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.     

基于外场实验的风力机叶片三维效应研究

针对一台33 kW水平轴风电机组开展了外场实验,得到其叶片7个断面翼型的压力分布曲线;基于求解时均N-S方程对风轮进行三维数值模拟,以及将叶片各断面作为二维翼型进行数值计算,分别得到各断面翼型的压力分布曲线及升阻力系数．通过将外场实验、三维和二维数值计算所得压力分布曲线及升阻力系数进行对比分析,研究了三维效应对风力机气动性能的影响．研究表明,从叶尖到叶根各断面翼型的压差先增大后逐渐减小,叶片表面压力分布曲线比较明显地反映了从叶尖到叶根流动分离的变化;叶片表面压力分布的三维数值计算结果较二维计算结果更加接近于外场实验值;风力机叶片表面的三维流动对叶片的气动性能影响较大,在叶尖和叶根部分尤为突出.     

A numerical investigation on the dynamic stall of a vertical axis wind turbine

In the last years, for home user, the wind turbine with vertical axis (VAWT) began to be more attractive due benefits in exploitation. In terms of aerodynamics, when the wind speed approaches the speed of operation (low value of tip speed ratio -TSR) the blade airfoil exceeds the critical angle of incidence for static conditions. Angle of incidence varies quickly across blade and the blade works in dynamic stall condition. The goal of the present work is to investigate the two-dimensional dynamic stall phenomenon around the NACA 0012 airfoil at relatively low Reynolds. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

边界条件对梁类结构系统刚度的影响

车身骨架是由大量梁类结构单元构成的.除了这些梁的截面形状和尺寸外,边界条件也对系统刚度影响很大.讨论了各种边界条件和载荷模式下的梁系统的合成刚度.基于两端固支的均匀截面梁的弯曲和扭转刚度,研究了各联结刚度的大小对系统刚度的贡献,并绘制了相应的影响曲线.最后,通过上述解析公式和有限元法计算了某汽车仪表板横梁系统的实际弯曲和扭转刚度.文中获得的静态刚度公式对其它梁类结构也适用。     

气动、结构、载荷相协调的大型风电叶片自主研发进展

从叶片设计的3个关键环节（气动设计、结构设计和载荷评估）出发,对叶片自主研发进展进行了总结分析．在气动设计方面,概述了计算流体动力学（computational fluid dynamics, CFD）方法、涡方法和叶素动量（blade element momentum, BEM）方法,并依据工程中广泛应用的BEM方法,指出了低风速区风电叶片的解决思路;在结构设计方面,简要概述了基于梁模型的传统设计分析方法,分析了其在大型复合材料叶片薄壳结构上的不足,并对有限元方法（finite element method, FEM）在叶片结构分析中的应用进展进行了介绍;在载荷评估方面,介绍了其对叶片和整机其它部件的影响,阐述了载荷预估方面的工作进展．然后,通过分析3个关键环节之间的相互关系,得到如下结论:建立气动、结构和载荷相协调的叶片优化设计体系,才能真正满足高效低成本的需要．最后,指明了需要进一步研究的主要方向,即高效低载翼型研究,结构非线性有限元分析,气动-结构耦合研究,设计标准制定．最终目标是建立适合中国风资源特点的叶片研发体系,推动我国风电产业发展.     

Nonlinear equations of a timoshenko-type theory of laminated anisotropic shells

In recent years analysis of the stress—strain state of shell structures made out of composite materials has been based on refined shell theories which take into account strains in the direction normal to the reference surface. There are several approaches to the formulation of the refined theories. One can point to shell theories developed on the basis of variational principles (e.g., [1, 2]) as well as theories created with the help of iterational processes (e.g., [3–6]). A resolving system of nonlinear equations for laminated anisotropic shells has been derived in the proposed research based on the Reissner variational principle [7, 8]. A similar linear theory which takes into account the strain e₃₃ also has been developed in [1]. If the shear stiffnesses of the layers differ greatly from each other in the transverse direction, then one can treat the shell structure as a single-layer shell of nonuniform structure. In this case it is advisable to solve a problem of the type of a uniform shell with minimal stiffnesses.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 501–507, May–June, 1979.     

