Fatigue load computation of wind turbine gearboxes by coupled finite element,multi‐body system and aerodynamic analysis

The main concern of the present publication is the computation of dynamic loads of wind turbine power trains, with particular emphasis on planetary gearbox loads. The applied mathematical approach relies on a non‐linear finite element method, which is extended by multi‐body system functionalities, and aerodynamics based on the blade element momentum theory. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling and analysis of floating spar‐type wind turbine drivetrain

This paper studies the drivetrain dynamics of a 750 kW spar‐type floating wind turbine (FWT). The drivetrain studied is a high‐speed generator, one‐stage planetary, two‐stage parallel and three‐point support type. The response analysis is carried out in two steps. First, global aero‐hydro‐elastic‐servo time‐domain analyses are performed using HAWC2. The main shaft loads, which include the axial forces, shear forces and bending moments, are obtained in this integrated wind–wave response analysis. These loads are then used as inputs for the multi‐body drivetrain time‐domain analyses in SIMPACK. The investigations are largely based on comparisons of the main shaft loads and internal drivetrain responses from 1 h simulations. The tooth contact forces, bearing loads and gear deflections are the internal drivetrain response variables studied. The comparisons are based on the mean values, standard deviations and maximum values extrapolated using a 10 ^{? 5} up‐crossing rate. Both operational and parked conditions are considered. The investigation consists of three parts. First, the responses are compared between the FWT and its equivalent land‐based version. Second, the contributions from the main shaft loads (shear forces, axial forces and bending moments) and nacelle motions are investigated individually. Third, an improved four‐point support (4PT) system is studied and compared against the original three‐point support system for the FWT. The results show that there are general increases in the standard deviations of the main shaft loads and internal drivetrain responses in the FWT. In addition, these increases are a result of the increased main shaft loads in the FWT, especially the non‐torque loads. Last, the 4PT system, when applied to a FWT drivetrain, significantly reduces the tooth contact forces and bearing loads in the low‐speed stage, but this result comes at the expense of increased main bearing radial loads. Copyright © 2013 John Wiley & Sons, Ltd.     

750 kW风力机组齿轮箱动力学仿真分析

风力发电机组系统运行时产生剧烈的振动,对齿轮箱的运行精度和齿轮寿命的影响非常大。针对这一情况,文章对齿轮箱进行了重新设计、建模。基于多体系统动力学方法、模态振动、冲击-接触理论,以750 kW型风机齿轮箱为研究对象,通过对齿轮箱的仿真分析,得出齿轮啮合和碰撞力以及动能随时间的变化曲线。文章还对高速齿轮轴进行了模态分析,得到弯曲模态振型图,并将高速齿轮轴、行星轮、行星架和齿轮Z1变为柔体进行应力分析,得到齿轮的应力分布图,为齿轮箱总体动力学特性分析及齿轮箱优化设计奠定基础。     

Multi‐flexible‐body Dynamic Analysis of Horizontal Axis Wind Turbines

This article presents a structural dynamic analysis of horizontal axis wind turbines (HAWTs) using a new methodology. The methodology is based on representing a HAWT as a multi‐flexible‐body system with both rigid‐ and flexible‐body subsystems. The rigid‐body subsystems (nacelle, hub) are modelled as interconnected sets of rigid bodies using Kane's method. Kane's method leads to compact equations of motion for rigid‐body mechanisms. The flexible‐body subsystems (blades, tower) are modelled using geometrically exact, non‐linear beam finite elements derived from a mixed variational formulation for the dynamics of moving beams. The use of the mixed formulation allows for the direct determination of constraint forces and moments within the beam finite element and at the boundaries, thus allowing simple connectivity between the finite elements and rigid bodies. The equations for the rigid and flexible subsystems are coupled to obtain a unified framework that models the dynamic behaviour of the complete system. Linearization of the dynamic equations about the steady state solution yields system equations with periodic coefficients that must be solved by Floquet theory to extract the dynamic characteristics. Numerical studies are presented to investigate the natural frequencies and mode shapes for a HAWT with flexible blades and tower. Copyright © 2002 John Wiley & Sons, Ltd.     

