Model-Based Degree Estimation of Unbalance and Misalignment in Flexible Coupling-rotor System

The condition of rotor system must be assessed in order to develop condition-based maintenance for rotating machinery. It is determined by multiple variables such as unbalance degree, misalignment degree, the amount of bending deformation of the shaft, occurrence of shaft crack of rotor system and so on. The estimation of the degrees of unbalance and misalignment in flexible coupling-rotor system is discussed. The model-based approach is employed to solve this problem. The models of the equivalent external loads for unbalance and misalignment are derived and analyzed. Then, the degrees of unbalance and misalignment are estimated by analyzing the components of the equivalent external loads of which the frequencies are equal to the 1 and 2 times running frequency respectively. The equivalent external loads are calculated according to the dynamic equation of the original rotor system and the differences between the dynamical responses in normal case and the vibrations when the degree of unbalance or misalignment or both changes. The denoise method based on bandpass filter is used to decrease the effect of noise on the estimation accuracy. The numerical examples are given to show that the proposed approach can estimate the degrees of unbalance and misalignment of the flexible coupling-rotor system accurately.

Effects of Tightening Torque on Dynamic Characteristics of Low Pressure Rotors Connected by a Spline Coupling

A rotor dynamic model is built up for investigating the effects of tightening torque on dynamic characteristics of low pressure rotors connected by a spline coupling.The experimental rotor system is established using a fluted disk and a speed sensor which is applied in an actual aero engine for speed measurement.Through simulating calculation and experiments,the effects of tightening torque on the dynamic characteristics of the rotor system connected by a spline coupling including critical speeds,vibration modes and unbalance responses are analyzed.The results show that when increasing the tightening torque,the first two critical speeds and the amplitudes of unbalance response gradually increase in varying degrees while the vibration modes are essentially unchanged.In addition,changing axial and circumferential positions of the mass unbalance can lead to various amplitudes of unbalance response and even the rates of change.

INVESTIGATION OF ACTIVE CONTROL FOR DYNAMIC STABILITY OF HELICOPTER ROTOR－BODY COUPLING

A study is conducted on the feasibility of helicopter ground and air resonanceby using actively controlled tabs mounted at the trailing edge of an aerofoil. A method isdeveloped to obtain the optimal feedback control law through constructing a referencemodel according to requirements of stability levels in the modal space. The effects of rotorspeed and length and location of tabs on the control law are analyzed, and it is found possible that a controller can be designed into constant feedback gain against rotor speed andto feed back only to the dominant system states to eliminate the unstable range of rotorspeed.

Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.

Structural Parameter Analyses on Rotor Airloads with New Type Blade-Tip Based on CFD/CSD Coupling Method

For accurate aeroelastic analysis,the unsteady rotor flowfield is solved by computational fluid dynamics(CFD)module based on RANS/Euler equations and moving-embedded grid system,while computational structural dynamics(CSD)module is introduced to handle blade flexibility.In CFD module,dual time-stepping algorithm is employed in temporal discretization,Jameson two-order central difference(JST)scheme is adopted in spatial discretization and B-L turbulent model is used to illustrate the viscous effect.The CSD module is developed based on Hamilton′s variational principles and moderate deflection beam theory.Grid deformation is implemented using algebraic method through coordinate transformations to achieve deflections with high quality and efficiency.A CFD/CSD loose coupling strategy is developed to transfer information between rotor flowfield and blade structure.The CFD and the CSD modules are verified seperately.Then the CFD/CSD loose coupling is adopted in airloads prediction of UH-60A rotor under high speed forward flight condition.The calculated results agree well with test data.Finally,effects of torsional stiffness properties on airloads of rotors with different tip swept angles(from 10° forward to 30° backward)are investigated.The results are evaluated through pressure distribution and airloads variation,and some meaningful conclusions are drawn the moderated shock wave strength and pressure gradient caused by varied tip swept angle and structural properties.

Dynamic response of large increased pressure wind tunnel rotor-gear coupling system with parallel misalignment

To study the misalignment of gear coupling, this paper analyzed the distortion of the tooth of gear coupling on the base of gear coupling’s motion under parallel misalignment, and derived the specific expression of additive radial force, which produced by the rotor’ torque. The motion differential equations of the large increased pressure wind tunnel rotor-gear coupling system were derived by the finite element method. Newmark integral method was applied to calculate the dynamic response of the system with parallel misalignment. The numerical results show that: under the effect of additive radial force, the static misalignment can arouse 2X frequency component lateral vibration; the dynamic misalignment can arouse2X,4X,6X multiple frequency components lateral vibration. The 2X frequency component is obvious. The additive radial force of the gear coupling can arouse lateral vibration with even multiple frequency components.

