Paper presented at CIGRE 97 (Conférence Internationale des Grands Rèseaux Electriques), Yokohama, October 29, 1997 Vibrational Behaviour of the Turbogenerator Stator End Winding in Case

of Electrical Failures K. Senske S. Kulig J. Hauhoff, D. Wünsch Siemens AG University of Dortmund Gerhard-Mercator University Mülheim a.d.Ruhr Gesamthochschule Duisburg

1 Abstract In the following the investigations on the electromechanical behaviour of the stator end winding of an air-cooled Siemens tur-bogenerator induced by electromagnetic bar forces is elaborated. The paper starts with an analysis of the sta-tor bar properties as well as the determina-tion of the representative rigidities and equivalent E-modules. This is followed by a presentation of the 3D model for the com-plete end winding, including the brackets, the end plate and bracings as well as a dis-cussion of the appropriate natural frequen-cies. Finally, the time response of the elec-trical bar forces for rated operating condi-tions and the most severe failure, a three-phase fault, are calculated. In an analysis of the total electrical and mechanical system’s forced vibration the bar displacement changing with time and the forces acting in the brackets and bracings are determined.

2 Introduction The turbogenerators belong to the largest and most expensive electrical machines. Their development is always dominated by the attempt to improve the output factor. Improvement has up to now primarily achieved by more capable calculation pro-cedures and the application of modern man-ufacturing methods and better materials. The stator end winding is one of the most intensively stressed unit components (Fig.1). When designing this component it is tried to achieve a vibration level as low as possi-ble, to minimise the appropriate abrasion of the insulation. In addition in case of failure, extreme forces are acting on bandages and brackets that may result in severe damage,

if they were inadequately dimensioned. Due to the very complex structure and the boundary conditions difficult to assess, cal-culations concerning stator end windings have been incomplete up to now. Optimisation with respect to operational behaviour has only been possible on the basis of empirical findings and experimen-tal investigations. The complex set up of the winding bars, the complicated interac-tion of different materials as well as the process engineering treatment of bandages and bars have allowed just rough analytical calculations.

Fig. 1: End Winding of An Air-Coole Turbo- generator Only in the most recent years, the develop-ment of modern, powerful finite-element programs offered a tool to model such com-plex structures and to describe forces and loads by failure studies. Necessary, how-ever, for those calculations are both exten-sive knowledge on the dynamics of large systems and comprehensive practical ex-perience regarding the design and the op-

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eration of turbogenerators. Furthermore, considerable expenditure to set up the cal-culation model and for the calculation it-self has to be taken into consideration. To manage this task, a research project was initiated by Siemens AG in co-operation with the Institute for Design Engineering and Mechanical Conveying and Handling (University of Duisburg). Its objective has been to develop a suitable finite-element based calculation process for the design of stator end windings of large turbogenera-tors. In addition to the calculation of natural modes and frequencies, the analysis of forced vibrations shall be possible. Another target has been to determine the end wind-ing stresses under dynamic operating forces. In order to cover both systems - the electri-cal and the mechanical -, two models had to be set up, the spatial FE-model of the me-chanical structure and the 3D calculation of the time functions of the forces acting on all locations of the end winding. Such an inter-disciplinary task is a new job for the calcu-lator having to establish the exact boundary conditions as well as to assess the effect of both partial systems.

3 Set Up of The End Winding The end winding design varies from manu-facturer to manufacturer and is essentially determined by the cooling type selected for the stator winding. Therefore, in the study three different unit types with different end winding design were investigated. Fig. 1 is a typical example of the end winding of a 170 MVA air-cooled Siemens design tur-bogenerator.This generator has been taken as a reference model when presenting the investigation results, as extensive meas-urements of the end winding vibrations could be performed, thus enabling the com-plete validation of the calculation model. The stator end winding of this turbogenera-tor consists of the involute shaped stator winding bars, the ends of which are brazed in pairs to turns. The individual turns are braced together by bandages out of glass-

silk tapes. The end winding is supported on the pressure plate clamping the stator core, by GFK boards being bolted to the bracket plates. In order to brace the winding bars more effectively and increase the total strength of the entire structure, enclosing GFK rings are applied. Also to these rings the bars are joined by bandages. Following manufacture, the stator core including the windings is impregnated in epoxy resin for HV insulation and subsequently cured re-sulting in a further increasing rigidity.

