JP7762059B2 - Wire manufacturing method - Google Patents

Description

This disclosure relates to a method for manufacturing an electric wire.

An electric wire for high-frequency power transmission is known, in which multiple conductors are arranged on the outer surface of a core material (see Patent Document 1).

JP 2013-251101 A

In high-frequency power transmission, the skin depth in the conductor becomes smaller, resulting in greater current loss. Therefore, to transmit high-frequency power efficiently, it is necessary to increase the conductor density within the skin depth range where the current is concentrated.

One aspect of the present disclosure aims to provide a method for manufacturing an electric wire that can reduce losses in high-frequency power transmission.

One aspect of the present disclosure is a method for manufacturing an electric wire comprising an insulating, cylindrical or columnar core material, a cylindrical assembly conductor arranged to surround the core material, and an insulating coating that covers the assembly conductor.

The electric wire manufacturing method includes the steps of: determining the radius and number of the multiple conductor wires that make up the assembly conductor based on the occupied cross-sectional area of the assembly conductor in a specific region whose distance from the outer surface of the assembly conductor is equal to or less than the skin depth; arranging the multiple conductor wires along the outer surface of the core material; forming the assembly conductor by concentrically twisting the multiple conductor wires around the core material; and covering the core material and assembly conductor with an insulating covering.

With this configuration, multiple conductor strands are concentrically twisted around a core material to form an assembly conductor, thereby increasing conductor density. Furthermore, the radius and number of multiple conductor strands can be determined so that the cross-sectional area occupied by the assembly conductor within the skin depth range is increased. This results in an electric wire that can reduce losses in high-frequency power transmission.

In one aspect of the present disclosure, in the determining step, the occupied cross-sectional area may be determined by subtracting the area of a second region, which is inside the specific region, from the area of a first region, which is inside the outer peripheral surface of the assembly conductor, in the cross section of the electric wire, and the outer diameter of the assembly conductor used to calculate the occupied cross-sectional area may be a function of the radius of the multiple conductor wires before they are concentrically twisted and the number of multiple conductor wires arranged in a row circumferentially around the core material. This configuration makes it possible to achieve a balance between the arrangement efficiency of the conductor wires and the occupied cross-sectional area.

In one aspect of the present disclosure, in the determination step, the sum of the cross-sectional areas of the multiple conductor wires within the specific region may be used as the occupied cross-sectional area, and the number of multiple conductor wires arranged radially of the core material within the specific region used to calculate the occupied cross-sectional area may be a function of the skin depth and the radius of the multiple conductor wires before being concentrically twisted. This configuration can ensure the occupied cross-sectional area and reduce current loss while avoiding the risk of increased manufacturing costs.

In one aspect of the present disclosure, each of the multiple conductor wires may be a twisted wire formed by twisting multiple wires together. This configuration can reduce the resistance per unit cross-sectional area of the assembly conductor.

1A and 1B are schematic cross-sectional views of an electric wire according to an embodiment. FIG. 2 is a flowchart showing a method for manufacturing an electric wire according to the embodiment. FIG. 3 is a schematic diagram showing the procedure for calculating the occupied cross-sectional area in the first method. FIG. 4 is a graph showing an example of the relationship between the occupied cross-sectional area and the number of conductor wires in the first method. 5A and 5B are schematic diagrams showing unit areas in the second method. 6A, 6B, 6C, and 6D are schematic diagrams showing the procedure for calculating the occupied cross-sectional area in the second method. FIG. 7 is a graph showing an example of the relationship between the occupied cross-sectional area and the radius of the conductor wire in the second method.

Hereinafter, embodiments to which the present disclosure is applied will be described with reference to the drawings.
1. First embodiment
[1-1. Configuration]
The method for manufacturing an electric wire according to this embodiment is carried out for the purpose of obtaining an electric wire 10 shown in FIG. 1A or FIG. 1B.

<Electric wire>
The electric wire 10 is not particularly limited in its application, but is particularly suitable for transmitting high-frequency current. The electric wire 10 is used, for example, as a coil for contactless power supply to moving objects such as railway cars, automobiles, and conveying devices in factories, as internal wiring or power supply lines in electric blast furnaces, and the like.