A NEW AEROMECHANICAL STABILITY ANALYSIS METHODOLOGY FOR COUPLED ROTOR/FUSELAGE SYSTEM OF HELICOPTERS

The aeromechanical st ability for the coupled rotor/fuselage system of helicopters in forward flight i s investigated. The periodic time-varying equations of motion are developed thr ough building a new 24DOF coupled rigid/elastic blended element based on the fle xible multibody system theory in this paper. It accounts for the effects of prec one, sweep, and the moderately large elastic deflections on the blade and elasti city of shaft and fuselage of the helicopter. The dynamic coupling between the r igid motion of blades about the flap, lag and pitch hinges of articulated rotor and moderately large elastic deflections are included. There is no restriction o n the rotation amplitudes of flap, lag and pitch in the formulation. The stabili ty of periodic solution is studied using the Floquet theory. The transition matr ix is calculated by the Newmark integration method. The aeromechanical stability of a new helicopter is studied. The results show that it is stable in the given forward flight. But the instability arises with the decrease of the bending and torsion stiffness of the shaft.

Analytical Model of Elastomeric Lag Damper Kinematic Coupling and Its Effect on Helicopter Air Resonance in Hover

For an elastomeric lag damper with nonlinear properties and kinematic couplings, its differential equation about equilibrium position was derived in a rotating frame. The equation was then transformed into a non-rotating frame by multi-blade transformation and incorporated into the rotor/airframe differential equations for eigen analysis. The effects of damper steady displacement and kinematic couplings on helicopter air resonance in hover were analyzed. The results demonstrate that the elastomeric damper can increase helicopter dynamic stability; however, its available damping will decrease as its steady displacement increased. For the notional rotor system, the damper steady displacement will decrease when kinematic couplings are introduced, and hence the regressive lag modal damping can be increased.

Numerical Optimization on Aerodynamic/Stealth Characteristics of Airfoil Based on CFD/CEM Coupling Method

Based on computational fluid dynamics （CFD）/computational eleetromagnetics method （CEM） coupling method and surrogate model optimization techniques, an integration design method about aerodynamic/stealth characteristics of airfoil is established. The O-type body-fitted and orthogonal grid around airfoil is first generated by using the Poisson equations, in which the points per wave and the normal range satisfy the aerodynamic and electromagnetic calculation accuracy requirement. Then the aerodynamic performance of airfoil is calculated by sol- ving the Navier-Stokes （N-S） equations with Baldwin-Lomax （B-L） turbulence model. The stealth characteristics of airfoil are simulated by using finite volume time domain （FVTD） method based on the Maxwell＇s equations, Steger-Warming flux splitting and the third-order MUSCL scheme. In addition, based upon the surrogate model optimization technique with full factorial design （FFD） and radial basis function （RBF）, an integration design about aerodynamic/stealth characteristics of rotor airfoil is conducted by employing the CFD/CEM coupling meth- od. The aerodynamic/stealth characteristics of NACA series airfoils with different maximum thickness and camber combinations are discussed. Finally, by choosing suitable lift-to-drag ratio and radar cross section （RCS） ampli- tudes of rotor airfoil in four important scattering regions as the objective function and constraint, the compromised airfoil with high lift-to-drag ratio and low scattering characteristics is designed via systemic and comprehensive ana- lyses.

RESEARCH ON MODELING AND CHARACTERISTICS OF THE SPINDLE DYNAMIC COUPLING ABSORBERING SYSTEM OF A SUPER-PRECISION SURFACE GRINDING MACHINE

The bearing is described by constrain matrix, and the spindle system of a NCsurface grinding machine is simplified as elastic-coupling beam, then modal synthesis method is usedto establish the dynamic model of beam. Moreover, the response of the end of rotor is analyzed, andthe natural frequency, principle mode and other dynamic characteristics of the coupling system arestudied, the law of bearing stiffness to coupling frequency and amplitude of rotor is also found.Finally, according to the actual condition, a dynamic absorber is designed. The simulation andexperimental results show that the amplitude of spindle can be declined effectively when the dynamicabsorber is attached.

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.

Nonlinear Dynamic Analysis of Coupled Gear-Rotor-Bearing System with the Effect of Internal and External Excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

Nonlinear aeroelastic coupled trim and stability analysis of rotor-fuselage

Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method （TEM）. The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.

INFLUENCES ON COUPLED LATERAL AND TORSION VIBRATION BEHAVIOR OF RUB-IMPACT ROTOR BY ROTOR-TO-STATOR CLEARANCE

With the establishment of the nonlinear coupled lateral and torsion vibrationequations of rub-impact Jeffcott rotor and through numerical simulations, the influences on lateraland torsion vibration behavior by rotor-to-stator clearance are analyzed, which prove that there isstrong impact on coupled lateral and torsion vibration behavior. Smaller the clearance is, morecomplex the motion of rotor is. When the clearance is larger, the frequency spectrum of rub-impactrotor is mainly composed of 1/2X, 1/3X and 1/4X components. With the decrease of clearance,quasi-periodic and chaotic motions will be present. Under different clearances, the bifurcationdiagrams of lateral and torsion vibrations can be divided into rub-free zone, rub-light zone andthree complex motion zones in which the motion trend of lateral vibration is similar to that of thetorsion vibration. Compared with the lateral vibration, the torsion vibration is of more motionforms and more abundant frequency components in amplitude spectrum.

