Dynamic Characteristics Of Rotor-bearing System Subjected To Base Motions

An aero-engine mounted on an aircraft is inevitably subjected to external excitations provided by the aircraft as the base of the engine,which may lead to severe vibrations,complicated movements,and even abnormal operation of the rotor system.Therefore,it is necessary to investigate the dynamic characteristics of aero-engine rotor-bearing system subjected to base motions,in order to provide support for optimizing structural design,improving structural reliability,and enhancing vibration resistance.Through coordinate transformation,the motions of aircraft can be converted into the motions of rotor base.Combining base motion excitations with rotor-bearing system,a systematic approach is proposed to investigate the dynamic characteristics of a single-or dual-rotor system subjected to base motions.Using Lagrange's principle,the steady-state and transient equations of motion for the finite elements relative to moving base are derived,including rigid disks,mass unbalances,shaft segments with uniform or tapered cross-section and bearings.The factors are taken into account including rotary inertia,gyroscopic moment,transverse shear deformation,rotating angular acceleration,and deterministic base motions(translational and rotational components).The results show that compared with fixed base,base translations just add external force vectors,while base rotations bring on parametric damping and stiffness matrices as well as additional force vectors.Base axial rotation keeps the system isotropic,while base lateral rotations lead to anisotropy and break the symmetry of dynamic behavior.Using state-space vector method,steady-state characteristics of the single-or dual-rotor system subjected to base motions are analyzed via critical speeds,mode shapes,unbalance responses during base rotations,frequency responses due to base harmonic excitations,and shaft orbits.Using Newmark-Hilber-Hughes-Taylor(Newmark-HHT)integration method,transient characteristics of the single-or dual-rotor system excited by mass unbalance and base motions during start-up are illustrated.The influence of factors are discussed on the transient responses of the rotor system with fixed base,including acceleration/deceleration and rotating angular acceleration.Using control variable method,the effects of base motion parameters on the steady-state and transient responses of the single-or dual-rotor system are analyzed,including the angular velocities of the axial rotation or lateral rotations,and the magnitude and frequencies of harmonic translations.The above results indicate that compared with fixed base,base axial rotation contributes significantly to the critical speeds and resonant amplitudes of the rotor systems.For the single(dual)rotor system,when the direction of base axial rotation is identical to the rotating direction of the(low pressure)rotor,with the increase of base angular velocity,the critical speeds decrease gradually.Base lateral rotations generate additional gyroscopic moments,which deviates the shaft center from the bearing centerline.The deviation becomes greater with the increase of the lateral angular velocity of the base or the rotating speed of the rotor.Base harmonic translations can lead to forward and backward whirl resonances.The frequency of base harmonic translation affects orbit shapes significantly.In contrast,the magnitude of base translation has a large influence on orbit amplitudes.When the harmonic frequency of base translation gets close to excited frequencies of low-pressure or high-pressure rotor,obvious beat vibrations appear in the time waveform.Owing to base harmonic translation,the transient responses are amplified gradually in the whole speed range.When the magnitude is too high,the resonant amplitudes will be even probably submerged in the responses excited by base translation.Especially for the dual-rotor system,the impacts of co-rotating or counter-rotating,low-pressure or high-pressure rotor excitation on the vibration characteristics are also discussed.Compared with direct Campbell diagram,for calculating the critical speeds of dual-rotor system,dual-rotor critical speed map leads to a wider range of application,especially for the case that the speed ratio varies significantly during operation.On the premise of the same structure,the first three critical speeds of counter-rotating dual-rotor are lower than those of co-rotating dual-rotor.Due to gyroscopic moment,the resonance frequencies of the low-pressure rotor excitation(LRE)are not identical to those of the high-pressure rotor excitation(HRE),regardless of co-rotating or counter-rotating.The transient responses at a specific cross-section are closely related to co-rotating or counter-rotating,unbalance distribution,critical speeds and mode shapes,thereby varying along the axial direction.The above mentioned rotor systems excited by base motions are linear systems.Furthermore,for the nonlinear rotor system supported by a squeeze film damper(SFD)with centering spring,it is assumed that the journal has a static eccentricity.The nonlinear vibration responses of the squeeze film damped rotor system subjected to base motions are investigated by means of time waveform,shaft orbit,frequency spectrum and Poincarémap.Bifurcation diagram is used to analyze the motion behavior of the rotor system changing with rotating speed or harmonic frequency of base translation.The results show that when the journal has a static eccentricity,even if the base is fixed,the whirl orbit of the journal is no longer circular,the center of the orbit is offset,and the second-order frequency is stimulated.With static eccentricity,the fluctuation of the eccentricity ratio is larger.Under base axial rotation,the center of the journal orbit is still located at the static eccentric point,while it deviates from the static eccentric point in the case of base lateral rotation,and the deviation direction depends on the direction of the lateral rotation.Excited by base harmonic translation,the frequency components of the responses contain not only integral multiples of the fundamental frequency k?(k(28)1,2),but also the harmonic frequency of base translation?~z,and even the combined frequenciesk??j?~z(k,j(28)1,2).When subjected to base harmonic translation,the system responses transform from periodic motion to period-doubling or quasi-periodic bifurcation.The maneuvering flight of aircraft is regarded as a kind of base excitation for rotor-bearing system.A dynamic model of a rotor system with a squeeze film damper during maneuvering flight is established,considering not only the unbalance forces,oil-film force and gravity,but also the additional inertial force and the instantaneous static eccentricity of the journal caused by maneuvering flight.In order to achieve turning maneuver,the parameters between yawing and rolling should be matched properly.The influence of maneuvering speed,maneuvering radius,rotating speed and mass unbalance on the transient responses of the rotor system are discussed during turning and diving-climbing maneuver.The results indicate that when an aircraft conducts a maneuvering flight,the offset direction of the whirl orbit center is determined by the centrifugal acceleration of the aircraft and the additional gyroscopic moment.The journal performs a nonsynchronous whirl around the instantaneous static eccentricity.The magnitude of the instantaneous static eccentricity is related to the additional load during maneuvering flight and the supporting stiffness of the rotor system.Increasing maneuvering velocity or decreasing maneuvering radius,the rotor vibration will enter earlier into or withdraw later from the relatively large eccentric condition.The shaft center deviates from the original bearing centerline,high-order harmonic frequencies appear in the vibration responses,and the shape of rotor trajectories is gradually flattened.During maneuvering flight,rotating in the vicinity of critical speeds in addition to excessive mass unbalances should be prevented.The impacts of complicated maneuver on the nonlinear dynamic characteristics of rotor-bearing system should be considered.