3.1 Modelling of The End Winding The rigidity of the end winding structure is essentially determined by the set up and geometry of the bar as well as the location and the type of the bandages. The technical state of art of today’s hardware and soft-ware still does not allow to produce a com-plete geometry based end winding model implicitly considering the exact strand de-sign of a bar as well as the bandage charac-teristics. To get an adequate FE model, therefore, the bars and bandages are to be replaced by suitable sub-models to obtain handy model sizes. These sub-models must not essentially modify the vibrational be-haviour and thus the mass and rigidity dis-tribution of the entire model. As the dy-namic properties of the winding bars and bandages were to the most part unknown at the beginning of the research activities, measurements to establish the required characteristics for the model and to validate the sub-models have been indispensable. 3.2 Equivalent Geometry and represen-

tative Rigidity of a Stator Bar The stator bars consist of solid Cu conduc-tors being individually coated with an insu-lating varnish and bonded to each other. The Cu conductors in series are enclosed by an HV insulation. This insulation is achieved by bandaging with glass silk tapes impregnated in epoxy resin and cured. In case of directly gas or liquid cooled bars additional stainless steel ducts are available for the cooling agent. The bar edges of the winding bars describe involute functions being projected on a tapered shell face. Fig.

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2 shows the typical structure of a stator bar with indirect air-cooling.

cross-over insulation

outer corona protection

micalastic insulation

insulation of solid conductors

vanish coat of solid conductors

cross-over filler

Fig. 2: Stator Bar with Indirect Air-Cooling The strand structure described is very com-plex and makes it nearly impossible to pro-vide a detailed FE model of the total end winding. Therefore, the stator bar has to be modelled as a solid body exhibiting real outer dimensions. It is out of a substitute material, having the same dynamic proper-ties as the real bar. The appropriately re-quired reliable values for mass distribution, the rigidities and the damping of the stator bars have not been available at the begin-ning of the investigations. Thus, both meas-urements and FE-calculations were per-formed to determine these values.

3.2.1 Experimental Investigations of The Stator Bar

To measure the rigidity parameters of the winding bars, static bending tests around two axes (flat and high side) on one-sidedly clamped, straight bar parts were performed that had been especially produced for this test. Another free oscillation test helped to verify the results and to additionally assess the dynamic data. Fig. 3 shows the test ar-rangement used.

Fig. 3: Test Arrangement to Measure The Dy-namic Properties of A Stator Bar The most important results of both meas-urements are comprised in Table 1. Measuring Results on Winding Bar TLRI 108/36 Bar dimensions 27.8 mm x 97.6mm x 1300 mm Weight per meter 20.83 kg/m Flat side High side E.I (Nm2) (stat.meas.) 13.5 103 157 103

E.I (Nm2) (free oscill.) 13.7 103 159 103

l. natural frequency (Hz) 25.0 - Damping dimension D 0.016 0.016

Table 1: Measuring Results for The Winding Bar Based on the tests, the product of elasticity module E and moment of inertia I is deter-mined which establishes stator bar rigidity. Comparing the results of both tests shows that under the given assumptions of an one-sidedly clamped bar (Euler-Bernoulli bar ) converting the measured values leads to reproducible results. The deformation of the clamping point has to be taken into consid-eration, however. The Leer damping dimension D was calcu-lated by the logarithmic decrement δ, that is defined as a natural logarithm of the ratio of subsequent vibration amplitudes :

ϑ =⎛⎝⎜

⎞⎠⎟

+

1 1

1nA

A nln

n = number of amplitudes evaluated

D =+

ϑ

π ϑ4 2 2

3

Supplementary tests showed that the Leer damping dimension increases with growing excitation amplitudes. Due to the compo-nents of non-metallic materials, the static and dynamic characteristics differ to only some extent.

3.2.2 High-Resolution FE Model The experimental determination of bar ri-gidities is time and cost intensive; espe-cially in case of new designs measuring is not possible. Therefore, various bar models were investigated covering the effect of the stacked set up in different ways. The result was that good coincidence with the defor-mation behaviour measured could only be reached by the high-resolution FE volume model according to Fig. 4 (1).

