Study On The Performance Of Aerodynamic Tilting-Pad And Compliant Foil Bearings

The aerodynamic bearings are successfully used in high speed rotating machines such as turbo expanders because of their excellent performance. The systematically experimental and theoretical researches on the static and dynamic performance of this type of bearings and the dynamic analysis of the related rotor systems are very important for the bearing design and application, especially for advancing the performance and widening the application of the bearings. This dissertation presents the theory and the numerical calculation method for predicting the performance of the aerodynamic tilting-pad bearing and related rotor systems. And it firstly builds an actively control model for controlling the vibration of the rotor systems supported by tilting-pad gas bearings based on applying the piezo-electric actuators and PID feedback control systems. Furthermore, a test rig is established to predict the static and dynamic performance of the compliant foil gas bearings. The main contents of this dissertation are listed as follows:1. The compressible gas-lubricated static Reynolds equation is iteratively solved by means of the finite element method for calculating the static performance of the tilting-pad gas bearing. Based on the computational results, the influences of the bearing parameters, such as bearing preload, compressible number on the static performance of the bearing are studied.2. Two computational methods for calculating the dynamic stiffness and damping coefficients of the tilting-pad bearings are presented with the assumption that the pads and the journal perturb with the same frequency. Now, the gas-lubricated dynamic Reynolds equation is solved by means of the partial derivative method in the complex number domain. By comparing the results, these two methods are proved to be validity for calculating the dynamic coefficients of the tilting-pad bearings. Moreover, according to the numerical simulation results, the effects of the bearing parameters on the dynamic coefficients are discussed. And the frequency dependency of the dynamic stiffness and damping coefficients of the tilting-pad gas bearings are explained more thoroughly. Furthermore, the each function of the perturbation frequency of the journal and the pads on these dynamic coefficients are firstly discussed.3. By using the limit theory, the limits of the dynamic stiffness and damping coefficients of the tilting-pad bearings are calculated when the dimensionless perturbation frequency tends to zero and infinite. It provides a computational method for predicting the static stiffness and damping coefficients of the tilting-pad bearings and makes it possible to research the dynamic performance of the tilting-pad gas bearings in the whole frequency range.4. Basing on whether the pads tilting degrees of freedom are included in the moving equations or not, two calculation models for the stability analysis of the rotor systems supported by tilting-pad self-acting gas bearings are given. The stability of the rotor systems are analyzed according to the eigenvalues of the system in which the frequency dependency of the dynamic stiffness and damping coefficients are taken into account. It perfects the stability analysis of the rotor systems supported by tilting-pad gas bearings. The results indicate the eigenvalues and the stability of the rotor system obtained by these two models are well agreement each other.5. By using the piezo-electric actuators and PID feedback control systems, an actively control model are firstly established for controlling the vibration of the rotor systems. The optimal control rules between the voltages and displacements of the rotor systems are obtained by means of the optimal control theory. Applying this actively control model, the unbalance responses of the rotor systems can be effectively restrained and the theoretical basis is provided for further improving the stability of the rotor systems supported by the tilting-pad gas bearings.6. A multifunctional test rig is built for testing the static and dynamic performance of the compliant foil journal and thrust bearings. And the testing methods of the static and dynamic performance of the foil bearings are given. The lift-off speed of compliant foil bearing is identified more accurately by simultaneously using the frictional moment method and the displacement response frequency spectra method. The dynamic stiffness and damping coefficients of compliant foil journal bearing are evaluated by means of the least mean square in the time domain. And the effects of the excitation frequency on these dynamic coefficients are mainly investigated. Furthermore, the lift-off speed of compliant foil thrust bearing is first identified by using the displacement response frequency spectra method.