Multi‐body modelling and analysis of a planet carrier in a wind turbine gearbox

There have been some recent efforts to numerically model and analyse the wind turbine gearbox. To date, much of the focus has been on increasing model refinement and demonstrating its added value. This paper takes a step back and examines in detail the modelling and analysis of an important wind turbine gearbox component, the planet carrier, in a multi‐body setting. The planet carrier studied in this work comes from the 750 kW wind turbine gearbox used in the National Renewable Energy Laboratory's Gearbox Reliability Collaborative project. The study is performed in two parts. First, the influence of subcomponents mated to the planet carrier in the gearbox assembly is investigated in detail. These components consist of the planet pins, bearings and the main shaft. In the second part of the study, the flexible body modelling of the planet carrier for use in multi‐body simulations is examined through the use of condensed finite element and multi‐body simulation models. Both eigenvalue analyses and time domain simulations are performed. Comparisons are made regarding the eigenfrequencies, categorized mode shapes and the maximum and minimum planet carrier rim deflections from the time domain simulations. The mode shapes are categorized into seven distinct deformation patterns. An actual load case from the dynamometer tests, a 100% rated torque loading, is used in the time domain simulations. The results from this comprehensive study provide an insight into the proper modelling of a wind turbine planet carrier in a multi‐body setting. Copyright © 2012 John Wiley & Sons, Ltd.     

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 novel power splitting drive train for variable speed wind power generators

In this paper a novel electrically controlled power splitting drive train for variable speed wind turbines is presented. A variable speed wind turbine has many advantages, mainly it can increase the power yield from the wind, alleviate the load peak in the electrical-mechanical drive train, and posses a long life time, also, it can offer the possibility to store the briefly timely wind-conditioned power fluctuations in the wind rotor, in which the rotary masses are used as storages of kinetic energy, consequently, the variable speed wind turbines are utilized in the wind power industry widely. In this work, on the basis of a planetary transmission a new kind of drive train for the variable speed wind turbines is proposed. The new drive train consists of wind rotor, three-shafted planetary gear set, generator and servo motor. The wind rotor is coupled with the planet carrier of the planetary transmission, the generator is connected with the ring gear through an adjustment gear pair, and the servo motor is fixed to the sun gear. By controlling the electromagnetic torque or speed of the servo motor, the variable speed operation of the wind rotor and the constant speed operation of the generator are realized, therefore, the generator can be coupled with the grid directly. At the nominal operation point, about 80% of the rotor power flow through the generator directly and 20% through the servo motor and a small power electronics system into the grid. As a result, the disadvantages in the traditional wind turbines, e.g. high price of power electronics system, much power loss, strong reaction from the grid and large crash load in the drive train will be avoided.     

Residual signal feature extraction for gearbox planetary stage fault detection

Faults in planetary gears and related bearings, e.g. planet bearings and planet carrier bearings, pose inherent difficulties on their accurate and consistent detection associated mainly to the low energy in slow rotating stages and the operating complexity of planetary gearboxes. In this work, statistical features measuring the signal energy and Gaussianity are calculated from the residual signals between each pair from the first to the fifth tooth mesh frequency of the meshing process in a multi‐stage wind turbine gearbox. The suggested algorithm includes resampling from time to angular domain, identification of the expected spectral signature for proper residual signal calculation and filtering of any frequency component not related to the planetary stage. Two field cases of planet carrier bearing defect and planet wheel spalling are presented and discussed, showing the efficiency of the followed approach and the possibility of characterizing a fault as localized or distributed. Copyright © 2017 John Wiley & Sons, Ltd.     

Sources of time‐varying contact stress and misalignments in wind turbine planetary sets

Recent data shows that 90% of large wind turbines include a gearbox, and industry forecasts expect this figure to remain relatively stable. With global annual volumes (2009) of around 18,600 units, the quality, cost and performance of gearboxes is of paramount importance to the wind sector. The industry has been focusing some attention on gearbox reliability, as demonstrated by a growth in the number of specific seminars and collaborative programs on this topic. One aspect that needs to be brought to an industry‐wide forum is the understanding of the complexity of bearing design in the gearbox and the careful attention that needs to be paid to ensure a reliable gearbox design. This paper seeks to address this issue by clear demonstration of design issues using a model of the gearbox from the National Renewable Energy Lab's Gearbox Reliability Collaborative. Detailed models are presented with focus on determining the quality of the function of the planetary gear stages. Key design drivers are discussed such as the quality of alignment at the gears and bearings and the loads and stresses seen on these components. Under a design load case with a significant rotor off‐axis moment the stresses in the planet gears and bearings are investigated. It is shown how the misalignment of the planet pins varies with the rotation of the planetary set and how subsequently time‐varying contact stresses and load distributions occur in the planet gears and bearings. These factors strongly influence the fatigue life of the gearbox components as well as the level of vibration. Design tools are then used to demonstrate how small variations in the clearances of the planet carrier bearings can have a big effect on the quality of the design. Numerical studies show where optimal clearance settings lie and how the misalignment of the planetary set can be improved. Furthermore, a demonstration is made of how redesign of the bearing arrangement and subsequent optimization of the planet tooth geometry further improves the misalignment and results in significantly reduced time‐varying contact stresses, better load distribution and reduced vibration. It is illustrated that small clearances, such as in the carrier bearings, can have a large effect on the performance of the design and a study shows how to identify and reduce time‐varying misalignment and contact stresses resulting in lower vibration, lower fatigue and a more reliable product. Copyright © 2011 John Wiley & Sons, Ltd.     

