表面硬化滚道风电主轴轴承的疲劳寿命分析

建立一种针对表面硬化滚道三排圆柱滚子风电主轴轴承的疲劳寿命分析方法。首先,在卡迪尔坐标系中建立三排圆柱滚子风电主轴轴承的5自由度力学模型,分析计算在外部5个方向载荷联合作用下轴承的内部滚子载荷分布;然后,建立圆柱滚子与表面硬化滚道之间的弹塑性接触有限元模型,计算得到滚子接触载荷作用下滚道次表面的脉动应力分布;最后,根据Goodman方程将滚道脉动应力幅值转化为交变应力幅值,运用Basquin应力-寿命理论计算得到风电主轴轴承的疲劳寿命。结果表明,轴承的下风向外圈滚道承受来自风轮的推力载荷,其疲劳寿命最短;径向外圈滚道承受风轮的重力载荷,其疲劳寿命最长。轴承的疲劳寿命取决于下风向滚道。     

Scour influence on the fatigue life of operational monopile‐supported offshore wind turbines

Offshore wind turbines supported on monopiles are an important source for renewable energy. Their fatigue life is governed by the environmental loads and in the dynamic behavior, depending on the support stiffness and thus soil‐structure interaction. The effects of scour on the short‐term and long‐term responses of the NREL 5‐MW wind turbine under operational conditions have been analyzed by using a finite element beam model with Winkler springs to model soil‐structure interaction. It was found that due to scour, the modal properties of the wind turbine do not change significantly. However, the maximum bending moment in the monopile increases, leading to a significant reduction in fatigue life. Backfilling the scour hole can recover the fatigue life, depending mostly on the depth after backfilling. An approximate fatigue analysis method is proposed, based on the full time‐domain analysis for 1 scour depth, predicting with good accuracy the fatigue life for different scour depths from the quasi‐static changes in the bending moment.     

General static load‐carrying capacity of four‐contact‐point slewing bearings for wind turbine generator actuation systems

Four‐contact‐point slewing bearings are widely used in wind turbine generators (WTGs) to adjust the orientation of the blades and the nacelle to fully exploit wind resources. These bearings must withstand static and fatigue loads; however, at the first stages of the design process, the bearings are commonly selected by considering only static loads. This paper presents a further step of a previous theoretical work published by the authors in the field of the static load‐carrying capacity of four‐contact‐point slewing bearings under axial, radial and tilting‐moment loads. In that work, a generalization of the works by Sjoväll and Rumbarger was presented, providing an acceptance surface of the bearing in the load space. The contact angle of the balls was assumed to be load independent. The present work improves that development by considering the influence of the variability of the contact angle with the applied load, and as a result, the acceptance surface has been redefined. By comparing the results with those of the finite element model published by the authors, it is proven that the new model presented in this work is more realistic than the previous one. Thus, it is believed that this methodology can be easily applied for the initial selection of blade and yaw bearings in WTGs. Copyright © 2012 John Wiley & Sons, Ltd.     

考虑齿圈柔性的风电行星轮系动态啮合特性研究

针对集中参数法难以考虑齿圈柔性而有限元法计算量大的问题,以风电行星轮系为研究对象在集中参数/有限元混合法基础上提出一种揭示内啮合齿轮副延长啮合现象的分析方法。首先采用集中参数法建立风电行星轮系的动力学模型,并求解获得动态啮合力;随后,运用有限元法建立行星轮系内啮合齿轮副的有限元模型,并开展静态接触分析从而获得内啮合齿轮副各啮合位置发生多齿啮合时的变形阈值;最后,将集中参数模型获得的动态啮合力施加在内齿圈有限元模型上计算出内齿圈的动态响应,并结合发生多齿啮合时的变形阈值,从而揭示在不同负载和支撑数量下内齿圈上多齿啮合的分布区域,获得接触应力和齿根应力,分析啮合齿对数量改变前后对应力的影响。结果表明：考虑齿轮柔性后,内啮合齿轮副会出现除理论啮合齿对外其他齿对相接触的现象;随着负载扭矩的增大,内齿圈上三齿啮合首先发生在支撑两侧,随后三齿啮合发生区域不断增加;当行星轮与内齿圈间的啮合由理论两齿啮合变为三齿啮合时,其齿面接触应力和齿根应力小于其在相同时刻只计入两齿啮合时的应力值。     

Planetary gear load sharing of wind turbine drivetrains subjected to non‐torque loads

