Vibration and flutter of stiff-inplane elastically tailored composite rotor blades

Aeroelastic response, blade and hub loads, and shaft-fixed aeroelastic stability is investigated for a helicopter with elastically tailored stiff-inplane composite rotor blades. A free wake model for nonuniform rotor inflow is integrated with a recently developed finite-element-based aeroelastic analysis for helicopters with tailored composite blades. Pitch-flap and pitch-lag elastic couplings, introduced through the anisotropy of the plies in the blade spar, have a significant effect on the dynamic elastic torsion response. Positive and negative pitch-flap couplings reduce vertical hub shear forces approximately 20% in the high vibration transition flight regime, however, negative pitch-flap elastic coupling significantly increases inplane hub shear forces at all flight speeds. The influence of pitch-flap, pitch-lag, and extension-torsion elastic couplings on the rotating frame blade bending moments is small. Ply-induced composite couplings have a powerful effect on blade stability in both hover and forward flight. Positive pitch-flap, positive pitch-lag, and positive extension-torsion couplings each have a stabilizing effect on lag mode damping. Negative pitch-lag coupling has a strong destabilizing effect on blade lag stability, resulting in a mild instability at moderate flight speeds.     

Application of CFRP as a rotor shaft material

Conclusions Theoretical analysis and tests performed on rotors with composite shaft show that there is a sufficiently wide rotation stability region in the rotor parameter space despite comparatively high damping of a polymeric composite with respect to steel. Optimum parameters of the shaft (lay-up, thickness) and bearing (radial stiffness, damping) can be found within this region for each given rotor ensuring a low vibration level at critical frequencies.If rotor system parameters are far enough from the instability threshold, maximum vibration level is observed when rotor passes the first eigenfrequency zone. Further increase of rotation frequency leads to a rotor self-centering, and vibration level does not change passing the second eigenfrequency zone. The rotor response is not sensitive to small changes in rotor system parameters. If rotor system parameters are close to the instability threshold, vibration level at the second eigenfrequency dominates, and a small variation of bearing parameters causes significant changes in the vibration level.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 227–240, March–April, 1995.     

Rotor dynamics behavior of turbo-expander involving droplet impact

ABSTRACT

This paper dedicates on the rotor dynamics behaviour research on the turbo-expander rotor system involving droplet impact. A stochastic model based on Beta distribution and Bernoulli distribution of droplet generation is established and the formulations of droplet impact forces are deduced, which is applied on the rotor dynamics equations of the tilting pad bearing supported turbo-expander considering the temperature gradient for a further analysis. A time domain research is carried out and a conclusion that continuously droplet impact will perturb the steady vibration of the turbo-expander rotor system is obtained. Monte Carlo method is implemented for a statistics dynamics research and the results suggests that in the design of expander impellers, in order to decrease the uncertainty brought by droplet impact, the number of channels should be as few as possible, the droplet impact should be controlled to occur uniformly, and the collision, entrainment of the primary droplets and the stripping of the liquid film on the blade should be strictly restrained.     

Dynamic analysis and experiment investigation of a cracked dual-disc bearing-rotor system based on orbit morphological characteristics

The paper is aimed to examine dynamic behaviors of a dual-disc bearing-rotor system in multi-fault state, and the crack detection based on the orbit morphological characteristics and vibration responses is proposed. Dynamic response and vibration signal analysis are two significant studies in rotor system. Most researchers have simulated the nonlinear dynamics and analyzed the fault signal using various methods separately. However, the fault feature from vibration signal is tightly connected with the dynamic mechanism in the rotor system, especially in rotor system with coupling multi-fault. In the paper, the dynamic model of the dual-disc bearing-rotor system is established, which takes into account the effects of crack, rub-impact and nonlinear oil-film forces. The vibration responses and the effect of crack on dual-disc rotor system with multi faults are investigated. The existence of crack and the coupling effect of multi faults enrich dynamic behavior of the dual-disc bearing-rotor system, and the response near the 1/2 subcritical speed provides a criterion for crack detection. Experiment investigation is attempted for the first time, which is based on the changes of crack depth and rotation speed for multi-fault dual-disc rotor system. The analysis of the dynamic response and the orbit morphological characteristics from experiment can effectively detect the crack information.     