Fig. 4: FE Volume Model of A Straight Stator Bar This model considers both the HV insula-tion and all solid conductors with the ap-propriate varnish coats and relevant mate-rial characteristics. The varnish coats are joined with the insulation and the strands. Due to the varnish coat being thin with re-spect to length and the multi-layer structure of the stator winding bar, elements are to be precisely set resulting in high memory re-quirements and long computation times, preventing such the application of this bar model in the FE-model. As the movement of the varnish layers to each other are of minor importance, the contact problem has to not be taken into consideration. Con-fronting the results of measurement to those of computation in Table 2 illustrates that

there is a good coincidence with the high-resolution FE volume model. Measured and calcu-lated rigidity values of the bar specimen

measurement FEM % E lx (flat side) (Nm2) 324 305 -5.9

% E lx (high side) (Nm2) 3.729 3.745 0.4% Table 2: Calculated and meas rigidity data Using this FE model it was possible to bring measurements and calculations in union also for other bar types. Such, the deformation behaviour of newly developed bars can be calculated in advance.

3.2.3 Substitute Bar Model Based on the measured or calculated rigidi-ties, two, in this case different E-modules can be calculated for the flat and high side by inserting the moments of inertia of the FE model. Accordingly, anisotropic mate-rial had to be used as substitute material for the geometry based solid bar, the material matrix of which had to be entered in the element specific, local co-ordinate system. In order to simplify modelling and to in-crease the model’s degrees of freedom, the anisotropic behaviour is not reflected by an anisotropic material but additional shell elements in the boundary faces. Applying the Steiner equations the rigidity values can be determined for this stacked model from the axial plane area moments of the partial faces. The material parameter for the sub-stitute bar can be adapted to the measured values via the thickness of the layer. Veri-fying the parameters of the partial model takes place by comparing the measured and calculated rigidities or the vibrational be-haviour. Table 3 confronts the measured values to the calculated. By coupling the shell elements, the node turning degrees of freedom are not consid-ered. Pre-tests performed have proven that this simplification will not affect the re-sults.

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Natural Frequencies Calculated 1st natural

mode 2nd natural mode

3rd natural mode

Test bar- rigidi-ties of static measure-ment

24.9 Hz 84.3 Hz 156 Hz

Substitute model of straight bar with shell ele-ments

25.2 Hz 86.3 Hz 161 Hz

Table 3: Comparison of calculated and measured bar natural frequencies

3.3 Modelling of Bandages The bandages holding the stator bar struc-ture firm and assuring the connection to the bracket, decisively influence the dynamic end winding behaviour. Therefore, it is of central importance to correctly determine the appropriate rigidity. Just analytical cal-culations of the rigidity values based on known material characteristics are not pos-sible as the effect of the layers on each other and the influence of the epoxy resin impregnation as well as the subsequent cur-ing process cannot be established. There-fore, also in this case measurements are unavoidable.

3.3.1 Measurements on The Bandages To measure bandage rigidity, a servo-hydraulic test stand of the Institute for De-sign Engineering and Mechanical Convey-ing and Handling was used (Fig. 5). The rigidities of the bandages between bars and bracket and bar was measured in a static and dynamic test. In case of the static test, load was slowly but continuously in-creased to fracture. In the vibration test, the dynamic characteristics being relevant un-der practical conditions were determined while load increased periodically. As tem-perature dependency of the characteristics had also to be expected, it was reasonable to perform the investigations at 25°C and 80°C. Thus, the results allow to assess the influence of end winding temperature in-creases on natural vibration behaviour.

Fig. 5: Tearing a Bandage on the Test Stand Table 4 shows that the rigidity values under tensile load are generally less than those under compression. Any heat up results in reduced rigidity values, especially under tensile load. The dynamically measured rigidity values are in any case higher than comparable static values at the same operat-ing point. Characteristic Bandages

between Bars

Bandages between Bracket and Bar

Rigidity under tension and 25°C (106 N/m)

13.6 - 18.4 17.4 - 18.2

Rigidity under pressure and 25°C (106 N/m)

24.0 18.0

Linearized rigidity at 25°C (106 N/m)

14.0 17.8

Rigidity under tension and 80°C (106 N/m)

6.3 9.9

Rigidity under pressure and 80°C (106 N/m)

22.0 16.5

Linearized rigidity at 80°C (106 N/m)

7.1 11.8

Dynamic rigidity at 80°C (106 N/m)

8.9 15.3

Rigidity in Fracture Area at 80°C (106 N/m)

