Claims:
We claim
1. A stationary induction apparatus comprising
2. A stationary induction apparatus as claimed in claim 1, in which said helical winding is formed with a plurality of duct spacers interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially bisecting point and its neighboring portions of said helical winding is greater than that of said duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially bisecting point and its neighboring portions of said helical winding.
3. A stationary induction apparatus as claimed in claim 1, in which said helical winding is formed with a plurality of duct spacers interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially trisecting points and their neighboring portions of said helical winding is greater than that of the duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially trisecting points and their neighboring portions of said helical winding.
4. A stationary induction apparatus comprising
5. A stationary induction apparatus as claimed in claim 4, in which each of said plurality of cylindrical winding layers of said multilayer cylindrical winding is formed at a substantially uniform winding pitch in the axial direction of the winding, and said helical winding is formed with a plurality of duct spacers interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially bisecting point and its neighboring portions of said helical winding is greater than that of the duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially bisecting point and its neighboring portions of said helical winding.
6. A stationary induction apparatus as claimed in claim 4, in which each of said plurality of cylindrical winding layers of said multilayer cylindrical winding is formed at a substantially uniform winding pitch in the axial direction of the winding, and said helical winding is formed with a plurality of duct spacers interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially trisecting points and their neighboring portions of said helical winding is greater than that of the duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially trisecting points and their neighboring portions of said helical winding.
7. A stationary induction apparatus comprising
8. A stationary induction apparatus as claimed in claim 7, in which said low voltage helical winding is formed of a plurality of insulated conductors bundled in the radial direction and helically wound in a plurality of turns, and a plurality of duct spacers are interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially bisecting point and its neighboring portions of said low voltage winding.
9. A stationary induction apparatus comprising
10. A stationary induction apparatus as claimed in claim 9, in which said low voltage helical winding is formed of a plurality of insulated conductors bundled in the radial direction and helically wound in a plurality of turns, and a pluraltiy of duct spacers are interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially bisecting point and its neighboring portions of said low voltage winding.
11. A stationary induction apparatus comprising
12. A stationary induction apparatus as claimed in claim 11, in which said low voltage helical winding is formed of a plurality of insulated conductors bundled in the radial direction and helically wound in a plurality of turns, and a plurality of duct spacers are interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially bisecting point and its neighboring portions of said low voltage winding.
13. A stationary induction apparatus comprising
14. A stationary induction apparatus as claimed in claim 13, in which said low voltage helical winding is formed of a plurality of insulated conductors bundled in the radial direction and helically wound in a plurality of turns, and a plurality of duct spacers are interposed in the radial direction between the bundles of said plurality of insulated conductors, and the axial thickness of the duct spacers interposed between the bundles of said plurality of insulated conductors at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the bundles of said plurality of insulated conductors at portions other than said axially bisecting point and its neighboring portions of said low voltage winding.
15. A stationary induction apparatus comprising
16. A stationary induction apparatus as claimed in claim 7, in which said low voltage discal winding is formed of a stack of a plurality of discal coil sections interconnected in series with a plurality of duct spacers interposed therebetween, said discal coil sections being formed of insulated conductors wound in the radial direction in a plurality of turns, and the axial thickness of the duct spacers interposed between a plurality of discal coil sections at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the discal coil sections at portions other than said axiall bisecting point and its neighboring portions of said low voltage winding.
17. A stationary induction apparatus comprising
18. A stationary induction apparatus as claimed in claim 17, in which said low voltage discal winding is formed of a stack of a plurality of discal coil sections interconnected in series with a plurality of duct spacers interposed therebetween, said discal coil sections being formed of insulated conductors wound in the radial direction in a plurality of turns, and the axial thickness of the duct spacers interposed between a plurality of discal coil sections at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the discal coil sections at portions other than said axially bisecting point and its neighboring portions of said low voltage winding.
19. A stationary induction apparatus comprising
20. A stationary induction apparatus as claimed in claim 19, in which said low voltage discal winding is formed of a stack of a plurality of discal coil sections interconnected in series with a plurality of duct spacers interposed therebetween, said discal coil sections being formed of insulated conductors wound in the radial direction in a plurality of turns, and the axial thickness of the duct spacers interposed between a plurality of discal coil sections at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the discal coil sections at portions other than said axially bisecting point and its neighboring portions of said low voltage winding.
