JP5306796B2 - Laminated iron core for outer rotor type motor and manufacturing method thereof - Google Patents

Description

TECHNICAL FIELD The present invention relates to a laminated core for an outer rotor type motor in which a plurality of segment core pieces continuous in a strip shape are wound spirally and laminated, and a method for manufacturing the same.

Conventionally, a laminated core for an outer rotor type motor (hereinafter also simply referred to as a laminated core) in which a plurality of magnetic pole portions are formed on the outer side in the radial direction of the yoke portion has been used.
This laminated iron core was manufactured by laminating a plurality of core pieces punched out from an iron core material (for example, strip material), but they were connected to each other at the connecting portion to improve the yield of the iron core material. A plurality of segment core pieces have been punched from the core material, spirally wound and laminated (for example, see Patent Document 1).
However, each segment core piece constituting the above-described laminated iron core has a configuration in which one magnetic pole piece portion is provided in one yoke piece portion, and the following problems have occurred.

For example, the number of connecting portions is large, and the mechanical strength of the wound laminated core is not always strong.
Further, when the adjacent segment core pieces are bent at the connecting portion, the thickness of the connecting portion becomes thicker than other portions, and as a result, a gap is generated between the segment core pieces of the layers adjacent to each other in the vertical direction. An extra pressurizing process for eliminating the gap is required, and the efficiency of the motor is reduced, which adversely affects the quality of the motor.
Therefore, as shown in FIGS. 7 and 8, a plurality (here, five) of magnetic pole piece portions 81 are formed on the outer side in the radial direction of the yoke piece portion 80, and are coupled to each other by a connecting portion 82 to form a straight line. The adjacent arc-shaped segment core pieces 83 arranged are punched out of the core material 84 with a die, bent at the connecting portion 82 and spirally wound and laminated to produce a laminated core 85.

JP 2000-116037 A

However, since the connecting portion 82 that connects the adjacent segment core pieces 83 is provided at the tip end in the radial direction of the magnetic pole piece 81, it is formed between the adjacent segment core pieces 83 arranged in a straight line. The gap 86 was large. As a result, the length of the core material 84 necessary for punching one segment core piece 83, that is, the material required length (feeding pitch) must be increased, resulting in a decrease in the yield of the core material 84. It was. Note that the required length of the core material 84 for manufacturing one segment core piece 83 is that the connecting portion 82 is provided at the tip end in the radial direction of the magnetic pole piece 81, so that the outer diameter of the laminated core 85 is , Determined by the number of divisions of the segment core piece 83.

This invention is made | formed in view of this situation, and it aims at providing the laminated core for outer rotor type | mold motors which can improve the yield of iron core material, and its manufacturing method.

The laminated core for the outer rotor type motor according to the first invention that meets the above object has a plurality of magnetic pole piece portions formed radially outside the yoke piece portion, and is connected to each other at the connecting portion and arranged linearly. Adjacent segment core pieces are bent at the connecting portion, the side end portions of the segment core pieces are aligned, or the inner arc portions of the yoke piece portions are arranged on the same circle, and a plurality of continuous segments. In the laminated core for the outer rotor type motor, in which the core pieces are spirally wound and laminated,
The connecting portions of the segment core pieces are provided between the radially intermediate position and the base position of the magnetic pole piece portion or at the radially outer position of the yoke piece portion, and the adjacent segments arranged linearly. The interference piece where the iron core pieces overlap or the magnetic pole piece part in the radially outer region connected to the interference part and the interference part was removed.

In the laminated core for an outer rotor type motor according to the first aspect of the invention, it is preferable that the connecting portions provided in the upper and lower adjacent layers are shifted in the circumferential direction.

In the laminated core for an outer rotor type motor according to the first aspect of the present invention, the connecting portion at the circumferential end of the segment core piece is disposed at a radially outer position of the yoke piece, and the end of the segment core piece It is preferable to remove the magnetic pole piece portion that is divided into two in the circumferential direction.

In the laminated core for an outer rotor type motor according to the first aspect of the present invention, it is preferable that the magnetic pole piece portion to be removed remains a non-interfering portion on the radially inner side of the segment core piece arranged linearly.