2.6 12.9

Table 4: Results of Rigidity Measurements on Bandages A frequency dependency of the values can-not be shown in the frequency range up to 20 Hz. Moreover, the stress-strain curve indicates definite tendencies of creepage becoming evident in a severe drop of the rigidity values. This behaviour is explicitly

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obvious in case of the bandages between the bars. Comparisons of the measuring results of various bandage shapes show that based on the geometrical dimensions, the conversion of rigidity values of geometrical similar bandages is possible. Thus, on the basis of known measuring results also exact evalua-tions of the characteristics of new bandage shapes can be performed. 4 Spatial FE Model of The End Winding A geometrical volume model to calculate the vibrational behaviour could be set up using the 3D CAD data and the material data known. The above determined charac-teristics for the bars and bandages were applied. Fig. 6 shows the complete FE model structure of the generator investi-gated.

ring bottomstator bar

end windingconnection

Fig. 6: Complete FE Model of The Generator Investigated In addition to the bars and bandages the model comprises the end plate and junction plates. Both were modelled from shell ele-ments. The pressure plate is limiting the system. Its deformation is given by imprinted boundary conditions at the transition to the core. Also the GFK rings, including the relevant bandages, that reinforce the end winding in radial direction, are part of the model. Establishing the real mass distribution in the end winding is possible without any

problems by adapting the density. The ri-gidity values of the bars are given with highest accuracy applying the above intro-duced equivalent bar model. Bandages between the bars or for bracket attachment are modelled by crossed spring elements exhibiting spring rigidity solely in longitudinal axis direction. The rigidity values of these equivalent spring elements are calculated from experimentally deter-mined rigidity data. In this case as a first assumption the rigidity values based on the results of the vibrational tests are taken being averaged by linear regression. Using spring elements has the programmatic ad-vantage that the rigidity values can be modified without any difficulties and it is thus easy to perform parameter studies helping to analyse bandage. When setting up the components it has to be strictly noted that the correct location of all force applica-tion points on the joints is assured.

5 Natural Modes and Frequencies By means of the introduced complete end winding model all natural frequencies and modes of the entire end winding were cal-culated for the frequencies ranging from 0 Hz to 150 Hz. As a tool, the integrated pro-gramme system I-DEAS Masterseries 4.0 was used on HP workstation C100. The calculations in the frequency ranges inves-tigated resulted in 10 natural frequencies with the appropriate natural modes. Table 5 lists the first 5 natural modes. Natural Mode

Natural Frequency

Characteristics

1 77.9. Hz 2-node vibrations, tilting 2 84.9 Hz 4-node vibration 3 103.6 Hz 6-node vibration 4 121.7 Hz 8-node vibration 5 137.4 Hz 10-node vibration Table 5: Natural frequencies and Modes of The End Winding Due to the spatial extension of the end winding and its inhomogenous structure, complicated natural modes come up exhib-iting both relative movements of the indi-vidual bars to each other and bandage strain. Nevertheless, similarities of the

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global deformation to the characteristic natural modes of a ring acc. to Timo-schenko (2) can be established. Thus, e.g. to some extent the 2nd natural mode can be identified as a 4-node vibration, Fig. 7

Fig. 7: Natural Mode of The End Winding In case of this natural mode different radial deformations along the unit axis can be observed. On the core, at those points where

Fig. 8: Natural Mode of The End Winding the bars are rigidly tied to the core, they remain circular and will then continuously change to an ellipse in the area of the bar connections. The highest vibration amplitu-des occur at the bar connections. The 3rd

natural mode behaves in a similar way, Fig.8. This vibration can be considered a 6-node vibration acc. to Timoschenko.

5.1 Verification of The FE Model Decisive for this study and its successful completion was the fact that there was a real generator available as measuring object which could undergo comprehensive meas-uring sequences in the Siemens AG test field to determine natural modes and fre-quencies as well as the force characteristics. In the beginning, models supplied the natu-ral modes measured, the natural frequencies calculated, however, were too low with respect to the values measured. In order to determine the cause for these differences, model improvements and extensive pa-rameter studies were executed. When analysing the natural modes of the initial model, penetrations within the range of the spacers between the bars as well as at the joints to the brackets became evident. The reason was the assumption of linear spring characteristics of the appropriate bandages in the FE model. In the actual end winding spacers are inserted between the bars producing such significantly more rigid joints with respect to compressive load than the modelled bandage characteris-tics. Rigidity will also definitely increase in case of bar and bracket contact. To avoid modelling non-linear characteris-tics, the rigidity was increased by an itera-tive process at the points of penetration until they had vanished. In the initial model the friction of the con-tact pieces inserted between the bars and pre-tightened by bandages had also not been taken into consideration. This contact has, however, as later calculations have shown, an essential effect on the location of natural frequencies. Friction was applied to the model by introducing lateral rigidity values preventing the relative movement of the bars to each other. Both improvements allowed that the calculation results of the reference model could be well adapted to the results measured. The reference model

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supplies for the four-node vibration, the frequency of which was determined as 86 Hz, a frequency of 84.9 Hz.