Dynamic modeling and analysis of wind turbine drivetrain considering the effects of non-torque loads

With the increase of the rotor diameter and the deterioration of operating conditions, modern wind turbines suffer from more and more significant time-varying non-torque loads, which increases the burden of turbine structures especially the gearbox. Based on an aeroelastic loose coupling approach and assembly of the finite element method, an integrated drivetrain coupling analysis model including blade module, aerodynamic module, and gearbox module is established in this study. This proposed model is validated by comparing the calculation results with previous literature. Taking National Renewable Energy Laboratory 5-MW wind turbine as the research object, the gearbox vibration responses, gear meshing forces and bearing forces under non-torque loads caused by blade gravity, wind shear (WS), tower shadow (TS) and yawed inflow are studied in detail. Results show that the y-direction displacements of the gearbox, sun gear 1, sun gear 2 and gear are larger than those in x-direction because F_y or M_x generated by blade gravity, WS and TS dominates the non-torque loads. The non-torque loads lead to a non-uniform planet load sharing especially for the planetary gear stage 1. Because of the fluctuations of non-torque loads, not only the rotation frequencies of the corresponding carrier but also the multiple frequencies of the carrier 1 are observed in the frequency spectrums. The non-torque loads are mainly borne by carrier 1 bearings. Except for the blade gravity, the bearing forces caused by other unsteady inflows have obvious fluctuations.     

An optimization procedure for the design of prop-rotors in high speed cruise including the coupling of performance,aeroelastic stability,and structures

An optimization procedure is developed to address the complex problem of designing prop-rotors in high speed cruise. The objectives are maximization of the aerodynamic efficiency in high speed cruise and minimization of the total rotor weight. Constraints are imposed on aeroelastic stability in cruise and rotor thrust. An isotropic box beam is used to model the principal load carrying member in the blade. Design variables include blade sweep and twist distributions, rotational velocity in cruise, and the box beam wall thickness. Since the optimization problem is associated with multiple design objectives, the problem is formulated using a multiobjective formulation technique known as the Kreisselmeier-Steinhauser function approach. The optimization algorithm is based on the method of feasible directions. A hybrid approximate analysis technique is used to reduce the computational expense of using exact analyses for every function evaluation within the optimizer. The results are compared to two reference rotors, unswept and swept. The optimum result shows significant improvements in the propulsive efficiency in cruise and reductions in the rotor weight without loss of aeroelastic stability or thrust, when compared to the reference unswept rotor. The swept reference rotor is initially unstable and the optimization procedure has been successful in producing a blade design which is fully stable with significant improvements in efficiency and blade weight. Off-design studies performed indicate that the optimum rotor maintains high propulsive efficiency over a wide range of operating conditions.     

On some regularities in dynamic response of cyclic periodic structures

The paper deals with cyclic periodic structures modelling bladed disk assemblies of blades with friction elements for vibration damping. These elements placed between adjacent blades reduce the vibration amplitudes by means of dry friction resulting from centrifugal forces acting on the elements and relative displacements of the blades. However, the application of these friction elements results in an additional dynamical coupling which together with mistuning of some system parameters (e.g., blade eigenfrequency or contact parameters) may cause localization of vibration. In the present paper a linear approximation of such a system is investigated. The structure composed of cyclic periodic cells modelled each as a clamped-free beam interacting with each other by means of viscoelastic elements of complex stiffness is applied for dynamic system analysis. In case of free vibrations as well as in case of steady-state dynamic response to a harmonic pressure field, a perfect periodic structure and the structures with periodically mistuned parameters (blade eigenfrequencies and contact parameters) are studied. Some regularities in the dynamic response of the systems with mistuning have been noticed. Despite the fact that only a linear approximation has been used, the results and conclusions can be applied for models which describe the blade interaction in a nonlinear way.     

1:2 and 1:3 internal resonance active absorber for non-linear vibrating system

Vibration and dynamic chaos should be controlled in either structures or machines. An active vibration absorber for suppressing the vibration of the non-linear plant when subjected to external and parametric excitations is studied in the presence of one-to-two and one-to-three internal resonance. The main attention is focused on the study of the active control and stability of two systems, which can be used to reduce vibrations due to rotor blade flapping motion. The method of multiple scale perturbation technique is applied to determine four first-order non-linear ordinary differential equations that govern the modulation of the amplitudes and phases in the presence of internal resonance of the two systems with quadratic and cubic order of control. These equations are used to determine the steady state solutions and their stability. The stability study of non-linear periodic solution for two cases (1:2 and 1:3 internal resonance) and the stability of the obtained numerical solution are investigated using frequency, force-response curves and phase-plane method. Also, effects of some parameters on the steady state solution of the vibrating system are investigated and reported in this paper. Variation of some parameters leads to the bending of the frequency, force-response curves and hence to the jump phenomenon occurrence. The reported results are compared to the available published work.     

