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.

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.

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.

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.

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.

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

Based on computational fluid dynamics(CFD)/computational electromagnetics 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 solving 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 method.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)amplitudes 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 analyses.

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.

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.

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.

转子-机匣耦合系统碰摩非线性特征研究

转子-机匣碰摩问题是航空发动机中最常见故障之一。在临界转速附近,转子振动幅值会急剧增大,超过转子-机匣初始间隙就会引起碰摩。为了进一步探究碰摩机理,建立了考虑阻尼的非线性碰摩力模型并将其耦合在转子-机匣系统模型中,采用四阶Runge-Kutta法求解,给出了不同转速下转子-机匣系统的响应分岔图,研究了转子-机匣系统的振动响应。同时,分别讨论了碰撞恢复系数、碰摩间隙对转子运动和碰摩力的影响。结果表明:碰撞恢复系数减小会导致转子-机匣嵌入深度增大,从而导致碰摩力增大。碰摩间隙会改变碰摩的频率,且随着间隙的减小,碰摩的频率增大。

存在初始静偏心的储能飞轮转子动力学特性

以大功率储能飞轮转子系统为研究对象,探究电机转子存在初始静偏心时飞轮动力学特性的变化规律。首先使用能量法求出电机转子不平衡磁拉力(UMP)与转子偏心位移之间的关系,采用Timoshenko梁单元模型建立包含UMP的飞轮转子机电耦合动力学模型,计算分析电机转子初始偏心量和偏心方向对飞轮稳态和瞬态特性的影响,得出以下结论:随着偏心量的增大,上轴承处轴心轨迹出现嵌套圆环,频谱出现3种频率成分且幅值增大,升速响应曲线共振峰的峰值增大,对应转速减小;当偏心方向改变且旋转一周时,转频等成分的幅值、升速响应曲线共振峰值产生明显的周期规律变化。

氦气轮机转子动力学特性优化设计

基于ANSYS软件对某一型号的氦气轮机柔性转子进行了转子动力学特性的计算分析与优化设计。首先对转子的初始模型进行了临界转速计算,并识别影响转子固有频率的关键部位,通过加强其弯曲刚度,初步提高了转子的临界转速。进一步将转子分段并用柔性膜盘联轴器连接,计算得到氦气轮机转子的临界转速大幅提高,使其在设计转速下可视为刚性轴,保证了氦气轮机转子的转子动力学安全。

弹性环挤压油膜阻尼器支撑下的柔性转子系统动力学分析

弹性环挤压油膜阻尼器(Elastic ring squeeze film damper, ERSFD)具有良好的支撑作用和减振效果,但由于其结构和流场耦合行为极为复杂,使得已有的物理模型难以完整表现出ERSFD的力学特性.为了进一步探究ERSFD的力学机理,本文借助有限元仿真平台,采用双向流固耦合的计算方法,剖析弹性环与油膜之间的相互作用,获取ERSFD中油膜压力的分布规律.在此基础上,利用最小二乘法进一步拟合出ERSFD等效刚度、等效阻尼与转子轴颈扰动位移的映射关系,并将其分别引入柔性转子系统动力学模型中.通过数值计算研究了ERSFD支撑下柔性转子系统的振动响应,分别给出了不同转速下转子系统的响应分岔图、轴心轨迹等.同时,通过对比分析,进一步揭示了ERSFD所诱发出的转子系统丰富的非线性动力学行为,有助于对ERSFD轴承支撑特性的理解.

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。