Elastohydrodynamics Applied to Active Tilting-Pad Journal Bearings

The static and dynamic properties of tilting-pad journal bearings with controllable radial oil injection are investigated theoretically. The tilting pads are modeled as flexible structures and their behavior is described using a three-dimensional finite element framework and linear elasticity. The oil film pressure and flow are considered to follow the modified Reynolds equation, which includes the contribution from controllable radial oil injection. The Reynolds equation is solved using a two-dimensional finite element mesh. The rotor is considered to be rigid in terms of shape and size, but lateral movement is permitted. The servovalve flow is governed by a second order ordinary differential equation, where the right hand side is controlled by an electronic input signal. The constitutive flow-pressure relationship of the injection orifices is that of a fully developed laminar velocity profile and the servovalve is introduced into the system of equations by a mass conservation consideration. The Reynolds equation is linearized with respect to displacements and velocities of the nodal degrees of freedom. When all nodal points satisfy static equilibrium, the system of equations is dynamically perturbed and subsequently condensed to a $2×2$ system, keeping only the lateral motion of the rotor. As expected, bearing dynamic coefficients are heavily influenced by the control parameters and pad compliance.