Dynamic Analysis And Experimental Investigation On A New Type Of Active Bump-type Foil Bearing-rotor System

Gas foil bearings(GFBs)consist of elastic foil and rigid bearing housings,they are flexibly dydrodynamic gas bearings in which ambient gases are used as their lubricants.Because of the advantages of high rotational speed,long service life,low cost,oil-free lubrication,and compact structure,they can significantly enhance the DN value(speed of the rotor surface),energy density and efficiency of rotating machineries.GFBs have been widely used in air cycle machines,high speed motors,high speed blowers/compressors,micro turbojet engines,micro gas turbines,air compressor for vehicle fuel cell and so on.However,because of nonlinear dynamic characteristics of GFBs,the rotor-GFBs system suffers severe subsynchronous vibrations with high amplitudes which weakens the stability of system and hinders the application of GFBs.Traditional “passive” solutions are optimizing the performances of GFBs through improving structure designs of bearings.However,the structures and performances of bearings designed by the "passive" solution can not be changed actively after the assembly of bearings,and the performances of bearings can't be controlled actively when the working conditions of equipment are changed.To solve the above problems,in this paper,on the basis of fully understanding the lubrication mechanism of GFBs,a new type of active bump-type foil bearing(ABFB)was innovatively put forward.An "active" solution for optimizing bearing performance and improving the high-speed stability of bearing-rotor system was put forward through introducing active control structure and control method.In this paper,the main research methods and achievements are as follows:Based on the requirements of radial preloading for GFBs and the retro-piezoelectric effect of piezoelectric actuator,an active substructure including piezoelectric actuators,flexible hinges,lever amplifier and preloading devices was designed.The static analysis of the active substructure was carried out by using the finite element method(FEM),and the theoretical model of the active structure was established based on the second Cartesian theorem.The correctness of the theoretical model of the active substructure was verified on the test rig.Based on the Link-Spring model of bump foil and one dimensional FEM model of top foil,the mechanical model of foil structure was deduced.The mechanical model of elastic support structure was deduced on the basis of coupling theoretical model of the active substructure with mechanical model of foil structure in series.The static push-pull test was utilized to verify the correctness of the mechanical model.Based on the mechanical model of elastic support structure coupled with the compressible gas Reynolds equation,the theoretical lubrication model of the ABFB was derived.The finite difference method(FDM)and Newton-Raphson method were utilized to solve the static lubrication model of the ABFB.The pressure distribution,eccentricity and attitude angle of the ABFB under different control voltages were predicted.Based on the hypothesis of small perturbation method and the calculation results of static performances,the dynamic lubrication model of the ABFB was solved by using the FDM and Newton-Raphson method.The effects of control voltage,nominal clearance and width of flexure hinge on the dynamic stiffness coefficients and dynamic damping coefficients of the ABFB were predicted.The predicted results indicated that the ABFB could change its static and dynamic performances by actively changing the control voltage.The static and dynamic performances of ABFB provided important theoretical references for the design and active control of the bearing.The lift-off test rig for the ABFB was built.The influences of different control voltages on the lift-off performances of the bearing were measured.The test rig of rotor-ABFB system was built.The effects of different control voltages and unbalanced masses of the rotor on the dynamic responses of the rotor system with constant rotational speed and during the deceleration process were measured.The effectiveness of the ABFB was verified.Based on the hypothesis of small perturbation method,the dynamic stiffness coefficients and dynamic damping coefficients of the ABFB were calculated.The theoretical model of the rotor was established by using the FEM.The dynamic model of the rotor-ABFB system was derived by coupling the dynamic coefficients of the ABFB and the theoretical model of the rotor.The rotordynamic responses of the rotor-ABFB system at different rotational speeds were calculated.The critical speeds and peak amplitudes of the rotor under different control voltages were predicted.Based on the theoretical model of rigid rotor and the non-linear supporting force model of bearings,the nonlinear theoretical model of the rotor-ABFB system with considerations of rigid rotor,lubricated film and foil structure was established.The rotordynamic responses of the rotor-ABFB system during the deceleration process and under different unbalanced displacements were predicted,which were in good agreement with the measured data of corresponding rotating tests.The validity of the nonlinear theoretical model of the rotor-ABFB system was verified.The non-linear dynamic responses of the rotor-ABFB system were analyzed.The influences of key parameters including control voltage,nominal clearance,width of flexure hinge and static load of rotor on the rotordynamic responses of the rotor-ABFBs system were analyzed and discussed by means of rotor axial trajectory,Poincare mapping,fast Fourier transform of vertical vibration,minimum film thickness and power loss description during one rotational cycle.The vibration control test rig was established in which the rotor was supported by two ABFBs.The effects of linearly increasing voltage on the amplitude of the rotor at different constant rotating speeds were measured.The feedback relationship between the measured vibration of rotor and the output DC voltage was established by using proportional,integral and differential(PID)control algorithm.The effects of PID closed-loop control under constant rotational speed and during coast down and speed up and down process were measured.The feasibility of building the closed-loop control for the rotor-ABFBs system was proved.The results of control tests shown that the rotor amplitudes could be actively controlled in a small range at different rotational speeds by using the PID control algorithm.In conclusion,an ABFB was proposed based on the innovative design of active substructure.By actively changing the control voltage,the active control of the static and dynamic performances of the bearing was realized,and the subsynchronous vibrations with large amplitude of the rotor-ABFB system were actively suppressed.The rotor amplitudes of the rotor-ABFBs system could be controlled in a small range at different rotational speeds by using the PID control algorithm.The effects of different design parameters,working conditions and control voltages on the static and dynamic performances of bearings and the non-linear dynamic response of the bearing-rotor system were studied by using theoretical calculation and experimental measurement.The predicted results and experimental data shown that the ABFB could actively and effectively suppress the vibration of the rotor-ABFBs system.The ABFB could actively optimize the bearing performances and improve the high-speed stability of the rotor-ABFBs system according to the working conditions.It is an effective "active" solution.