Identification of loading conditions resulting in roller slippage in gearbox bearings of large wind turbines

The dynamic loads on the rollers inside the bearings of large wind turbine gearboxes operating under transient conditions are presented with a focus on identifying conditions leading to slippage of rollers. The methodology was developed using a multi‐body model of the drivetrain coupled with aeroelastic simulations of the wind turbine system. A 5 MW reference wind turbine is considered for which a three‐stage planetary gearbox is designed on the basis of upscaling of an actual 750 kW gearbox unit. Multi‐body dynamic simulations are run using the ADAMS software using a detailed model of the gearbox planetary bearings to investigate transient loads inside the planet bearing. It was found that assembly and pre‐loading conditions have significant influence on the bearing's operation. Also, the load distribution in the gearbox bearings strongly depends on wind turbine operation. Wind turbine start‐up and shut‐down under normal conditions are shown to induce roller slippage, as characterized by loss of contacts and impacts between rollers and raceways. The roller impacts occur under reduced initial pre‐load on opposite sides of the load zone followed by stress variation, which can be one of the potential reasons leading to wear and premature bearing failures. Copyright © 2017 John Wiley & Sons, Ltd.     

Using transfer path analysis to assess the influence of bearings on structural vibrations of a wind turbine gearbox

Noise and vibration issues can be dealt with using several approaches. Using the source–transfer path–receiver approach, a vibration issue could be solved by attenuating the source, modifying the transfer path or by influencing the receiver. Applying this approach on a wind turbine gearbox would respectively correspond with lowering the gear excitation levels, modifying the gearbox housing or by trying to isolate the gearbox from the rest of the wind turbine. This paper uses a combination of multi‐body modelling and typical transfer path analysis (TPA) to investigate the impact of bearings on the total transfer path and the resulting vibration levels. Structural vibrations are calculated using a flexible multi‐body model of a three‐stage wind turbine gearbox. Because the high‐speed mesh is often the main source of vibrations, focus is put on the four bearings of this gear stage. The TPA method using structural vibration simulation results shows which bearing position is responsible for transmitting the highest excitation levels from the gears to the gearbox housing structure. Influences of bearing stiffness values and bearing damping values on the resulting vibration levels are investigated by means of a parameter sensitivity study and are confirmed with the results from the TPA. Because both the TPA and the parameter sensitivity analysis revealed a big influence on radial stiffness for a certain bearing, this was investigated in more detail and showed the big importance of correct axial bearing position. The main conclusions of this paper are that the total vibration behaviour of a wind turbine gearbox can be altered significantly by changing both bearing properties such as stiffness, damping and position, and bearing support stiffness. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessment of a comprehensive aeroelastic tool for horizontal‐axis wind turbine rotor analysis

This paper presents the development of a computational aeroelastic tool for the analysis of performance, response and stability of horizontal‐axis wind turbines. A nonlinear beam model for blades structural dynamics is coupled with a state‐space model for unsteady sectional aerodynamic loads, including dynamic stall effects. Several computational fluid dynamics structural dynamics coupling approaches are investigated to take into account rotor wake inflow influence on downwash, all based on a Boundary Element Method for the solution of incompressible, potential, attached flows. Sectional steady aerodynamic coefficients are extended to high angles of attack in order to characterize wind turbine operations in deep stall regimes. The Galerkin method is applied to the resulting aeroelastic differential system. In this context, a novel approach for the spatial integration of additional aerodynamic states, related to wake vorticity and dynamic stall, is introduced and assessed. Steady‐periodic blade responses are evaluated by a harmonic balance approach, whilst a standard eigenproblem is solved for aeroelastic stability analyses. Drawbacks and potentialities of the proposed model are investigated through numerical and experimental comparisons, with particular attention to rotor blades unsteady aerodynamic modelling issues. Copyright © 2016 John Wiley & Sons, Ltd.     

