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.

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.

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.

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).

EXPERIMENTAL INVESTIGATION OF AERODYNAMICINTERACTION EFFECT OF ROTOR WAKE ONFUSELAGE OF HELICOPTER

The interaction effect of rotor wake on fuselage of helicopter was investigated with experimental method. The results from experiment have proved that for the drag of fuselage the effect of rotor airflow is closely in connection with both the flight speed and the collective pitch of blades, while for the thrust and pitch moment of fuselage the collective pitch angle of blades plays more important role. A simple and effective computing method about aerodynamic interaction can be derived from the measured data. In order to implement the experiment, a fuselage model, a special sensor, the measurement and data acquisition and processing system were designed and manufactured according to the special requirements of this research project, thereby a good base was built up for carrying out experiments successfully with high quality.

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.

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.

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.

冲击激励下轴线失准转子-磁轴承系统不对中定量研究

为研究和识别转子系统在轴承处发生的平行角度混合不对中,提出一种频谱辨识转子-磁轴承系统固有不对中量大小的方法.采用动量矩定理将圆盘不平衡力对转轴的影响等效到转子轴向力上,建立考虑轴向径向耦合效应的刚性双偏置圆盘转子-磁轴承系统的动力学模型;通过SIMULINK仿真得到系统时域下的位移和电流响应,分析不对中条件下转子系统动力学特性,并利用快速傅里叶变换将时域响应转换为频域响应,基于频域下最小二乘算法得到转子系统不对中量大小.结果表明:在冲击激励影响条件下,采用该方法计算的不对中量大小误差均在5.0%以内,当转子受到外界扰动力时,该算法能够准确定量识别转子的不对中量,可为不对中转子-磁轴承系统故障诊断及自修复提供理论参考.

双并列转子永磁电机非对称负载运行特性

双并列转子电机在驱动两侧非对称负载时,轻载侧电机的功角较低,产生了电机材料浪费,效率低等问题。为提升电机整体输出功率,基于双并列转子电机基本理论采用解析法求得电机驱动转矩平均值的表达式,进而提出轻载侧绕组提前的结构设计。而后以一台12极72槽双并列转子电机为例,建立其磁网络模型,通过麦克斯韦应力张量法得出驱动转矩的解析计算式,分析转子偏差角对电机基本转矩脉动的影响,得出最佳绕组提前槽数。最后,针对电机转矩脉动较大的问题,使用响应曲面法,以基本转矩脉动为目标函数,以永磁体偏心距、永磁体极弧系数、并接区高度作为自变量对电机进行优化,有效降低电机转矩脉动,验证了绕组前置的结构改进对提升电机非对称状态下的输出转矩具有显著效果。

带后掠桨尖旋翼/螺旋桨的悬停气弹特性分析

针对旋翼/螺旋桨的大负扭和后掠桨尖设计在桨叶内部所带来的严重应力应变集中问题,结合三维结构动力学模型、旋翼气动模型和旋翼配平方法,对复合材料旋翼/螺旋桨进行了综合建模与气弹载荷分析,并通过悬停实验验证了综合模型的准确性。对比分析了无负扭、大负扭和大负扭带后掠桨尖的桨叶气弹特性,发现大负扭导致桨叶应力集中区域扩大,后掠桨尖使桨尖过渡区域的应力集中区域扩大,集中程度加剧。