Tilting-Pad Journal Bearings With Active Lubrication Applied as Calibrated Shakers: Theory and Experiment

In recent years, a continuous research effort has transformed the conventional tilting-pad journal bearing (TPJB) into a mechatronic machine element. The addition of electromechanical elements provides the possibility of generating controllable forces over the rotor as a function of a suitable control signal. Such forces can be applied in order to perform parameter identification procedures “in situ,” which enables evaluation of the mechanical condition of the machine in a noninvasive way. The usage of a controllable bearing as a calibrated shaker requires obtaining the bearing specific frequency dependent calibration function, i.e., the transfer function between control signal and force over the rotor. This work presents a theoretical model of the calibration function for a TPJB with active lubrication. The bearing generates controllable forces by injecting pressurized oil directly into the bearing clearance. The injected flow is controlled by means of a servovalve. The theoretical model includes the dynamics of the hydraulic system using a lumped parameter approach, which is coupled with the bearing oil film using a modified form of the Reynolds equation. The oil film model is formulated considering an elastothermohydrodynamic lubrication regime. New contributions to the mathematical modeling are presented, such as the inclusion of the dynamics of the hydraulic pipelines and the obtention of the bearing calibration function by means of harmonic analysis of a linearized form of the controllable bearing constitutive equations. The mathematical model is used to study the relevance and effects of different parameters on the calibration function, aiming at providing general guidelines for the active bearing design. Finally, experimental results regarding the calibration function and the usage of the studied bearing as a calibrated shaker provide insight into the possibilities of application of this technology.