A finite element model for pre‐stressed or post‐tensioned concrete wind turbine towers

Wind turbine support towers have been traditionally formed of structural steel tubular sections, being fabricated in large sections under factory conditions before being transported to site for erection. Given the trend towards developing turbines with hub heights in excess of 90 m, it is now necessary to develop towers of concrete and other materials that can provide improved dynamic properties and ease transportation difficulties over the structural steel solutions. Concrete towers of this height require pre‐stressing to overcome high vertical stresses induced in bending, which would otherwise lead to cracking in the concrete, with a resulting reduction in the tower's natural frequency. In order to properly understand the behaviour of concrete towers, it is necessary to take account of both material and geometric non‐linearity. Material non‐linearity of concrete is well understood, and geometric non‐linearity arises because of the imposition of an initial stress into the concrete by way of the application of pre‐stress. In this paper, a finite element model is proposed, which will describe the concrete as a continuum of four‐noded, two‐dimensional Reisser–Mindlin shell elements. The pre‐stressing tendons are to be represented by one‐dimensional bar elements, with an imposed pre‐stress. For the numerical examples considered in the paper, tendons are modelled to be post‐tensioned and debonded. The effect of varying the design parameter of magnitude of pre‐stress and the time dependence of pre‐stress force has been investigated using the model described. The impact that concrete compressive strength had on overall tower stiffness was also investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

100kW风力发电机叶片疲劳分析

结合有限元分析方法和叶片振动试验方法,利用最少的试验设备,检测出叶片危险部位的相应数据,以提高疲劳试验的可靠性。通过理论计算和数学建模相结合的方法,确定叶片阴阳两面最大变形位置,使试验条件更符合叶片的实际工况。分析试验结果显示,被测叶片达到了设计标准的要求。     

Long‐term contact fatigue analysis of a planetary bearing in a land‐based wind turbine drivetrain

This paper presents an approach for performing a long‐term fatigue analysis of rolling element bearings in wind turbine gearboxes. Multilevel integrated analyses were performed using the aeroservoelastic code HAWC2, the multibody dynamics code SIMPACK, the three‐dimensional finite element code Calyx and a simplified lifetime prediction model for rolling contact fatigue. The National Renewable Energy Laboratory's 750 kW wind turbine and its planetary bearing were studied. Design load cases, including normal production, parked and transient load cases, were considered. To obtain the internal bearing load distribution, an advanced approach combining a finite element/contact mechanics model and a response surface model were used. In addition, a traditional approach, the Harris model, was also applied for comparison. The long‐term probability distribution of the bearing raceway contact pressure range was then obtained using Weibull and generalized Gamma distribution functions. Finally, we estimated the fatigue life of the bearing, discussed the differences of the methods used to obtain the bearing internal loads and analyzed the effects of the environmental conditions and load cases on the results. The Harris model may underestimate the inner raceway life by 55.7%, which can cause large load fluctuations along the raceways. The bearing fatigue life is very sensitive to the wind distribution and less affected by the transient and parked load cases. Copyright © 2014 John Wiley & Sons, Ltd.     

Low‐cost mounting arrangements for building‐integrated wind turbines

Micro‐generation is being widely promoted as a way for householders in the UK and elsewhere to take part in ‘the Green Revolution’. Building‐integrated wind turbines (BIWTs) provide a way to do this, enabling people to reduce their contribution to the problems of both climate change and decreasing fossil fuel availability. Although energy yields from BIWTs for many householders have been shown to be low, there are still situations where such turbines can make a useful contribution to electricity generation, e.g. in windier areas and for isolated detached buildings. The standards for the installation of BIWTs are still being developed including those for the safe mounting of turbines on domestic buildings. This paper investigates the current trend for mounting small wind turbines on the walls of domestic premises and compares this with an approach which uses roof timbers. It identifies the main characteristics of building construction which affect the integrity of such installations. European and British standards have been used to calculate wind and gravitational loads. Finite element models are used to derive working stresses and, hence, some basic principles of good design. The likely costs of wall and roof mounting are then compared. Installation and health and safety issues are also examined briefly. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical validation of a finite element thin‐walled beam model of a composite wind turbine blade

