Study On Nonlinear Dynamics Of Squeeze Film Damper-rolling Bearing-Rotor Systems

A squeeze film damper(SFD)is a common vibration damper used in the areo-engine.It is made up of a rolling bearing,a bearing pedestal and the oil film filled in the clearance formed by the bearing and the pedestal.It is a kind of a structure utilizing the oil film to absorb the oscillation energy to attenuate vibration.Comparing with other dampers,it has small and light characteristics.Howerver,the oil film force is related to stiffness and damper which present nonlinear for the velocity and displacement of the journal.Therefore,the design of the parameters is difficult,and the ?two steady state‘ jump phenomenon and the non-synchronous response even chaos behaviors caused by improper parameters have been reported by many scholars.The trial and error method or experimental method is usually used for the parameter design at present,rather than the theoretical analysis method.Besides,only the complex phenomena of SFDs coupling with other nonlinear factors are reported,the relationship between phenomena and parameters need to be researched.Thus,it is meaningful to study the relationship through theoretical methods and discuss the effects on oscillation attenuation for different conditions to suppress harmful vibration.In this paper,different kinds of SFD-rotor system are established,the bifurcation characteristics of SFD-rotor system with single excitation frequency are first analyzed by theoretical method,later,the dynamic characteristics of SFD embedding in dual-excitation frequencies system,parametrical excitation coupling external excitation system and dual-rotor system are respectively studied.The detail content is contained as follow:The rigid rotor-SFD motion equations are formulized,in which the oil film force are obtained by the short bearing approximate model considering the Reynolds boundary condition.The bifurcation equations are gained through the averaging method and analyzed by the singularity theory.There are three bifurcation modes with different local topology configurations: the normal motion,?two steady state‘ motion,and unable going cross critical speed motion.The transition sets is the boundary of the three kinds of bifurcations,and they provide guidance for choosing the proper parameters.Furthermore,the motion equations containing the fluid inertia force are also analyzed,the bifurcation modes are as same as former,while the effects of the fluid inertia on hysteresis sets is obvious.However,the effect recedes with the decrease of bearing parameter,and the effect of fluid inertia can be neglected qualitatively when the bearing parameter below a certain value.Besides,the quantitative effect exists only on the peak of resonance region.The soft-hard charactertisic can exist in the condition of inter-resonance condition.The nonlinear characteristics of SFD-rotor system containing two external excitation frequencies are studied by using two-dimension harmonic balance method embedding pseudo-arc length algorithm and Runge-Kutta algorithm.It is shown that the various jump phenomena between periodic solution and quasi-periodic solution,which can be concluded as two types based on the bifurcation mechanism: the saddle-node bifurcation and the secondary Hopf bifurcation.The saddle-node bifurcation often occurs in cubic nonlinear system,while the secondary Hopf bifurcation makes the periodic solution lose stability and evolve into quasi-periodic motion with small vibration amplitude,then leads this quasi-periodic motion jump to another quasi-periodic motion with large vibration amplitude in the corresponding frequency domain.The nonlinear characteristics of high order modal is sensitive to ratio of frequencies,they can show as soft stiffness characteristic,soft and hard stiffness coexist characteristic and hard stiffness characteristic,even new unstable region and quasi-periodic solution.The nonlinear vibration can be suppressed by adjusting parameters such as clearance and viscosity,though the effect is not obvious under some frequency ratios.Thus,the frequency ratio is a key parameter to control the vibration of system.The nonlinear dynamics of rotor system containing rolling bearings and squeeze film dampers with the external excitation and parametrical excitation are studied by the numerical integration method.Due to the complex excitations,besides the various order primary resonance regions,such as passing frequency resonance region of rolling bearing,1/2 subharmonic resonance region of passing frequency,1/2 subharmonic resonance region of the second primary resonance and some quasi-periodic region.The jump phenomenon may occur in these regions.With increase of number of rolling balls,the amplitude of passing frequency resonance and 1/2 subharmonic resonance of passing frequency decease,and jump phenomenon vanish,and the odd number of balls shows more stable characteristic than even number.The damper effect of SFD is not obvious in the passing frequency resonance region,while it is obvious the hysteresis region and quasi-periodic region diminish in the primary resonance due to the effect of the SFD.The combined selection of the proper number of rolling elements and proper SFD can suppress the vibration and jump phenomenon in kinds of resonance region,avoid the harmful nonlinear phenomenon.The motion equation of intershaft bearing-dual rotor system is formalized,and the effects of bearing clearance and distribution of SFD on the system response of intershaft bearing-dual rotor system are discussed.Due to the nonlinear characteristic of intershaft bearing,the response of the system shows the combination frequency resoanances,and the amplitude increase with the increase of clearance.At the resonance peak,the equivalent stiffness of intershaft bearing for horizontal direction and vertical direction are equal,their variation tendencies are the same as frequency-amplitude curves,while the variation tendencies of the equivalent stiffness of vertical direction is opposite to frequency-amplitude curves and its stiffness value is larger than that of horizontal direction.The different distribution for SFD affect the performance of vibration absorption on different vibration modal shape: the SFD at the front support of the low pressure rotor effectively suppress the second order primary resonance,the SFD at the rear support of the low pressure rotor effectively suppress the first order primary resonance,the effect of SFD at the front support of high pressure rotor is auxiliary damping.The disturbution for SFD should choose the maxium displacement in each vibration shape and the support with maxium radius to guarantee the effect on vibration suppression and avoid nonlinear phenomenon.This paper provides a strategy to evaluate the proper operation parameters for the SFD and theory basis for application of SDFs under different conditions,the results is meaningful to avoid harmful nonlinear phenomenon such as jump and synchronous response.