5.2 Excitability of Natural Modes Only those end winding vibration modes of the total spectre of the natural modes calcu-lated are excited, the spatial characteristics of which are favourable - so-called easily excitable natural modes - and which are near to the excitation frequency. Further-more, vibration size is essentially depend-ent on a coincidence in spatial extension and time characteristics of the appropriate vibration modes and force distribution. The natural frequencies near to the system fre-quency of 50 or 60 Hz and twice the value, 100 or 120 Hz, are of special interest. End windings can be excited by: • electromagnetic forces due to the stator

and rotor currents in stationary and tran-sient conditions at simple and double system frequency,

• foot excitation due to core vibrations at double system frequency and

• foot excitation due to unbalances in the rotating shaft at simple system frequency being transmitted to the end winding via the housing and core.

Accordingly, consideration of all natural frequencies calculated is not reasonable. To find the dominant natural modes, a model response analysis was performed for the total model, introducing an excitation of F F t F f= = < <0 0 1 1 150sin ;ω K N Hz Hz at one point, while the system responses are calculated at various other evaluation points. In the course of these investigations four locations at the top bar, the bottom bar, the bracket and the ring were covered lying opposite to the excitation location. It is thus assured that an individual evaluation point is not situated on a nodal point by accident. Fig. 9 illustrates these positions.

ring

top stator bar

excitation

end windingconnection

bottom statorbar

Y

XZ

Fig.9: Position of Force Excitation and Points of Analysis Based on the transfer functions where the component amplitude is plotted against frequency for an evaluation point, the fre-quencies of the excitable natural modes can be easily established by analysing the local peaks. The amount of mechanical damping of the entire end winding was established in the test field on a real-sized unit in the course of a short-circuit run at variable speed and subsequent free decay of the 4-node vibra-tion to D = 0.016. Modal damping influ-ences the amplitude only, the location of the extreme points in the transfer functions remains unchanged to the most part. The characteristic transfer functions between ring and top bar of the TLRI 108/36 unit have been shown for the three dynamic components in X,Y,Z direction in Fig. 10. Fig. 9 shows the definition of the co-ordinate axes. In the curves all the natural modes given in Table 5 are given. As expected, these natu-ral modes are excited to a different degree as shown by the size of the relevant reso-nance tips. The individual resonance tips are given in the curves for all three co-ordinate directions. The extension, how-ever, is different showing the interaction between excitation direction and the forma-tion of the natural mode evident. Fig. 10

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Fig.10: Transfer Functions between Ring and Top Bar illustrates that natural mode 2 is most sensi-tive to excitation. The resonance tips of natural modes 3, 4 and 5, however, are very distinct, as well, making them easily excit-able. Analysing the vibration modes as well as the transfer functions, makes clear that despite of its inhomogenous structure the end winding behaves like an homogenous solid body in the frequency range up to 150 Hz. The natural modes with distinct single bar vibrations occur in higher frequency ranges only which cannot be excited in the end windings designed. 6 Deformation of The End Winding Un-

der The Influence of Electromagnetic Forces

6.1 Electromagnetic Forces

In both stationary and transient operation electrical currents pass the end winding bars producing electromagnetic forces in interaction with the magnetic field. These excite vibrations in the end winding struc-ture. With respect to the design of the unit data regarding the vibrational behaviour in steady-state operation as well as the most severe failures such as line-to-line or 3-pole terminal short-circuits and faulty synchro-nisation with 180° slip angle is of highest interest. The upcoming forces and deforma-tions have to be taken up by the end wind-ing structure and the brackets, without per-manently damaging the bandages, mounting rings or brackets.