The electric wire 10 includes an assembly conductor 11 , an insulating coating 12 , and a core material 13 .
The assembly conductor 11 has a cylindrical shape and is arranged to surround the core material 13. The assembly conductor 11 is formed by concentrically twisting a plurality of conductor wires 11A bundled into a cylindrical shape around the core material 13. The conductor wires 11A are compressed in the radial direction of the electric wire 10 by the concentric twisting, thereby reducing their diameter.

The conductor wires 11A are made of a metal such as copper or a copper alloy. Each of the multiple conductor wires 11A is a twisted wire formed by twisting together multiple metal wires. The conductor wires 11A are twisted in a spiral shape around the core material 13.

The insulating coating 12 is a cylindrical insulator that covers the assembly conductor 11. The insulating coating 12 is arranged on the outer surface of the assembly conductor 11. The insulating coating 12 is formed, for example, from an insulating resin.

The core material 13 is a cylindrical (see Figure 1A) or columnar (see Figure 1B) insulator. The core material 13 is arranged inside the assembly conductor 11, i.e., in the hollow portion of the assembly conductor 11. The multiple conductor wires 11A that make up the assembly conductor 11 are arranged along the outer surface of the core material 13.

<Wire manufacturing method>
As shown in FIG. 2, the electric wire connecting method of this embodiment includes a determining step S10, an arranging step S20, a concentric twisting step S30, and a covering step S40.

<Decision process>
In this process, the radius and number of the multiple conductor wires 11A that make up the assembly conductor 11 are determined based on the occupied cross-sectional area of the assembly conductor 11 in a specific region R whose distance from the outer peripheral surface of the assembly conductor 11 is equal to or less than the skin depth δ.

The skin depth δ refers to the distance over which, due to the skin effect, when a high-frequency current flows through the assembly conductor 11, the current decreases to 1/e of the skin current (i.e., the current flowing on the outer surface of the assembly conductor 11). In other words, the specific region R is the region through which a current of at least 1/e of the skin current flows.

The skin depth δ is calculated by the following formula (1): In formula (1), f is the frequency [Hz], μ _r is the relative permeability of the conductor, μ ₀ is the permeability of a vacuum, and σ is the conductivity of the conductor [S/m].
δ=1/(π・f・μ _r・μ ₀・σ) ^1/2 ...(1)

The calculation of the occupied cross-sectional area of the assembly conductor 11 and the determination of the radius and number of conductor wires 11A are performed using the first or second method described below.

(First Method)
The first method is intended for the case where a plurality of conductor wires 11A are arranged in one layer (i.e., so as not to overlap in the radial direction of the electric wire 10) in the specific region R. In the first method, the specific region R is densely filled with a plurality of conductor wires 11A, and the occupied cross-sectional area S is calculated on the assumption that no gaps exist between the conductor wires 11A in the specific region R.

In other words, in the first method, the occupied cross-sectional area S is calculated by subtracting the area of the second region in the cross section of the wire 10 that is inward from the outer peripheral surface of the assembly conductor 11.

Specifically, the area obtained by subtracting the area of the second circle C2 from the area of the first circle C1 shown in Figure 3 (i.e., the area of the specific region R sandwiched between the first circle C1 and the second circle C2) is defined as the occupied cross-sectional area S of the assembly conductor 11. Note that Figure 3 shows the conductor wires 11A before they are concentrically twisted.

The first circle C1 is the smallest circle that encompasses the multiple conductor strands 11A after they have been concentrically twisted (i.e., smoothed), and coincides with the outer circumference of the assembly conductor 11. Therefore, the radius rc of the first circle C1 is half the outer diameter of the assembly conductor 11. The second circle C2 is a concentric circle of the first circle C1, with a radius obtained by subtracting the skin depth δ from the radius of the first circle C1.

The occupied cross-sectional area S of the assembly conductor 11 in the specific region R is calculated by the following formula (2) using the radius rc of the first circle C1.
S=π・rc ² −π・(rc−δ) ² ...(2)

The radius rc of the first circle C1 is calculated by the following formula (3): In formula (3), rm is the radius of the core material 13 (i.e., ½ of the outer diameter), t is the thickness of the assembly conductor 11, ra is the radius of the conductor wires 11A before being concentrically twisted, and n is the number of conductor wires 11A arranged on the outer peripheral surface of the core material 13.
rc=rm+t=( rm2 +n・ra2 ^{) 1/2} ... ⁽ 3)

In this way, the outer diameter of the assembly conductor 11 (i.e., the radius of the first circle C1) used to calculate the occupied cross-sectional area S (specifically, the area of the first circle C1) is expressed as a function rc(ra, n) of the radius ra of the multiple conductor wires 11A before they are concentrically twisted and the number n of the multiple conductor wires 11A arranged in the circumferential direction of the core material 13, as shown in equation (3).