An analytical formulation was developed to estimate the load‐sharing and planetary loads of a three‐point suspension wind turbine drivetrain considering the effects of non‐torque loads, gravity and bearing clearance. A three‐dimensional dynamic drivetrain model that includes mesh stiffness variation, tooth modifications and gearbox housing flexibility was also established to investigate gear tooth load distribution and non‐linear tooth and bearing contact of the planetary gears. These models were validated with experimental data from the National Renewable Energy Laboratory's Gearbox Reliability Collaborative. Non‐torque loads and gravity induce fundamental excitations in the rotating carrier frame, which can increase gearbox loads and disturb load sharing. Clearance in the carrier bearings reduces the bearing stiffness significantly. This increases the amount of pitching moment transmitted from the rotor to the gear meshes and disturbs the planetary load share, thereby resulting in edge loading. Edge loading increases the likelihood of tooth pitting and planet‐bearing fatigue, leading to reduced gearbox life. Additionally, at low‐input torque, the planet‐bearing loads are often less than the minimum recommended load and thus susceptible to skidding. Copyright © 2014 John Wiley & Sons, Ltd.     

A framework for isogeometric‐analysis‐based optimization of wind turbine blade structures

Early‐stage wind turbine blade design usually relies heavily on low‐fidelity structural models; high‐fidelity, finite‐element‐based structural analyses are reserved for later design stages because of their complex workflows and high computational expense. Yet, high‐fidelity structural analyses often provide design‐governing feedback such as buckling load factors. Mitigation of the issues of workflow complexity and computational expense would allow designers to utilize high‐fidelity feedback earlier, more easily, and more often in the design process. Thus, a blade analysis framework that employs isogeometric analysis (IGA), a simulation method that overcomes many of the aforementioned drawbacks associated with traditional finite element analysis (FEA), is presented. IGA directly utilizes the mathematical models generated by computer‐aided design (CAD) software, requiring less user interaction and no conversion of parametric geometries to finite element meshes. Furthermore, IGA tends to have superior per‐degree‐of‐freedom accuracy compared with traditional FEA. Issues unique to IGA in the context of wind turbine blade design, such as coupling of thin‐shell components, are addressed, and a design approach that combines reduced‐order aeroelastic analysis with IGA is outlined. Aeroelastic analysis is used to efficiently provide dynamic kinematic data for a wide range of wind load cases, while IGA is used to perform buckling analysis. The value of incorporating high‐fidelity analysis feedback into blade design is demonstrated through optimization of the NREL/SNL 5 MW wind turbine blade. A variety of potential designs are produced with reduced blade mass and material cost, and IGA‐based buckling analysis is shown to provide design‐governing constraint information.     

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

Aerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.     

Model predictive control of a wind turbine using short‐term wind field predictions

As wind turbines become larger and hence more flexible, the design of advanced controllers to mitigate fatigue damage and optimise power capture is becoming increasingly important. The majority of the existing literature focuses on feedback controllers that use measurements from the turbine itself and possibly an estimate or measurement of the current local wind profile. This work investigates a predictive controller that can use short‐term predictions about the approaching wind field to improve performance by compensating for measurement and actuation delays. Simulations are carried out using the FAST aeroelastic design code modelling the NREL 5 MW reference turbine, and controllers are designed for both above rated and below rated wind conditions using model predictive control. Tests are conducted in various wind conditions and with different future wind information available. It is shown that in above rated wind conditions, significant fatigue load reductions are possible compared with a controller that knows only the current wind profile. However, this is very much dependent on the speed of the pitch actuator response and the wind conditions. In below rated wind conditions, the goals of power capture and fatigue load control were considered separately. It was found that power capture could only be improved using wind predictions if the wind speed changed rapidly during the simulation and that fatigue loads were not consistently reduced when wind predictions were available, indicating that wind predictions are of limited benefit in below rated wind conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

A fast stochastic solution method for the Blade Element Momentum equations for long‐term load assessment

Unsteady power output and long‐term loads (extreme and fatigue) drive wind turbine design. However, these loads are difficult to include in optimization loops and are typically only assessed in a post‐optimization load analysis or via reduced‐order methods. Both alternatives yield suboptimal results. The reason for this difficulty lays in the deterministic approaches to long‐term loads assessment. To model the statistics of lifetime loads they require the analysis of many unsteady load cases, generated from many different random seeds—a computationally expensive procedure. In this paper, we present an alternative: a stochastic solution for the unsteady aerodynamic loads based on a projection of the unsteady Blade Element Momentum (BEM) equations onto a stochastic space spanned by chaos exponentials. This approach is similar to the increasingly popular polynomial chaos expansion, but with 2 major differences. First, the BEM equations constitute a random process, varying in time, while previous polynomial chaos expansion methods were concerned with random parameters (ie, random but constant in time or initial values). Second, a new, more efficient basis (the exponential chaos) is used. This new stochastic method enables us to obtain unsteady long‐term loads much faster, enabling unsteady loads to become accessible inside wind turbine optimization loops. In this paper we derive the stochastic BEM solution and present the most relevant results showing the accuracy of the new method.     