The optimised FE model of the end winding fulfils the prerequisite of analysing the forced system behaviour. It is necessary, however, to specify the time characteristics of the field of force along the involutes of all bars. I.e., in addition to the 3-dimensional analysis of the mechanical structure, calculating the 3-D fields of the electromagnetic forces changing with time is also required. This is a very complex task as the resulting magnetic field in the end winding is produced by both rotor and sta-tor currents and it is additionally influenced by the adjacent magnetic components such as the core in the housing. With respect to this objective a computer programme is used, based on the Biot-Savart law and the reflection of the stator magnetic potential in the rotor. Time functions of the stator currents were determined by means of the NETOMAC (3) programme applying the extended Park generator model. Calculations are quite extensive and the data amount to be han-dled extremely voluminous; thus, in case of the reference generator with 54 turns and 12 sections per involute, each of the 3 force components gets 648 functions. Each of the 1944 functions is described with 1200 points in a period of 1 second. The resulting field of force rotates on cir-cumference of the end winding and de-creases according to the appropriate cur-rents. In Fig. 11 instantaneous pictures of the field of force following a 3-pole termi-nal short-circuit for four moments t = 0.029 s, 0.030 s, 0.031 s and 0.032 s at one plane of the end winding is given. The spatial distribution of the field of force changes continuously, showing the form-tion of a group according to the coil struc-ture of the winding - 12 on circumference.

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t = 0.032 st = 0.031 s

t = 0.030 st = 0.029 s

Fig. 11: Instantaneous Pictures of The Force of Field in One End Winding Plane Following a 3- Pole Terminal Short-circuit The forces have the „clover-leaf distribu-tion“ known from previous investigations and are in no way sinusoid. If the forces in different end winding planes are compared, it becomes evident that they are highest next to the core, decreasing continuously to the bar end. Due to the decaying stator and rotor currents in case of failure, the appro-priate forces will also decrease. Fig. 12 shows the time history of the force compo-nents Fx, Fy, Fz after a 3-pole terminal short-circuit for the evaluation points on the top bar .

Fig. 12: Force Components after 3-Pole

Terminal Short-Circuit Contrary to expectations, the 50 Hz content dominates in the time history of forces at the beginning. They decrease, however, after 0.5 s to 10% of the initial value leav-ing thus, only the 100 Hz content. The 50 Hz component is due to the direct compo-

nents of the current decreasing with the stator time constant TA. This is different to nominal operation where just the 100 Hz component is existent.

6.2 End Winding Deformation After the mechanical model of the end winding was set up and the time functions of the electromagnetic forces were avail-able, it was possible to determine the forced vibrations for the above defined failures. The calculation results are time functions of displacements at all points of the model, on the basis of which the load in all end wind-ing components, especially the brackets, mounting rings and bandages can be estab-lished. The analysis of the individual failures re-quires high calculation and time expendi-tures as the deformation values are to be determined for each element node and each time step in a given time period. On the one hand the time interval has to be small enough to scan the natural frequencies ex-cited. On the other hand the interval has to be long enough to reflect all function tips and to cover the decaying transient switch-on processes. In order to limit the evalua-tion expenditure, it is reasonable to watch the functions of the displacements at repre-sentative positions only. They have to be selected such that they cover the vibrations on circumference and in axial direction and additionally contain the deformation peaks expected. Furthermore, the four locations at the top bar, the bottom bar, the bracket and on the ring, illustrated in Fig. 9, are investi-gated. As an example Fig. 13 shows the time his-tory of the X, Y, Z components of the node displacements at the point of evaluation on the top bar acc. to Fig. 9 for nominal opera-tion. Fig. 14 shows the appropriate curves for the 3-pole terminal short-circuit.

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Fig. 13: Time history of the X, Y, Z components of the node displacements at the point of evaluation on the top bar for nominal operation As expected, the end winding acts mostly as a homogenous ring, resulting in a 4-node vibration according to the relevant excita-tion force with 100 Hz at nominal opera-tion. The maximum amplitude occurs at the front end windings reaching maximum val-ues of about 30 µm. This is in the accept-able range for generators of this type and indicates a rigid end winding design. In case of a 3-pole terminal short-circuit, the peak value of the electromagnetic forces is about 100fold higher than the value at nominal operation. This results in a defi-nitely higher vibration level in Fig. 14.