In the laminated core for an outer rotor type motor according to the first aspect of the present invention, the magnetic pole piece shortened by shortening the outer side in the radial direction of the magnetic pole piece part divided into two by the adjacent segment iron core pieces from the other magnetic pole piece part It is preferable to arrange the connecting part at the outer end of the part.

In the laminated core for an outer rotor type motor according to the first invention, the connecting portion of the segment core piece is positioned radially outside the yoke piece portion and between the magnetic pole piece portions of the adjacent segment core pieces. Preferably, the front side interference part of the magnetic pole piece part is removed.

In the manufacturing method of the laminated core for the outer rotor type motor according to the second aspect of the invention, a plurality of magnetic pole piece portions are formed on the radially outer side of the yoke piece portion, and are connected to each other at the connecting portion to form a straight line. While forming a plurality of arranged segment core pieces, bending the connecting portion and aligning the side end portions of the adjacent segment core pieces, or arranging the inner arc portion of the yoke piece portion on the same circle, In the method of manufacturing a laminated core for an outer rotor type motor in which a plurality of continuous segment core pieces are spirally wound and laminated,
When forming the segment core pieces, the connecting portion is formed between the intermediate position in the radial direction of the magnetic pole piece portion and the base position, or at the radially outer position of the yoke piece portion, and is arranged linearly. An interference portion where adjacent segment core pieces overlap or the magnetic pole piece portion in the radially outer region connected to the interference portion and the interference portion is removed.

In the method for manufacturing a laminated core for an outer rotor type motor according to the second invention, it is preferable that the connecting portions of the segment core pieces provided in layers adjacent to each other in the vertical direction are shifted in the circumferential direction.

The laminated core for an outer rotor type motor and the method for manufacturing the same according to the present invention include a connecting portion of the segment core piece between a radial intermediate position of the magnetic pole piece portion and a base position, or a radially outer position of the yoke piece portion. Therefore, the length of the iron core material required for punching one segment iron core piece can be made shorter than before, and the amount of iron core material used can be reduced. Since the adjacent segment core pieces arranged in a straight line are removed, or the magnetic pole pieces in the radially outer region connected to the interference portions and the interference portions are removed, the adjacent segment core pieces are The overlapping portions are eliminated, and the segment core pieces having the same shape can be punched from the core material.
Thereby, the yield improvement of an iron core material can be aimed at and the laminated core for outer rotor type motors can be manufactured economically.

Moreover, when the connection parts provided in the upper and lower adjacent layers are shifted in the circumferential direction, the coupling strength of each segment core piece can be strengthened. Furthermore, the mechanical strength of the wound laminated core is sufficiently strong.

If the non-interfering portion on the radially inner side of the segment core pieces arranged in a straight line is left in the magnetic pole piece portion to be removed, the magnetic pole piece portion can be partially left. It is possible to suppress a decrease in magnetic characteristics of the magnetic pole portion formed by stacking the layers.

When the outer side in the radial direction of the magnetic pole piece divided into two by the adjacent segment core pieces is shorter than the other magnetic pole piece, and the connecting part is arranged at the outer end of the shortened magnetic pole piece, Since it can remain, the fall of the magnetic characteristic of the magnetic pole part comprised by laminating | stacking several magnetic pole piece parts can further be suppressed.

Further, when the connecting portion is formed at the radially outer position of the yoke piece portion and between the magnetic pole piece portions of the adjacent segment core pieces, and the front interference portion of the magnetic pole piece portion is removed, The removal amount can be minimized, and the decrease in efficiency of the manufactured laminated core can be further reduced.

Next, embodiments of the present invention will be described with reference to the accompanying drawings for understanding of the present invention.
Here, FIG. 1 is an explanatory view before lamination of adjacent segment core pieces of the laminated core for outer rotor type motor according to the first embodiment of the present invention, and FIG. 2 (A) shows the adjacent segment core pieces. FIG. 4B is an explanatory diagram when the adjacent segment core pieces are laminated, FIG. 3 is a partially enlarged perspective view of the laminated core for the outer rotor type motor, and FIG. Explanatory drawing before lamination | stacking of the segment core piece adjacent to the laminated core for outer rotor type | mold motors concerning the 2nd Embodiment of this invention, (B) is explanatory drawing at the time of lamination | stacking of the adjacent segment core piece, FIG. (A) is explanatory drawing before lamination | stacking of the adjacent segment core piece of the laminated core for outer rotor type motors concerning the 3rd Embodiment of this invention, (B) is the description at the time of lamination | stacking of the adjacent segment core piece. FIG. 6 (A) shows the fourth aspect of the present invention. Illustration prior to lamination of the segment core pieces adjacent the outer rotor type motor for a laminated core according to the embodiment of facilities, (B) is an explanatory view at the time of stacking of the segment core pieces adjacent the.

