WO2023277694A1 - Winding of an electric machine made of multistrand conductors with two or more twisting levels - Google Patents

Winding of an electric machine made of multistrand conductors with two or more twisting levels Download PDF

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Publication number
WO2023277694A1
WO2023277694A1 PCT/NO2022/050131 NO2022050131W WO2023277694A1 WO 2023277694 A1 WO2023277694 A1 WO 2023277694A1 NO 2022050131 W NO2022050131 W NO 2022050131W WO 2023277694 A1 WO2023277694 A1 WO 2023277694A1
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Prior art keywords
twisting
level
winding
electric machine
conductors
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PCT/NO2022/050131
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French (fr)
Inventor
ZhaoQiang Zhang
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Alva Industries As
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Priority to EP22833732.5A priority Critical patent/EP4364174A1/en
Publication of WO2023277694A1 publication Critical patent/WO2023277694A1/en

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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K3/00—Details of windings
    • H02K3/04—Windings characterised by the conductor shape, form or construction, e.g. with bar conductors
    • H02K3/28—Layout of windings or of connections between windings
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K3/00—Details of windings
    • H02K3/04—Windings characterised by the conductor shape, form or construction, e.g. with bar conductors
    • H02K3/12—Windings characterised by the conductor shape, form or construction, e.g. with bar conductors arranged in slots
    • H02K3/14—Windings characterised by the conductor shape, form or construction, e.g. with bar conductors arranged in slots with transposed conductors, e.g. twisted conductors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K2203/00—Specific aspects not provided for in the other groups of this subclass relating to the windings
    • H02K2203/15—Machines characterised by cable windings, e.g. high-voltage cables, ribbon cables