The radius ra of the conductor wire 11A satisfies the following formula (4) with respect to the radius rm of the core material 13 and the number n of conductor wires 11A.

From equations (2), (3), and (4), when the radius rm of the core material 13 is fixed, the occupied cross-sectional area S is a function of the number n of conductor wires 11A. As shown in Figure 4, the occupied cross-sectional area S decreases as the number n of conductor wires 11A increases. The rate of decrease in the occupied cross-sectional area S decreases as the number n of conductor wires 11A increases.

The number n of conductor wires 11A is limited to a number equal to or less than the number that ensures the required occupied cross-sectional area S. On the other hand, as the number n of conductor wires 11A decreases, the radius ra of the conductor wires 11A increases. In other words, the smaller the number n of conductor wires 11A, the larger the portion of the conductor wires 11A that is located outside the specific region R, and the lower the placement efficiency of the conductor wires 11A.

From the above, by setting the number of conductor wires 11A to the value of n at which the rate of decrease in S with an increase in n (i.e., the differential value) first exceeds a predetermined threshold, it is possible to achieve a balance between placement efficiency and the occupied cross-sectional area S.

As described above, in the first method, the number n of the multiple conductor wires 11A is determined based on the occupied cross-sectional area S expressed by equations (2), (3), and (4).

(Second Method)
The second method is intended for the case where a plurality of conductor wires 11A are arranged in multiple layers (i.e., stacked in multiple stages in the radial direction of the electric wire 10) in the specific region R.

In the second method, the occupied cross-sectional area S is calculated assuming that gaps exist between the multiple conductor wires 11A in the specific region R. In other words, in the second method, the occupied cross-sectional area S of the assembly conductor 11 is calculated as the sum of the cross-sectional areas of the multiple conductor wires 11A within the specific region R.

Specifically, as shown in Figure 5A, the specific region R is first divided into rectangular unit regions R0, each with a side length equal to the skin depth δ and a side length equal to 2ra. Note that in Figure 5A, the left side of the figure is the radially outer side of the electric wire 10. Furthermore, ra is the radius of the conductor wires 11A (conductor wires W1-W4 in Figure 5A) before being concentrically twisted.

In unit region R0, the second conductor wire W2 and the third conductor wire W3 of two intermediate layers are arranged between the first conductor wire W1 of the outermost layer and the fourth conductor wire W4 of the innermost layer. The first conductor wire W1 and the fourth conductor wire W4 are arranged so that their central axes are aligned in the radial direction of the electric wire 10. Note that while the first conductor wire W1 is arranged in a single layer in Figure 5A, it may also be arranged in multiple layers (i.e., multiple wires aligned radially).

The second conductor wire W2 and the third conductor wire W3 are in contact with the first conductor wire W1 and the fourth conductor wire W4, respectively. The second conductor wire W2 and the third conductor wire W3 are also in contact with each other in the circumferential direction of the electric wire 10. The point of contact between the second conductor wire W2 and the third conductor wire W3 is on the line segment connecting the center of the first conductor wire W1 and the center of the fourth conductor wire W4.

In a cross section perpendicular to the central axis of the electric wire 10, the first conductor wire W1 is entirely contained within the unit area R0. On the other hand, a portion of the fourth conductor wire W4 (i.e., the area close to the core material 13) is not contained within the unit area R0.

Half of the second conductor wire W2 and half of the third conductor wire W3 in the circumferential direction of the electric wire 10 are not included in the unit area R0. Therefore, the sum of the cross-sectional area of the portion of the second conductor wire W2 included in the unit area R0 and the cross-sectional area of the portion of the third conductor wire W3 included in the unit area R0 is equal to the cross-sectional area of one virtual conductor wire W5, as shown in Figure 5B.

The virtual conductor wire W5 overlaps the first conductor wire W1 and the fourth conductor wire W4 in the unit region R0. In the second method, the occupied cross-sectional area S is calculated using the unit region R0 as the sum of the cross-sectional area of the first conductor wire W1, the cross-sectional area of the portion of the virtual conductor wire W5 that is included in the specific region R, and the cross-sectional area of the portion of the fourth conductor wire W4 that is included in the specific region R.