As shown in FIGS. 1 to 3, the laminated core for an outer rotor type motor (hereinafter also simply referred to as a laminated core or a stator core) 10 according to the first embodiment of the present invention is radially outward of the yoke piece 11. A plurality of magnetic pole piece portions 12 are formed at the connecting portion 13 and the adjacent segment core pieces 14 that are connected to each other in a straight line are bent at the connecting portion 13 so that the side end portion 15 of the segment core piece 14 is bent. In addition, the inner arc portion 16 of the yoke piece portion 11 is arranged on the same circle, and a plurality of continuous segment core pieces 14 are spirally wound and stacked. The portion 12 is provided between the radial intermediate position P1 and the base position P2 or at the radially outer position P3 of the yoke piece. In addition, the side edge part 15 of the adjacent segment core piece 14 may contact | abut, and may have a slight clearance gap. This will be described in detail below.

The laminated iron core 10 is made of, for example, a plurality of segment core pieces 14 arranged linearly connected by a connecting portion 13 from a magnetic steel sheet (not shown), which is an iron core material having a thickness of about 0.5 mm. As shown in FIGS. 2 (A), 2 (B), and FIG. 3, the punched continuous segment core pieces 14 are wound and sequentially laminated. Here, as a method of stacking and joining the plurality of segment core pieces 14, any one of caulking, welding, and adhesion can be applied, or any two or more can be used in combination.
Each segment core piece 14 is provided with a plurality of slots 17 on the outer side in the radial direction to form the magnetic pole piece 12, and the yoke piece 11 is formed on the inner side in the radial direction. The number of magnetic pole pieces 12 (slots 17) formed in one yoke piece 11 is such that the number n of magnetic pole pieces 12 is not a divisor of the number N of all magnetic pole parts per round of the laminated core 10. (However, in the case of two or more windings, n may be a multiple of N), that is, here five (for example, three or four may be sufficient).

As shown in FIG. 1, the segment core pieces 14 are arranged at the end portions in the circumferential direction of the segment core pieces 14 and at the radially outer positions of the yoke pieces 11 (corresponding to the base positions of the magnetic pole pieces 12). The connection part 13 connected to is provided.
In the case of a conventional segment core piece (two-dot chain line in FIG. 1), the connecting portion 13 is formed at the end of the segment core piece, and magnetic pole pieces 18 and 19 that are divided in the circumferential direction are formed. It was the position that had been. However, when the connecting portion 13 is provided in this portion, the adjacent segment core pieces 14 arranged in a straight line are formed before the plurality of continuous segment core pieces 14 are spirally wound, that is, at the time of punching with a mold. Interference portions of the magnetic pole piece portions 18 and 19 indicated by two-dot chain lines are generated, and punching of a predetermined shape cannot be performed.
Therefore, the pole pieces 18 and 19 including the interference portion and the radially outer region connected to the interference portion are removed.
Thereby, the material required length required for the punching of the segment core piece 14 can be shortened, and the yield of the core material can be improved.

As shown in FIG. 2A, when the adjacent segment core pieces 14 connected by the connecting portion 13 are bent and wound by the connecting portion 13, a portion without the magnetic pole piece portion 12 is generated. .
Therefore, as shown in FIGS. 2B and 3, when the plurality of segment core pieces 14 are wound and stacked, the connecting portion 13 provided between the adjacent segment core pieces 14 is connected to the stacked core. The positions of the magnetic pole piece portions 12 are adjusted by shifting to the different positions in the stacking direction, that is, shifting in the circumferential direction so that the connecting portions 13 of the segment core pieces 14 adjacent in the stacking direction are arranged at different positions. In the present embodiment, when the segment core pieces 14 are stacked, the magnetic pole piece portions 12 are shifted in the circumferential direction by two pieces, but may be shifted one by one, or three or more. Also good.
As a result, when the manufactured laminated core 10 is viewed in plan, the magnetic pole portion can be formed at the same pitch on the outer peripheral portion of the laminated core 10 by eliminating the portion without the magnetic pole portion constituted by the laminated magnetic pole piece portions 12. .