Definitions

  • the present invention is related to a winding of an electric machine made of multistrand conductors with two or more twisting levels, according to the preamble of claim 1.
  • Electric machines are used in a wide range of applications. Electric machines are continuously under development for improvement and other areas of use. One continuous development task is to provide electric machines with a desirable high efficiency performance. To be able to provide electric machines with high efficiency, the losses will have to be reduced. For electric machines, operating at elevated frequencies, one way to achieve loss reduction is by using multistranded transposed conductors, such as Roebel bars, Litz wires or similar.
  • Litz wire is a particular type of multistrand wire or cable. It is often used in electric machines operated at high frequencies.
  • the Litz wire is designed to reduce the skin effect and proximity effect losses. It consists of many thin wire strands, individually insulated and twisted together into bundles, following one of several carefully prescribed patterns. It often involves several levels, or bunching steps (number of twisting operations). The result of these winding patterns is to equalize the proportion of the overall length over which each strand is at the outside of the conductor without worsening the mechanical property.
  • Roebel bar is another alternative addressing the challenge of skin and proximity effects.
  • Roebel bars are several parallel sub-conductors, usually of rectangular cross-section, isolated from one another and specially layered with a specific and precisely defined twist (or transposition).
  • Roebel bars are costly and therefore usually limited to electric machines with a high output in the upper kilowatt and megawatt range, unlike Litz wire, used both for small and large electric machines.
  • Windings made of multistrand conductors like Litz wire, Roebel bars and similar, are well described in prior art, and some examples can be found in EP1930918A2, US2002050395A1, CN103545023A, JP2016024974A, CN108352214A, WO 2019086666 Al, CN 207217136 U and JP S57196857 A.
  • one-level twisting is the same as “strand-level twisting"
  • two-level twisting includes strand-level twisting and "top-level twisting”
  • three-level twisting includes strand-level twisting, "mid-level twisting" and top-level twisting.
  • length of lay The distance required to complete one revolution of a strand around the diameter of the conductor is called “length of lay” or “helical twisting pitch”.
  • the active length of the electric machine should be N times the twisting pitch (N is a positive integer).
  • N is a positive integer.
  • prior art fails to describe a winding design for adaptation of dimension of the active parts of an electric machine to existing multistrand conductors, such as Litz wires or similar, with defined pitches at different twisting levels.
  • the main object of the present invention is to provide a winding of an electric machine partly or entirely solving the mentioned drawbacks of prior art solutions.
  • An object of the present invention is to provide a winding of an electric machine made of multistrand conductors with two or more twisting levels reducing the circulating currents and the related losses to their theoretical minimum.
  • An object of the present invention is to provide a winding of an electric machine made of multistrand conductors enabling the use of multistrand conductors with defined pitches at different twisting levels.
  • a winding of an electric machine made of multistrand conductors with two or more twisting levels is defined by the technical features of claim 1. Preferable features of the winding are described in the dependent claims.
  • Active length of an electric machine is according to the present invention defined as the length where the winding is exposed to the main magnetic field. It can be equal to the length of the core or the magnets in the direction perpendicular to the direction of rotation or lateral movement of the electric machine.
  • the electric machine active length (l a ) is defined as either the axial length of magnets/rotor-core for a radial-flux permanent magnet electric machine, or the radial length of magnets/rotor-core for an axial flux permanent magnet electric machine.
  • helix twisting pitch of multistrand conductors is designated as p.
  • p 2 is defined as the pitch for top level twisting and p t is defined as the pitch for strand- level twisting.
  • p 3 is defined as the pitch for top-level twisting
  • p 2 is defined as the pitch for mid-level twisting
  • p t is defined as the pitch for strand-level twisting.
  • the pitch for each level is thus according to the present invention related to the own coordinate of each twisting level.
  • An equivalent pitch p t is according to the present invention defined for two-layer twisting through
  • k should be 1 to reduce the circulating current to zero (theoretical minimum). Practically, the twisting operation is not perfectly done, therefore, there should be used a range for k to cover the manufacture imperfection. According to the present invention, the range is specified to 0.85-1.15. The closer k is to 1, the lower circulating currents can be expected.
  • N 1, in this case, the conductor length is minimal while the circulating current is minimal, and therefore the conductor resistance is minimal.
  • the winding according to the present invention is applicable for both ironless and slotless electric machines.
  • the multistrand conductors are Litz wire or Roebel bars.
  • Fig. 1 is a principle drawing of a winding according to the present invention with multiple levels of twisting
  • Fig. 2 is a principle drawing explaining what a helix pitch of a conductor
  • Fig. 3 is a principle drawing of a winding formed by a Litz wire with a single level of twisting
  • Fig. 4 is a principle drawing of one embodiment of a winding according to the present invention formed by a Litz wire with two levels of twisting
  • Fig. 5 is a principle drawing of another embodiment of a winding according to the present invention formed by a Litz wire with three levels of twisting,
  • Fig. 6 is a principle drawing of a further embodiment of a winding according to the present invention formed by a Litz wire with two levels of twisting, and
  • Fig. 7 is a principle drawing of the cross-section of a stator of an electric machine provided with a winding according to the present invention.
  • multistrand conductors of a winding according to the present invention are represented by Litz wire. It should be understood that the same principles may be applied to other types of twisted multilayer conductors.
  • FIG. 1 showing a principle drawing of winding according to the present invention made of multistrand conductors 10 in the form of a Litz wire having three levels of twisting.
  • the lowest (first) level is a so-called “strand-level twisting” where a bundle 12 is made of twisted individual strands 11.
  • the next (second) level of twisting which also is called “mid-level twisting”
  • the third level twisting which also is called “top-level twisting” is made by twisting several of the second-level bundles 13 into a third-level bundle 14.
  • FIG. 2 showing a principle drawing of a Litz wire 10, wherein the parameter of helix pitch (p) of the wire is explained by illustration of the Litz wire 10 consisting of twisted strands 11 wherein one of the strands 110 is shaded.
  • Figure 3 showing a principle drawing of a winding made of multistrand conductors in the form of a Litz wire 10 with a single level of twisting, where single conductors (strands) 11 are twisted together in a bundle.
  • FIG. 4 showing a principle drawing of one embodiment of a winding according to the present invention made of multistrand conductors formed by a Litz wire 10 with two levels of twisting, where several first-level bundles 12 are twisted into one second-level bundle 13.
  • FIG. 5 showing a principle drawing of another embodiment of a winding according to the present invention made of multistrand conductors formed by a Litz wire 10 with three levels of twisting.
  • the first level bundles 12 consist of twisted individual strands 11, as shown in Figure 1, wherein each of the second-level twisted bundles 13 consist of several first-level twisted bundles 12 and the third level bundle 14, consist of several second-level twisted bundles 13. It is noteworthy that the direction of twisting is the same on the second-level 13 and the third-level 14 bundles.
  • FIG. 6 showing a principle drawing of a further embodiment of a winding according to the present invention made of multistrand conductors formed by a Litz wire 10 with two levels of twisting, where several first-level bundles 12 are twisted into one second-level bundle 13. It is noteworthy that the direction of twisting is different on the first-level 12 and the second-level 13 bundles.
  • FIG. 7 showing a cross-sectional principle drawing of a stator of an electric machine, including iron core 15, slot area 16 filled with a winding according to the present invention, and end-windings 17.
  • the winding in the example in Figure 7 is made of multistrand conductors formed by a Litz wire with two levels of twisting, wherein the expression governing the winding design is kNp 1 p 2 a Pi ⁇ Pz
  • the present invention is applicable for all kinds of electric machines using multilevel conductor twisting, including both machines with and without iron cores, also including any spatial configurations and topologies, radial-flux topologies, axial-flux topologies and other variants.
  • the multistrand conductors can be both Litz wire, Roebel bars or other types of multilevel twisted conductors.
  • Dimensions of the active parts, in particular active length, of an electric machine can be adjusted to fit the available multistrand conductors with defined pitches at different twisting levels, likewise, the pitches of the multistrand multilevel conductors can be adjusted to fit the given dimensions of the electric machine.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Windings For Motors And Generators (AREA)
  • Coils Of Transformers For General Uses (AREA)

