Theoretical Analysis And Experimental Investigation On Nonlinear Dynamic Behaviors Of Rotor Supported On Gas Foil Bearings

Gas foil bearings(GFBs)are hydrodynamic gas bearings with elastic foil structure supporting the pressured air film.Rotor systems supported on GFBs(rotor-GFBs systems)have the advantages of high efficiency,clean and oil-free,long life,low cost and so on.The rotor-GFBs systems are suitable for developments of micro turbo-machineries in high rotational speed and high temperature operation and can be applied to the aerospace and aviation industries.Due to the geometric and physical parameters of the foil structure,the force supplied by GFBs are highly nonlinear.Meanwhile,dynamic behavior of high speed rotor is also quite complex.The two mentioned factors limit the developments and applications of rotor-GFBs system.In this dissertation,models and corresponding tests are established to evaluate the dynamic performance of rotor-GFBs system.Effects of bearing parameters and extra loads on the nonlinear system response are investigated.The subsynchronous vibrations which are common in rotor-GFBs system are analyzed.The main researches and achievements are as follow:Based on the basic process of static load-deflection test,the criterion of GFBs nominal clearance are presented according to characters of the nonlinear supporting force of foil structure.The methods to calculate the instant rotor speeds and time-frequency results of vibration data are established.The in-series stiffness model of bearing and rotor are used to estimate the rotor-GFBs system dynamic performance and the find out the source of subsynchronous vibrations.According to the vibration data from tests,nominal clearance and nonlinear supporting force of foil structure do affect the synchronous and subsynchronous vibrations.From the aspects of experiments,the parameters of GFBs and their effects on the rotor system are investigated.The compressible lubricant gas film is calculated with the Reynolds equations based on the assumption of Newtonian fluid.The foil structure is modeled with the Link-Spring model.Dynamic coefficients of the GFBs are the perturbation of the static results of the two mentioned models.The system dynamic model of rotor system are derived with the Timoshenko beam theory.Linear modal analysis of rotor-GFBs system are conducted with the calculated bearing dynamic coefficients.Nonlinear transient dynamic simulations are conducted with the modified nonlinear supporting force of the foil structure data from static load-deflection tests.Comparisons are discussed with the synchronous and subsynchronous data from tests and simulations.The advantages and disadvantages in linear and nonlinear rotor-GFBs models are summarized.From the aspects of theory,the effects of foil structure on the nonlinear response of rotor-GFBs system are discussed.To simplify the analysis of the nonlinear stiffness of foil structures,the model of bump foils in-parallel are applied.To simplify the estimation of the nonlinear stiffness of GFBs,the model of foil structure and gas film in-series are used.With the coupling of rotordynamic response analysis,the transient model considering the compressible gas film,the elastic foil structure and shaft whirl are derived.The transient model show good agreements with the corresponding test data,especially in the frequency domain.The source of subsynchronous motions are discussed with the stiffness model mentioned above.With help of transient shaft orbits,Poincare map and amplitude spectrum,the effects of nominal clearance,foil structure stiffness,foil structural loss factor and static load on the amplitude,frequency and operational shapes are discussed.From the aspects of theoretical analyses and experimental investigations,the source and impact factors of nonlinear dynamic performance of the rotor-GFBs system are discussed.To investigate effects of extra static and imbalance loads on the nonlinear dynamic performance of rotor-GFBs system,the test rigs used to add extra loads on the shaft are manufactured.To overcome the errors due to the wear of shaft surface,the vibration data are compensated with the slow-roll vector at low speed and key-phaser signal from digital laser tachometer.The coast-down tests are conducted under different conditions of static and imbalance loads.The synchronous and subsynchronous motions are compared and discussed to find out the effects of extra load on the nonlinear transverse vibration of rotorGFBs system.The relationship between the bearing drag force and rotor speed are derived and used to explain the coast-down time extents with different extra loads.From the aspects of theoretical analyses and experimental investigations,the effects of extra loads of shaft on the nonlinear dynamic performance of rotor-GFBs system are discussed.The static modal reduction method is derived to reduce the time-cost of simulations.The reduced model is compared with the linear free modal analysis and show good tolerable errors.To improve the robustness of the transient dynamic model of rotor-GFBs system,the Wilson-theta method is applied to solve the second order partial equation groups.One test with various static load condition is conducted to calibrate the transient dynamic model.The source of subsynchronous in rotor-GFBs system are discussed with simulation data under different static and dynamic loads.Moreover,when the extra static loads or imbalance loads are large enough,the subsynchronous vibrations will disappear as the natural frequency of the rotor system is improved by the extra loads.Unfortunately,these phenomena are only found out in the theoretical simulations and are hard to be proved in experimental investigations.The operational deflection shape of the subsynchronous motions are compared and separated from that happed in the rotor system supported on the oil bearings.From the theoretical analysis,the effects of static and imbalance loads on the rotor-GFBs system subsynchronous vibrations are discussed.In conclusion,to overcome the applying limitations of rotor-GFBs system due to high nonlinear vibrations,experimental investigations with bearing static load-deflection test rigs and transverse vibration test rigs are conducted to estimate the effects of GFBs parameters and extra loads on the nonlinear dynamic performance of rotor-GFBs system.The simplified models that explain the nonlinearity of foil structure and GFBs are discussed.Moreover,the linear and nonlinear models are able to estimate the nonlinear performance of rotor-GFBs system.The theoretical analysis and experimental investigations in this thesis are useful to understand the nonlinearity of the rotor system and helpful to the widespread applications of rotor-GFBs system.