Hansen, Anders Melchior

Larsen, Torben J.

Rasmussen, Flemming

Online Research Database In Technology

                       General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.  • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal   If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.     Downloaded from orbit.dtu.dk on: Dec 18, 2017Gearbox loads caused by double contact simulated with HAWC2Hansen, Anders Melchior; Rasmussen, Flemming; Larsen, Torben J.Published in:ProceedingsPublication date:2011Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Hansen, A. M., Rasmussen, F., & Larsen, T. J. (2011). Gearbox loads caused by double contact simulated withHAWC2. In Proceedings European Wind Energy Association (EWEA).Gearbox loads caused by double contact simulated withHAWC2Anders M. Hansen†, Flemming Rasmussen†, Torben J. Larsen††Wind Energy Department, Risø-DTU, DK-4000 Roskilde, Denmarkanmh@risoe.dtu.dk”EWEC conference 2011, Brussels”1 AbstractThe aim of the work presented in this paper is to investigate if a special event named ”double contact” betweenindividual gear wheels inside a gear box can be the cause for some of the frequent occurrences of gearbox failuresexperienced in modern wind turbines. The investigation is made by interfacing a simulation model of the dynamicbehaviour of a gearbox to the aeroelastic code HAWC2. The response of the coupled simulation models are thenanalysed in order to see if and under which circumstances the double contact event occurs and which loads areachieved inside the gearbox.The paper introduces first the double contact hypothesis as motivation for the study. Then the generalisedinterface to HAWC2 is described which is used to couple the gearbox model and the wind turbine model in HAWC2.The simulation model of the gearbox is then described and the gearbox model and the wind turbine model arejoined and the coupled response is obtained and analysed with special attention to the double contact event.Finally, conclusions are made.2 Double contact theoryEven though gearboxes using planetary stages have been used for centuries, the drive train layout normally used inwind turbines, see Figure 1, has special design features, which might cause problems not seen in other planetarystage applications. Apart from the torque transfer from low speed side to high speed side, the gear box alsoworks as a second main bearing of the main shaft. Hereby all force reactions from the rotor as well as thegravity and inertial loads from the gear box itself will be transferred through the main bearings between carrierand housing down to the gear box suspension normally consisting of two rubber bushing arrangements. A specialand important feature of the planetary gear is the load alleviating effect of the floating sun-wheel suspension.This floating sun-wheel suspension allows for small movements of the sun-wheel, which ensures an excellent loaddistribution between the three planets. The theory of this section is that the load transfer through the mainbearings can be influenced by a double contact situation inside the planetary stage if an unfortunate ratio betweenbearing clearance and teeth clearance occurs.A double contact is a situation where the tooth is in normal contact on the driving side and at the same timein contact on the back side as illustrated in Figure 3. Such a double contact situation is not considered a problemif it only occurs between one set of planet-sun and planet-ring teeth connections, but in the case where doublecontact on two sets of planet-sun and planet-ring connections occurs simultaneously a completely changed loadsharing between the planet wheels occurs. The reason for the changed load sharing during a double-contact isthat the two planet wheels involved with the double-contact makes a small rotation which forces the sun-wheel tobe in contact with only these two planets. The third planet is then completely unloaded which causes the inputtorque to be taken by two instead of three planets causing an increased load at the teeth and bearings during thismoment of contact.In the quest for the explanation of the many gear box failures especially seen in the period from 1995 to 2005,the dynamics of the traditional drive train layout, has previously been investigated. In a research project fundedby the Danish Energy Agency, a dynamical model of the drive train arrangement was modeled by Larsen et. al[1],[2]. In this model the main components in the drive train was modeled using a lumped spring/mass approachcoupled to a 2D spring mass model of the planetary stage, originally formulated by Lin and Parker [3]. The drivetrain model is illustrated in Figure 2. The tooth contact in the planetary stage illustrated in Figure 2 is modeledusing linear springs for the tooth flexibility and lumped inertia for the