21. A stationary induction apparatus comprising
22. A stationary induction apparatus as claimed in claim 21, in which said low voltage discal winding is formed of a stack of a plurality of discal coil sections interconnected in series with a plurality of duct spacers interposed therebetween, said discal coil sections being formed of insulated conductos wound in the radial direction in a plurality of turns, and the axial thickness of the duct spacers interposed between a plurality of discal coil sections at the axially bisecting point and its neighboring portions of said low voltage winding is greater than that of the duct spacers interposed between the discal coil sections at portions other than said axially bisecting point and its neighboring portions of said low voltage winding.
Description:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to stationary induction apparatus.
2. Description of the Prior Art
Stationary induction apparatus such as transformers and reactors of large capacity employed in power circuits comprise essentially an iron core, windings disposed to surround the iron core, and electrical insulators for electrically insulating the windings from the iron core as well as one winding from the other.
Commonly, the electrical insulator described above is formed from paper comprised essentially of fibrous materials. For example, Kraft paper, Manila paper or pressboard is generally used to form such members as insulating coverings for conductors of individual coils constituting the wiring, insulating cylinders disposed between the windings, insulating rings disposed above and beneath the windings and interposed between the core fastening members and the yokes of the iron core, and inter-coil duct pieces disposed radially between the coils in suitably spaced relation from each other.
When short-circuit trouble occurs in the power transmission system for the stationary induction apparatus formed from materials as described above, an excessively large short-circuit current flows through the related winding of the apparatus, and this short-circuit current cooperates with the radial component of leakage flux in the apparatus to impart an excessively large electromagnetic force to the winding in its axial direction. The axial electromagnetic force acts to create alternate compression and vibration between the coils in the winding and the inter-coil duct pieces as well as between the winding and the insulating rings. Due to the vibration created in this manner, gaps are produced between the coils and the inter-coil duct pieces as well as between the upper and lower ends of the winding and the insulating rings, and because of the presence of the gaps, an excessively large impact is imparted between the coils and the inter-coil duct pieces as well as between the upper and lower ends of the winding and the insulating rings in the succeeding period of vibration.
It is known that the winding in the electrical apparatus of this kind has the natural vibrations or the natural frequencies of the first order, second order and third order which lie in the vicinity of 30 cycles per second, 70 cycles per second and 120 cycles per second, respectively. Thus, these natural frequencies of the winding are very close to the power source frequency, 50 hertz or 60 hertz, and twice its double frequency, 100 hertz or 120 hertz. Since the natural frequencies of the winding are thus very close to the power source frequencies which impart vibration to the winding, the displacement due to the vibration is quite large, and in some cases, resonance takes place to further enlarge the above displacement. As a result, the winding is subject to permanent plastic deformation due to the abovedescribed impact or displacement until finally it is broken.
The inter-coil duct pieces and the insulating rings described above must have the function of insulating the individual coils from each other and insulating the windings from the earth, and at the same time, the function of mechanically holding the individual coils and the entire windings. However, these inter-coil duct pieces and insulating rings have a certain limit in their mechanical strength because of the fact that they consist essentially of paper material. As a result, these intercoil duct pieces and insulating rings are quite weak against the electromagnetic force and impact described above and are liable to move out of their predetermined position to be easily broken down. The collapse of the duct pieces and insulating rings would further promote the deformation of the winding.
SUMMARY OF THE INVENTION
It is therefore an object of the present invention to provide a stationary induction apparatus having a winding structure which does not easily deform even if a short-circuit current occurring in an associated system may flow into the winding.
Another object of the present invention is to provide a stationary induction apparatus having means for shifting the vibration mode of an inner one of the windings to a higher order so that the winding may not resonate with the frequency of a power source and the frequency which is twice the power source frequency.
The present invention contemplates the provision of a stationary induction apparatus having a mechanically stable and strong winding in which, on the basis of the result of analysis of the electromagnetic force applied to the winding in the case of short-circuiting, the number of natural vibrations of the winding is so set that it is higher than the frequency of a power source and is suitably shifted from the value which is twice the power source frequency in order to thereby suppress the axial vibrational compression and displacement of the winding due to impartation thereto of the electromagnetic force.