Here, when the number of all magnetic pole pieces per round of the laminated iron core in plan view is m and the number of magnetic pole pieces per segment iron core piece (same as the number of slots) is n, When the number of segment core pieces per round necessary for shifting one piece by two pieces in the stacking direction is k, the following relationship is established. Here, it is calculated that the removed magnetic pole piece is also present.
(M + 2) / n = k
Here, m, n, and k are positive integers, respectively, and can be variously changed according to the manufacturing conditions of the laminated core.
When the number of magnetic pole pieces shifted in the stacking direction is one or three or more, it is necessary for one turn by changing “2” in the above formula to the number to be shifted, that is, one or three or more. The number of segment iron core pieces is obtained.
As a result, as shown in FIG. 3, there is a portion in which the magnetic pole pieces are not partially formed in the stacking direction of the stacked cores 10, but the number of segment core pieces 14 is generally large. Little effect on efficiency loss.

Then, the manufacturing method of the laminated core for outer rotor type | mold motors concerning the 1st Embodiment of this invention is demonstrated, referring FIGS. 1-3.
First, while conveying an electromagnetic steel sheet (not shown), using one or a plurality of molds (not shown), as shown in FIG. A plurality of segment core pieces 14 are punched out.
When punching out the segment core pieces 14, the connecting portions 13 at the ends in the circumferential direction of the segment core pieces 14 are formed at radially outer positions of the yoke pieces 11, and adjacent segment core pieces arranged in a straight line. The magnetic pole piece portions 18 and 19 that are divided into two in the circumferential direction shown in FIG. 1 are not formed, including the interference portion with which 14 overlaps and the magnetic pole piece portion in the radially outer region connected to the interference portion.

And while winding the continuous segment core piece 14 with a rotating shaft, the connecting part 13 is bent, the inner arc part 16 of the yoke piece part 11 is arranged on the same circle, and a plurality of continuous arranged linearly. The segment core pieces 14 are spirally wound and laminated, and the laminated core 10 is manufactured while further shifting the connecting portions 13 of the segment core pieces 14 adjacent in the vertical direction in the circumferential direction.
Thereby, when the manufactured laminated iron core 10 is viewed in a plan view, it is possible to eliminate a portion without the magnetic pole portion constituted by the laminated magnetic pole piece portions 12.

Next, laminated cores for outer rotor type motors according to second to fourth embodiments of the present invention will be described with reference to FIGS. 4 to 6 respectively.
The segment core piece 20 constituting the laminated core for the outer rotor type motor according to the second embodiment of the present invention shown in FIG. 4 (A) has a connecting portion 21 at the end in the circumferential direction of the segment core piece 20. At the end of the segment core piece 20, it is formed at the base position of the magnetic pole pieces 22 and 23 divided in the circumferential direction (the radially outer position of the yoke piece 11).
Each of the magnetic pole piece portions 22 and 23 in which the connecting portions 21 of the adjacent segment core pieces 20 are formed has a shape in which a non-interference portion on the radially inner side of the segment core pieces 20 arranged linearly remains.
For this reason, the adjacent segment core pieces 20 are in a state in which the end face 24 of the magnetic pole piece portion 22 of the adjacent segment core piece 20 and the end face 25 of the magnetic pole piece portion 23 are in contact with each other at the time of punching with a mold. . Note that the pole piece portion may be arranged with the end face having a gap.

When manufacturing a laminated core using such a segment core piece 20, while winding the continuous segment core piece 20 around a rotating shaft, as shown in FIG. The inner arc portion 26 of the yoke piece portion 11 is arranged on the same circle, a plurality of continuous segment core pieces 20 are spirally wound and laminated, and a laminated iron core is manufactured while the connecting portion 21 is shifted in the circumferential direction. To do.
As a result, when the manufactured laminated iron core is viewed in plan, the magnetic pole piece portions 22 and 23 remain, so that the magnetic pole piece portions 12 and 23 are formed as compared with the case where the magnetic pole piece portions 22 and 23 are not provided. A decrease in magnetic characteristics of the magnetic pole portion can be suppressed.