wheel bodies. The main results from thatinvestigation was that the load alleviating effect of the floating sun-wheel suspension together with the limitedinertia of the sun-wheel caused a very fine load distribution in all investigated load cases. Another result of theinvestigation was that the inertia of the gear box mounted on the main shaft and gear stay suspension througha carrier that was surprisingly flexible caused vibration modes mainly dominated by the gear box translation withfrequencies down to 10Hz, which is in the frequency range of the aerodynamic input loads. However, the analysisdid not give a reason for the gear box failures. One limitation of the analysis was that the drive train model wasnot coupled to the rest of the turbine.The behaviour of the planetary gear stage was further investigated by Parker et al.[4]. The focus of this analysiswas directly on the double contact situation. The model used for the analysis was again the original model byLin and Parker, [3], but now also equipped with extra non-linear springs representing the clearance between theteeth and inside the bearings and an extra set of springs for the double contact, see Figure 3. In this analysisperformed with constant input torque and gravity loading it was clearly seen that a change in loads occurred. Aload increase for the planetary bearings by a factor of 1.75 is seen in Figure 4.Figure 1: Traditional layout of wind turbine drive train. The gear box which consists of a planetary stageand two parallel stages also works as the second main bearing on the main shaft.ks1u1η1ζ1kr1u2ζ2kr2ks2ks3kr3η2kcuuckruurψ2kp1kp3kp3ζ3η3u3kp2Planet2Planet1kcrxkcryksuuskp1kp2Planet3ksryksrxζζζηηηmc,carriermr,ringms,sunA-AL1 L3L2mgmcmshθ θkmykgx,kcxAAFigure 2: Left: Compression forces in a normal tooth contact situation of a planetary gear stage. Right:Dynamical model used to investigate the drive train dynamics with particular focus on gear teeth and bearingforces.Figure 3: Left: Example of a double contact situation where the backside of the teeth are also in contact.Right: Double contact springs inserted (with red). Springs are non-linear and only active during compression.Only double contact spring is illustrated for the two lower planets even though they are also present for theupper planet.Figure 4: Preliminary analysis of the double-contact situation. It can be seen that planet forces are highlyun-equal depending on the azimuth position during a double-contact situation even though the input torqueis constant.3 The solution of externally formulated equations of motions togetherwith the HAWC2 core DOFsThe gearbox model used for this paper uses a new interface which enables externally formulated equations ofmotions to be solved together with the core equations of motions in the HAWC2 code.The external system interact with the HAWC2 model through a set of constraint equations which describeshow the external system degrees of freedom (DOFs) and the HAWC2 DOFs are related. Both the EOMs for theexternal system and the constraint equations are specified in an external DLL which is then called by the HAWC2solver during the simulation.In order for HAWC2 to be able to solve the combined EOMs, the external system DLL must return some specificinformation to HAWC2. To understand what is required by the DLL, it is useful to explain how the EOMs areformulated in HAWC2. The basic assumption is that the EOMs for the external system can be formulated by useof some kind of variational principle, such as e.g. the Virtual Work Principle or Hamiltons Principle - if so, thesum of virtual work, δW , for the internal (i.e. the HAWC2 system, subscript i) and external system (subscript e)is:δW = δWi + δWe = δqi ·Bi + δqe ·Be = 0In the 2nd last part of the equation above, the virtual work is expressed as a function of the virtual DOFs, δqiand δqe for the internal and external DOFs, respectively. The virtual work must be zero for the systems to bein equilibrium for all the virtual variations of the DOFs which requires the vectors Bi and Be to be equal to 0.(Note that if the external system is a simple mass/damper/spring system with external forces acting on it, thenBe = M · q¨e +C · q˙e +K · qe − FThe vectors Bi and Be express the un-constrained EOMs for the systems. The systems are not interactingwith each other since they do not share any DOFs. If somehow the systems were constrained to move in a certainmanner relative to each other, we would have to introduce external forces acting on both systems in order toobtain the constrained movement of the systems. This is done by introducing the Lagrange Multiplier Method,cf. [5], which adds some extra virtual energy to the system virtual energy necessary to satisfy the constraints.The constrained movement between the systems are formulated in a set of constraint