Blade Mode Shapes Research Articles

Vibration and Damping Analysis of Carbon Fiber Wind Turbine Blade with Viscoelastic Damping Treatment

The paper have described the vibration and damping analysis of carbon fiber wind turbine blade with viscoelastic damping treatment using commercial ANSYS program. The wind turbine system including a carbon fiber layer and a viscoelastic damping layer was attached on inside of carbon layer. Firstly, the natural frequencies and mode shape of pure carbon fiber turbine blade were compared with viscoelastic damping treated turbine blade using modal analysis. There were 1mm, 2mm, 3mm thickness damping layer finite element model to be constructed. The results show the little changes in lower first mode but getting smaller with higher modes. Finally, the frequency response functions of damped and undamped turbine blade were calculated for investigating the damping effect of viscoelastic damping layer. As shown in the results, the viscoelastic damping layer has good damping effect for vibration control of carbon fiber wind turbine blade.

A Study on Fluid Self-Excited Flutter and Forced Response of Turbomachinery Rotor Blade

Complex mode and single mode approach analyses are individually developed to predict blade flutter and forced response. These analyses provide a system approach for predicting potential aeroelastic problems of blades. The flow field properties of a blade are analyzed as aero input and combined with a finite element model to calculate the unsteady aero damping of the blade surface. Forcing function generators, including inlet and distortions, are provided to calculate the forced response of turbomachinery blading. The structural dynamic characteristics are obtained based on the blade mode shape obtained by using the finite element model. These approaches can provide turbine engine manufacturers, cogenerators, gas turbine generators, microturbine generators, and engine manufacturers with an analysis system to remedy existing flutter and forced response methods. The findings of this study can be widely applied to fans, compressors, energy turbine power plants, electricity, and cost saving analyses.

Effects of extreme wind shear on aeroelastic modal damping of wind turbines

ABSTRACTWind shear is an important contributor to fatigue loads on wind turbines. Because it causes an azimuthal variation in angle of attack, it can also affect aerodynamic damping. In this paper, a linearized model of a wind turbine, based on the non‐linear aeroelastic code BHawC, is used to investigate the effect of wind shear on the modal damping of the turbine. In isotropic conditions with a uniform wind field, the modal properties can be extracted from the system matrix transformed into the inertial frame using the Coleman transformation. In shear conditions, an implicit Floquet analysis, which reduces the computational burden associated with classical Floquet analysis, is used for modal analysis.The methods are applied to a 2.3 MW three‐bladed pitch‐regulated wind turbine showing a difference in damping between isotropic and extreme shear conditions at rated wind speed when the turbine is operating closest to stall. The first longitudinal tower mode decreases slightly in damping, whereas the first flapwise backward whirling and symmetric modes increase in damping. This change in damping is attributed to an interaction between the periodic blade mode shapes and the azimuth‐dependent local aerodynamic damping in the shear condition caused by a beginning separation of the flow. Copyright © 2012 John Wiley & Sons, Ltd.

Correlation of helicopter rotor aeroelastic response with HART‐II wind tunnel test data

PurposeThis paper aims to validate a comprehensive aeroelastic analysis for a helicopter rotor with the higher harmonic control aeroacoustic rotor test (HART‐II) wind tunnel test data.Design/methodology/approachAeroelastic analysis of helicopter rotor with elastic blades based on finite element method in space and time and capable of considering higher harmonic control inputs is carried out. Moderate deflection and coriolis nonlinearities are included in the analysis. The rotor aerodynamics are represented using free wake and unsteady aerodynamic models.FindingsGood correlation between analysis and HART‐II wind tunnel test data is obtained for blade natural frequencies across a range of rotating speeds. The basic physics of the blade mode shapes are also well captured. In particular, the fundamental flap, lag and torsion modes compare very well. The blade response compares well with HART‐II result and other high‐fidelity aeroelastic code predictions for flap and torsion mode. For the lead‐lag response, the present analysis prediction is somewhat better than other aeroelastic analyses.Research limitations/implicationsPredicted blade response trend with higher harmonic pitch control agreed well with the wind tunnel test data, but usually contained a constant offset in the mean values of lead‐lag and elastic torsion response. Improvements in the modeling of the aerodynamic environment around the rotor can help reduce this gap between the experimental and numerical results.Practical implicationsCorrelation of predicted aeroelastic response with wind tunnel test data is a vital step towards validating any helicopter aeroelastic analysis. Such efforts lend confidence in using the numerical analysis to understand the actual physical behavior of the helicopter system. Also, validated numerical analyses can take the place of time‐consuming and expensive wind tunnel tests during the initial stage of the design process.Originality/valueWhile the basic physics appears to be well captured by the aeroelastic analysis, there is need for improvement in the aerodynamic modeling which appears to be the source of the gap between numerical predictions and HART‐II wind tunnel experiments.