Development of a finite element solution module for the analysis of the dynamic behavior and balancing effects of an induction motor system

The study developed a multipurpose finite element solution module with the theoretical groundwork originated from principles of rotordynamics. This module is capable of solving many of the related rotating machine problems such as of the high speed gas bearing spindles and the electric machines. The goal of this paper is to utilize the developed solution module in investigating various aspects of the vibration behavior of an induction motor system for solving its failure problem of the shaft. Some of the crucial factors to the quality and performance of the motor, such as the vibration amplitude as resulted from the bearing wear, damping effects, mass unbalance, and the passing of system resonance critical speeds, are all investigated in the study. An efficient dual-rotor model is verified to have excellent accuracy when comparing the calculated frequency response function (FRF) with that from modal testing. The results of the transient orbit analysis indicate that the bearing stiffness and damping dominates the vibration amplitude remarkably. The effects both from the bearing damping as well as from the clamping–damping between the silicon steel core and the rotating shaft are all examined. It is noticed that the bearing damping plays the major role in the restraint of the vibration amplitudes of the rotor. For the analysis of vibration suppression with different eccentricities of the unbalanced masses, it is found that the adding of balance masses will normally suppress the vibration amplitude effectively until the point where an optimum amount that causes the minimum balanced vibration amplitudes is observed. Both the qualitative and quantitative analyses for the effectiveness of the balance mass added with different eccentricity ratios are studied. Thus, the critical adding mass ratio (i.e. the adding mass ratio at the minimum balanced amplitude factor) can also be predicted through its linear relationship with the eccentricity ratio. Based on all the findings through the study, it is concluded that the approach not only can solve the realistic shaft vibration failure problems of a motor and the demonstrated processes are also believed to be able to help the designers to have better command of motor performance at the system design stage.     

A mathematical model for horizontal axis wind turbine blades

A mathematical model describing the nonlinear vibration of horizontal axis wind turbine (HAWT) blades is proposed in this paper. The system consists of a rotating blade and four components of deformation including longitudinal vibration (named axial extension), out-of-plane bend (named flap), in-plane/edgewise bend (named lead/lag) and torsion (named feather). It is assumed that the center of mass, shear center and aerodynamic center of a cross section all lie on the chord line, and do not coincide with each other. The structural damping of the blade, which is brought about by materials and fillers is taken into account based on the Kelvin–Voigt theory of composite materials approximately. The equivalent viscosity factor can be determined from empirical data, theoretical computation and experimental test. Gravitational loading and aerodynamic loading are considered as distributed forces and moments acting on blade sections. A set of partial differential equations governing the coupled, nonlinear vibration is established by applying the generalized Hamiltonian principle, and the current model is verified by previous models. The solution of equations is discussed, and examples concerning the static deformation, aeroelastic stability and dynamics of the blade are given.     

Stall-delay modelling of wind turbine blades

Most aerodynamic design tools for horizontal-axial wind turbines are based on the blade-element momentum theory (BEM). Due to the nature of this theory, the design tools need 2-D steady sectional lift and drag curves as an input. In practice, flow over a wind turbine rotor blade is neither two-dimensional nor steady, and is affected by rotation. Pioneering experiments have identified a consequence: at inboard rotor blade sections stall is delayed. This so-called Himmelskamp effect [1] gives a larger lift than predicted and, as a result, a higher power and loading than expected. Consequently, an aerodynamic model is needed to explain and predict sectional lift and drag under rotating conditions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

迷宫密封不平衡转子动力系统的稳定性与分岔

研究迷宫密封对不平衡转子系统动力稳定性的影响.存在不平衡量的转子在旋转过程中受到周期激励,低转速时,转子作与激励同频率的周期运动,随着转速的提高,达到一定阈值时周期运动开始失稳.对迷宫密封的气动力采用Muszynska非线性力学模型,用打靶法求解转子运动周期解,并根据Floquet理论分析了周期解的稳定性及失稳后的动力学特性.     

