Thermoelastohydrodynamic tilt pad journal bearing simulation and application to rotor-bearing model

Abstract

A general approach for incorporating heat transfer and elastic deformation effects into a tilt pad journal bearing simulation model is presented. A global analysis method is used, which includes variable viscosity and heat transfer effects in the fluid film, elastic deformation and heat conduction effects in the pads, and elastic deformation effect in the pivots. An upwinding technique is used in the finite element formulation of the energy equation to handle numerical instability due to the convective term. The thermal cavitation model is used in the cavitated region. Deflection modes with their associated parameters are used to approximate deformation of top surface of the pads. Equations of motion (sum of forces in the perpendicular and tangential directions, and sum of moments applied on a pad) are satisfied for each pad. The dynamic coefficients of a single pad are calculated at the equilibrium state of the bearing, based on numerical perturbation of these equations with respect to related parameters. These parameters include journal position, pad rotation, pivot deformation, and mode related ones. The synchronously reduced (eight) dynamic coefficients, used for conventional stability and unbalance codes, are generated assuming the frequency of the pad motion to be identical to the frequency of the shaft motion. The stiffness and damping coefficients are calculated and compared with experimental and numerical results from the existing literature. The calculated dynamic coefficients are used to predict the instability onset speed of the rotor-bearing system. The finite element model of the rotor-bearing system is used to evaluate the eigenvectors and eigenvalues. The system is stable if the real part of the complex eigenvalue is negative. The effects of complex eigenvalue-dependent coefficients and synchronously reduced coefficients on the rotor-bearing systems are investigated. The effects of heat transfer and elastic deformation on the dynamic coefficients and the rotor-bearing stability are demonstrated. The current research assists the researchers and the engineers to predict the instability onset point accurately.