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  • Modeling, Identification and Control, Vol. 33, No. 1, 2012, pp. 111, ISSN 18901328

    Modeling and Parameter Identification of

    Deflections in Planetary Stage of Wind Turbine

    Gearbox

    Morten Haastrup 1 Michael R. Hansen 2 Morten K. Ebbesen 2 Ole . Mouritsen 3

    1Vestas Wind Systems A/S, DK-8200 Aarhus, Denmark. E-mail: [email protected]

    2Department of Engineering, University of Agder, N-4879, Grimstad, Norway E-mail: {michael.r.hansen,morten.k.ebbesen}@uia.no

    3Department of Mechanical and Manufacturing Engineering, Aalborg University, DK-9220 Aalborg , Denmark,E-mail: [email protected]

    Abstract

    The main focus of this paper is the experimental and numerical investigation of a 750[kW] wind turbinegearbox. A detailed model of the gearbox with main shaft has been created using MSC.Adams. Special fo-cus has been put on modeling the planet carrier (PLC) in the gearbox. For this purpose experimental datafrom a drive train test set up has been analyzed using parameter identification to quantify misalignments.Based on the measurements a combination of main shaft misalignment and planet carrier deflection hasbeen identified. A purely numerical model has been developed and it shows good accordance with theexperimental data.

    Keywords: Flexible bodies, wind turbine, Multibody dynamics, parameter identification

    1 Introduction

    A common topology of wind turbine drive trains in-cludes a gearbox with the main purpose of increasingthe speed of the rotor to a value suited to the gener-ator, power electronics and grid at hand. The steadyincrease in power rating of wind turbines together withthe constraint on the blade tip speed has led to higherdemands for gear ratio and, subsequently, to a highercomplexity in the gearbox layout and in the load distri-bution. This trend has further emphasized the gearboxas a crucial element in any reliability assessment of awind turbine.

    Since model based prediction of performance, in gen-eral, and reliability, in particular, holds many advan-tages the obvious conclusion from the above is to em-ploy models that take into account more degrees of

    freedom and more phenomena when doing time do-main simulation of drive trains. This should, however,be done carefully since certification in the wind tur-bine industry is based on simulation of large time se-quences. This work focuses on the investigation of theimportance of including gearbox component flexibilitywith special emphasis on the planet carrier (PLC) ofthe planetary stage normally found in a wind turbinegearbox. In that respect the work can be viewed as acontinuation of Haastrup et al. (2011) that focused onthe distribution of the torsional flexibility of the drivetrain. Also, the work can be viewed as an integralpart of the Gearbox Reliability Collaborative (GRC)initiated and managed by the National Renewable En-ergy Laboratory (NREL) where a 775[kW] gearbox hasbeen subjected to extensive testing. Part of the instru-mentation involves proximity sensors used to measure

    doi:10.4173/mic.2012.1.1 c 2012 Norwegian Society of Automatic Control

    http://dx.doi.org/10.4173/mic.2012.1.1

  • Modeling, Identification and Control

    Hub flange

    Main shaft (MS)

    Planet carrier (PLC)

    Sun shaft

    Low speed shaft (LS) IMS

    HS

    MS sleeve

    T

    Radial load

    Figure 1: Naming of the main components.

    the axial and radial motion and deflection of specificpoints of the PLC. The aim of this paper is to utilizethese measurements to set up and calibrate a modelthat properly describes the behavior of the PLC witha minimum of complexity and computational costs.

    Many different approaches have been suggested onhow to model planetary gears. In the following papersresearchers are investigating vibration phenomena us-ing analytical approaches: Al-shyyab and Kahraman(2007), Kahraman (1994), Lin and Parker (1999).Others reach the same objective using finite ele-ment Parker et al. (2000a), Parker et al. (2000b) andRigaud et al. (2006). Common for all of these papersis that they present methods for prediction of noiseand/or vibration of gearboxes. Before computers be-came sufficiently fast to solve large finite element analy-ses (FEA) and multi body simulations (MBS) the sameobjectives were reached using analytical models. A sur-vey is given in Ozguven and Houser (1988).

