The combined effects of couple stresses and the pressure dependent viscosity of lubricant on the non-linear dynamic response of an unbalanced flexible rotor supported by coated journal bearings

Abstract

On the basis of the V. K. Stokes micro-continuum theory and the Barus’ law, 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 unbalanced Jeffcott's flexible rotor supported by coated hydrodynamic journal bearings are investigated in this work. 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 rotor-dynamic equations with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses and the piezo-viscosity of lubricant on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be overlooked. As expected, these effects are more noticeable for oils blended with polymers characterized by higher length molecular chains