Dynamic response of a horizontal axis wind turbine blade under aerodynamic,gravity and gyroscopic effects

This work presents analytical and numerical dynamics studies of a horizontal axis wind turbine blade subjected to aerodynamic, centrifugal, gravity, and gyroscopic loads. The blade, assimilated to a long beam of variable cross section, is composed of homogeneous and isotropic material. It is discretized with blade elements of constant sections. Using Finite Element Method (FEM), the assembly of these elements constitutes an approximate model of the blade. The analytical study consists on defining the elementary matrices of rigidity, mass, and gyroscopic coupling between vibration and the blade rotation, as well as the elementary vector of the external loads. The numerical study deals with the resolution of the linear system of equations of the blade motion. Then, it will be possible to calculate its static and dynamic responses for a practical case. The numerical results show that the blade presents cyclic deformations under the considered loadings. These sustained vibrations directly affect the fatigue life of the blade, leading to a significant reduction in the operational efficiency of the wind turbine.     

Theoretical analysis of coupled torsional, warping and distortional waves in a straight thin-walled box beam by higher-order beam theory

When a thin-walled box beam is subjected to a dynamic torsional load, warping and distortional deformations of its cross section are coupled with torsional deformation. Due to the coupling, the wave propagation along the beam axis becomes considerably complicated. However, there appears no in-depth investigation on dispersion phenomena. It is difficult to see the intriguing interconnection of branches of the dispersion curves by means of numerical solutions of three-dimensional elastodynamic equations. Thus, we aim to analytically investigate the dispersion relation and wave reflection phenomena by using a one-dimensional higher-order beam theory that is capable of representing the three aforementioned deformations. Through this study, the interconnections of real, imaginary and complex branches of the dispersion relation for low frequencies are revealed and reflection and transmission phenomena occurring at a joint of two beams of different cross-sectional dimensions are also investigated.     

Dynamic aeroelastic response and active control of composite thin-walled beam structures in compressible flow

The dynamic aeroelastic response and its active control of composite beam structures in compressible flow and exposed to gust and explosive type loads are examined. Modeling of the structures is based on a refined composite thin-walled beam theory and incorporate a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, and rotatory inertia. The unsteady compressible aerodynamic loads for arbitrary small motion in the time domain are derived based on the concept of indicial functions. The sliding mode control (SMC) and linear-quadratic Gaussian (LQG) control methodology with sliding mode observer are used for the purpose of control. The beam structures are restricted to circumferentially asymmetric lay-up construction and the influence of ply angle, flight speed, and external excitations on the response and its active control are specifically investigated. A number of conclusions are outlined at the end.     

基于虚拟仪器的风力发电机组噪声分析系统*

该文基于LabVIEW虚拟技术设计了一款界面友好、操作便捷、实用性强的噪声测试分析系统。重点阐述了频率计权算法设计,依据IEC 61672-1:2002标准中频率计权规范,对比分析了快速傅里叶变换法和数字滤波器法在实现频率计权结果中的差异。在此基础上,根据IEC 61400-11-2012《风力发电机组噪声测试方法》标准,结合LabVIEW中的声音与振动工具包以及高级信号处理等函数,实现后续功能,使系统具有比较完备噪声测试分析功能。最后,以内蒙古风电场采集到的风力发电机组噪声数据为例,进行风力发电噪声分析系统的仿真验证,并对分析结果做了归纳总结。     

Dynamic response of thin-walled structures by variable kinematic one-dimensional models

This paper investigates the accuracy capabilities of using variable kinematic modeling in compact and thin-walled beam-like structures with dynamic loadings. Carrera Unified Formulation (CUF) is employed to introduce refined one-dimensional (1D) models with a variable order of expansion for the displacement unknowns over the beam cross-section. Classical Euler–Bernoulli and Timoshenko beam theories are obtained as particular cases of these variable kinematic models while a higher order expansion permits the detection of in-plane cross-section deformation, since it leads to shell-like solutions. Finite element (FE) method is used to provide numerical results and the Newmark method is implemented as a time integration scheme. Some assessments with closed form solutions are discussed and comparisons with shell-type results obtained with commercial FE software are made. Further analyses address both compact and thin-walled cross-sections. In particular, the case of a deformable thin-walled cylinder loaded by time-dependent internal forces is discussed. The results clearly show that finite elements which are formulated in the CUF framework do not introduce additional numerical problems with respect to classical beam theories. Comparisons with elasticity solutions prove that the present 1D CUF model offers an accuracy in analyzing thin-walled structures which is typical of shell or three-dimensional models with a remarkable reduction in the computational cost required.     