In accordance with the present invention, the ampereturn distribution in the axial direction of the winding may be varied so that the electromagnetic force developed in the axial direction of the winding has a distribution with a mode of the fourth or higher order in order thereby to attain the effect similar to that which is attained by increasing the number of natural vibrations of the winding itself.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a vertical sectional side elevational view showing part of the winding structure wound around an iron core in the stationary induction apparatus of the present invention.
FIG. 2 is a sectional view taken on the line II--II in FIG. 1.
FIG. 3 is a diagrammatic illustration of leakage flux distribution in a two-winding transformer.
FIGS. 4a, 4b and 4c are diagrammatic illustrations of the distribution of electromagnetic forces developed in the axial direction of the winding when short-circuit takes place in an associated system.
FIGS. 5a and 5b are diagramatic illustrations of the mode of electromagnetic force distribution and the form of normal vibrations of various orders, respectively.
FIGS. 6a and 6b are diagrammatic illustrations of the distribution of the participation factor Ki corresponding to the mode of various orders.
FIGS. 7a, 7b through 9a, 9b and FIG. 10 are diagrammatic illustrations of various arrangements of the low-voltage winding according to the present invention and corresponding distributions of the electromagnetic force developed in the axial direction of the winding, respectively.
FIG. 11 is an illustrative drawing showing the arrangement of a helical winding and the local increase of the axial pitch of the bundles of the helical winding in an example of the embodiment of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring to FIGS. 1 and 2 showing the internal structure of a two-winding transformer, a pair of concentric windings 4 and 7 are disposed to surround an iron core 1. As is commonly known, the transformer iron core 1 comprises a leg portion 1a which is assembled by laminating a multiplicity of steel sheets and yoke portions 1b which are assembled by laminating a multiplicity of concentric iron sheets and are magnetically coupled to the top and bottom of the leg portion 1a. The leg portion 1a and yoke portions 1b are fastened together by suitable means. An insulating cylinder 2 of pressboard fits on the leg portion 1a of the iron core 1. A plurality of rod-like insulating spacers 3, commonly made of pressboard, are bonded to the outer peripheral surface of the insulating cylinder 2 in suitably parallelly spaced relation from each other.
The low-voltage winding 4 of the transformer is disposed to surround the leg portion 1a of the iron core 1 with the spacers 3 interposed therebetween and comprises a multiplicity of coils 41, 42, 43, . . . . . 4i, 4i+1, . . . . . 4n-2, 4n-1 and 4n wound in its axial direction. These coils are successively electrically connected with each other to form a discal winding, or insulated conductors 4a constituting the individual coils are bundled and continuously wound to form a helical winding. A plurality of inter-coil duct pieces 51, 52, 53, . . . 5i, 5i+1, . . . . . 5n, and 5(n+1) are radially disposed between the adjacent coils in suitably spaced relation from each other. The inner end of each duct piece situated on the side of the inner periphery of the coil makes a dovetail joint with the corresponding insulating spacer 3. Insulating layers 6 comprising a plurality of concentric insulating cylinders are disposed to surround the outer peripheral surface of the low-voltage winding 4 so that oil gaps formed between the adjacent cylinders and the insulating cylinders constitute the main insulation.
The high-voltage winding 7 is disposed to surround the main insulation and is commonly in the form of a discal winding or a cylindrical winding. In the illustrated embodiment, the high-voltage winding 7 is in the form of a discal winding. The high-voltage winding 7 comprises an alternate arrangement of coils 71, 73, . . . 7n-2 and 7n formed by winding insulated conductors 7a from the outer periphery toward the inner periphery of the winding and coils 72, 74, . . . 7n-3 and 7n-1 formed by winding the insulated conductors 7a from the inner periphery toward the outer periphery of the winding. A plurality of inter-coil duct pieces 81, 82, 83, . . . 8n-1, 8n and 8n+1 are radially disposed between the adjacent coils in suitably spaced relation from each other. The inner end of each duct piece situated on the side of the inner periphery of the coil makes a dovetail joint with a corresponding one of insulating spacers 9 parallelly disposed on the outermost layer of the main insulation.
Shielding rings 10 are disposed on the upper and lower ends of the low-voltage winding 4. Shielding rings 11 are disposed on the upper and lower ends of the high-voltage winding 7. These shielding rings 10 and 11 are made by covering a conductor with an insulating tape. Insulating rings 12 are interposed between the yoke portions 1b of the iron core 1 and the shielding rings 10. Insulating rings 13 are interposed between the yoke portions 1b of the iron core 1 and the shielding rings 11. These insulating rings 12 and 13 support insulatingly the low-voltage winding 4 and the high-voltage winding 7 in their vertical direction.
