Blade Tip Response Research Articles

Vibration Control of Large Wind Turbine Blades with Unidirectional Cable Pendulum Damper

A unidirectional cable pendulum damper is proposed to mitigate vibration responses of large-scale wind turbine blades in the edgewise direction, and the effectiveness of the proposed device for vibration response control is investigated. First, the configuration and working principles of the vibration damper are introduced. Second, the Euler–Lagrange equation of the single blade vibration damping system with the vibration damper is derived based on the Hamilton’s principle. At last, considering the effect of blade rotation, the wind load that applied on the blade was calculated using the rotating sample spectrum. The dynamic responses of blades are also calculated using the MATLAB/Simulink platform. The peak value and standard deviation of blade responses were taken as evaluation indexes to evaluate the vibration control efficiency of the device with varying the parameters such as the mass ball pendulum length, the fixed pulley block installation position, the stiffness and the pre-stress of the flexible cable. The optimal parameters of the vibration damper are investigated and obtained based on the assumption that no pounding happens between the mass ball of the vibration damper and the inner wall of the blade. Results show that the length of the mass ball pendulum and the installation position of the fixed pulley block, the values of which are within a reasonable range, can ensure the optimal performance of the vibration damper. The displacement of the mass sphere can be effectively reduced by increasing the stiffness of the flexible cable, and the pre-stress shows marginal beneficial effect on the damping performance and the displacement control of the mass sphere. Using the optimum parameters, the vibration damper can keep the mass ball within a safe running distance. The reduction of the peak value and the standard deviation of the blade displacement can reach 89.36% and 89.83%, respectively. The proposed device space can effectively reduce the blade tip response of the wind turbine by occupying less space. Moreover, the size of the device installation space can be changed by adjusting the weight ball swing length, which is suitable for the vibration control of the wind turbine blade edgewise direction.

Theoretical modeling and vibration control for pre-twisted composite blade based on LLI controller

Theoretical modeling and vibration control for divergent motion of thin-walled pre-twisted wind turbine blade have been investigated based on “linear quadratic Gaussian (LQG) controller using loop transfer recovery (LTR) at plant input” (LLI). The blade section is a single-celled composite structure with symmetric layup configuration of circumferentially uniform stiffness (CUS), exhibiting displacements of vertical/lateral bending coupling. Flutter suppression for divergent instability is investigated, with blade driven by nonlinear aerodynamic forces. Theoretical modeling of CUS-based structure is implemented based on Hamilton variational principle of elasticity theory. The discretization of aeroelastic equations is solved by Galerkin method, with blade tip responses demonstrated. The LLI controller is characterized by LTR at the plant input. The effects of LLI controller are achieved and illustrated by displacement responses, controller responses and frequency spectrum analysis, respectively.

Full-Annulus Simulation of Nonsynchronous Blade Vibration Excitation of an Axial Compressor

A high speed 1–1/2 axial compressor stage is simulated in this paper using an unsteady Reynolds-averaged Navier–Stokes (URANS) solver for a full-annulus configuration to capture its nonsynchronous vibration (NSV) flow excitation with rigid blades. A third-order weighted essentially nonoscillatory scheme for the inviscid flux and a second-order central differencing for the viscous terms are used to resolve nonlinear unsteady fluid flows. A fully conservative rotor/stator sliding boundary condition (BC) is employed with multiple-processor capability for rotor/stator sliding interface that accurately captures unsteady wake propagation between the rotor and stator blades while conserving fluxes across the rotor/stator interfaces. The predicted dominant frequencies using the blade tip response signals are not harmonic to the engine order, which is the NSV excitation. The simulation is based on a rotor blade with a 1.1% tip-chord clearance. Comparison with the previous 1/7 annulus simulations show that the time-shifted phase-lag BCs used in the 1/7 annulus are accurate. For most of the blades, the NSV excitation frequency is 6.2% lower than the measurement in the rig test, although some blades displayed slightly different NSV excitation frequencies. The simulation confirms that the NSV is a full annulus phenomenon. The instability of the circumferential traveling vortices in the vicinity of the rotor tip due to the strong interaction of incoming flow is the main cause of the NSV excitation. This instability is present in all blades of the rotor annulus. For circumferentially averaged parameters like total pressure ratio, NSV is observed to have an effect on the radial profile, particularly at radial locations above 70% span. A design with a lower loading of the upper blade span and a higher loading of the midblade spans is recommended to mitigate or remove NSV.