Abstract

Winding of an electric machine, wherein the winding is made of multistrand conductors (10) with two or more twisting levels, wherein the active length of the electric machine and twisting pitches of the multistrand conductors (10) are in a certain relation described by a mathematical expression.

Description

Winding of an electric machine made of multistrand conductors with two or more twisting levels
The present invention is related to a winding of an electric machine made of multistrand conductors with two or more twisting levels, according to the preamble of claim 1.
Background
Electric machines are used in a wide range of applications. Electric machines are continuously under development for improvement and other areas of use. One continuous development task is to provide electric machines with a desirable high efficiency performance. To be able to provide electric machines with high efficiency, the losses will have to be reduced. For electric machines, operating at elevated frequencies, one way to achieve loss reduction is by using multistranded transposed conductors, such as Roebel bars, Litz wires or similar.
Litz wire is a particular type of multistrand wire or cable. It is often used in electric machines operated at high frequencies. The Litz wire is designed to reduce the skin effect and proximity effect losses. It consists of many thin wire strands, individually insulated and twisted together into bundles, following one of several carefully prescribed patterns. It often involves several levels, or bunching steps (number of twisting operations). The result of these winding patterns is to equalize the proportion of the overall length over which each strand is at the outside of the conductor without worsening the mechanical property.
Roebel bar is another alternative addressing the challenge of skin and proximity effects. Roebel bars are several parallel sub-conductors, usually of rectangular cross-section, isolated from one another and specially layered with a specific and precisely defined twist (or transposition). Roebel bars are costly and therefore usually limited to electric machines with a high output in the upper kilowatt and megawatt range, unlike Litz wire, used both for small and large electric machines.
Windings made of multistrand conductors, like Litz wire, Roebel bars and similar, are well described in prior art, and some examples can be found in EP1930918A2, US2002050395A1, CN103545023A, JP2016024974A, CN108352214A, WO 2019086666 Al, CN 207217136 U and JP S57196857 A.
There will be at least one level, two levels or three levels of twisting of the multistrand conductors: one-level twisting is the same as "strand-level twisting", • two-level twisting includes strand-level twisting and "top-level twisting”, and
• three-level twisting includes strand-level twisting, "mid-level twisting" and top-level twisting.
The distance required to complete one revolution of a strand around the diameter of the conductor is called "length of lay” or "helical twisting pitch".
It is known that, besides the skin and proximity effect, one more problem in the electric machines made of multistrand conductors is circulating currents flowing along the length of the conductors. These circulating currents are induced due to the difference of the exposure of individual strands and contours formed by the strands to the magnetic field crossing the contours. The circulating currents are a hindering factor for optimal machine efficiency.
It is also known that, for reducing the circulating currents, the active length of the electric machine should be N times the twisting pitch (N is a positive integer). For achieving both the lowest circulating current and the lowest winding resistance, it is preferable to have N = 1. For example, the article "Transpositions in Stator Bars of Large Turbogenerators" by Johann Flaldemann (IEEE Trans. Energy Conversion, vol. 19, No. 3, September 2004) discloses that when the first Roebel bar was invented, it had 360 degree (N = 1) in the active length.
Flowever, this solution is only applicable to windings with one-level twisting. The prior art solutions fail to disclose solutions for windings made of multistrand conductors with multiple layers of twisting wherein each layer may have different direction of twisting and different pitch.
Thus, the disadvantage of prior art solutions is that they fail to disclose a winding design for reduction or total elimination of the circulating currents in the multistrand windings with more than one level of twisting.
Further, prior art fails to describe a winding design for adaptation of dimension of the active parts of an electric machine to existing multistrand conductors, such as Litz wires or similar, with defined pitches at different twisting levels.
Consequently, prior art further fails to disclose a solution for design and production of highly efficient electric machines utilizing multistrand windings with more than one level of twisting.
It is accordingly a need for a winding of an electric machine solving the problem of circulating currents enabling the use of multistrand conductors twisted at different levels with different pitches and in different directions. So far, there is no information available in the public resources on how to reduce the circulating current and the related loss when windings are constructed with multiple-step twisting, in which there are pitches for each individual level. The technical problem of how to reduce circulating current is thus not straightforward. It is accordingly a need for a winding design of an electric machine enabling production of highly efficient electrical machines.