Specifically, in the second method, as shown in Figure 6A, the first area S1, second area S2, and third area S3 of the unit area R0 are calculated.

6B, the first area S1 (see FIG. 6A) is the sum of the cross-sectional area S11 of the entire first conductor wire W1 and the cross-sectional area S12 of the virtual conductor wire W5 that is radially outward of the fourth conductor wire W4. The cross-sectional area S11 can be calculated using the following formula (5).
S11=i・πra ² ...(5)

i is the total number of first conductor wires W1 (i.e., the number contained in unit area R0), and is the largest integer obtained when the skin depth δ is divided by the diameter 2ra of the first conductor wires W1, as expressed in equation (6) below.

The cross-sectional area S12 is the area of a sector with a central angle of (2π-θ) and can be calculated using the following equations (7) and (8).

(ji) is the number of virtual conductor wires W5 included in the unit area R0. j is the largest integer obtained when the skin depth δ is divided by 3 ^1/2 ra, as expressed by the following formula (9), and (ji) is 1 or 0.

The number j obtained by equation (9) is the number of conductor wires 11A arranged side by side in the radial direction of the core material 13 within the specific region R. In this way, the number of conductor wires 11A in the radial direction used to calculate the occupied cross-sectional area S is expressed as a function j(δ, ra) of the skin depth δ and the radius ra of the conductor wires 11A before being concentrically twisted.

As shown in Figure 6C, the second area S2 (see Figure 6A) is the cross-sectional area S21 of the portion of the virtual conductor wire W5 included in the unit area R0 minus the cross-sectional area 12 used in calculating the first area S1.

The cross-sectional area S21 is the area of a sector with a central angle of (2π-α) and can be calculated using the following equations (10) and (11).

As shown in Figure 6D, the third area S3 (see Figure 6A) is the area S31 of the sector with a central angle β minus the area S32 of the isosceles triangle, and can be calculated using the following equations (12) and (13).

From the first area S1, the second area S2, and the third area S3, the cross-sectional area S0 of the assembly conductor 11 in the unit region R0 can be calculated by the following formula (14).
S0=S1+S2+S3=(S11+S12)+(S21-S12)+S3
=S11+S21+S3...(14)

The occupied cross-sectional area S of the assembly conductor 11 in the specific region R can be calculated by the following formula (15): In formula (15), S10 is the area of the unit region R0, and S20 is the area of the specific region R.
S=(S0/S10)・S20...(15)

As shown in Figure 7, the occupied cross-sectional area S obtained by equation (15) decreases as the radius ra of the conductor wire 11A increases. Furthermore, the rate of decrease in the occupied cross-sectional area S decreases as the radius ra of the conductor wire 11A increases.

The radius ra of the conductor wire 11A is limited to a value equal to or less than the value that ensures the required occupied cross-sectional area S. On the other hand, if the radius ra of the conductor wire 11A becomes smaller, the strength of the wire and ease of manufacturing decrease. Therefore, if the radius ra is made too small, there is a risk of reduced quality and increased manufacturing costs.

From the above, the value of ra at which the rate of decrease of S with respect to an increase in ra (i.e., the differential value) first exceeds a predetermined threshold value is set as the radius of the conductor wire 11A, and the number of conductor wires 11A is determined according to this radius, thereby ensuring the occupied cross-sectional area S while avoiding the risks described above.

In this way, in the second method, the radius ra of the multiple conductor wires 11A is determined based on the occupied cross-sectional area S expressed by equation (15).

<Placement process>
In this step, a plurality of conductor wires 11A are arranged along the outer peripheral surface of the core material 13. The number and radius of the conductor wires 11A to be arranged are determined in the determination step S10.

<Concentric twisting process>
In this step, the plurality of conductor wires 11A are twisted concentrically around the core material 13 to form the assembly conductor 11. The concentric twisting compresses the plurality of conductor wires 11A toward the center of the core material 13.

<Coating process>
In this step, the core material 13 and the assembly conductor 11 after the concentric stranding step S30 are covered with an insulating cover 12. In this way, an electric wire 10 for high frequency power transmission is obtained.

