Envelope and order domain analyses of a nonlinear torsional system decelerating under multiple order frictional torque

Sen O. T., Dreyer J. T., Singh R.

MECHANICAL SYSTEMS AND SIGNAL PROCESSING, vol.35, pp.324-344, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35
  • Publication Date: 2013
  • Doi Number: 10.1016/j.ymssp.2012.09.008
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.324-344
  • Keywords: Friction-induced machinery vibration, Signal processing for speed-dependent process, Analytical methods, Nonlinear dynamics, Harmonic balance method, Hilbert transform, HARMONIC-BALANCE METHOD, CLEARANCE NONLINEARITY, FREQUENCY-RESPONSE, CONTINUATION
  • Istanbul Technical University Affiliated: Yes


The broader goal of this article is to re-examine the classical machinery shut down vibration problem in the context of a two degree of freedom nonlinear torsional system that essentially describes a braking system example. In particular, resonant amplifications during deceleration, as excited by a multi-order rotor surface distortion and pad friction regime, are investigated using a nonlinear model, and the order domain predictions are successfully compared with an experiment. Then a quasi-linear model at higher speeds is proposed and analytically solved to obtain closed form expressions for speed-dependent torque as well as its envelope curve. The Hilbert transform is also utilized to successfully calculate the envelope curves of both quasi-linear and nonlinear systems. Finally, the multi-term harmonic balance method is applied to construct semi-analytical solutions of the nonlinear torsional model, and the order domain results are successfully compared with measurements. New analytical solutions provide more insight to the speed-dependent characteristics given instantaneous frequency excitation. (C) 2012 Elsevier Ltd. All rights reserved.