Non-stationary dynamic analysis of a wind turbine power drivetrain: Offshore considerations

This paper presents a multi-body model for studying the non-stationary dynamic behaviour of a wind turbine power drivetrain. The model includes some offshore considerations, such as the extra degrees of freedom and boundary conditions that installation on an offshore floating platform can add. The studied problem is an offshore implementation, with seafloor depths of the order of a hundred metres, making it necessary to use a floating platform. Special attention is paid to the characteristics of the combined offshore buoy support and detailed model of the power train, in order to assess the impacts of buoy movement on forces on gears and bearings. A multi-body analysis code was used to develop the model, and a conventional wind turbine set-up was implemented as an example. Gearbox dynamic behaviour was simulated for common manoeuvres such as a start-up and an emergency stop, and the results are presented and discussed.     

Dynamic characteristics of curved nanobeams using nonlocal higher-order curved beam theory

Here, an analytical approach for the dynamic analysis, viz., free and forced vibrations, of curved nanobeams using nonlocal elasticity beam theory based on Eringen formulation coupled with a higher-order shear deformation accounting for through thickness stretching is investigated. The formulation is general in the sense that it can be deduced to analyse the effect of various structural theories pertaining to curved nanobeams. It also includes inplane, rotary and coupling inertia terms. The governing equations derived, using Hamiltons principle, are solved in conjunction with Naviers solutions. The free vibration results are obtained employing the standard eigenvalue analysis whereas the displacement/stress responses in time domain for the curved nanobeams subjected to rectangular pulse loading are evaluated based on Newmarks time integration scheme. The formulation is validated considering problems for which solutions are available. A comparative study is done here by different theories obtained through the formulation. The effects of various structural parameters such as thickness ratio, beam length, rise of the curved beam, loading pulse duration, and nonlocal scale parameter are brought out on the dynamic behaviours of curved nanobeams.     

Nonlinear parametric instability of wind turbine wings

Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability of a wind turbine wing has been analysed based on a two-degrees-of-freedom model with one modal coordinate representing the vibrations in the blade direction and the other vibrations in edgewise direction. The functional basis for the eigenmode expansion has been taken as the linear undamped fixed-base eigenmodes. It turns out that the system becomes unstable at certain excitation amplitudes and frequencies. If the ratio between the support point motion and the rotational frequency of the rotor is rational, the response becomes periodic, and Floquet theory may be used to determine instability. In reality the indicated frequency ratio may be irrational in which case the response is shown to be quasi-periodic, rendering the Floquet theory useless. Moreover, as the excitation frequency exceeds the eigenfrequency in the edgewise direction, the response may become chaotic. For this reason stability of the system has in all cases been evaluated based on a Lyapunov exponent approach. Stability boundaries are determined as a function of the amplitude and frequency of the support point motion, the rotational speed, damping ratios and eigenfrequencies in the blade and edgewise directions.     

风力发电机自循环蒸发内冷系统稳定性的研究

自循环蒸发内冷系统的冷却效率高,可以实现无泵自循环,运行安全可靠,基本免维护,因此适合在大型风力发电机中使用.蒸发内冷系统的稳定性对风力发电机的安全运行十分重要,本文基于非线性分岔理论及其数值延拓法,对自循环蒸发内冷系统应用于风力发电机的的静态稳定性进行了深入研究.获得了系统静态分岔解图,分析了系统演化特性,同时分析了系统分岔现象的参数效应.搭建了实验平台,通过实验观测到了自循环蒸发内冷系统的静态分岔现象,验证了理论计算的正确性.     

