1、02FTM4Multibody-System-Simulation of DriveTrains of Wind Turbinesby: B. Schlecht, T. Schulze and J. Demtrder,Dresden University of TechnologyTECHNICAL PAPERAmerican Gear Manufacturers AssociationMultibody-System-Simulation of Drive Trains ofWind TurbinesB. Schlecht, T. Schulze and J. Demtrder, Dresd
2、en University of TechnologyThestatementsandopinionscontainedhereinarethoseoftheauthorandshouldnotbeconstruedasanofficialactionoropinion of the American Gear Manufacturers Association.AbstractDimensioningofwindturbinesadequatelytotheirexpectedoperationloadingespeciallyforOff-Shore-Applicationswith se
3、veral MW output power requires a very good knowledge of the dynamic loads of all possible operationalsituations.Toreducetheneedofriskyandexpensivemeasurementsitissuggestedtostudythedynamicbehaviorofthewind turbine drive train by using the Multibody-System-Simulation. The actual possibilities of this
4、 method aredemonstratedinthefirstpartofthispaperforabuiltwindturbineof600kWpoweroutput.Thesecondpartdealswiththemodelingofasingle-stageplanetarygearboxina750-kW-Turbinetakingalsointoaccounttheparameterexcitationofthe tooth contact. This gear box model covers all relevant aspects to analyze drive tra
5、ins of wind turbines up to 3 MWpoweroutput.Themodelexpansiontoatwo-stageplanetarygearboxallowsthedynamicanalysisofwindturbineswithanoutputhigherthan4MW.Furtherresearchworkinthenearfuturewillconcentrateontheconnectionbetweenthewindsimulation models for the rotor and drive train on the one hand and th
6、e coupling with the generator and the electricalnetwork on the other hand with special regard to the control concepts.Copyright2002American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Virginia, 22314October, 2002ISBN: 1-55589-804-11 Multibody-System-Simulation of Drive Train
7、s of Wind Turbines Prof. Dr.-Ing. Berthold Schlecht, Dipl.-Ing. Tobias Schulze, Dipl.-Ing. Jens Demtrder Institute of Machine Elements and Machine Design Dresden University of Technology, Mommsenstrasse 13, D-01062 Dresden, Germany E-Mail: schlecht.bertholdimm.tu-dresden.de tobias.schulzeimm.tu-dres
8、den.de NEG Micon A/S, Alsvej 21, DK-8900 Randers, Denmark E-Mail: jdeneg-micon.dk Introduction and Task During the last years the share of wind power in relation to the total energy production in Germany has increased continuously with an annual growth of 35 %. The main reasons are the Eco-friendlin
9、ess and a steady improvement of the used technology in connection with a continuous increase of the power output of the single wind turbine. 10 years ago the power output per unit was less than 300 kW, todays standard turbines have an power output of 1.5 MW. Some manufacturers have put into operatio
10、n turbines of 2.5 MW and the whole wind industry branch works on the development of turbines with 5 to 6 MW power output which will only be suitable for Off-Shore-applications due to their large size. Because of the large power output increase the turbines have reached dimensions where operational i
11、nfluences have to be taken into account that are not comparable to stationary industrial plants. That means in detail high load peaks, load alternation influences in the drive train, high light load periods and aeroelastic vibrations at the rotor blades. In every case especially the drive train has
12、to withstand very high dynamic loads because it connects directly the rotor (transforming the wind energy in rotational energy) with the generator (transforming the rotational energy into electrical energy). That means that both the dynamics of the wind loads and the dynamics of the electrical netwo
13、rk act on the drive train. Very often deformations of the tower and the nacelle structure occur leading to additional loads on the drive train 1, 2. A prerequisite for dimensioning a drive adequately for the expected strain is to know the kind of strain action as a function of time. According to the
14、 “Richtlinie fr die Zertifizierung von Windkraftanlagen of the Germanischer Lloyd (GL) the representative cumulative frequency distribution of the location has to be taken into account 3. It can be determined by measurement or calculation. It is easiest to measure the behavior under operational stra
15、in in the case of a built machine. In the past, measurements to this effect were quite frequently made on wind turbines 4, 5. The high quality of these measurements does, however, require an enormous technical expenditure - apart from the fact that the object to be measured must be available. In the
16、 case of a projected installation or a new or further development, this kind of measuring technique for determining strain is not possible, as there is no object available for measurements during the starting phase. According to the GL-Guideline 3 the wind turbine could be dimensioned with a simplif
17、ied single-stage cumulative frequency distribution and taking into account dynamic loads by the application factor kAanalogous to DIN 3990 6. In general the application factor amounts to kA= 1,5, for rotors with three blades it is allowed to use kA= 1,3 3. Investigations of drive trains in other app