Drive train dynamics assessment and speed controller design in variable speed wind turbines

This paper deals with the speed controller design in DFIG based wind turbines, and investigates stability and performance of the drive train dynamics against different control strategies. It is shown that speed controller design based on the single mass drive train model may result in unstable mechanical modes, because it ignores the dynamics of the flexible shaft. Then, another control approach, known as feedforward compensation of the shaft torsional torque, is examined. It is shown that this control method results in poorly damped oscillations of torsional torque and turbine speed during the transient conditions. The open loop transfer function from the electromagnetic torque to the generator speed contains a dual quadratic function representing the dynamics of flexible shaft. The dual quadratic function comprises resonant and anti-resonant frequencies that greatly affect the stability of the drive train dynamics. Next, a step-by-step procedure for designing the speed controller based on the two-mass drive train model is proposed. The proposed speed controller provides stable closed loop system, zero tracking error, low-frequency disturbance rejection, and open-loop gain attenuation at the resonant frequency. At the end, performance of the proposed controller is investigated by the time domain simulations.     

Effects of floating sun gear in a wind turbine's planetary gearbox with geometrical imperfections

This paper addresses the effect of gear geometrical errors in wind turbine planetary gearboxes with a floating sun gear. Numerical simulations and experiments are employed throughout the study. A National Renewable Energy Laboratory 750 kW gearbox is modelled in a multibody environment and verified using the experimental data obtained from a dynamometer test. The gear geometrical errors, which are both assembly dependent and assembly independent, are described, and planet‐pin misalignment and eccentricity are selected as the two most influential and key errors for case studies. Various load cases involving errors in the floating and non‐floating sun gear designs are simulated, and the planet‐bearing reactions, gear vibrations, gear mesh loads and bearing fatigue lives are compared. All tests and simulations are performed at the rated wind speed. For errorless gears, the non‐floating sun gear design performs better in terms of gear load variation, whereas the upwind planet bearing has more damage. In the floating sun gear scenario, the planet misalignment is neutralized by changing the sun motion pattern and the planet gear's elastic deformation. The effects of gear profile modifications are also evaluated, revealing that profile modifications such as crowning improve the effects of misalignment. Copyright © 2014 John Wiley & Sons, Ltd.     

Aeroelastic analysis of a floating offshore wind turbine in platform‐induced surge motion using a fully coupled CFD‐MBD method

Modern offshore wind turbines are susceptible to blade deformation because of their increased size and the recent trend of installing these turbines on floating platforms in deep sea. In this paper, an aeroelastic analysis tool for floating offshore wind turbines is presented by coupling a high‐fidelity computational fluid dynamics (CFD) solver with a general purpose multibody dynamics code, which is capable of modelling flexible bodies based on the nonlinear beam theory. With the tool developed, we demonstrated its applications to the NREL 5 MW offshore wind turbine with aeroelastic blades. The impacts of blade flexibility and platform‐induced surge motion on wind turbine aerodynamics and structural responses are studied and illustrated by the CFD results of the flow field, force, and wake structure. Results are compared with data obtained from the engineering tool FAST v8.     

Improving wind turbine drivetrain designs to minimize the impacts of non‐torque loads