FIG. 3 shows the manner of distribution of leakage flux in a two-winding transformer as described above. With the leakage flux distribution as such, when a short-circuit current flows into one of the windings, a large electromagnetic force is developed in the internally disposed low-voltage winding 4 and the externally disposed high-voltage winding 7. Such an electromagnetic force is commonly of the order of several hundred tons.
FIG. 4 shows the distribution of the electromagnetic force developed in the axial direction of the low-voltage winding 4. In FIG. 4a, it will be seen that electromagnetic forces f1, f2, f3, f4, . . . fi, fi+1, fi+2, . . . . fn-1 and fn are developed in the respective coils 41, 42, 43, 44, . . . 4i, 4i+1, 4i+2, . . . 4n-1 and 4n when the short-circuit current flows into the winding. The electromagnetic forces developed in the coils have a distribution as shown in FIG. 4b from which it will be seen that the electromagnetic forces are substantially opposite to each other on opposite sides of the central portion of the winding 4 and are maximum at the upper and lower ends of the winding 4 where the radial component of the leakage flux is large. However, the electromagnetic force developed in the individual coil is transmitted intact to the adjacent coils since the inter-coil duct pieces 51, . . . 5n+1 are generally merely interposed between the adjacent coils. As a result, the electromagnetic forces described above are combined together and the resultant force produces a maximum compression at the central portion of the winding 4. The resultant force is distributed in the form of Σf as shown by the solid line in FIG. 4c in which the vertical axis represents the axial length L of the winding 4 and the horizontal axis represents the developed mechanical force F.
In the case of a transformer, for example, its electromagnetic force distribution takes generally the form of the second order corresponding to the distribution of the radial components of the leakage flux. Therefore, the vibration mode of the second order corresponding to this manner of distribution is most liable to appear. Since the number of natural vibrations in the case of the vibration mode of the second order lies in the vicinity of 70 cycles per second as described previously and is thus close to the power source frequency, the displacement due to vibration becomes correspondingly greater.
Now, a participation factor Ki is used to define the relation between the electromagnetic force distribution and the mode of natural vibration of respective orders. The participation factor Ki represents the rate at which the electromagnetic force distribution participates in the vibration mode of the its order and can be given by the following equation: ##SPC1##
where F(x) is the electromagnetic force distribution, and Ui(x) is the mode of natural vibration of the ith order, that is, the normal mode of vibration of the ith order.
The participation factor Ki can be increased by bringing the mode of F(x) as close to the mode of Ui(x) as possible. FIG. 5 is a diagrammatic illustration of the above relation. FIG. 5a shows the mode of the electromagnetic force distribution F(x) and FIG. 5b shows the normal mode of vibration of the ith order, for example, those of the first order, second order and fourth order. In FIGS. 5a and 5b, x represents the axial length of the winding. In FIG. 5a, the mode shown by the solid line represents the electromagnetic force distribution of the second order in a conventional transformer, while the mode shown by the one-dot chain line represents the electromagnetic force distribution of the fourth order which is improved in accordance with the present invention.
Since the vibration mode tends to be induced in relation to the electromagnetic force distribution, a vibration mode of higher order can be developed when the electromagnetic force distribution is shifted to its higher order. On the basis of the above fact, the vibration mode can be shifted to a number of natural vibrations of higher order by varying the electromagnetic force distribution while keeping the numbers of natural vibrations of various orders unchanged. In such an arrangement, the electromagnetic forces cancel each other at the numbers of natural vibrations of lower orders, and the displacement of the winding can be made correspondingly smaller. This is equivalent to the effect as when the number of natural vibrations of the winding is increased.
In FIG. 6a there is shown the state in which the number of natural vibrations of the winding itself is shifted to a higher order without varying the electromagnetic force distribution as well as the participation factor Ki. The solid curve in FIG. 6a represents the distribution of the participation factor Ki in a conventional transformer and it will be apparent that the participation factor has a peak in the vibration mode of the second order. The distribution of the participation factor Ki can parallelly be shifted toward a higher order by shifting the number of natural vibrations of the winding toward its higher order. The dotted curve in FIG. 6a shows the fact that a peak appears in the vibration mode of the third order, while the one-dot chain curve shows the fact that a peak appears in the vibration mode of the fourth order.