Fig. 14: Time History of The Node Displacements at The Evaluation Point on The Top Bar for The 3-Pole Terminal Short-Circuit The vibrations rapidly decay, however, due to the severely dropping exciting force (s. Fig. 12) and the high mechanical end wind-ing damping. The maximum vibration am-

plitude of about 1000 µm is also evident at the front end windings 367 ms after the failure and will then drop to 178 µm after 500 ms. It is obvious in this case that in the begin-ning 50 Hz of the exciting force dominate, while 100 Hz come up only after those have decayed. De-exciting the generator pro-vokes that the currents drop to zero after a few seconds. Accordingly, the exciting forces vanish, as well. In this time range the process is characterised by the natural 85 Hz vibration; it decays, however, quickly due to the relatively high damping effect. As observed when analysing the natural modes, the end winding is vibrating like a homogeneous solid body under the effect of the electromagnetic forces. This becomes evident in Fig. 15 showing the deformation of the end winding for four different peri-ods.

t = t0 + 0.83 ms t = t0

t = t0 + 1.67 ms t = t0 + 2.49 ms

Fig. 15: End Winding Deformation under The Effect of Electromagnetic Forces After significant vibration properties have been illustrated in the above figures, table 6 compares the calculated and measured re-sults for all cases of load and evaluation locations. Analysing the vibration amplitudes as well as the appropriate time histories proves that

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the largest movement takes place in radial direction, component R. In this direction also the highest magnetic forces come up while end winding rigidity is lowest. Com-parison with the appropriate measurements were possible for a limited number of points only. The calculated vibration level coincides well with the measured one.

7 Conclusion By applying a 3-D FEM model, a new way for adequately designing end windings has been shown. The multitude of new findings regarding the behaviour of the end winding could only be gained, however, by high expenditures regarding the set up of the mechanical model and the 3D force calcula-tions. Thus, it only reasonable to apply this method when designing larger units or new unit types. For these units today modern

parametric 3D-CAD systems are used for design allowing to apply the geometry to the FE-model. Thus, reduction of the mod-elling expenditure as well as of expenditure regarding the calculation of the electro-magnetic forces is achieved. Uncertainties when laying down the model parameters currently predominantly regard the deter-mination of bandage rigidity as well as the simulation of the non-homogenous conduc-tor bar. Therefore, a multitude of measure-ments has been performed in this investiga-tion to back up the calculation results. With the increasing number of units investigated, the safety of calculation results improves, reducing such the experimental part. Fur-ther more detailed investigations for vari-ous unit types are currently performed to get precise results with respect to local forces and loads.

case of load steady-state operation 3-pole terminal

short circuit evaluation point calculation measurement calculation R

in mm Phi in °

Z in mm

R in mm

Phi in °

Z in mm

R in mm

Phi in °

Z in mm

console 10.5 h 3.0 4.6 1.0 5.5 2.5 - 171.6 245.2 47.7 GFK-ring 9.75 h 3.1 2.8 0.2 3.0 8.0 - 205.6 116.4 11.4 bottom stator bar 9.75 h

15.1 10.7 16.8 16.0 2.5 - 823.9 401.6 652.3

Table 6: Comparison of Calculated and Measured Node Displacements

8 References 1] Wünsch, D. ; Mankenda, N. ; Ambrosi, M.

L. ; Hauhoff, J.: Dynamisches Betriebsver-halten des Wickelkopfes vom Turbogenera-tor TLRI 108/36 der Siemens AG : 2. Zwi-schenbericht 1996. Gerhard-Mercator-Universität - GH Duisburg, Konstruktions-lehre und Fördertechnik, 1996 - Unveröf-fentlichter Bericht

[2] Timoschenko S., Joung D.H., Wearer.W.: Vibration Problems in Engineering, New York, Wiley & Sons, 1974 [3] B. Kulicke:

Digitalprogramm NETOMAC zur Simmu-lation elektromechanischer und

-magnetischer Ausgleichsvorgänge in Drehstromnetzen. Elektrizitätswirtschaft 78 (1979), S. 18-23

[4] H. Berger, W. Fritz, P. Juen: Wickelkopfbeanspruchung bei Fehl-synchronisation von Turbogeneratoren. ETZ-A Bd. 96 (1975) H. 4, S. 188-194.

[5] H. Berger, T.S: Kulig, D. Lambrecht: Turbosätze bei elektrischen Störfällen- Modellierung, Beanspruchungen, Schutzmaßnahmen. Paper 69 presented at the AIM International Seminar for Modern Power Plants, Lìege, Belgium, Oct. 26- 30, 1981

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