This paper presents a numerical validation of a thin‐walled beam (TWB) finite element (FE) model of a realistic wind turbine rotor blade. Based on the theory originally developed by Librescu et al. and later extended to suit FE modelling by Phuong, Lee and others, this computationally efficient yet accurate numerical model is capable of capturing most of the features found in large blades including thin‐walled hollow cross section with variable thickness along the section's contour, inner reinforcements, arbitrary material layup and non‐linear anisotropic fibre‐reinforced composites; the present application is, for the time being, restricted to linearity. This one‐dimensional (1D) FE model allows retaining information of different regions of the blade's shell and therefore approximates the behaviour of more complex three‐dimensional (3D) shell or solid FE models more accurately than typical 1D FE beam models. A 9.2 m rotor blade, previously reported in specialized literature, was chosen as a case study to validate the static and dynamic behaviour predicted by a TWB model against an industry‐standard 3D shell model built in a commercial software tool. Given the geometric and material complexities involved, an excellent agreement was found for static deformation curves, as well as a good prediction of the lowest frequency modes in terms of resonance frequencies, mode shapes and frequency response functions; the highest (sixth) frequency mode shows only a fair agreement as expected for an FE model. It is concluded that despite its simplicity, a TWB FE model is sufficiently accurate to serve as a design tool for the recursive analyses required during design and optimization stages of wind turbines using only readily available computational tools. Copyright © 2011 John Wiley & Sons, Ltd.     

Load sharing behavior analysis method of wind turbine gearbox in consideration of multiple-errors

Conducting a further analysis on loading sharing among compound planetary gear system in wind turbine gearbox, and making a meshing error analysis on the eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of wind turbine gearbox respectively. In view of the floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of all gears, this paper establishes a refined mathematical model of two-stage power split loading sharing coefficient calculation in consideration of multiple errors. Also obtains the regular curves of the load sharing coefficient and floating orbits of center gears, and conducts a load sharing coefficient test experiment of compound planetary gear system to verify the research results, which can provide scientific theory evidence for proper tolerance distribution and control in design and process.     

Aero‐structural dynamics of a flexible hub connection for load reduction on two‐bladed wind turbines

In this study, an innovative concept for load reduction on the two‐bladed Skywind 3.4 MW prototype is presented. The load reduction system consists of a flexible coupling between the hub mount, carrying the drive train components including the hub assembly, and a nacelle carrier supported by the yaw bearing. This paper intends to assess the impact of introducing a flexible hub connection on the system dynamics and the aero‐elastic response to aerodynamic load imbalances. In order to limit the rotational joint motion, a cardanic spring‐damper element is introduced between the hub mount and the nacelle carrier flange, which affects the system response and the loads. A parameter variation of the stiffness and damping of the connecting spring‐damper element has been performed in the multi‐body simulation solver Simpack. A deterministic, vertically sheared wind field is applied to induce a periodic aerodynamic imbalance on the rotor. The aero‐structural load reduction mechanisms of the coupled system are thereby identified. It is shown that the fatigue loads on the blades and the turbine support structure are reduced significantly. For a very low structural coupling, however, the corresponding rotational deflections of the hub mount exceed the design limit of operation. The analysis of the interaction between the hub mount motion and the blade aerodynamics in a transient inflow environment indicates a reduction of the angle of attack amplitudes and the corresponding fluctuations of the blade loading. Hence, it can be concluded that load reduction is achieved by a combination of reduced structural coupling and a mitigation of aerodynamic load imbalances. Copyright © 2016 John Wiley & Sons, Ltd.     

Stochastic dynamic response analysis of a tension leg spar‐type offshore wind turbine

This paper presents a stochastic dynamic response analysis of a tension leg spar‐type wind turbine subjected to wind and wave actions. The dynamic motions, structural responses, power production and tension leg responses are analyzed. The model is implemented using the HAWC2 code. Several issues such as negative damping, rotor configuration (upwind or downwind rotor) and tower shadow effects are discussed to study the power performance and structural integrity of the system. The operational and survival load cases considering the stochastic wave and wind loading are analyzed to investigate the functionality of the tension leg spar‐type wind turbine. Amelioration of the negative damping applied for this concept reduces the structural dynamic responses, which are important for fatigue life. It is found that the responses induced by wave and wind actions at the wave frequencies are not affected much by the aerodynamic excitation or damping forces. Because of the nonlinear effects of the tension leg, all of the motion responses are strongly coupled. The global responses of upwind and downwind versions of the turbine are found to be close because the tower shadow has a limited effect on the global responses. However, the structural dynamic responses of the blades are more affected by the tower shadow. In this study, the extrapolation methods are applied to efficiently estimate the maximum responses. The maximum response is found to occur in the survival cases as a result of the wave actions and the increased aerodynamic drag forces on the tower. The results show that the maximum responses corresponding to the up‐crossing rate of 0.0001 (corresponding to the maximum response within a 3 hour period) can be expressed by the mean plus 3 to 5 standard deviations. Copyright © 2012 John Wiley & Sons, Ltd.     