Object
The main object of the present invention is to provide a winding of an electric machine partly or entirely solving the mentioned drawbacks of prior art solutions.
An object of the present invention is to provide a winding of an electric machine made of multistrand conductors with two or more twisting levels reducing the circulating currents and the related losses to their theoretical minimum.
It is further an object of the present invention to provide a winding of an electric machine made of multistrand conductors with two or more twisting levels adapted the design of the electric machine.
An object of the present invention is to provide a winding of an electric machine made of multistrand conductors enabling the use of multistrand conductors with defined pitches at different twisting levels.
It is an object of the present invention to provide a winding of an electric machine made of multistrand conductors enabling adaptation of the pitches of the multistrand multilevel conductors for the given dimensions of the electric machine.
Further objects of the present invention will appear from the following description, claims and attached drawings. The invention
A winding of an electric machine made of multistrand conductors with two or more twisting levels is defined by the technical features of claim 1. Preferable features of the winding are described in the dependent claims.
For description and clarity of the present invention, some definitions will now be given.
Active length of an electric machine is according to the present invention defined as the length where the winding is exposed to the main magnetic field. It can be equal to the length of the core or the magnets in the direction perpendicular to the direction of rotation or lateral movement of the electric machine. According to the present invention, the electric machine active length (la) is defined as either the axial length of magnets/rotor-core for a radial-flux permanent magnet electric machine, or the radial length of magnets/rotor-core for an axial flux permanent magnet electric machine.
In the present invention, helix twisting pitch of multistrand conductors is designated as p. For two- layer twisting, p2 is defined as the pitch for top level twisting and pt is defined as the pitch for strand- level twisting. For three-layer twisting, p3 is defined as the pitch for top-level twisting, p2 is defined as the pitch for mid-level twisting and pt is defined as the pitch for strand-level twisting. The pitch for each level is thus according to the present invention related to the own coordinate of each twisting level.
An equivalent pitch pt is according to the present invention defined for two-layer twisting through
1 1 1 1 1 1 1 the expression — = — + — and for three-layer twisting through the expression — = — + — + — ,
Pt Pi Pz Pt Pi Pz Pz
1 1 wherein, when the twisting direction in the 2nd (or 3rd) level is same as the first level, — (or — ) take
Vz Vz plus sign; otherwise they take minus sign.
By using the defined equivalent pitch and the electric machine active length, we can write the expression describing the situation where the circulating currents are minimized or eliminated as: la = kNpt, where k is a value between 0.85 and 1.15, N is a nonzero positive integer.
Ideally, if there are perfect twisting operations, k should be 1 to reduce the circulating current to zero (theoretical minimum). Practically, the twisting operation is not perfectly done, therefore, there should be used a range for k to cover the manufacture imperfection. According to the present invention, the range is specified to 0.85-1.15. The closer k is to 1, the lower circulating currents can be expected. Preferably, N = 1, in this case, the conductor length is minimal while the circulating current is minimal, and therefore the conductor resistance is minimal.
To generalize the above expressions to cover any number of levels of twisting one can write the relationship between the electric machine's active length (la) and the twisting pitches (p) as the two expressions
Figure imgf000006_0001
and la = kNpt. where L is the number of twisting levels, pt is the pitch for strand level twisting, pt is the pitch for any higher-level twisting and wherein, when the twisting direction of the higher-level twisting is the same as the strand level, s = +1 and, when the twisting direction of the higher-level twisting is opposite to the strand level, s = —1.
A more general mathematical expression linking the electric machine's active length (la) and the twisting pitches (p) can be written as follows:
Figure imgf000006_0002
The winding according to the present invention is applicable for both ironless and slotless electric machines.
According to one embodiment of the present invention, the multistrand conductors are Litz wire or Roebel bars.
Further preferable features and advantageous details of the present invention will appear from the following example description, claims and attached drawings.
Example
The present invention will below be described in further details by way of example embodiments with references to the attached drawings, where: Fig. 1 is a principle drawing of a winding according to the present invention with multiple levels of twisting,