Non‐torque loads induced by the wind turbine rotor overhang weight and aerodynamic forces can greatly affect drivetrain loads and responses. If not addressed properly, these loads can result in a decrease in gearbox component life. This work uses analytical modeling, computational modeling and experimental approaches to evaluate two distinct drivetrain designs that minimize the effects of non‐torque loads on gearbox reliability: a modified three‐point suspension drivetrain studied by the National Renewable Energy Laboratory (NREL) Gearbox Reliability Collaborative (GRC) and the Pure Torque® drivetrain developed by Alstom. In the original GRC drivetrain, the unequal planetary load distribution and sharing were present and they can lead to gear tooth pitting and reduce the lives of the planet bearings. The NREL GRC team modified the original design of its drivetrain by changing the rolling element bearings in the planetary gear stage. In this modified design, gearbox bearings in the planetary gear stage are anticipated to transmit non‐torque loads directly to the gearbox housing rather than the gears. Alstom's Pure Torque drivetrain has a hub support configuration that transmits non‐torque loads directly into the tower rather than through the gearbox as in other design approaches. An analytical model of Alstom's Pure Torque drivetrain provides insight into the relationships among turbine component weights, aerodynamic forces and the resulting drivetrain loads. In Alstom's Pure Torque drivetrain, main shaft bending loads are orders of magnitude lower than the rated torque and hardly affected by wind speed, gusts or turbine operations. Copyright © 2014 John Wiley & Sons, Ltd.     

风电机组行星轮系柔性齿圈疲劳寿命研究

为探究风电机组行星轮系柔性内齿圈在动态啮合力作用下的疲劳损伤规律,建立考虑内齿圈结构柔性的行星轮系动力学模型,运用瞬态动力学进行仿真计算得到内齿圈结构应力时域历程,并通过试验验证该动态应力仿真结果的正确性。运用雨流循环计数法及Goodman平均应力修正法得到对称循环应力,随后结合Miner线性损伤理论计算内齿圈结构的弯曲疲劳寿命,分析内齿圈结构变形引起应力变化对疲劳寿命的影响,探讨不同轮缘厚度、支撑数量及不同负载下内齿圈结构疲劳寿命的变化规律。结果表明：内齿圈疲劳寿命受到齿圈结构变形和轮齿变形的共同作用,轮缘越薄内齿圈结构变形越剧烈,各轮齿间寿命差距越大,两支撑间各轮齿疲劳寿命波动趋势越复杂;当齿圈柔性较大时,其最大应力由齿圈结构变形引起且疲劳破坏点由齿根向齿槽偏移,齿圈柔性较小时其疲劳寿命主要取决于轮齿变形。     

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.     

计入齿圈柔性的风电机组行星传动动态特性研究

为研究齿圈柔性对风电机组行星齿轮传动系统动态特性的影响,将连续体的柔性齿圈离散成多段刚性轮齿段,以连接处的扭簧扭转刚度来量化齿圈的柔性特点。在行星架随动坐标系下,综合考虑啮合刚度、支撑刚度和齿圈柔性等因素,建立计入齿圈柔性的行星传动系统平移—扭转耦合动力学模型,继而分析齿圈柔性、齿圈支撑点数目与负载力矩对齿圈变形及系统啮合力的影响,并进一步揭示太阳轮浮动轨迹在不同齿圈支撑点数目下的表现特点。研究结果表明:工作过程中的柔性齿圈产生较大的弹性变形,致使太阳轮与行星轮啮合力幅值出现长周期波动,且其频谱中出现多个转频成分,经对比发现该转频分别为行星架转频、ζ倍行星架转频及2ζ倍行星架转频(ζ为齿圈支撑点数目)。当支撑点数目与行星轮个数满足倍数关系时,太阳轮浮动轨迹较为规律,其外轮廓与刚性齿圈条件下一致;否则,浮动轨迹外轮廓呈现出具有ζ个瓣叶的花瓣状。     

Review on wind turbines with focus on drive train system dynamics

The strong growth within the wind technology market, underpinned by policy goals around the world, has highlighted the demand for advanced engineering analysis to improve wind turbine (WT) design, both in terms of reliability and design of larger turbines. This paper presents a review of the latest research that has been carried out in modeling and analysis of load transmission in WT drive train systems and their components. Common failure roots are elaborated, and probable hypotheses are presented. A modeling approach is derived by classification into engineering, mathematical and computational models with a focus on gearbox modeling efforts. Precise understanding of drive train system dynamics and load transmission is necessary for a cost efficient and robust system design to enhance reliability and reduce the maintenance costs. Design optimization of WTs and their subsystems will make future WTs more attractive compared with fossil and nuclear power plants, and it is therefore an important issue for a more sustainable environment. Copyright © 2014 John Wiley & Sons, Ltd.     

A new multibody modelling methodology for wind turbine structures using a cardanic joint beam element

This paper presents a new multibody modelling methodology for wind turbine structures. The methodology is based on the hybrid multibody system being composed of rigid, flexible bodies, force elements and joints. With a cardanic joint beam element based on the Timoshenko beam theory, the flexible bodies, e.g. rotor blades and tower, shafts, are modelled by a set of rigid bodies connected by cardanic joints geometrically and constrained by spring forces elastically, thus a whole wind turbine structure can be represented by a discrete system of rigid bodies, springs, and dampers. Using some concepts of the differential geometry, the Lagrange's motion equations of the multibody system are represented in explicit form. With this model, the global natural vibrations of a wind turbine structure of 600 kW are analysed.     