Some properties of filled polyvinyl chloride

The effect of TiO₂, SiO₂, and carbon fillers on rigid, partly plasticized PVC has been investigated. Interaction in the polymer-filler system improves certain important properties — hardness, stiffness, wear resistance, etc., — the effect of the fillers being highly specific.M. V. Lomonosov Odessa Technological Institute. Translated from Mekhanika Polimerov, No. 1, pp 124–126, January–February, 1970.     

大型近海水平轴风力机转轮的空气动力学性能优化判据

以近海风能工程为研究目标,对具有不同特性参数（设计风速、叶尖线速度和转轮实度）的大容量（1～10 MW）风力机转轮的气动性能与几何特性进行分析与研究．首先提出大型机组转轮气动性能优化判据:在其直径最小的前提下具有尽可能高的年可用风能特性因数以及与之相关的风能利用系数,因而可捕获最多风能,使年发电量最大．接着给出影响它的几个主要气动参数,如转轮设计风速、叶尖线速度以及转轮实度,并分析风力机在近海气象条件下运转时上述两个气动指标随这些参数变化的规律．提供的气动分析方法及结果可作为大型近海风力机转轮气动性能的评价基础．     

Dynamic analysis of elastic beams under uncertainty

We consider minimax estimation of the state of semi-infinite elastic beams under uncertainty using initial, boundary, and external dynamic inputs (concentrated and distributed forces, bending and torsional moments) and state observations. The errors of all measurements and observations are assumed to be in a given ellipsoidal region. The problems are solved using standard classical solutions of elastoplastic beams, Lur'e's symbolic method, and the theory of minimax filtering of noise in linear dynamic systems.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 64–70, 1991.     

Three‐dimensional boundary layer on wind turbine blades

This paper describes a three‐dimensional analysis of the laminar boundary layer that develops on the blades of an horizontalaxis wind turbine. The main aim was to investigate a fundamental phenomenon: the effect of rotation on the blade boundary layer of a wind turbine in conjunction with the widely observed phenomenon of stall‐delay. The separation position in retarded flows with pressure gradients is calculated and compared for the rotation and non‐rotation cases. It is concluded that the stall is linearly postponed due to the Coriolis force and the separation point is delayed as a result of increasing rotation speed or decreasing blade spanwise position. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the stiffness of the elastic core on the buckling mode and the critical load for glass-reinforced plastic cylindrical shells in axial compression

The effect of the stiffness of the core, treated as a three-dimensional elastic body, on the buckling mode and the critical load is investigated for orthotropic cylindrical shells in axial compression. Parametric equations that permit the easy determination of the critical loads are obtained together with an expression for the stiffness parameter at which the buckling mode changes. The effect on the critical load of a central opening in the core is considered.Translated from Mekhanika Polimerov, No. 5, pp. 931–939, September–October, 1971.     

Contact problems for beams and plates with low shear stiffness

The low shear stiffness and strength of unidirectionally reinforced plates and beams predetermines the choice of calculation model in specific problems [4]. The contact problem is considered for a glass-reinforced plastic plate resting on a Winkler foundation; the deformation properties of the plate are described by the equations of an orthotropic material; the investigation is based on generalized applied theories of the Timoshenko and Ambartsumyan types [5–8], which permit the high shear compliance of thin-walled structures to be taken into account.L'vov Polytechnic Institute; Ivan Franko Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 4, pp. 715–720, July–August, 1970.     