equations gathered in theconstraint vector g(qi,qe) = 0. For each constraint equation, a new DOF (called a Lagrange multiplier) isintroduced and collected in the vector λ. Now the virtual constraint energy is added to the system virtual energy,like this0 = δW + δ(λ · g)= δW + δλ · g + δg · λ= δqi ·(Bi + (∇qig)T· λ)+ δqe ·(Be + (∇qeg)T· λ)+ δλ · g= δqi · (Bi +Gi · λ) + δqe · (Be +Ge · λ) + δλ · g, ∀δqe, ∀δqi, ∀δλThe last line in the equation above introduces the gradient matrices Ge and Gi (or rather the transpose ofthat), which contain the derivatives of the constraint vector wrt. qe and qi, respectively. Since the total virtualenergy must be zero for all virtual variations of the DOFs, we finally get these EOMs:Bi +Gi · λ = 0Be +Ge · λ = 0g = 0It is now clear which tasks the external DLL needs to do in order to couple an external system with the HAWC2model:• The un-constrained EOMs for the external system, Be, need to be formulated, along with• the constraint vector, g, and the gradient matrices, Ge and Gi.The two bulleted tasks above are really not dependent and they can be specified separately in external DLLs,providing the possibility to do simulations of external systems without constraining them to any internal systems.Also, constraints between internal systems can be defined without having to introduce an external systems.Further, which is not really clear from the description above, it is also possible to specify constraints betweenindividual external systems, so that it is possible to couple two (or more) external systems together.4 Gearbox modelThe gearbox model was formulated with the aim of providing a flexible tool to model all kinds of gearboxes,both parallel and planetary gear stages and multiple stages as well. This was achieved by setting up the dynamicequations for a single gear wheel in a floating frame of reference giving each gear wheel 12 degrees of freedom -6 for the floating frame and 6 for local displacements and rotations inside the floating frame (see Figure 5). Thegear wheels can subsequently be grouped so that they share the same floating frame of reference.Figure 5: The figure shows kinematics of a single gear wheel, here one of the planet wheels. The displacementof the floating frame of reference is given by the vector R(t) and the rotation is given by the rotation matrixA(t). The wheel offset is defined by Ri0 and the orientation of the local displacements of the wheel isdefined by the rotation matrix Ai1. The local displacement and rotation are described by ui(t) and Ai2(t),respectively.Springs can be defined related to the local DOFs. Further, springs and dampers between groups of gear wheelscan be modelled with external force models combined with appropriate constraint equations. Normally suchsprings are introduced to model bearing stiffness. A dead band can also be defined for the springs in order tomodel bearing clearance.The model of the gear tooth interaction is modeled by a spring/damper model combined with an appropriateconstraint equation which accounts for the relative movement between interacting gear teeth. The force modelis defined so that it only allows pressure forces to occur between the individual gear teeth. Furthermore, a deadband can be defined in order to model backlash.5 Coupled analysisIn this section the combined aeroelastic response of the gearbox and the wind turbine during operation in turbulentwind is analysed with special attention to the double contact event.For the present turbine, the shaft is supported by two bearings, one near the rotor (front) and another embeddedin the gear box (rear). The force reaction at the rear bearing perpendicular to the shaft is mainly composed of aconstant contribution from the gravity on the rotor and a time varying contribution from the aerodynamic loadingon the rotor. The time varying load is generated when the blades pass the fluctuations in wind speed (due towind shear, tower shadow, and turbulence) over the rotor disc and therefore there will be orientations relative tothe blades which are loaded more than others. Since the location of the planets are fixed relative to the blades,one should expect the initial mounting of the rotor relative to the planets in the gearbox (at least for the 1st gearstage) to be of importance. This hypothesis is also investigated.The three Figures 6, 7, and 8 show results from an aeroelastic simulation with the same input parameters, i.e.same turbine model (600kW stall regulated), same mean wind (10m/s) and same turbulence time series. Only thegearbox models differ. The turbine is started at low rotor RPM and the generator is cut out. After approximately12 sec. the rotor has reached the cut-in speed and the generator is activated. The four graphs in each plot showthe gear tooth reaction forces on planet wheel #1 between