    To model wind turbine gearboxes a gear modelis required and some gear models for use in MBShas been suggested. Lundvall et al. (2004) proposesa gear model that imposes flexibility to the rigidbody motion. The flexibility is obtained using FEMand tribology theory. Another method proposedby Blankenship and Singh (1995) implements full 3Dforces and moments relevant for a helical gear pair.Blankenship uses a combined stiffness to account forboth gear wheel, tooth and contact stiffness. Athird gear model suggested by Ebrahimi and Eberhard(2006) uses a lumped mass approach for model-ing the flexibility of gears. In the present papercommercial available modeling tools developed byMSC.SoftwareTM, see Table 1, is used in conjunctionwith measured data to set up guidelines for modelingplanetary gearboxes in wind turbine drive trains. Thegear model has a contact algorithm for detecting con-tact between mating gears taking profile modifications

    and contact stiffness into account.In the present paper a gear model developed by

    MSC.Software in Germany will be used. The modelhas a contact algorithm for detecting contact betweenmating gears taking profile modifications and contactstiffness into account. Ultimately the goal is to predictfatigue loads on gear, bearings and other componentsand noise emission. However, none of these models areexperimentally verified.

    Table 1: Software used in this paper

    Name Purpose

    MSC.Adams Multibody dynamicsMSC.Patran FEM pre and post processorMSC.Nastran FEM solver

    Adams/Gear AT Gear sover for MSC.AdamsAdams Gear Generator Gear sover for MSC.Adams

    MATLAB Parameter identification

    2 Identification of PLC motion

    The gearbox considered in this paper has three gearstages: one planetary and two parallel. The naming ofthe main components of the gearbox is shown in Fig-ure 1. The PLC motion is measured by six proximitysensors. Four of them are measuring axial displace-ments (along the x-axis) and two are measuring radialdisplacement (perpendicular to the x-axis). All thedisplacements are measured relative to the housing ofthe gearbox, i.e., any displacement is a combination ofrigid body motion of the PLC relative to the housingas well as deflection of both the PLC and the housing.In order to produce valid experimental data, two faceson the PLC have been machined, as shown in Figure2, and they are used as measuring reference.

    2

  • Haastrup et al., Planet Carrier Motion

    Machined faces

    x = 47

    s47es40e

    Rs

    MS sleeve s137e

    s227e

    x

    x

    y

    z

    z

    Figure 2: CAD drawing showing the location of theproximity sensors.

    All sensors are mounted on the inside of the mainflange of the gearbox. They are displaced a radiusRs = 412[mm] from the x-axis, see Figure 2, and, fur-ther, rotated different angles around the x-axis with0 corresponding to the z-axis. The four sensorsthat measure axial displacement are located at x =[47, 137, 227, 317] and the two sensors that measureradial displacement are located at x = [40

    , 310].

    The signals from the sensors are named after thelocation of the sensors, subsequently, the names are:s47e , s

    137e , s

    227e and s

    317e for the axial sensors and s

    40e

    and s310e for the radial.

    Measurements were conducted in four different loadcases, which are tests where 100% or 50% of a nominaltorque of T 360[kNm] was applied. In two of the

    load cases radial load was also applied by means of anon-torque radial loading device, see Haastrup et al.(2011). The load cases are listed in Table 2.

    Table 2: Load cases.

    Load case Torque Radial load

    LC1 100% 0LC2 50% 0LC3 100% 200[kN]LC4 100% 200[kN]

    2.1 Rigid body motion

    zH

    yH

    xH

    zPLC

    yPLC

    x(t)

    PLC

    H

    vH

    vPLC

    sv

    PLC

    H

    Rs

    v

    Figure 3: Definition coordinate systems and angles.

    Identification of the PLC motion requires a modelthat is capable of showing the same behavior as can beobserved in the measurements. From the observationstwo models are proposed: The first model concernsonly rigid body motion (M1) while the second modelalso takes into account the deformation of the PLC(M2).Two coordinate systems have been employed to de-

    scribe the assumed rigid body motion of the PLC.Firstly, there is a fixed coordinate system (xH , yH ,zH) that is shown in Figure 3 and which is alignedwith the global coordinate system (x, y, z) shown inFigure 2. Secondly, a coordinate system fixed to thePLC (xPLC , yPLC , zPLC) is defined. This coordinatesystem is rotated around the xH -axis of the fixed co-ordinate system with an angle x(t), see Figure 3. Therigid body model assumes that the motion of the PLC

    3

  • Modeling, Identification and Control

    can be described by a constant displacement, dx, alongthe xH -axis, along with a constant tilt H around afixed tilt axis that is obtained by rotating the zH -axisan angle H around the xH -axis. Similarly, a constanttilt PLC around a rotating tilt axis that is obtainedby rotating the zPLC -axis an angle PLC around thexPLC = xH -axis. In all this gives five parameters to beidentified: dx, H , H , PLC , and PLC that describethe rigid body motion of the PLC. In the followingequations x(t) denotes the rotation of the PLC definedas the rotation of the PLC-coordinate system relativeto the H-coordinate system. The simulated sensor sig-nals