It will be understood that, according to the present invention, the vibration mode can be shifted toward a high order by increasing the number of natural vibrations of the winding. It will be further understood that the same purpose can be attained by varying the electromagnetic force distribution in a manner as described above so as to improve the vibration mode in order that the peak is shifted toward a higher order. The latter state is shown in FIG. 6b. More precisely, the peak of the participation factor Ki is shifted from its previous position in the vibration mode of the second order to a position in the vibration mode of the fourth order so that consequently the participation factor corresponding to the vibration mode of the second order is reduced.
It will be understood from the above description that the displacement or force can be decreased as a whole by arranging in such a manner that the winding has a vibration mode of the fourth or higher order.
FIGS. 7 through 9 illustrate a few forms of a two-winding transformer employing the above arrangement.
In a two-winding transformer shown in FIG. 7a, a low-voltage winding 16 is disposed around a leg portion 14a of an iron core 14 with an insulating cylinder 15 interposed therebetween, and a high-voltage winding 18 is disposed outside of the low-voltage winding 16 with an insulating cylinder 17 forming the main insulation interposed therebetween. Both these low-voltage and high-voltage windings 16 and 18 are supported at their upper and lower ends on an upper yoke portion 14b and lower yoke portion 14c of the iron core 14 through clamp rings and insulating rings. More precisely, the low-voltage winding 16 is supported at its upper and lower ends on the upper ad lower yoke portions 14b and 14c of the iron core 14 by means of clamp rings 19a, 19b and insulating rings 20a, 20b respectively. The high-voltage winding 18 is also supported at its upper and lower ends on the upper and lower yoke portions 14b and 14c of the iron core 14 by means of clamp rings 21a, 21b and insulating rings 22a, 22b respectively.
These low-voltage and high-voltage windings 16 and 18 consist of a multiplicity of coil sections formed by winding insulated conductors in a manner similar to that shown in detail in FIGS. 1 and 2. Inter-coil duct pieces are interposed between these coil sections to provide a passage of insulating oil between the coil sections so as to cool the windings and ensure required insulation. Referring to FIG. 7a, the low-voltage winding 16 consists of a multiplicity of coil sections 24 formed by insulated conductors 23, and inter-coil duct pieces 25 are interposed between these coil sections 24. Similarly, the high-voltage winding 18 consists of a multiplicity of coil sections 27 formed by insulated conductors 26, and inter-coil duct pieces 28 are interposed between these coil sections 27.
In FIG. 7a, the inter-coil duct pieces 25a located in the axially middle portion of the low-voltage winding 16 have a greater thickness along the axial direction of the winding as compared with the remaining inter-coil duct pieces 25 located close to the upper and lower ends of the winding so that the coil sections 24 in this portion are spaced apart from each other by a larger gap than those in the remaining portions. In addition, the number of turns of the insulated conductors forming the coil sections 24 in this portion of the winding having such an enlarged gap is reduced compared with the number of turns in the remaining portions so that the ampereturn product of the middle portion of the low-voltage winding 16 is reduced compared with that of the corresponding portion of the high-voltage winding 18.
Such a local reduction in the ampere-turns of the middle portion only of the low-voltage winding 16 disposed opposite to the high-voltage winding 18 radially inside the latter has an advantage in that the electromagnetic forces developed in the axial direction of the low-voltage winding 16 can be distributed in a manner as seen in FIG. 7b and an improved vibration mode of the fourth order can be obtained in which the mode of the vibration mode lies at exactly the central portion of the winding. That is, independent modes appear in the upper and lower portions of the mode and the electromagnetic forces are distributed in the upper portion in directions opposite to each other as shown by F1 and F2, while the electromagnetic forces are distributed in the lower portion in directions opposite to each other as shown by F3 and F4. By this arrangement, therefore, the number of natural vibrations of the winding becomes considerably high compared with the number of exciting vibrations due to the electromagnetic forces and the displacement due to vibration can be reduced considerably. Thus, the electromagnetic forces developed in the winding in the event of a short-circuit can be reduced.