Blade Tip Clearance Flow and Compressor Nonsynchronous Vibrations: The Jet Core Feedback Theory as the Coupling Mechanism

This paper investigates the role of tip clearance flow in the occurrence of nonsynchronous vibrations (NSVs) observed in the first axial rotor of a high-speed high-pressure compressor in an aeroengine. NSV is an aeroelastic phenomenon where the rotor blades vibrate at nonintegral multiples of the shaft rotational frequencies in operating regimes where classical flutter is not known to occur. A physical mechanism to explain the NSV phenomenon is proposed based on the blade tip trailing edge impinging jetlike flow, and a novel theory based on the acoustic feedback in the jet potential core. The theory suggests that the critical jet velocity, which brings a jet impinging on a rigid structure to resonance, is reduced to the velocities observed in the blade tip secondary flow when the jet impinges on a flexible structure. The feedback mechanism is then an acoustic wave traveling backward in the jet potential core, and this is experimentally demonstrated. A model is proposed to predict the critical tip speed at which NSV can occur. The model also addresses several unexplained phenomena, or missing links, which are essential to connect tip clearance flow unsteadiness to NSV. These are the pressure level, the pitch-based reduced frequency, and the observed step changes in blade vibration and mode shape. The model is verified using two different rotors that exhibited NSV.

Aeroelastic Analysis of Rotors With Flexible Disks and Alternate Blade Mistuning

A new reduced-order aeroelastic model using the principal shapes (AMPSs) of modes is presented. Rotors with flexible disks and alternate blade mistuning can challenge the fidelity of flutter prediction techniques that assume uniform blade-to-blade geometry and mode shape invariance with nodal diameter pattern. The AMPS method, however, accounts for alternating blade geometry as well as varying blade mode shapes, providing accurate flutter predictions for a large number of modes from a small number of computational fluid dynamics simulations. AMPS calculations on rotors with alternate blade mistuning are presented and compared to other prediction techniques. The results provide insight into how alternate blade mistuning affects aerodynamic coupling and the flutter characteristics of a rotor.

On-line fan blade damage detection using neural networks

This paper presents a methodology for monitoring the on-line condition of axial-flow fan blades with the use of neural networks. In developing this methodology, the first stage was to utilise neural networks trained on features extracted from on-line blade vibration signals measured on an experimental test structure. Results from a stationary experimental modal analysis of the structure were used for identifying global blade mode shapes and their corresponding frequencies. These in turn were used to assist in identifying vibration-related features suitable for neural network training. The features were extracted from on-line blade vibration and strain signals which were measured using a number of sensors.The second stage in the development of the methodology entails utilising neural networks trained on numerical Frequency Response Function (FRF) features obtained from a Finite Element Model (FEM) of the test structure. Frequency domain features obtained from on-line experimental measurements were used to normalise the numerical FRF features prior to neural network training. Following training, the networks were tested using experimental frequency domain features. This approach makes it unnecessary to damage the structure in order to train the neural networks.The paper shows that it is possible to classify damage for several fan blades by using neural networks with on-line vibration measurements from sensors not necessarily installed on the damaged blades themselves. The significance of this is that it proves the possibility to perform on-line fan blade damage classification using less than one sensor per blade. Even more significant is the demonstration that an on-line damage detection system for a fan can be developed without having to damage the actual structure.

Contribution to experimental validation of linear and non-linear dynamic models for representing rotor–blade parametric coupled vibrations

This work makes a theoretical and experimental contribution to the problem of rotor–blades dynamic interaction. A validation procedure of mathematical models is carried out with the help of a simple test rig, built by a mass–spring system attached to four flexible rotating blades. With this test rig, it is possible to highlight some dynamic effects and experimentally simulate the structural behaviour of a windmill in two dimensions (2-D model). Only lateral displacement of the rotor in the horizontal direction is taken into account. Gyroscopic effect due to angular vibrations of the rotor is eliminated in the test rig by attaching the rigid rotor to a flexible foundation. The blades are modelled as Euler–Bernoulli beams. Using three different approaches to describe the beam deformation one achieves: (a) a linear model; (b) a linear beam model with second order terms; (c) a fully non-linear model. Tip masses at the end of the blades emphasize the coupling between the dynamic and elastic terms. The shape functions are chosen in order to reduce the mathematical model, so that only the first bending mode of the beam is taken into account. The resulting equations of motion have five degrees of freedom and illustrate linear, non-linear and time-dependent terms in a very transparent way. Although neither gyroscopic effect due to rotor angular vibrations nor higher blade mode shapes are considered in the analysis, the equations of motion of the rotor–blades system are still general enough for the purpose of the work: validation of different linear and non-linear models with time dependent (periodic) coefficients. Experiments are carried out in the time and frequency domains while the rotor operates with different constant angular velocities.