[1-2. Effects]
According to the embodiment described above in detail, the following effects can be obtained.
(1a) The conductor density can be increased by forming the assembly conductor 11 by concentrically twisting a plurality of conductor element wires 11A around the core material 13. In addition, the radius ra and the number n of the plurality of conductor element wires 11A can be determined so that the occupied cross-sectional area S of the assembly conductor 11 within the skin depth δ is large. As a result, the electric wire 10 can be obtained, which can reduce loss in high-frequency power transmission.

(1b) The first method makes it possible to achieve a balance between the layout efficiency of the conductor wires 11A and the occupied cross-sectional area S.
(1c) The second method makes it possible to avoid the risk of increased manufacturing costs while ensuring the occupied cross-sectional area S and reducing current loss.

(1d) Each of the multiple conductor wires 11A is a twisted wire formed by twisting multiple wires together, thereby reducing the resistance per unit cross-sectional area of the assembly conductor 11.

2. Other Embodiments
Although the embodiments of the present disclosure have been described above, it goes without saying that the present disclosure is not limited to the above-described embodiments and can take on various forms.

(2a) In the electric wire manufacturing method of the above embodiment, the multiple conductor wires do not necessarily have to be twisted wires.

(2b) The function of one component in the above embodiments may be distributed among multiple components, or the functions of multiple components may be integrated into one component. Furthermore, part of the configuration of the above embodiments may be omitted. Furthermore, at least part of the configuration of the above embodiments may be added to or substituted for the configuration of another of the above embodiments. All aspects included within the technical concept identified by the wording of the claims are embodiments of the present disclosure.

10...electric wire, 11...assembly conductor, 11A...conductor wire, 12...insulating coating, 13...core material.

Claims (6)

A method for manufacturing an electric wire comprising an insulating cylindrical or columnar core material, a cylindrical assembly conductor arranged to surround the core material, and an insulating coating covering the assembly conductor,
determining the radius and number of the plurality of conductor wires constituting the assembly conductor;
a step of arranging the plurality of conductor wires along an outer peripheral surface of the core material;
forming the assembly conductor by concentrically twisting the plurality of conductor wires around the core material;
a step of covering the core material and the assembly conductor with an insulating coating;
Equipped with
In the determining step, the radius and the number of the plurality of conductor wires are determined based on a comparison between a rate of change in the occupied cross-sectional area of the assembly conductor in a specific region whose distance from the outer peripheral surface of the assembly conductor after the concentric twisting is equal to or less than the skin depth when at least one of the number and the radius of the plurality of conductor wires before the concentric twisting is changed and a predetermined threshold value.
Manufacturing method of electric wire. A method for manufacturing an electric wire according to claim 1,
In the determining step, the number of the conductor wires constituting the assembly conductor is determined to be the number such that, when the number of the conductor wires before the concentric twisting is increased, the rate of decrease in the occupied cross-sectional area of the assembly conductor in the specific region first exceeds the predetermined threshold.
Manufacturing method of electric wire. In the determining step,
the occupied cross-sectional area is calculated by subtracting the area of a second region that is more inward than the specific region from the area of a first region that is more inward than the outer circumferential surface of the assembly conductor in a cross section of the electric wire,
2. The method for manufacturing an electric wire according to claim 1, wherein the outer diameter of the assembly conductor used in calculating the occupied cross-sectional area is a function of radii of the plurality of conductor wires before being concentrically twisted and the number of the plurality of conductor wires arranged side by side in the circumferential direction of the core material. A method for manufacturing an electric wire according to claim 1,
In the determining step, a radius at which a reduction rate of the occupied cross-sectional area of the assembly conductor in the specific region first exceeds the predetermined threshold when the radius of the plurality of conductor wires before the concentric twisting is increased is determined as the radius of the plurality of conductor wires constituting the assembly conductor.
Manufacturing method of electric wire. In the determining step,
the sum of the cross-sectional areas of the plurality of conductor wires in the specific region is defined as the occupied cross-sectional area;
2. The method for manufacturing an electric wire according to claim 1, wherein the number of the plurality of conductor wires arranged side by side in the radial direction of the core material within the specific region used for calculating the occupied cross-sectional area is set as a function of the skin depth and a radius of the plurality of conductor wires before being concentrically twisted. The method for manufacturing an electric wire according to claim 1 , wherein each of the plurality of conductor wires is a stranded wire formed by twisting a plurality of wires together.