Stability Analysis on Rotor Systems Supported by Self-acting Tilting-pad Gas Bearings with Frequency Effects

The recent research on stability of gas bearing-rotor systems still mostly adopts the same method as in oil-lubricated bearing-rotor systems.The dynamic coefficients of gas bearings in the case that the perturbation frequencies are same as the rotating speed are used to carry out the stability analysis of rotor systems.This method does not contact the frequency characteristics of dynamic stiffness and damping coefficients of gas bearings with the dynamical behaviors of rotor systems.Furthermore,the effects of perturbation frequencies on the stability of systems are not taken into account.In this paper,the dynamic stiffness and damping coefficients of tilting-pad gas bearings are calculated by the partial derivative method.On the base of solution of dynamic coefficients,two computational models are produced for stability analysis on rotor systems supported by tilting-pad gas bearings according to whether the degrees of the freedom of pads tilting motions are included in the equations of motion or not.In the condition of considering the frequency effects of dynamic coefficients of tilting-pad gas bearings,the corresponding eigenvalues of the rigid and first five vibration modes of the system with the working speeds of 8-30 kr/min are computed through iteratively solving the equations of motion of rotor-system by using two computational models,respectively.According to the obtained eigenvalues,the stability of rotor system is analyzed.The results indicate that the eigenvalues and the stability of rotor system obtained by these two computational models are well agreement each other.They all can more accurately analyze the stability of rotor systems supported by tilting-pad gas bearings.This research has important meaning for perfecting the stability analysis method of rotor systems supported by gas bearings.

Rapid solution for analysis of nonlinear fluid film force and dynamic behavior of a tilting-pad journal bearing-rotor system with turbulent and thermal effects

To analyze the nonlinear dynamics of a tilting-pad journal bearing(TPJB)-rotor system with high accuracy and speed,the database method(DM)is modified to rapidly determine the nonlinear fluid film force(NFFF)of a TPJB while considering turbulent and thermal effects.A high-accuracy,large-capacity NFFF database for a single pad is constructed by numerically solving the turbulent adiabatic hydrodynamic model for five equivalent state variables of the journal,which are discretized in the pad coordinates.The remaining variables are not discretized in the DM.A combined linear and parabolic interpolation polynomial based on the database is established to accurately calculate the NFFF of the tilting pads;thus,the NFFF of a four-pad TPJB is obtained in the bearing coordinates.The DM is applied to analyze and compare the nonlinear dynamic behavior of a water-lubricated TPJB-Jeffcott rotor system with and without turbulent and thermal effects.The present DM solution without these effects and the previous DM solution are shown to be consistent.The results demonstrate the importance of the flow regime and the negligibility of temperature increases in the nonlinear dynamics of a water-lubricated TPJB.This work contributes to the accurate and efficient analysis of the nonlinear dynamics of high-speed TPJBs and low-viscosity-fluid-lubricated TPJBs.

Nonlinear dynamic analysis of low viscosity fluid-lubricated tilting-pad journal bearing for different design parameters

To reveal nonlinear dynamic rules of low viscosity fluid-lubricated tilting-pad journal bearings(TPJBs),the effects of design parameters on journal center orbits and dynamic minimum film thicknesses of water-lubricated TPJBs with and without static loads are investigated.The hydrodynamic bearing force used in the nonlinear dynamic analysis is an approximate analytical solution including the turbulence effect.The results reveal the methods for vibration suppression and load capacity improvement and give an optimal pivot offset and clearance ratio that can maximize the minimum film thickness.The results also show that four-pad TPJBs with loads between pads are preferred due to good dynamic performance and load capacity.This study would provide some guidance for nonlinear design of low viscosity fluid-lubricated TPJBs under dynamic loads.

Effect of presence of lifting pocket on the THD performance of a large tilting-pad thrust bearing

Hydrostatic assistance is a commonly used method to improve limited load carrying ability of tilting-pad thrust bearings during transient states of operation of vertical shaft hydro-generators.Despite of special hydraulic equipment(as pumps,valves,etc.),it also requires manufacturing of special recesses/pockets at pad sliding surfaces,into which oil is injected under high pressure.It allows to lift the rotor before start-up of the machine and form a hydrostatic film between pads and collar.There is a quite wide variety of geometry of recesses(shape,depth,and size)met in practical large bearing applications.The presence of a hydrostatic pocket(usually located in the sliding surface above the pivot area,where thin film,high oil pressure and temperature are observed)affects bearing performance under hydrodynamic operation.In theoretical researches,there is an almost common practice not to include hydrostatic recess in thermohydrodynamic(THD)or thermoelastohydrodynamic(TEHD)analysis.This is probably due to the problems with obtaining solution for oil film geometry with pocket,the order of magnitude of the pocket depths being larger than gap thickness.In this paper,an attempt was taken to study the effect of lifting pocket on THD performance of a large tilting-pad thrust bearing of Itaipu power plant.Bearing performance was evaluated including recess shape for several cases of its depth.The results show that hydrostatic recess changes calculated bearing properties quite significantly,especially in vicinity of the pocket.

The Prediction of Dynamic Coefficients for Tilting-Pad Journal Bearings Based on an AGA-BP Neural Network

To provide real-time dynamic coefficients of tilting-pad journal bearings( TPJBs) for the dynamic analysis of a rotor-bearing system accurately,an improved error back propagation( BP) neural network model is built in this paper.First,the samples are gained by solving the Reynolds equation with the finite differential method based on hydrodynamic lubrication theory.Secondly,the adaptive genetic algorithm( AGA) is applied to optimize the initial weights and thresholds of the BP neural network before training.Then,with a number of trial calculations,the optimum parameters for the neural network are obtained.Finally,an application case of the neural network is given as well as the results analysis.The results show that the AGA can efficiently prevent the training of the neural network from falling into a local minimum,and the AGA-BP neural network of dynamic coefficients for TPJBs built in this paper can meet the demand of engineering.