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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 7064590, 11 pages
Research Article

The Nonsmooth Vibration of a Relative Rotation System with Backlash and Dry Friction

1Liren College of Yanshan University, Qinhuangdao 066004, China
2College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China

Correspondence should be addressed to Shuo Li; nc.ude.usy.liamuts@ilouhs

Received 2 May 2017; Accepted 14 August 2017; Published 7 November 2017

Academic Editor: Viktor Avrutin

Copyright © 2017 Minjia He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate a relative rotation system with backlash and dry friction. Firstly, the corresponding nonsmooth characters are discussed by the differential inclusion theory, and the analytic conditions for stick and nonstick motions are developed to understand the motion switching mechanism. Based on such analytic conditions of motion switching, the influence of the maximal static friction torque and the driving torque on the stick motion is studied. Moreover, the sliding time bifurcation diagrams, duty cycle figures, time history diagrams, and the K-function time history diagram are also presented, which confirm the analytic results. The methodology presented in this paper can be applied to predictions of motions in nonsmooth dynamical systems.