Comparison of simulators for variable‐speed wind turbine transient analysis

This paper presents a comparison of three variable‐speed wind turbine simulators used for a 2 MW wind turbine short‐term transient behaviour study during a symmetrical network disturbance. The simulator with doubly fed induction generator (DFIG) analytical model, the simulator with a finite element method (FEM) DFIG model and the wind turbine simulator with an analytical model of DFIG are compared. The comparison of the simulation results shows the influence of the different modelling approaches on the short‐term transient simulation accuracy. Copyright © 2005 John Wiley & Sons, Ltd.     

Comparison of the near‐wake between actuator‐line simulations and a simplified vortex model of a horizontal‐axis wind turbine

The flow around an isolated horizontal‐axis wind turbine is estimated by means of a new vortex code based on the Biot–Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind‐turbine conditions (Tjæreborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near‐wake structure and local forces along the blade. The results from the Tjæreborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator‐line approach but with a negligible computational effort. Copyright © 2015 John Wiley & Sons, Ltd.     

发动机主轴承座结构强度分析研究

建立了包括缸体、框架、轴瓦、曲轴及连接螺栓的发动机主轴承座网格模型,通过指定不同的接触区域、接触条件、载荷、约束边界条件及多点约束,分别建立了螺栓预紧、轴瓦过盈、曲轴动压力及热负荷四种工况主轴承座强度分析有限元模型。采用二阶修正单元并通过接触主从面上单元的对应性来保证计算精度和收敛性,采用小滑移接触算法计算出各工况下主轴承座的应力和变形情况,根据计算结果,对主轴承座的强度、变形、滑移表面的滑动以及轴瓦背面的压力分布进行了评价,对主轴承座结构提出了改进意见,改进方案满足结构设计要求。     

Fatigue design load calculations of the offshore NREL 5 MW benchmark turbine using quadrature rule techniques

A novel approach is proposed to reduce, compared with the conventional binning approach, the large number of aeroelastic code evaluations that are necessary to obtain equivalent loads acting on wind turbines. These loads describe the effect of long‐term environmental variability on the fatigue loads of a horizontal‐axis wind turbine. In particular, Design Load Case 1.2, as standardized by IEC, is considered. The approach is based on numerical integration techniques and, more specifically, quadrature rules. The quadrature rule used in this work is a recently proposed “implicit” quadrature rule, which has the main advantage that it can be constructed directly using measurements of the environment. It is demonstrated that the proposed approach yields accurate estimations of the equivalent loads using a significantly reduced number of aeroelastic model evaluations (compared with binning). Moreover, the error introduced by the seeds (introduced by averaging over random wind fields and sea states) is incorporated in the quadrature framework, yielding an even further reduction in the number of aeroelastic code evaluations. The reduction in computational time is demonstrated by assessing the fatigue loads on the NREL 5 MW reference offshore wind turbine in conjunction with measurement data obtained at the North Sea, for both a simplified and a full load case.     

Fatigue assessment of offshore wind turbines on monopile foundations using multi‐band modal expansion

Offshore wind turbines (OWTs) are subjected to both quasi‐static loads originating from variations in the thrust force and dynamic loads linked to turbulence, waves and turbine dynamics. Both types of loads contribute to fatigue life progression and thus define the turbine's age. As a structural health monitoring solution, one could thus directly measure the stress history at fatigue critical locations. However, for OWTs on monopile foundations some fatigue critical locations are located below the seabed. Installing strain sensors at these hotspots is therefore impossible for existing wind turbines. This measurement restriction is overcome by reconstructing the full‐field response of the structure based on the limited number of accelerometers and strain sensors (installed at a few easily accessible locations) and a calibrated finite element model of the system. The system model uses a multi‐band modal expansion approach constituted of the quasi‐static and dynamic contributions. These contributions are superimposed to reconstruct the stress history at all degrees of freedom of the finite element model, and the subsequent assess fatigue life consumption at all fatigue hot spots of the OWT. In this paper, the proposed virtual sensing technique is validated by predicting the stresses in the transition piece with 12 days of consecutive measurements from an operational OWT. The data set contains both variations in environmental and operating conditions as well as extreme events. Finally, a full‐field strain assessment in the tower and foundation system of the OWT is demonstrated. Copyright © 2017 John Wiley & Sons, Ltd.     