The Coupled CFD/Free-Wake Method for Numerical Prediction of Rotor BVI Noise

A coupled Navier-Stokes/free-wake method is developed to predict the rotor aerodynamics and wake.The widely-used Farassat 1 Aformulation is adopted to predict the rotor noise.In the coupled method,the Reynolds-averaged Navier-Stokes(RANS)solver is established to simulate complex aerodynamic phenomena around blade and the tip-wake is captured by a free-wake model without numerical dissipation in the off-body wake zone.To overcome the time-consuming of the coupling strategy in previous studies,a more efficient coupling strategy is presented,by which only the induced velocity on the outer boundary grid need to be calculated.In order to obtain blade control settings,a delta trimming procedure is developed,which is more efficient than traditional trim method in the calculation of Jacobian matrix.Several flight conditions are simulated to demonstrate the validity of the coupled method.Then the rotor noise of operational load survey(OLS)is studied by the developed method as an application and the computational results are shown to be in good agreements with the available experimental data.

NONLINEAR NUMERICAL ANALYSIS OF A FLEXIBLE ROTOR EQUIPPED WITH SQUEEZE COUPLE STRESS FLUID FILM JOURNAL BEARINGS

This study performs a dynamic analysis of a rotor supported by two squeeze couple stress fluid film journal bearings with nonlinear suspension. The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the dimensionless parameter l＊. It is found that the system is more stable with higher dimensionless parameter l＊. Thus it can conclude that the rotor-bearing system lubricated with the couple stress fluid is more stable than that with the conventional Newtonian fluid. The modeling results thus obtained by using the method proposed in this paper can be used to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided.

Transient Analysis of a Reactor Coolant Pump Rotor Seizure Nuclear Accident

The reactor coolant pump(RCP)rotor seizure accident is defined as a short-time seizure of the RCP rotor.This event typically leads to an abrupt flow decrease in the corresponding loop and an ensuing reactor and turbine trip.The significant reduction of core coolant flow while the reactor is being operated at full load can have very negative consequences.This potentially dangerous event is typically characterized by a complex transient behavior in terms of flow conditions and energy transformation,which need to be analyzed and understood.This study constructed transient flow and rotational speed mathematical models under various degrees of rotor seizure using the test data collected from a dedicated transient rotor seizure test system.Then,bidirectional fluid-solid coupling simulations were conducted to investigate the flow evolution mechanism.It is found that the influence of the impeller structure size and transient braking acceleration on the unsteady head(Hu)is dominant in rotor seizure accident events.Moreover,the present results also show that the rotational acceleration additional head(Hu1)is much higher than the instantaneous head(Hu2).

基于流固耦合的大型立式轴流泵机组运行稳定性分析

轴(贯)流泵机组在中国南水北调、“一带一路”等泵站群建设中运用广泛.为了研究大型轴流泵不同运行工况下流体激励力对机组振动的影响,采用CFX和Mechanical联合实现轴流泵叶片非定常应力的流固耦合计算模拟.流场计算基于RANS方法的N-S方程,结构计算采用弹性结构力学方程,使用任意拉格朗日-欧拉ALE法求解,得到了轴流泵转子变形、应力分布及模态特征.研究结果表明,叶频与压力波动频率一致,叶轮旋转是造成压力脉动的主要原因;叶片的最大变形出现在叶片轮缘处,叶片最大应力出现在叶片与轮毂连接处;在叶轮0.6~1.4倍额定转速内,难以找到转子各阶固有频率与叶频及其倍频均保持一定差值的合理转速,但在忽略次要共振可能性后,存在最优转速以达到固有频率和各阶主频的合理差值.

HIGHER ORDER SPECTRAL ANALYSIS IN FAULT DIAGNOSIS OF ROTORS

The nonlinear properties of rotating machinery vibration signals are presented. The relationship between faults and quadratic phase coupling is discussed. The mechanism that gives rise to quadratic phase coupling is analyzed, and the coupling models are summarized. As a result, higher order spectra analysis is introduced into fault diagnosis of rotors. A brief review of the properties of higher order spectra is presented. Furthermore, the bicoherence spectrum is employed to extract the features that signify the machinery condition. Experiments show that bicoherence spectrum patterns of different faults are quite different, so it is proposed to identify the faults in rotors.

ZERO MODE NATURAL FREQUENCY AND NONLINEAR VIBRATION OF COUPLED LATERAL AND TORSION OF A LARGE TURBINE GENERATOR

Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF andvibrations resulted by it are studied. First, calculating method of the ZMNF excited byelectromagnetic in vibrational system of coupled mechanics and electrics are given from the view ofmagnetic energy. Laws that the ZMNF varies with active power and exciting current are obtained andare verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system isstudied by considering rest eccentricity, rotating eccentricity and swing eccentricity. UsingLargrange-Maxwell equation when three phases are asymmetric derives differential equation of thecoupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics ofresonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF willoccur in turbine generators by the action of electromagnetic. Because ZMNF varies withelectromagnetic parameters, resonance can occur when exciting frequency of the rotor speed is fixedwhereas exciting current change. And also find that a generator is in the state of large amplitudein rated exciting current.