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Lubricants 2015, 3(2), 281-310; doi:10.3390/lubricants3020281

Nonlinear Dynamic Response of an Unbalanced Flexible Rotor Supported by Elastic Bearings Lubricated with Piezo-Viscous Polar Fluids

1
Laboratoire de Mécanique et Structures, Université 8 mai 1945 Guelma, BP 401, Guelma 24000, Algeria
2
Université de Lyon, CNRS INSA-Lyon, LaMCoS, UMR5259, Villeurbanne F-69621, France
*
Author to whom correspondence should be addressed.
Academic Editor: Michel Fillon
Received: 1 November 2014 / Revised: 11 January 2015 / Accepted: 22 January 2015 / Published: 16 April 2015
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Abstract

On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains. View Full-Text
Keywords: couple-stress piezo-viscous fluid; flexible rotor; elastic bearing; modified Reynolds equation; nonlinear dynamic approach; finite element method; Euler scheme; transient lubrication problem; polymer additives couple-stress piezo-viscous fluid; flexible rotor; elastic bearing; modified Reynolds equation; nonlinear dynamic approach; finite element method; Euler scheme; transient lubrication problem; polymer additives
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. (CC BY 4.0).

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MDPI and ACS Style

Lahmar, M.; Bou-Saïd, B. Nonlinear Dynamic Response of an Unbalanced Flexible Rotor Supported by Elastic Bearings Lubricated with Piezo-Viscous Polar Fluids. Lubricants 2015, 3, 281-310.

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