density evolution, discretization is applied to both space and time. The transition probability between adjacent time instants is assumed to be Gaussian and the calculation of the probability density is made on a reduced finite space. The mean and variance, which are used to construct the Gaussian distribution, are obtained through a direct numerical integration scheme with one stochastic Newmark method. Statistic linearization technique is utilized within each individual time-step to find a linear equivalent of the original system with backlash nonlinearity. Through this method the evolution of the probability distribution function of the response displacement and the velocity is calculated. Three representative cases with different levels of constant load are investigated.

Copyright © 2012 by ASME



Interactive Graphics


Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In