18、lications but with comparable power output have shown in the past, that the lump sum consideration of dynamic loads by an application factor leads very often to unsatisfactory results 5, 7, 8. There is the general danger of wrong dimensioning. In the case of a wind turbine the over dimensioning is n
19、ot desirable because of the light weight design requirements. On the other hand a dimensioning of too low capacity causes failures of the drive train with production losses and high repair and maintenance costs. To avoid this problems 2one can either resort to analogy in order to obtain suitable loa
20、d assumptions, or derive conclusions from comparable kinematic chains to determine the strains to be expected, or use a suitable simulation procedure in order to accurately predict the operational strain that may occur. Furthermore simulation has the advantage that special load cases can also be con
21、sidered, cases which do not occur in normal operation, but are important for dimensioning, as they could, under certain circumstances, destroy the drive train or the entire turbine 9, 10, 11, 12, 13. Especially the last aspect will be of more significance for the dimensioning of wind turbines for Of
22、f-Shore-Applications. Therefore the following example of a wind turbine with 600 kW output rate (Fig. 1) should demonstrate the actual possibilities of the Multibody-System-Simulation to determine the dynamic behavior of drive trains. Creating a simulation model of the drive train Technical installa
23、tions are oscillatory continua with infinitely many degrees of freedom. A detailed investigation of a limited number of degrees of freedom is, as a rule, entirely sufficient for analyzing dynamic behavior. Consequently, it is sensible to look at a mathematical model that reflects the relevant featur
24、es of the real technical system as accurately as possible. Basically, we differentiate between models with distributed parameters - for example, elastic bodies in continuum mechanics - and models with concentrated parameters 14. For models with concentrated parameters, characteristics such as inerti
25、a, elasticity, viscosity and force of the real system are attributed to individual discrete elements. With the help of these discrete elements which comprise the rigid body, the massless spring and the massless damper, as well as drive and reaction forces or moments, it is possible to build general
26、three-dimensional multi-body-systems. Any restrictions on movement (linkages) between the bodies are realized with joints with specific properties. Such mechanical systems are described mathematically by ordinary coupled differential equations and algebraic equations. Fig. 1: Investigated Wind Turbi
27、ne NEG-Micon Type NTK 600/43 3 As mentioned at the beginning, the expected dynamic stresses on the drive train of a wind turbine in various load cases are to be investigated with the help of a simulation calculation. To achieve this purpose, the simulation model to be prepared must first of all sati
28、sfy the following requirements: The model must represent the conditions of the real system as accurately as possible. The connection between the real system and the reduction in the model should be noticeable at each point. It should be possible to calculate the system parameters on which the model
29、is based from the technical documents or from the real system itself with sufficient accuracy. A further essential aspect when making a simulation model is the choice of the system boundary. As the system boundary separates the simulation model from its surroundings, determining the system boundary
30、- and with it, dividing the system parameters in internal and external parameters - is of decisive influence on the complexity of the model. The external system parameters are described as independent quantities acting without being under any influence from the system. Owing to these independent qua
31、ntities the respective system answers for the interdependent state quantities appear inside the system boundary. The investigated drive train of the wind turbine is shown schematically in Fig. 2. Starting from the rotor, the torque is transmitted via a three-stage parallel axis helical gear with a f
32、langed on brake disc and a coupling to the generator with a total gear ratio of 1:56. Fig 3. shows the multibody simulation model ready for calculation with the program SIMPACK 15. The specialty of the model is that additionally to the torsional degree of freedom the translational degree of freedom
33、in axial direction has been considered. This feature allows the calculation of the inner reaction forces in the gear box, resulting from the external wind loads at the rotor and the electrical loads at the generator. On the basis of these forces the relevant cumulative frequency distributions for th