Fig. 2 is a principle drawing explaining what a helix pitch of a conductor,
Fig. 3 is a principle drawing of a winding formed by a Litz wire with a single level of twisting, Fig. 4 is a principle drawing of one embodiment of a winding according to the present invention formed by a Litz wire with two levels of twisting,
Fig. 5 is a principle drawing of another embodiment of a winding according to the present invention formed by a Litz wire with three levels of twisting,
Fig. 6 is a principle drawing of a further embodiment of a winding according to the present invention formed by a Litz wire with two levels of twisting, and
Fig. 7 is a principle drawing of the cross-section of a stator of an electric machine provided with a winding according to the present invention.
In following example description of the present invention, multistrand conductors of a winding according to the present invention are represented by Litz wire. It should be understood that the same principles may be applied to other types of twisted multilayer conductors.
Reference is now made to Figure 1 showing a principle drawing of winding according to the present invention made of multistrand conductors 10 in the form of a Litz wire having three levels of twisting. The lowest (first) level is a so-called "strand-level twisting" where a bundle 12 is made of twisted individual strands 11. The next (second) level of twisting, which also is called "mid-level twisting", is where several of the first-level twisted bundles 12 are twisted together into a second- level bundle 13. Finally, the third level twisting, which also is called "top-level twisting", is made by twisting several of the second-level bundles 13 into a third-level bundle 14.
Reference is now made to Figure 2 showing a principle drawing of a Litz wire 10, wherein the parameter of helix pitch (p) of the wire is explained by illustration of the Litz wire 10 consisting of twisted strands 11 wherein one of the strands 110 is shaded. Reference is now made to Figure 3 showing a principle drawing of a winding made of multistrand conductors in the form of a Litz wire 10 with a single level of twisting, where single conductors (strands) 11 are twisted together in a bundle.
Reference is now made to Figure 4 showing a principle drawing of one embodiment of a winding according to the present invention made of multistrand conductors formed by a Litz wire 10 with two levels of twisting, where several first-level bundles 12 are twisted into one second-level bundle 13.
Reference is now made to Figure 5 showing a principle drawing of another embodiment of a winding according to the present invention made of multistrand conductors formed by a Litz wire 10 with three levels of twisting. The first level bundles 12 consist of twisted individual strands 11, as shown in Figure 1, wherein each of the second-level twisted bundles 13 consist of several first-level twisted bundles 12 and the third level bundle 14, consist of several second-level twisted bundles 13. It is noteworthy that the direction of twisting is the same on the second-level 13 and the third-level 14 bundles.
Reference is now made to Figure 6 showing a principle drawing of a further embodiment of a winding according to the present invention made of multistrand conductors formed by a Litz wire 10 with two levels of twisting, where several first-level bundles 12 are twisted into one second-level bundle 13. It is noteworthy that the direction of twisting is different on the first-level 12 and the second-level 13 bundles.
Reference is now made to Figure 7 showing a cross-sectional principle drawing of a stator of an electric machine, including iron core 15, slot area 16 filled with a winding according to the present invention, and end-windings 17. The winding in the example in Figure 7 is made of multistrand conductors formed by a Litz wire with two levels of twisting, wherein the expression governing the winding design is kNp1p2 a Pi±Pz
When the direction of the twisting on the first level bundle 12 and the second level bundle 13 are different, the expression of the winding design becomes:
. _ fcJVp1p2 a
P1-P2 When the direction of the twisting on the first level bundle 12 and the second level bundle 13 are the same, the expression of the winding design becomes:
Figure imgf000009_0001
The above described embodiments can be combined and modified to form other embodiments which are within the scope of the claims.
Modifications
The present invention is applicable for all kinds of electric machines using multilevel conductor twisting, including both machines with and without iron cores, also including any spatial configurations and topologies, radial-flux topologies, axial-flux topologies and other variants.
The multistrand conductors can be both Litz wire, Roebel bars or other types of multilevel twisted conductors.
Dimensions of the active parts, in particular active length, of an electric machine can be adjusted to fit the available multistrand conductors with defined pitches at different twisting levels, likewise, the pitches of the multistrand multilevel conductors can be adjusted to fit the given dimensions of the electric machine.
List of designations
10 - Litz wire
11, 110 - single conductor (strand) 12 - first-level bundle (strand-level twisting)
13 - second-level bundle (mid-level twisting)
14 - third-level bundle (top-level twisting)
15 - iron core of an electric machine
16 - slot area with winding 17 - end-windings