Investigation of horizontal-axis wind turbine (HAWT) blade three-dimensional rotational e?ect based on ?eld experiments?

Field experiments are performed on a two-bladed 33 kW horizontal-axis wind turbine (HAWT). The pressures are measured with 191 pressure sensors positioned around the surfaces of seven spanwise section airfoils on one of the two blades. Three-dimensional (3D) and two-dimensional (2D) numerical simulations are performed, respectively, on the rotor and the seven airfoils of the blade. The results are compared with the experimental results of the pressure distribution on the seven airfoils and the lift coe?cients. The 3D rotational e?ect on the blade aerodynamic characteristics is then studied with a numerical approach. Finally, some conclusions are drawn as follows. From the tip to the root of the blade, the experimental di?erential pressure of the blade section airfoil increases at ?rst and then decreases gradually. The calculated 3D result of the pressure distribution on the blade surface is closer to that of the experiment than the 2D result. The 3D rotational e?ect has a signi?cant impact on the blade surface ?ow and the aerodynamic load, leading to an increase of the di?erential pressure on the airfoils and their lift coe?cient than that with the 2D one because of the stall delay. The in?uence of the 3D rotational e?ect on the wind turbine blade especially takes place on the sections with ?ow separation.     

Unwanted noise and vibration control using finite element analysis and artificial intelligence

A mechatronic approach integrating both passive and active controllers is presented in this study to deal with unwanted noise and vibration produced in an automobile wiper system operation. Wiper system is a flexible structure with high order, nonlinear model that is considered as a multi objective control problem since there is a conflict between its functionality quality in wiping and generated unwanted noise and vibration. A passive control technique using multi body system (MBS) model and finite element analysis (FEA) is introduced to identify the potential of the effectiveness of the physical parameters of wiper blade to give appropriate range to reduce the unwanted noise and vibration in the system. While, the significant contribution of active controller is to deal with uncertainties exerted to system within wiper operation. In passive control stage, natural frequencies of a uni-blade automobile wiper are determined using modal testing. Later, a 3-dimensional model of a wiper blade assembly is developed in multi body system design to investigate the good validation test and agreement of the physical behavior of the system in experiment with finite element analysis. Parametric modification via complex eigenvalue is adopted to predict instability of the wiper blade. In active control level, experimental data collected from the wiper system during its operation. A system identification model named nonlinear auto regressive exogenous Elman neural network (NARXENN) is developed for implying the active controller. A bi-level adaptive-fuzzy controller is brought in whose parameters are tuned simultaneously by a multi objective genetic algorithm (MOGA) to deal with the conflict interests in wiper control problem.     

Active vibration control of unbalanced flexible rotor–shaft systems parametrically excited due to base motion

Rotor vibrations caused by large time-varying base motion are of considerable importance as there are a good number of rotors, e.g., the ship and aircraft turbine rotors, which are often subject to excitations, as the rotor base, i.e. the vehicle, undergoes large time varying linear and angular displacements as a result of different maneuvers. Due to such motions of the base, the equations of vibratory motion of a flexible rotor–shaft relative to the base (which forms a non-inertial reference frame) contains terms due to Coriolis effect as well as inertial excitations (generally asynchronous to rotor spin) generated by different system parameters. Such equations of motion are linear but time-varying in nature, invoking the possibility of parametric instability under certain frequency–amplitude combinations of the base motion. An investigation of active vibration control of an unbalanced rotor–shaft system on moving bases is attempted in this work with electromagnetic control force provided by an actuator consisting of four electromagnetic exciters, placed on the stator in a suitable plane around the rotor–shaft. The actuator does not levitate the rotor or facilitate any bearing action, which is provided by the conventional suspension system. The equations of motion of the rotor–shaft continuum are first written with respect to the non-inertial reference frame (the moving base in this case) including the effect of rotor internal damping. A conventional model for the electromagnetic exciter is used. Numerical simulations performed on the flexible rotor–shaft modelled using beam finite elements shows that the control action is successful in avoiding the parametric instability, postponing the instability due to internal material damping and reducing the rotor response relative to the rigid base significantly, with sufficiently low demand of control current in comparison with the bias current in the actuator coils.     