改进的NSGA-Ⅱ算法研究风力机叶片多目标优化

将一种采用精英控制策略和动态拥挤方法用于快速非支配排序遗传算法（NSGA-Ⅱ）,并应用到风力机叶片的优化研究中,获得了一种新颖的风力机叶片多目标优化设计方法．作为应用算例,以设计风速下的功率系数最大和叶片质量最小为优化目标,用该方法设计了5 MW大型风力机叶片．优化结果表明,此算法在处理风力机多目标优化问题取得了良好的效果,给出的是一个Pareto最优解集,而不是传统优化方法追求的单个最优解,为风力机多目标优化设计提供新的思路和通用的算法．     

Effect of layer geometry and stiffness on the fields of normal stresses in multilayer beams under asymmetric bending

A mathematical model is suggested for calculating the bending stiffness and fields of normal stresses (strength) at any point in the cross section of a multilayer beam. It is found that the structure of the scalar field of normal stresses allows one to solve some optimization problems with multivariant parameters. The method is illustrated with an example of two-layer beams. The results of an investigation into the strength and stiffness of two-layer beams, with a geometric and (or) stiffness asymmetry, in asymmetric bending are presented. The kinetics of bending stiffness and strength in relation to variations in the geometric parameters of cross sections and in the ratio of elastic moduli of layers is examined. It is established that the normal stresses in multilayer beams under asymmetric bending considerably depend on the location of the flexural center, neutral plane, and bending stiffnesses relative to the principal axes of cross sections of the beams.     

Action of a powerful light beam on polypropylene film

The changes in the supermolecular structure of polypropylene films exposed to powerful light pulses have been investigated by optical microscopy. A pulse lasting 10^–3 sec produces melting of the polymer with subsequent recrystallization and the formation of a finely spherulitic structure. In connection with the change in supermolecular structure there is an increase in the breaking stress of the melted portion of the film. A pulse lasting 2·10^–8 sec causes melting and vaporization of individual parts of the spherulites in the irradiated region. The remainder of the polymer is such that orientation of the structural elements with respect to the radius—the maltese cross pattern of the original spherulites—is preserved.Mekhanika Polimerov, Vol. 2, No. 6, pp. 817–822, 1966     

Stress State of Multilayer Structural Elements Subjected to Static Loading and Optimization of Laminated Beams and Bars

The results of FEM investigation of the triaxial stress state in multilayer structural elements subjected to axial and bending loads are presented. The distribution regularities of the stiffness and stresses or strains depending on the geometric and mechanical characteristics of layers and their position in the cross section of beams and bars are examined. The optimization of these elements is carried out using the dependences of the Bareisis—Paulauskas method and the Optim-98 computer program created by the present authors. As the optimization criteria, the strength, stiffness, mass, and cost of the structural elements are considered.     

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.     

Progresses in application of computational ?uid dynamic methods to large scale wind turbine aerodynamics?

The computational ?uid dynamics (CFD) methods are applied to aerody-namic problems for large scale wind turbines. The progresses including the aerodynamic analyses of wind turbine pro?les, numerical ?ow simulation of wind turbine blades, evalu-ation of aerodynamic performance, and multi-objective blade optimization are discussed. Based on the CFD methods, signi?cant improvements are obtained to predict two/three-dimensional aerodynamic characteristics of wind turbine airfoils and blades, and the vorti-cal structure in their wake ?ows is accurately captured. Combining with a multi-objective genetic algorithm, a 1.5 MW NH-1500 optimized blade is designed with high e?ciency in wind energy conversion.     

Temperature-time dependence of the adhesion strength for polymer — Polymer systems

The temperature — time dependence of the adhesion strength has been studied for polymer systems differing in the thermodynamic compatibility of the substrate and adhesive and in the rate of polymerization of the latter. The fracture-activation energies of these systems have been calculated. It is shown that the temperature — time dependence of the adhesion strength varies depending on whether chemical intermolecular forces are responsible for the strength of the joint.Perm Scientific-Research Institute of Polymer Materials. A. M. Gor'kii Ural State University. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 665–671, July–August, 1968.     

Equivalence of the derived chains corresponding to a boundary-value problem on a finite interval,for polynomial operator pencils

Under investigation is the equivalence of derived chains constructed from root vectors of polynomial pencils of operators acting in a Hilbert space. These derived chains correspond to various boundary—value problems on a finite interval for an operator—differential equation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 83–95, January, 1990.