The segment core piece 30 constituting the laminated core for the outer rotor type motor according to the third embodiment of the present invention shown in FIG. 5 (A) is divided into two pieces by the adjacent segment core pieces 30; The outer side of 32 in the radial direction is shorter than the other magnetic pole piece 12, and a connecting portion 33 is formed at the outer end (tip position) of the shortened magnetic pole pieces 31 and 32.
When manufacturing a laminated core using such a segment core piece 30, while winding the continuous segment core piece 30 with a rotating shaft, as shown in FIG. The inner circular arc part 34 of the yoke piece part 11 is arranged on the same circle, a plurality of continuous segment core pieces 30 arranged in a straight line are spirally wound and stacked, and the connecting part 33 is arranged in the circumferential direction. A laminated iron core is manufactured while shifting.
As a result, when the manufactured laminated iron core is viewed in plan, the magnetic pole piece portions 31 and 32 remain, so that the magnetic pole piece portions 12 and 12 are formed as compared with the case where the magnetic pole piece portions 31 and 32 are not provided. A decrease in magnetic characteristics of the magnetic pole portion can be suppressed.

The segment core piece 40 constituting the laminated core for the outer rotor type motor according to the fourth embodiment of the present invention shown in FIG. 6 (A) has a connecting portion 41 at a radially outer position of the yoke piece portion 11. In addition, it is formed between the magnetic pole piece portions 42 and 43 located at the circumferential end portions of the adjacent segment core pieces 40.
The magnetic pole piece portions 42 and 43 formed on both sides of the connecting portion 41 have the opposite front side interference portions 44 and 45 (interference portions where adjacent segment core pieces 40 overlap in a straight line) are removed. .
For this reason, the adjacent segment core pieces 40 are arranged with a gap between the end face 46 of the magnetic pole piece portion 42 and the end face 47 of the magnetic pole piece portion 43 of the adjacent segment core piece 40 when punching with a mold. ing. The pole piece part from which the tip part has been removed may abut the end face thereof.

When manufacturing a laminated core using such a segment core piece 40, while winding the continuous segment core piece 40 with a rotating shaft, as shown in FIG. The inner arc portion 48 of the yoke piece portion 11 is arranged on the same circle, a plurality of continuous segment core pieces 40 arranged in a straight line are spirally wound and stacked, and the connecting portion 41 is further arranged in the circumferential direction. A laminated iron core is manufactured while shifting.
Thereby, when the manufactured laminated iron core is viewed in plan, the removal amount of the magnetic pole pieces 42 and 43 can be minimized, and the decrease in efficiency of the produced laminated iron core can be reduced.

As described above, the present invention has been described with reference to the embodiment. However, the present invention is not limited to the configuration described in the above embodiment, and the matters described in the scope of claims. Other embodiments and modifications conceivable within the scope are also included. For example, a case where a laminated core for an outer rotor type motor of the present invention and a manufacturing method thereof are configured by combining some or all of the above-described embodiments and modifications are also included in the scope of the present invention.
Further, in the above-described embodiment, the description has been given of the case where the connecting portion is provided at the intermediate position in the radial direction of the magnetic pole piece, the base position of the magnetic pole piece, or the radially outer position of the yoke piece. The position is not limited to this as long as the position does not affect the motor characteristics between the intermediate position in the radial direction to the base position or the radially outer position of the yoke piece.

It is explanatory drawing before lamination | stacking of the segment core piece adjacent to the laminated core for outer rotor type | mold motors which concerns on the 1st Embodiment of this invention. (A) is explanatory drawing at the time of bending the adjacent segment core piece at a connection part, (B) is explanatory drawing at the time of lamination | stacking of the adjacent segment core piece. It is a partial expansion perspective view of the laminated iron core for the outer rotor type motor. (A) is explanatory drawing before lamination | stacking of the segment core piece adjacent to the laminated core for outer rotor type | mold motors which concerns on the 2nd Embodiment of this invention, (B) is description at the time of lamination | stacking of the adjacent segment core piece. FIG. (A) is explanatory drawing before lamination | stacking of the adjacent segment core piece of the laminated core for outer rotor type motors concerning the 3rd Embodiment of this invention, (B) is the description at the time of lamination | stacking of the adjacent segment core piece. FIG. (A) is explanatory drawing before lamination | stacking of the adjacent segment core piece of the laminated core for outer rotor type | mold motors which concerns on the 4th Embodiment of this invention, (B) is description at the time of lamination | stacking of the adjacent segment core piece. FIG. It is explanatory drawing which shows the manufacturing method of the laminated core for outer rotor type motors which concerns on a prior art example. It is explanatory drawing of the segment core piece which comprises the laminated core for outer rotor type | mold motors.