Cyclostationary spectral analysis for the measurement and prediction of wind turbine swishing noise

This paper introduces cyclostationary spectral analysis as a new approach to analyzing and predicting the aerodynamic noise generated by wind turbines. This method is able to reveal new insights into the periodic character of the noise signal and is therefore ideally suited to the study of wind turbine noise. A new formulation is presented for the time variation of the noise spectrum due to wind turbines thereby providing insight into the character of the periodic variation in noise referred to as ‘swishing’. The character and mechanism of swishing noise is analyzed in detail.     

永磁同步风力发电机随机分岔现象的全局分析

永磁同步风力发电机在运行过程中不可避免地会受到风能的随机干扰,本文建立了在输入机械转矩存在随机干扰情况下永磁同步风力发电机的数学模型,采用胞映射方法分析了随机干扰强度变化时系统全局结构的演化行为,并通过数值模拟对理论分析进行验证.研究结果表明,随着随机干扰强度的增大,系统中会出现随机内部激变和随机边界激变,即由于随机吸引子与其吸引域内的随机鞍发生碰撞而产生的随机分岔现象和由于随机吸引子与其吸引域边界发生碰撞而产生的随机分岔现象.研究结果揭示了随机干扰对永磁同步风力发电机运行性能影响的机理,为永磁同步风力发电系统的运行和设计提供了理论依据.     

Mitigation of edgewise vibrations in wind turbine blades by means of roller dampers

Edgewise vibrations in wind turbine blades are lightly damped, and large amplitude vibrations induced by the turbulence may significantly shorten the fatigue life of the blade. This paper investigates the performance of roller dampers for mitigation of edgewise vibrations in rotating wind turbine blades. Normally, the centrifugal acceleration of the rotating blade can reach to a magnitude of 7–8g, which makes it possible to use this kind of damper with a relatively small mass ratio for suppressing edgewise vibrations effectively. The parameters of the damper to be optimized are the mass ratio, the frequency ratio, the coefficient of rolling friction and the position of the damper in the blade. The optimization of these parameters has been carried out on a reduced 2-DOF nonlinear model of the rotating wind turbine blade equipped with a roller damper in terms of a ball or a cylinder, ignoring the coupling with other degrees of freedom of the wind turbine. The edgewise modal loading on the blade has been calculated from a more sophisticated 13-DOF aeroelastic wind turbine model with due consideration to the indicated couplings, the turbulence and the aerodynamic damping. Various turbulence intensities and mean wind speeds have been considered to evaluate the effectiveness of the roller damper in reducing edgewise vibrations when the working conditions of the wind turbine are changed. Further, the optimized roller damper is incorporated into the 13-DOF wind turbine model to verify the application of the decoupled optimization. The results indicate that the proposed damper can effectively improve the structural response of wind turbine blades.     

Dynamic analysis of a beam with an intermediate elastic support

A survey of the literature shows that the title problem has not been studied to a great extent. In the present paper an approximate solution is obtained in the case of a beam with ends elastically restrained against rotation and an intermediate elastic support. When dealing with the forced vibrations situation a sinusoidally varying excitation is assumed.     

Variances of the vertical and horizontal wind measured by tower instruments and SODAR

At the Karlsruhe Nuclear Research Center, a monostatic Doppler SODAR has been operated near a 200 m high meteorological tower. Vertical profiles of the components of the wind vector and of the variances of the vertical wind and of the horizontal wind direction have been sampled continuously from the SODAR and the tower instruments as 30-min mean values. During seven episodes lasting more than 2 h, the instantaneous vertical wind speed was measured simultaneously by a sonic anemometer and the SODAR, and spectra were calculated. An intercomparison of the spectra and wind data measured directly by the SODAR and the tower instruments has been performed by a linear regression and correlation analysis referring to different height levels of measurement and stability classes.Systematic and statistically distributed differences among the data measured by the SODAR and the in situ instruments are discussed. Our investigation shows that the variance of only the vertical wind speed can be measured reliably by a SODAR. The variances of the horizontal wind direction and the elevation angle of the wind vector should not be used in a routine manner from a SODAR.     