Comparison Between Field Measurements and Analytical Results of Blade Tip Response of a Wind Turbine in Operation Considering the Spatial Correlation of Approaching Wind Velocity

Comparison Between Field Measurements and Analytical Results of Blade Tip Response of a Wind Turbine in Operation Considering the Spatial Correlation of Approaching Wind Velocity

The effect of the nonlinear velocity and history dependencies of the aerodynamic force on the dynamic response of a rotating wind turbine blade

Existing models for the analysis of offshore wind turbines account for the aerodynamic action on the turbine rotor in detail, requiring a high computational price. When considering the foundation of an offshore wind turbine, however, a reduced rotor model may be sufficient. To define such a model, the significance of the nonlinear velocity and history dependency of the aerodynamic force on a rotating blade should be known. Aerodynamic interaction renders the dynamics of a rotating blade in an ambient wind field nonlinear in terms of the dependency on the wind velocity relative to the structural motion. Moreover, the development in time of the aerodynamic force does not follow the flow velocity instantaneously, implying a history dependency. In addition, both the non-uniform blade geometry and the aerodynamic interaction couple the blade motions in and out of the rotational plane. Therefore, this study presents the Euler–Bernoulli formulation of a twisted rotating blade connected to a rigid hub, excited by either instantaneous or history-dependent aerodynamic forces. On this basis, the importance of the history dependency is determined. Moreover, to assess the nonlinear contributions, both models are linearized. The structural response is computed for a stand-still and a rotating blade, based on the NREL 5-MW turbine. To this end, the model is reduced on the basis of its first three free-vibration mode shapes. Blade tip response predictions, computed from turbulent excitation, correctly account for both modal and directional couplings, and the added damping resulting from the dependency of the aerodynamic force on the structural motion. Considering the deflection of the blade tip, the history-dependent and the instantaneous force models perform equally well, providing a basis for the potential use of the instantaneous model for the rotor reduction. The linearized instantaneous model provides similar results for the rotating blade, indicating its potential application for this scenario, and allowing for the definition of an added damping matrix, applicable for the dynamic analysis of rotating turbine blades.

Simulation Analysis of Casing Vibration Response and Its Verification Under Blade–Casing Rubbing Fault

A new rotor–stator rubbing model considering the blade–casing rubbing fault is put forward in this paper. The model couples the rotor together with its suspension (ball or roller bearings), the disk, the (multiple) blades, and the casing. In addition, the influence of the rotor–stator clearance on rubbing forces was considered. It can simulate rubbing faults for single-point rubbing on the casing and complete-cycle rubbing on the rotor. The new rubbing model was applied to the rotor–support–casing coupling model, and the casing acceleration response under rubbing faults was obtained by the time-integration approach. The casing acceleration response, blade tip response, and rubbing force were analyzed. An aero-engine rotor tester, including casing, was used to carry out the rubbing experiment for single-point rubbing on the casing and for whole-cycle rubbing on the rotor. The simulation results were found in highly consistent with the experimental results, which fully verified the effectiveness of the new blade–casing rubbing model.

A direct experimental–numerical method for investigations of a laboratory under-platform damper behavior