Explanation of symbols

10: laminated core for outer rotor type motor, 11: yoke piece, 12: magnetic pole piece, 13: connecting part, 14: segment core piece, 15: side end, 16: inner arc, 17: slot, 18 , 19: magnetic pole piece, 20: segment iron core piece, 21: connecting part, 22, 23: magnetic pole piece part, 24, 25: end face, 26: inner circular arc part, 30: segment iron core piece, 31, 32: magnetic pole piece Part, 33: connecting part, 34: inner arc part, 40: segment core piece, 41: connecting part, 42, 43: magnetic pole piece part, 44, 45: front side interference part, 46, 47: end face, 48: inside Arc part

Claims (8)

A plurality of magnetic pole piece portions are formed on the outer side in the radial direction of the yoke piece portion, and adjacent segment core pieces that are connected to each other at the connecting portion and arranged linearly are bent at the connecting portion, and In a laminated core for an outer rotor type motor in which side end portions are aligned or the inner arc portion of the yoke piece portion is arranged on the same circle and a plurality of continuous segment core pieces are spirally wound and laminated. ,
The connecting portions of the segment core pieces are provided between the radially intermediate position and the base position of the magnetic pole piece portion or at the radially outer position of the yoke piece portion, and the adjacent segments arranged linearly. A laminated iron core for an outer rotor type motor, wherein the interference portion where the iron core pieces overlap or the magnetic pole piece portion in the radially outer region connected to the interference portion and the interference portion is removed. 2. The laminated core for an outer rotor type motor according to claim 1, wherein the connecting portions provided in layers adjacent to each other in the vertical direction are shifted in the circumferential direction. The laminated core for outer rotor type motors according to any one of claims 1 and 2, wherein the connecting portion at a circumferential end of the segment core piece is disposed at a radially outer position of the yoke piece. A laminated iron core for an outer rotor type motor, wherein the magnetic pole piece portion that is divided into two in the circumferential direction is removed at an end portion of the segment iron core piece. 4. A laminated core for an outer rotor type motor according to claim 3, wherein the magnetic pole piece to be removed leaves a non-interfering portion on the radially inner side of the segment core piece arranged linearly. Laminated iron core for type motors. 3. The laminated core for an outer rotor type motor according to claim 1, wherein a radially outer side of the magnetic pole piece divided into two by the adjacent segment iron core pieces is shorter than the other magnetic pole pieces. And the said connection part has been arrange | positioned in the outer side edge part of this shortened magnetic pole piece part, The laminated core for outer rotor type | mold motors characterized by the above-mentioned. 3. The laminated core for an outer rotor type motor according to claim 1, wherein the connecting portion is located at a radially outer position of the yoke piece portion, and the magnetic pole piece portion of the adjacent segment core piece. 4. A laminated iron core for an outer rotor type motor, wherein the laminated core is formed between the magnetic pole pieces and the front side interference part of the magnetic pole piece part is removed. A plurality of magnetic pole piece portions are formed on the outer side in the radial direction of the yoke piece portion, and a plurality of segment core pieces arranged in a straight line by being connected to each other at the connecting portion are formed, and the segments adjacent to each other after being bent at the connecting portion For outer rotor type motors in which a plurality of continuous segment core pieces are spirally wound and laminated while aligning the side ends of the core pieces or arranging the inner arc portions of the yoke pieces on the same circle. In the method of manufacturing a laminated iron core,
When forming the segment core pieces, the connecting portion is formed between the intermediate position in the radial direction of the magnetic pole piece portion and the base position, or at the radially outer position of the yoke piece portion, and is arranged linearly. A method of manufacturing a laminated core for an outer rotor type motor, wherein an interference portion where adjacent segment core pieces overlap, or the magnetic pole piece portion in a radially outer region connected to the interference portion and the interference portion is removed. 8. The method of manufacturing a laminated core for an outer rotor type motor according to claim 7, wherein the connecting portions provided in upper and lower adjacent layers are shifted in the circumferential direction. .

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