地基激光测风雷达的光束扫描及风场反演

 激光测风雷达通过多普勒频移来确定激光束视线方向上的大气风场的速度矢量。由这些测得的矢量可反演大气风场群速的速度矢量。在本文中,我们将讨论利用单一LDV系统,激光束的扫描方式采用圆锥扫描,在扫描圆锥的垂直截面上取四个正交点上的多普勒风速矢量。通过这四个矢量,利用空间解析几何的知识,最终推导出观测视场上风场的水平和垂直方向的矢量分量。     

A procedure for the assessment of wind turbine noise

The noise assessment at the receivers due to wind turbines in operation is usually performed through outdoor measurements. Background noise and wind turbines noise (WTN) are related to wind speed and both contribute to the overall measured noise levels (environmental noise). Nevertheless, the relation between noise and wind speed is not easily predictable, especially when the wind farms are installed in hilly terrains, where the wind shear is truly remarkable. In Italy and in other countries, this kind of assessment is even more difficult to perform due to the national regulations that require to compute the difference between environmental and background noise levels with the same weather conditions. Thus, to get a reliable and approved measure of the residual noise it would be necessary to turn off the wind farm. This work suggests a technical procedure to simultaneously estimate the immission and the residual noise components measured nearby a wind farm when the residual noise is mainly generated by wind. This allows the evaluation of the noise impact produced by operational wind farms, without requiring the farm shut down. The method aims to be fairly straightforward, thus maintaining the required scientific basis to be used as an assessment procedure by consultants and public bodies.     

Complex signal analysis for wind turbine planetary gearbox fault diagnosis via iterative atomic decomposition thresholding

The vibration signals from complex structures such as wind turbine (WT) planetary gearboxes are intricate. Reliable analysis of such signals is the key to success in fault detection and diagnosis for complex structures. The recently proposed iterative atomic decomposition thresholding (IADT) method has shown to be effective in extracting true constituent components of complicated signals and in suppressing background noise interferences. In this study, such properties of the IADT are exploited to analyze and extract the target signal components from complex signals with a focus on WT planetary gearboxes under constant running conditions. Fault diagnosis for WT planetary gearboxes has been a very important yet challenging issue due to their harsh working conditions and complex structures. Planetary gearbox fault diagnosis relies on detecting the presence of gear characteristic frequencies or monitoring their magnitude changes. However, a planetary gearbox vibration signal is a mixture of multiple complex components due to the unique structure, complex kinetics and background noise. As such, the IADT is applied to enhance the gear characteristic frequencies of interest, and thereby diagnose gear faults. Considering the spectral properties of planetary gearbox vibration signals, we propose to use Fourier dictionary in the IADT so as to match the harmonic waves in frequency domain and pinpoint the gear fault characteristic frequency. To reduce computing time and better target at more relevant signal components, we also suggest a criterion to estimate the number of sparse components to be used by the IADT. The performance of the proposed approach in planetary gearbox fault diagnosis has been evaluated through analyzing the numerically simulated, lab experimental and on-site collected signals. The results show that both localized and distributed gear faults, both the sun and planet gear faults, can be diagnosed successfully.     

强流脉冲电子束作用下钽金属靶膨胀的轴向约束

研究了强流脉冲电子束与钽金属靶相互作用后靶材流体动力学膨胀的轴向约束问题。由于电子束在金属钛和钽内的能量沉积存在差异,未完全气化的钛箔对气化膨胀的钽材能够起到约束作用,并且可以通过吸收钽的能量来降低钽的膨胀速度。通过分析比较电子束在靶上形成孔洞的形貌以及高速相机拍摄得到的不同时刻靶材喷射的图像,证实了钛箔能够对钽金属靶的轴向膨胀起到一定的约束作用。尤其是电子束打靶过后1μs内的初始阶段,约束效果比较明显。