基于工况细化条件下数据统计分析的风电机组齿轮箱油温故障预警方法

文章针对风电机组齿轮箱油温劣化特征识别问题,提出了一种基于工况细化的异常变化检测和故障早期预警方法.该方法根据风机叶轮转速将机组运行数据进行细化分仓,在每个叶轮转速仓中建立基于概率统计分析的齿轮箱油温正常行为模型并设定其温度分布和温升变化的异常阈值;然后对现场机组齿轮箱油温变化进行监测,利用时序滑动窗口的评估方式实现风...     

Condition monitoring of spar‐type floating wind turbine drivetrain using statistical fault diagnosis

Operation and maintenance costs are significant for large‐scale wind turbines and particularly so for offshore. A well‐organized operation and maintenance strategy is vital to ensure the reliability, availability, and cost‐effectiveness of a system. The ability to detect, isolate, estimate, and perform prognoses on component degradation could become essential to reduce unplanned maintenance and downtime. Failures in gearbox components are in focus since they account for a large share of wind turbine downtime. This study considers detection and estimation of wear in the downwind main‐shaft bearing of a 5‐MW spar‐type floating turbine. Using a high‐fidelity gearbox model, we show how the downwind main bearing and nacelle axial accelerations can be used to evaluate the condition of the bearing. The paper shows how relative acceleration can be evaluated using statistical change‐detection methods to perform a reliable estimation of wear of the bearing. It is shown in the paper that the amplitude distribution of the residual accelerations follows a t‐distribution and a change‐detection test is designed for the specific changes we observe when the main bearing becomes worn. The generalized likelihood ratio test is extended to fit the particular distribution encountered in this problem, and closed‐form expressions are derived for shape and scale parameter estimation, which are indicators for wear and extent of wear in the bearing. The results in this paper show how the proposed approach can detect and estimate wear in the bearing according to desired probabilities of detection and false alarm.     

Environmental activism and vertical‐axis wind turbine preferences in California

Wind energy is widely recognized as a key element of the worldwide effort to limit greenhouse gas emissions. As compared with the general population, environmental activists have a much higher level of knowledge, interest, and capacity to affect the final outcome of a proposed wind turbine facility. To explore how their opinions on wind energy, particularly on vertical‐axis wind turbines, differ from the general public, we administered the same online experimental survey to a general population sample of adult Californians and to a self‐selected sample of online energy and environmental activists. We find that support for wind energy increases with the degree of environmental activism and engagement. The general public prefers vertical‐axis wind turbines in open spaces, away from one's residence. Location and price sensitivity, however, are weaker among activists. Among activists, attitudes about specific vertical‐axis wind turbine technologies are more crystalized and less susceptible to the information effects except on the topic of minimizing bird deaths.     

Modal re‐analysis of rotary wind turbine blades in refinement design

A modal re‐analysis approach is proposed for refinement designs of rotary wind turbine blades on the basis of matrix perturbation methods. The approach entails effects of stress stiffening, spin softening, uncertainty of material properties and structural modifications of blades. Three perturbation methods are used to conduct the re‐analysis approach, including the standard perturbation method and two improvements proposed by H. C. Hu and S. H. Chen, respectively. Numerical results of a typical wind turbine blade indicate that the two improved methods deliver better accuracy than the standard perturbation method in terms of eigenpairs. In application to blade designs, Chen's method is suitable for a multi‐step modal re‐analysis with explicit small parameters and cultivates the first‐order and second‐order perturbations of eigenpairs as well. In contrast, Hu's method is a better choice for a single‐step modal re‐analysis without determining any small parameter explicitly and directly offers approximate eigenpairs instead of somehow tedious perturbation processes. Copyright © 2012 John Wiley & Sons, Ltd.