Under-platform dampers are commonly adopted in order to mitigate resonant vibration of turbine blades. The need for reliable models for the design of under-platform dampers has led to a considerable amount of technical literature on under-platform damper modeling in the last three decades.Although much effort has been devoted to the under-platform damper modeling in order to avail of a predictive tool for new damper designs, experimental validation of the modeling is still necessary. This is due to the complexity caused by the interaction of the contacts at the two damper-platform interfaces with the additional complication of the variablity of physical contact parameters (in particularly friction) and their nonlinearity. The traditional experimental configuration for evaluating under-platform damper behavior is measuring the blade tip response by incorporating the damper between two adjacent blades (representing a cyclic segment of the bladed disk) under controlled excitation. The effectiveness of the damper is revealed by the difference in blade tip response depending on whether the damper is applied or not. With this approach one cannot investigate the damper behavior directly and no measurements of the contact parameters can be undertake. Consequently, tentative values for the contact parameters are assigned from previous experience and then case-by-case finely tuned until the numerical predictions are consistent with the experimental evidence. In this method the physical determination of the contact parameters is obtained using test rigs designed to produce single contact tests which simulate the local damper-platfom contact geometry. However, the significant limitation of single contact test results is that they do not reveal the dependence of contact parameters on the real damper contact conditions. The method proposed in this paper overcomes this problem.In this new approach a purposely developed test rig allows the in-plane forces transferred through the damper between the two simulated platforms to be measured, while at the same time monitoring in-plane relative displacements of the platforms. The in-plane damper kinematics are reconstructed from the experimental data using the contact constraints and two damper motion measurements, one translational and one rotational. The measurement procedures provide reliable results, which allow very fine details of contact kinematics to be revealed. It is demonstrated that the highly satisfactory performance of the test rig and the related procedures allows fine tuning of the contact parameters (local friction coefficients and contact stiffness), which can be safely fed into a direct time integration numerical model.The numerical model is, in turn, cross-checked against the experimental results, and then used to acquire deeper understanding of the damper behavior (e.g. contact state, slipping and sticking displacement at all contact points), giving an insight into those features which the measurements alone are not capable of producing. The numerical model of the system is based on one key assumption: the contact model does not take into account the microslip effect that exists in the experiments.Although there is room for improvement of both experimental configuration and numerical modeling, which future work will consider, the results obtained with this approach demonstrate that the optimization of dampers can be less a matter of trial and error development and more a matter of knowledge of damper dynamics.

A Class of Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies Undergoing Simultaneous Resonances—Part I: Theoretical Development

Blade tip timing is a technique for the measurement of vibrations in rotating bladed assemblies. Although the fundamentals of the technique are simple, the analysis of data obtained in the presence of simultaneously occurring synchronous resonances is problematic. A class of autoregressive-based methods for the analysis of blade tip timing data from assemblies undergoing two simultaneous resonances has been developed. It includes approaches that assume both sinusoidal and general blade tip responses. The methods can handle both synchronous and asynchronous resonances. An exhaustive evaluation of the approaches was performed on simulated data in order to determine their accuracy and sensitivity. One of the techniques was found to perform best on asynchronous resonances and one on synchronous resonances. Both methods yielded very accurate vibration frequency estimates under all conditions of interest.

A Class of Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies Undergoing Simultaneous Resonances—Part II: Experimental Validation

Blade tip timing is a technique for the measurement of vibrations in rotating bladed assemblies. In Part I of this work a class of methods for the analysis of blade tip timing data from bladed assemblies undergoing two simultaneous synchronous resonances was developed. The approaches were demonstrated using data from a mathematical simulation of tip timing data. In Part II the methods are validated on an experimental test rig. First, the construction and characteristics of the rig will be discussed. Then, the performance of the analysis techniques when applied to data from the rig will be compared and analysed. It is shown that accurate frequency estimates are obtained by all the methods for both single and double resonances. Furthermore, the recovered frequencies are used to calculate the amplitudes of the blade tip responses. The presence of mistuning in the bladed assembly does not affect the performance of the new techniques.

Simulation of Helicopter Rotor-System Structural Damage, Blade Mistracking, Friction, and Freeplay

Selected helicopter rotor faults are simulated by changes in stiffness, inertial, and aerodynamic properties of the damaged or mistracked blade(s). A rotor aeroelastic analysis based on finite elements in space and time and capable of modeling dissimilar blades is used to simulate the damaged rotor in forward flight. The various rotor faults modeled include chordwise imbalance, aerodynamic mistracking, localized cracks, distributed changes in blade stiffness properties modeling a stiffness defect and a manufacturing defect, friction and freeplay in the pitch-control system and the lag damper, and friction in the flap and lag hinge. Changes in blade tip response and rotor hub loads are identified for the selected faults and tables of rotor-system diagnostics are compiled.