Thermo-Hydrodynamic Analysis of Plain and Tilting Pad Bearings

The demand for higher efficiency and increased equipment compactness is pushing industrial compressors' designers towards the choice of higher rotor peripheral speed. As a consequence, modern bearing-rotor systems are subject to complex thermal phenomena inducing a renewed interest on their real working conditions. This work is about the validation of the in-house numerical code TILTPAD developed at the Department of Industrial Engineering of the University of Florence for the thermo-hydrodynamic analysis of both plain and tilting pad journal bearings performance. TILTPAD is a steady-state code based on a 2D thin-film approach able to find either the resulting hydrodynamic load using the shaft equilibrium position and the rotational speed (i.e., direct problem) or the shaft equilibrium position once the load and the rotational speed are prescribed (i.e., inverse problem). In order to calculate pads' pressure distribution a finite element approach is used to solve the Reynolds equation together with a mixed procedure to evaluate pads equilibrium positions. Two steady-state energy equations based on a Petroff-type simplification are implemented in the code. The first one is proposed in the work of Balbahadur and Kirk [1] while the second one is based on an improved mixing model and a temperature dependent viscosity. An iterative procedure is used between Reynolds and energy equations to account for the dependence of the dynamic viscosity on the temperature field. Super-laminar flow regimes are also modeled in the code by means of a simplified approach able to represents, with reasonable accuracy, the effects of Taylor-Couette vortex flows and of the transitional regimes up to the onset of a fully turbulent state. Under these hypotheses, the pressure field is slightly affected by the viscosity variation while dissipative effects are enhanced. The code has been validated by means of comparison with available experimental data. Particular attention is devoted to static working parameters (i.e., equilibrium position and frictional power loss), reproducing the global behavior of the bearing, although some local characteristic is also considered.