A Reduced-Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

A reduced-order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

A Method for Determination of Damping for Edgewise Blade Vibrations

AbstractViolent edgewise blade vibrations have in recent years been a large problem for some stall‐regulated wind turbines. Owing to the complexity of the phenomenon, it has been difficult to predict the risk of these vibrations with aeroelastic load prediction tools. One problem is the choice of parameters in the aeroelastic model, e.g. structural damping and aerodynamic aerofoil characteristics. In many cases a high degree of uncertainty in the predicted response exists and the need for experimental verification methods is obvious. In this work a new method to identify the effective damping for the edgewise blade mode shape for wind turbines has been developed. The method consists of an exciter mechanism which makes it possible to excite the edgewise blade mode shapes from the wind turbine nacelle. Furthermore, the method consists of an analysis method which enables a straightforward determination of the damping. The analysis method is based on a local blade whirl description of the edgewise blade vibrations. The method is verified on a Bonus wind turbine, and for this specific turbine the effective damping for edgewise blade vibrations has been determined. The results support the further development of aeroelastic models and show potential for fine‐tuning of parameters of importance for the edgewise blade vibration problem. Furthermore, the method can be used for experimental investigation of the risk of edgewise blade vibrations for a specific turbine. Copyright © 2000 John Wiley & Sons, Ltd.

Cascade Flutter Analysis of Cantilevered Blades

An analysis has been developed to treat the aeroelastic behavior of a cascade of cantilevered blades. The unique features of the formulation include consideration of (a) coupling between bending and torsion in each of the blade modes, (b) coupling among blade modes, (c) spanwise variation of blade mode shapes, (d) mechanical damping in each mode, (e) aerodynamic coupling among all blades of the assembly, and (f) mistuning. The methodology leads to a complex eigenvalue problem of the form [A (λ)] {x} = λ {x} the solution of which establishes the nature of stability and determines the flutter modes of vibration. A parametric study is made to examine the influence on flutter of (a) the strength of coupling between bending and torsion, (b) proximity of modal frequencies, (c) mass ratio, and (d) mistuning. Numerical results presented here are restricted to a twelve bladed system coupled aerodynamically. The flow conditions are assumed to be subsonic but the formulation of the problem and the organization of the computer program are such that other conditions can easily be considered in computation. The extension of the analysis to include mechanical coupling between the blades (through either shrouds or disk) is shown to be straightforward.

Rotating Blade Vibration Analysis Using Shells

Shallow shell theory and Ritz method are employed to determine the frequencies and mode shapes of turbomachinery blades having both camber and twist, rotating with non-zero angles of attack. Frequencies obtained for different degrees of shallowness and thickness are compared with results available in the literature, obtained from finite element analyses of nonrotating blades. Frequencies are also determined for a rotating blade, showing the effects of changing the (1) angular velocity of rotation (2) disk radius and (3) angle of attack, as well as the significance of the most important body force terms.

Measurement of Fan Vibration Using Double Pulse Holography

Supersonic unstalled flutter in gas turbine fans is a self-excited instability in which mechanical vibrations give rise to unsteady aerodynamic forces which drive the mechanical vibration. The phenomenon is very sensitive to the deflected shapes of the blades and to the spatial and temporal phases of the blades’ responses. This paper is concerned with the measurement of vibrational behavior on static fans and relating it to flutter. Accurate detailed data on the blade and disk vibration mode shapes of fans up to 2.2 m diameter has been measured using double pulse laser holography. Both axial and tangential components of the blade mode shape are obtained by taking holograms from two directions. The analysis of the holograms is performed with the aid of a computer linked television system which generates the required blade mode shapes directly from the photographs of the hologram reconstructions. The disk mode measurements on real fans have shown the existence of pairs of spatially orthogonal vibration modes which have similar shapes (e.g. both 4D) but slightly different natural frequencies. This frequency split between modes means that the flutter wave will experience a cyclic variation in amplitude and propagation speed as it travels round the fan. In addition, the temporal phase angle between twist and flap in a single blade, which is generally assumed to be 90 deg, will vary from blade to blade.

Dynamic characteristics of rotor blades

The transmission matrix method is used to determine the dynamic characteristics (natural frequencies and the associated mode shapes) of rotor blades. The problems treated are combined flapwise bending, chordwise bending, and torsion of twisted non-uniform blades and its special subcases. The orthogonality relations that exist between the natural modes are derived. The method is appealing because of its simplicity for programming for digital computer calculations and also the inputs are generated very easily since they are merely the coefficients of the differential equations of motion.

Modeling of gas turbine engine compressor blades for vibration analysis

stall flutter design system. Such an analysis must properly account for all the parameters important to aeroelastic stability before durable rotors can be confidently designed with minimum weight and performance penalties. Efforts at Pratt & Whitney Aircraft and the United Aircraft Research Laboratories to provide an accurate and dependable design system have recently been intensified. Major emphasis is being concentrated on developing an energy method of stability analysis. Attempts to generate the unsteady stalled cascade aerodynamics for the analysis include both theoretical investigations and experimental measurement of unsteady lift and moment in an oscillating cascade rig. The blade mode shape prediction is also being improved. NASTRAN is being developed for determining dynamic chordwise deflection, and shroud models are being improved to account more accurately for stiffness and boundary conditions (slippage). The ultimate goal of this work is a system that extends the state-ofthe-art to make stall flutter a problem that can be successfully handled during preliminary fan and compressor design.

Deflection and Vibration Analysis of a Flexible Fan Blade

Finite-element technique used to obtain deflected configuration, and natural frequencies and mode shapes of flex-fan blades, used in automobile cooling system, as function of speed of fan.