In FIG. 7a, the reduction in the number of turns of the insulated conductors and the enlargement of the gap between the coil sections has been referred to as a means for reducing the ampere-turns of the middle portion of the low-voltage winding disposed at the inside of the high-voltage winding. However, in the case of a winding such as a helical or cylindrical winding, it is generally difficult to reduce the number of turns at an intermediate portion of the winding. In such a case, the gap may solely be enlarged for effectively reducing the ampere-turns. According to another effective means for reducing the ampere-turns, the axial pitch of the conductor turn in the intermediate portion of the widing may be selected to be longer than that in the other portions.
FIG. 11 shows an example of the arrangement of a helical winding and the construction for locally increasing the axial pitch of the bundles of insulated conductors of the helical winding. As shown in the figure, there is a low-voltage winding 60, surrounded by a high-voltage winding 61. Duct pieces or duct spacers 65, 65a, 65b and 65c are provided and, among these duct pieces, each of the four duct pieces 65a at the axially middle portion of the low-voltage winding 60 has a width which is greater than the width of the other duct pieces 65. As a result, the axial density of ampere-turns of the low-voltage winding 60 is reduced at the moddle portion as compared with the other portions thereof. On the opposite ends of the winding, uppermost end duct piece 65b and lowermost end duct piece 65c, respectively, are provided.
Referring to FIG. 8a, a low-voltage winding 31 is disposed around a leg portion 29a of an iron core 29 with an insulating cylinder 30 interposed therebetween and is substantially trisected in the axial direction thereof. Spacers 32a and 32b having an especially large axial thickness are disposed at the trisected points of the low-voltage winding 31 so as to provide a gap larger than the gap formed by each of other inter-coil duct pieces 33. This arrangement provides an improved vibration mode of the sixth order in which two modes appear at the trisected points due to the fact that the electromagnetic forces developed in the axial direction of the winding are distributed in a manner as seen in FIG. 8b. A high-voltage winding 35 is disposed outside of the low-voltage winding 31 with an insulating cylinder 34 forming the main insulation interposed therebetween. According to the arrangement shown in FIG. 8a, therefore, the electromagnetic forces developed in the low-voltage winding can be distributed in the sixth order as shown by F1, F2, F3, F4, F5 and F6 in FIG. 8b, and it is possible to further reduce the resultant electromagnetic force.
Referring to FIG. 9a, a low-voltage winding 31 similar to that shown in FIG. 8a is substantially quadrisected in the axial direction thereof and spacers 32a, 32b and 32c having an especially large axial thickness are disposed at the quadrisected points of the low-voltage winding 31 so as to provide a gap larger than the gap formed by each of other inter-coil duct pieces 33.
A high-voltage winding 35 is disposed outside of the low-voltage winding 31 with an insulating cylinder 34 forming the main insulation interposed therebetween.
According to this arrangement, the electromagnetic forces developed in various parts of the low-voltage winding can be distributed in an improved vibration mode of a higher order or of the eighth order as shown by F1 to F8 in FIG. 9b and thus it is possible to further reduce the resultant electromagnetic force.
FIG. 10 shows an application of the present invention to a three-winding transformer. Referring to FIG. 10, a tertiary or low-voltage winding 38 is disposed around a leg portion 36a of an iron core 36 with an insulating cylinder 37 interposed therebetween. A medium-voltage winding 40 is disposed outside of the low-voltage winding 38 with an insulating cylinder 39 interposed therebetween, and a high-voltage winding 42 is disposed outside of the medium-voltage winding 40 with an insulating cylinder 41 interposed therebetween. All these windings are supported at their upper and lower ends on an upper yoke portion 36b and lower yoke portion 36c of the iron core 36 by means of insulating rings 43a, 43b, 44a, 44b, 45a and 45b respectively.
In the medium-voltage winding 40 and high-voltage winding 42, inter-coil duct pieces 48 and 49 of uniform axial thickness are disposed between coil sections 46 and 47 respectively, while in the case of the low-voltage winding 38 located at the innermost position, inter-coil duct pieces 50 in the middle portion of the winding 38 are in the form of spacers 50a, 50b and 50c having an especially large axial thickness so as to provide a larger gap in this portion. In this embodiment too, therefore, a vibration mode of the fourth order similar to that described with reference to FIG. 7a can be obtained. The spacers inserted in the low-voltage winding 38 may be disposed at trisected or quadrisected points of the winding 38 of the number of conductor turns in the portions adjacent to the equally divided points may be reduced so as to shift the vibration mode to a higher order.