1.5MW低风速风力发电机组主传动系统设计及动力学分析

低风速风力发电机组具有广阔的市场前景,其主传动系统的设计和分析是整个风机研发的关键技术之一。通过对风机各种传动系统结构形式的分析、对比和优化,设计了适于1.5 MW低风速风力发电机组的最佳传动方案,即内置式主轴、二级行星加一级平行轴齿轮传动的结构形式。采用多体动力学软件SIMPACK建立了该风机主传动系统的精确模型,找出系统的固有频率及激振源,并进行共振分析;对共振危险点进行时域仿真,根据仿真结果研究振动对风机系统的影响。最后根据系统的动态特性分析结果,验证所设计的主传动系统的可靠性。     

Analysis and estimation of transient stability for a grid-connected wind turbine with induction generator

Increasing levels of wind energy in modern electrical power system is initiating a need for accurate analysis and estimation of transient stability of wind turbine generation systems. This paper investigates the transient behaviors and possible direct methods for transient stability evaluation of a grid-connected wind turbine with squirrel cage induction generator (SCIG). Firstly, by using an equivalent lump mass method, a three-mass wind turbine equivalent model is proposed considering both the blades and the shaft flexibility of the wind turbine drive train system. Combined with the detailed electromagnetic transient models of a SCIG, the transient behaviors of the wind turbine generation system during a three-phase fault are simulated and compared with the traditional models. Secondly, in order to quickly estimate the transient stability limit of the wind turbine generation system, a direct method based on normal form theory is proposed. The transient models of the wind turbine generation system including the flexible drive train model are derived based on the direct transient stability estimation method. A method of critical clearing time (CCT) calculation is developed for the transient stability estimation of the wind turbine generation system. Finally, the CCT at various initial mechanical torques for different dynamical models are calculated and compared with the trial and error method by simulation, when the SCIG stator terminal is subjected to a three-phase short-circuit fault. The results have shown the proposed method and models are correct and valid.     

On design,modelling, and analysis of a 10‐MW medium‐speed drivetrain for offshore wind turbines

The design of a medium‐speed drivetrain for the Technical University of Denmark (DTU) 10‐MW reference offshore wind turbine is presented. A four‐point support drivetrain layout that is equipped with a gearbox with two planetary stages and one parallel stage is proposed. Then, the drivetrain components are designed based on design loads and criteria that are recommended in relevant international standards. Finally, an optimized drivetrain model is obtained via an iterative design process that minimizes the weight and volume. A high‐fidelity numerical model is established via the multibody system approach. Then, the developed drivetrain model is compared with the simplified model that was proposed by DTU, and the two models agree well. In addition, a drivetrain resonance evaluation is conducted based on the Campbell diagrams and the modal energy distribution. Detailed parameters for the drivetrain design and dynamic modelling are provided to support the reproduction of the drivetrain model. A decoupled approach, which consists of global aero‐hydro‐servo‐elastic analysis and local drivetrain analysis, is used to determine the drivetrain dynamic response. The 20‐year fatigue damages of gears and bearings are calculated based on the stress or load duration distributions, the Palmgren‐Miner linear accumulative damage hypothesis, and long‐term environmental condition distributions. Then, an inspection priority map is established based on the failure ranking of the drivetrain components, which supports drivetrain inspection and maintenance assessment and further model optimization. The detailed modelling of the baseline drivetrain model provides a basis for benchmark studies and support for future research on multimegawatt offshore wind turbines.     

Control design for mechanical hardware‐in‐the‐loop operation of dynamometers for testing full‐scale drive trains

Advanced testing methods are becoming more and more prevalent to increase the reliability of wind turbines. In this field, dynamometers that allow for system level tests of full‐scale nacelles will play an important role. Operating these test benches in a hardware‐in‐the‐loop (HiL) set‐up that emulates realistic drive train modes is challenging because of the relatively low stiffness of the load machines' drive trains. This paper proposes a control method for enabling the said operation mode. It is based on the idea that the HiL‐controller overrides the present unrealistic dynamics and directly imposes desired realistic dynamics on the test bench. A solution for the control problem is given and applied in a design study with a generic wind turbine and a test bench model obtained from construction data of a real test bench. In the design study, the HiL‐controller robustly imposes desired drive train dynamics on the test bench model. Despite measurement noise, unmodelled parametric uncertainty, and unmodelled delays, the first drive train mode is correctly reproduced. This is confirmed by a comparison with simulation results from a full servo‐aero‐elastic code. Furthermore, an implementation of the test bench model on a programmable logic controller showed the real‐time feasibility of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.