An Investigation of the Separate Flow and Stall-delay for Horizontal-Axis Wind Turbine

The flow characteristics and stall delay phenomenon of a stall regulated wind turbine rotor due to blade rotation in steady state non-yawed conditions are investigated. An incompressible Reynolds-averaged Navier-Stokes solver is applied to carry out the separate flow cases at high wind speeds from 11 m/s to 25 m/s with an interval of 2 m/s. The objective of the present research effort is to validate a first-principles based approach for modeling horizontal axis wind turbines (HAWT) under stalled flow conditions using NREL/Phase VI rotor data. The computational results are compared with the predicted values derived by a new stall-delay model and blade element momentum (BEM) method. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight

This paper focuses on the nonlinear vibration phenomenon caused by aircraft hovering flight in a rub-impact rotor system supported by two general supports with cubic stiffness. The effect of aircraft hovering flight on the rotor system is considered as a maneuver load to formulate the equations of motion, which might result in periodic response instability to the rotor system even the eccentricity is small. The dynamic responses of the system under maneuver load are presented by bifurcation diagrams and the corresponding Lyapunov exponent spectrums. Numerical analyses are carried out to detect the periodic, sub-harmonic and quasi-periodic motions of the system, which are presented by orbit diagrams, phase trajectories, Poincare maps and amplitude power spectrums. The results obtained in this paper will contribute an understanding of the nonlinear dynamic behaviors of aircraft rotor systems in maneuvering flight.     

Chaos via torus breakdown in the vibration response of a rigid rotor supported by active magnetic bearings

This work reports on a numerical study undertaken to investigate the response of an imbalanced rigid rotor supported by active magnetic bearings. The mathematical model of the rotor-bearing system used in this study incorporates nonlinearity arising from the electromagnetic force—coil current—air gap relationship, and the effects of geometrical cross-coupling. The response of the rotor is observed to exhibit a rich variety of dynamical behavior including synchronous, sub-synchronous, quasi-periodic and chaotic vibrations. The transition from synchronous rotor response to chaos is via the torus breakdown route. As the rotor imbalance magnitude is increased, the synchronous rotor response undergoes a secondary Hopf bifurcation resulting in quasi-periodic vibration, which is characterized by a torus attractor. With further increase in the rotor imbalance magnitude, this attractor is seen to develop wrinkles and becomes unstable resulting in a fractal torus attractor. The fractal torus is eventually destroyed as the rotor imbalance magnitude is further increased. Quasi-periodic and frequency-locked sub-synchronous vibrations are seen to appear and disappear alternately before the emergence of chaos in the response of the rotor. The magnitude of rotor imbalance where sub-synchronous, quasi-periodic and chaotic vibrations are observed in this study, albeit being higher than the specified imbalance level for rotating machinery, may possibly occur due to a gradual degradation of the rotor balance quality during operation.     

基于非线性能量阱的双频激励非线性系统减振

针对某型民用航空发动机双频带激励特点,建立了单自由度线性振子耦合非线性能量阱（nonlinear energy sink,NES）的动力学模型.根据典型双转子发动机在巡航状态下低、高特征频率比（1∶4.74）,为系统设定双频带简谐外激励.利用四阶Runge-Kutta算法,研究了耦合NES振子时系统的振动抑制特征,并从外激励频率对系统主振子动能、系统总体能量的影响等方面,与未耦合NES系统、耦合线性动力吸振器两种情况下的数值计算结果进行对比分析.研究结果表明NES对双频带外激励具有更好的振动抑制效果,用NES降低航空发动机振动有可行性.     

非线性不平衡弹性轴系动力学的安全裕度准则

给出了一个弹性转子系统的非线性动力学安全裕度准则.采用分解和聚合的方法将系统的积分空间与观察空间分离,在积分空间中得到高维系统的稳态轨迹;根据转子系统振动的国际标准确定安全准则的能量界限,在一系列观察空间中采用能量相比正面积准则计算安全裕度.给出了滑动轴承非线性油膜力条件下不平衡转子系统安全裕度计算的实例.所建议的安全裕度准则包括了工程中通用的稳定裕度的计算,它是解决非线性系统安全裕度和稳定裕度量化计算问题的一种有效方法.