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

• Published in: Lubricants Vol. 3; no. 2; pp. 281 - 310
• Main Authors: Lahmar, Mustapha, Bou-Saïd, Benyebka
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.06.2015
• Subjects: Computational fluid dynamics; couple-stress piezo-viscous fluid; elastic bearing; Euler scheme; finite element method; flexible rotor; Fluid flow; Lubricants; Mathematical analysis; modified Reynolds equation; nonlinear dynamic approach; Nonlinear dynamics; Nonlinearity; polymer additives; Rotors; Stresses; transient lubrication problem
• ISSN: 2075-4442; 2075-4442
• DOI: 10.3390/lubricants3020281

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.