Wind turbine main‐bearing loading and wind field characteristics

This paper investigates the relationship between wind turbine main‐bearing loads and the characteristics of the incident wind field in which the wind turbine is operating. For a 2‐MW wind turbine model, fully aeroelastic multibody simulations are performed in 3D turbulent wind fields across the wind turbine's operational envelope. Hub loads are extracted and then injected into simplified drivetrain models of three types of main‐bearing configuration. The main‐bearing reaction loads and load ratios from the simplified model are presented and analysed. Results indicate that there is a strong link between wind field characteristics and the loading experienced by the main bearing(s), with the different bearing configurations displaying very different loading behaviours. Main‐bearing failure rates determined from operational data for two drivetrain configurations are also presented.     

Implicit Floquet analysis of wind turbines using tangent matrices of a non‐linear aeroelastic code

The aeroelastic code BHawC for calculation of the dynamic response of a wind turbine uses a non‐linear finite element formulation. Most wind turbine stability tools for calculation of the aeroelastic modes are, however, based on separate linearized models. This paper presents an approach to modal analysis where the linear structural model is extracted directly from BHawC using the tangent system matrices when the turbine is in a steady state. A purely structural modal analysis of the periodic system for an isotropic rotor operating at a stationary steady state was performed by eigenvalue analysis after describing the rotor degrees of freedom in the inertial frame with the Coleman transformation. For general anisotropic systems, implicit Floquet analysis, which is less computationally intensive than classical Floquet analysis, was used to extract the least damped modes. Both methods were applied to a model of a three‐bladed 2.3 MW Siemens wind turbine model. Frequencies matched individually and with a modal identification on time simulations with the non‐linear model. The implicit Floquet analysis performed for an anisotropic system in a periodic steady state showed that the response of a single mode contains multiple harmonic components differing in frequency by the rotor speed. Copyright © 2011 John Wiley & Sons, Ltd.     

The dynamics of an offshore wind turbine in parked conditions: a comparison between simulations and measurements

Offshore wind turbines are complex structures, and their dynamics can vary significantly because of changes in operating conditions, e.g., rotor‐speed, pitch angle or changes in the ambient conditions, e.g., wind speed, wave height or wave period. Especially in parked conditions, with reduced aerodynamic damping forces, the response due to wave actions with wave frequencies close to the first structural resonance frequencies can be high. Therefore, this paper will present numerical simulations using the HAWC2 code to study an offshore wind turbine in parked conditions. The model has been created according to best practice and current standards based on the design of an existing Vestas V90 offshore wind turbine on a monopile foundation in the Belgian North Sea. The damping value of the model's first fore‐aft mode has been tuned on the basis of measurements obtained from a long‐term ambient monitoring campaign on the same wind turbine. Using the updated model of the offshore wind turbine, the paper will present some of the effects of the different design parameters and the different ambient conditions on the dynamics of an offshore wind turbine. The results from the simulations will be compared with the processed data obtained from the real measurements. The accuracy of the model will be discussed in terms of resonance frequencies, mode shapes, damping value and acceleration levels, and the limitations of the simulations in modeling of an offshore wind turbine will be addressed. Copyright © 2014 John Wiley & Sons, Ltd.     

Investigation of potential extreme load reduction for a two‐bladed upwind turbine with partial pitch

This paper presents a wind turbine concept with an innovative design combining partial pitch with a two‐bladed (PP‐2B) turbine configuration. Special emphasis is on extreme load reduction during storm situations at standstill, but operational loads are also investigated. In order to compare the loads and dynamics of the PP‐2B turbine, a partial pitch three‐bladed (PP‐3B) turbine and a normal pitch regulated three‐bladed (3B) turbine are introduced on the basis of solidity similarity scaling. From the dynamic comparisons between two‐ and three‐bladed turbines, it has been observed that the blade vibrations are transferred differently from the rotor to the tower. For a three‐bladed turbine, blade vibrations seen in a fixed frame of reference are split with ±1P only. A two‐bladed turbine has a similar split of ±1P but also includes contributions on higher harmonics (±2P, ±3P, … etc.). Further on, frequency split is also seen for the tower vibrations, where an additional ±2P contribution has been observed for the two‐bladed turbine. Regarding load comparisons, the PP‐2B turbine produces larger tower load variations because of 2P excitation during the operational cases. However, extreme loads are reduced by approximately 20% for the PP‐2B and 18% for the PP‐3B compared with the 3B turbine for the parked condition in a storm situation. Moreover, a huge potential of 60% is observed for the reduction of the extreme tower bottom bending moment for the PP‐2B turbine, when the wind direction is from ±90° to the turbine, but this also requires that the turbine is parked in a T‐configuration. © 2014 The Authors. Wind Energy published by John Wiley & Sons, Ltd.