sun/planet and ring/planet on the front side and backside of the tooth, respectively.The results shown in Figure 6 is the reference case with no clearance in the main bearing. In this case theforces on the end of the shaft perpendicular to the shaft are supported by the main bearing. The variation intooth forces are caused by variations in wind speed and hence the torque transmitted through the gearbox. Notooth forces on the back side of the gear teeth are observed which means that the gear box operates as intendedwithout any double contact events occurring.The gearbox used to generate the results in Figure 7 has low main bearing stiffness so that the forces on theshaft end are no longer supported by the main bearing. Instead the force is supported by the interaction betweenthe planet and the ring causing double contact between the gear teeth and increased tooth forces.The results shown in Figure 8 demonstrate the significance of how the rotor is mounted relative to the planetsin the gearbox. In this case the rotor and gearbox are rotated 60deg relative to the position used for the results inFigure 7, but otherwise the two gearboxes are identical. The tooth forces are seen to be larger in this case whichindicates that an optimum relative rotation between rotor and gearbox exists which minimizes the tooth forces incase of double contact. 0 50000 100000 150000 200000 250000 300000 0  10  20  30  40  50  60  70  80force [N]time [s]Planet 1: Tooth Reaction ForcesSun-planet  (front)Ring-planet (front)Sun-planet  (back)Ring-planet (back)Figure 6: Normal operation casewithout double contact. The vari-ation in loading is caused by tur-bulent wind speed variation. 0 50000 100000 150000 200000 250000 300000 0  10  20  30  40  50  60  70  80force [N]time [s]Planet 1: Tooth Reaction ForcesSun-planet  (front)Ring-planet (front)Sun-planet  (back)Ring-planet (back)Figure 7: Large carrier bearingclearance is applied which causesdouble contact. Loads are in-creased significantly. The rotor ismounted so that the three planetsare aligned with a blade. 0 50000 100000 150000 200000 250000 300000 0  10  20  30  40  50  60  70  80force [N]time [s]Planet 1: Tooth Reaction ForcesSun-planet  (front)Ring-planet (front)Sun-planet  (back)Ring-planet (back)Figure 8: Same gearbox as the oneto the left, but the mounting ofthe gearbox relative to the bladesis rotated 60deg. This results in aneven larger load increase.5.1 ConclusionThe coupled dynamic response of the gearbox and wind turbine was investigated during operation in turbulentwind with special emphasis on the double contact hypothesis. Three simulations were run in which only the gearbox differed. The differences in the responses were investigated and the following conclusions are made.High clearance in the planet carrier bearings in combination with low tooth clearance (backlash) increases therisk of double contact. If this occurs, the internal forces on teeth and planetary bearings are significantly increaseddue to an uneven load sharing between the planets. In this condition the radial forces transferred between theplanetary wheels and the ring are approximately added directly to the planet bearing forces in the driving directionand not as a square root sum, as one might expect.The additional planet bearing loads originating from the rotor bending moments are dependent upon how thethree planets in the gearbox are positioned relative to the three blades with a maximum depending upon turbinecharacteristics. This might contribute to the explanation of gearbox failures seen in the past and explain thevariability in failures of apparently identical turbines as the mounting azimuth position is random.References[1] T. J. Larsen, K. Thomsen, and F. Rasmussen. Dynamics of a wind turbine planetary gear stage. In ProceedingsCD-ROM. CD 2. European wind energy conference and exhibition 2003 (EWEC 2003). EWEA, 2003.[2] T. J. Larsen, K. Thomsen, and F. Rasmussen. Dynamics of a wind turbine planetary gear stage. TechnicalReport Risø-I-2112(EN), Risoe, National Laboratory, 2003.[3] J. Lin and Parker R. G. Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration.Journal of Vibration and Acoustics, vol. 121:pp. 316–321, 1999.[4] R. Parker, F. Rasmussen, and T. J. Larsen. Dynamic Modelling and Analysis of a Wind Turbine PlanetaryGear with Tooth Backlash and Bearing Clearance. In Poster presentation (EWEC 2006). EWEA, 2006.[5] Ted Belytschko, Wing Kam Liu, and Brian Moran. Nonlinear Finite Elements for Continua and Structures.John Wiley & Sons Ltd., 2000.

Gearbox loads caused by double contact simulated with HAWC2

http://orbit.dtu.dk/ws/files/5517600/Hansen_paper_EWEA2011presentation.pdf

Gearbox loads caused by double contact simulated with HAWC2

Abstract

Similar works

Full text

Available Versions

Online Research Database In Technology