34、e fatigue strength calculation of each shaft could be estimated. Furthermore external deformations of the surrounding structure and their influence on the drive train can be taken into account. Especially this aspect and the consideration of translational degrees of freedom in the gear box are of gr
35、eat advantage in comparison to the classical torsional vibration analysis because this model contains much more information regarding an adequate dimensioning due to the load data and the dynamical tuning of the drive train. Fig. 2: Schematic sketch of the drive train yz4Simulation ResultsFlex4Measu
36、red Dataof Wind TurbineMatlab/Simulink-Model for Characteristic Curve of Generator and to Simulate Switch Operations and Preparation of Measured DataSimpack-ModelRotationalSpeedRotorGeneratorTorqueBrakeTorqueAxial ForceRotationalAngleRotorRotationalSpeedGeneratorEvaluation and Visualisation of the S
37、imulationProgram SimpackFig. 3: Simulation model of the drive train On the generator side, the system boundary is on the rotor, i.e. the air gap moment on the machine is generated over a characteristic line that results from an evaluation of Klos equation for the asynchronous machine: KippMKippKipp2
38、MMssss=+Where Mmis the air gap moment on the machine, Mkippthe overturning moment, s the slip and skippthe pull-out slip. Any reactions from non-mechanical system components are in that way coupled to mechanical quantities. Even if the simulation program SIMPACK allows modeling the electrical machin
39、e in detail, we deliberately used the simplified approximation of the generator air gap moment through Klos equation, as the subject of the investigation is the stationary operation of the wind turbine and not its acceleration process. On the load side the system boundary is situated at the rotor hu
40、b. The reaction forces and moments at the hub have been calculated by the wind turbine manufacturer using a special wind simulation program FLEX 4 16. Another program for that purpose is called BLADED 17. Fig. 4 shows the calculated moments and forces at the rotor hub for a wind speed of 23 to 25 m/
41、s. Finally it has to be pointed out that the model creation represents the main part of the simulation procedure. The quality and the accuracy of the simulation model are mainly dependent on the know-how of the engineer and his special knowledge in this area of application. In the meantime the first
42、 attempts have been undertaken to create a model computer-aided 18. Results of the simulation of the drive train To start with, we made an analysis of natural frequencies by means of the linearized model. Discretizing the drive train into rigid masses and massless rigidities allows an exact assignme
43、nt of frequencies to the respective component of the drive train. This allows to draw conclusions on the excitability of undesirable vibrations 19. Table 1 shows the natural frequencies of the drive that are relevant for vibrations and gives their relative position in the drive train. The right colu
44、mn shows the calculated frequencies for a simple torsional model. All frequencies are of a torsional character. With this model it is only possible to determine the frequencies of 4.84 Hz and 67.13 Hz as the lowest Eigenfrequencies. Giving the model additional degrees of freedom in radial and axial
45、direction leads to a more complex model with more eigenfrequencies. The values for this model are given in the middle column. This model contains all frequencies appearing in the torsional model but additionally it contains a large number of low frequencies that are combined modes (translational and
46、 torsional) of the elements rotor hub, main shaft and gear box. To give an example, the natural frequency No. 4 of 4.84 Hz respectively 3.43 Hz is rotational and can be attributed to the main drive shaft. All other natural frequencies up to 59.93 Hz are combined modes 5(translational and torsional)
47、of the elements rotor hub, main shaft and gear box. It can be concluded from the natural shapes that the natural frequencies up to 67.13 Hz can be excited by the process. That means that an excitation from the wind load or due to the number of rotor blades and the circumferential speed would cause u
48、nwanted vibrations with the corresponding high amplitudes leading to an additional internal load on the drive train. Moments at Rotor kNm 2802602402002201801603002001000-100-200-3002001000-100-200-3000 10 20 30 40 50 60MxMyMzTime sec Forces at the Rotor kN 0 10 20 30 40 50 60701408090100110120130250
49、-250020015010050-50-100-150-20060708090100140110120130FxFyFzTime sec Fig 4: Simulated load input (moments and forces) at the rotor, calculated with FLEX 4 6 Table 1: Relevant natural frequencies of the drive train No. of Eigen-frequency SIMPACK-Model Hz Torsional Model Hz 1 0 02 1,65 - 3 3,05 -4 3,43 4,84 5 23,09 - 6 23,22 -7 24,98 - 8 36,16 -9 59,93 - 10 67,36 67,13 11 130,10 - 12 202,80 -13 242,62 236,16 14 259,11 -15 390,60 380,64 16 573,72 566,3017 621,83 604,73 18 1527,82 1513,66 19 1975,95 2039,40 20 2422,31 2412,34