Claims

Claims
1. A winding of an electric machine, wherein the winding is made of multistrand conductors (10) with two or more twisting levels, wherein active length (la) of the electric machine and twisting pitches (p) of the multistrand conductors (10) are linked by the expression
Figure imgf000011_0001
where k is a value between 0.85 and 1.15, L is the number of twisting levels, N is a nonzero positive integer, is the pitch for strand level twisting, p; is the pitch for any higher-level twisting, and wherein, when the twisting direction of higher-level twisting is same as the strand level, s = +1, and when the twisting direction of higher-level twisting is opposite to the strand level, s = —1.
2. A winding of an electric machine according to claim 1, wherein N = 1.
3. A winding of an electric machine according to claim 1, wherein k~l.
4. A winding of an electric machine according to claim 1, wherein the electric machine is ironless or slotless.
5. A winding of an electric machine according to claim 1, wherein the multistrand conductors (10) are Litz wire.
6. A winding of an electric machine according to claim 1, wherein the multistrand conductors (10) are Roebel bars.
PCT/NO2022/050131 2021-06-29 2022-06-09 Winding of an electric machine made of multistrand conductors with two or more twisting levels WO2023277694A1 (en)

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Citations (2)

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US20180226175A1 (en) * 2017-02-06 2018-08-09 Yazaki Corporation Aluminum composite twisted wire conductor, aluminum composite twisted wire, and wire harness
WO2019086666A1 (en) * 2017-11-06 2019-05-09 Thyssenkrupp Ag Device for producing stranded wires, a stranded wire and an electric machine having such a stranded wire

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Publication number Priority date Publication date Assignee Title
JPS57196857A (en) * 1981-05-29 1982-12-02 Hitachi Ltd Frequency generator
CN207217136U (en) * 2017-07-26 2018-04-10 深圳市嘉正欣实业有限公司 Silk-covered wire twisted wire and motor

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20180226175A1 (en) * 2017-02-06 2018-08-09 Yazaki Corporation Aluminum composite twisted wire conductor, aluminum composite twisted wire, and wire harness
WO2019086666A1 (en) * 2017-11-06 2019-05-09 Thyssenkrupp Ag Device for producing stranded wires, a stranded wire and an electric machine having such a stranded wire

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
SULLIVAN CHARLES R.; LOSSES LITZ-WIRE: "Analytical model for effects of twisting on litz-wire losses", 2014 IEEE 15TH WORKSHOP ON CONTROL AND MODELING FOR POWER ELECTRONICS (COMPEL), IEEE, 22 June 2014 (2014-06-22), pages 1 - 10, XP032628780, DOI: 10.1109/COMPEL.2014.6877187 *

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