JP2004087725A - Heat sink manufacturing method and heat sink - Google Patents

Abstract

An object of the present invention is to achieve both cooling efficiency and space saving.
Kind Code: A1 A comb-shaped member having a plurality of teeth, and a plurality of corrugated fins subjected to corrugation are disposed between the teeth, and the comb-shaped members are brazed. 10. A method of manufacturing a heat sink in which the heat sink 10 and the corrugated fin 17 are integrally joined,
The corrugated fins 17 are divided into a plurality of portions between the tooth portions 12, 12, and a heat treatment is performed in a state in which a spacer for pressing the corrugated fins 17 against the tooth portions 12 is inserted between the corrugated fins 17. And the corrugated fins 17 are brazed.
[Selection diagram] Fig. 1

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method for manufacturing a heat sink and a heat sink, and more particularly to a technology that is suitable for cooling a power module (power device element) of an automobile, an electric railway, a household appliance, an industrial machine, an electric power, and the like, and that can save space.
[0002]
[Prior art]
2. Description of the Related Art Conventionally, various types of aluminum heat sinks such as a heat sink made of an extruded material (die-cast material), a corrugated fin brazing heat sink, and a plate fin brazing heat sink have been used for cooling electric and electronic devices.
[0003]
[Problems to be solved by the invention]
In these prior arts, in reality, it is difficult to respond to a demand for higher efficiency of a cooling device that must cope with an inevitable higher density accompanying the recent reduction in the size of electric and electronic devices. In other words, it does not meet the requirements of improving the heat radiation performance with the same space volume and cooling conditions (cooling air volume and cooling air temperature), or miniaturizing the heat sink with the same or higher heat radiation performance.
[0004]
Aluminum extruded material is a type of injection molding in which aluminum material is extruded in a Tokoroten type through an extrusion mold, and in a heat sink made of aluminum die casting, the molten metal is filled in the mold cavity, and it is a kind of injection molding. In the manufactured heat sink 70, as shown in FIG. 7, the possible thickness of the fin 71 is about 1.0 mm or more, and it is not possible to take a fine fin structure capable of increasing a heat transfer area to air. Therefore, it is not possible to satisfy the recent demand for higher performance as heat transfer characteristics.
Furthermore, in such a structure, when the fin pitch is narrowed and the radiating area is to be increased while the fins 71 have the same thickness, the pressure loss of the cooling air passing between the fins 71 increases, and At the same time, there is a problem that the weight increases.
Further, when the thickness of the fin 71 is reduced to reduce the fin pitch, there is a problem that the fin efficiency, that is, the cooling efficiency is reduced.
[0005]
As the corrugated fin brazing heat sink 80, as shown in FIG. 8, a type in which an upright corrugated fin 82 is brazed to an aluminum plate 81 is exemplified. In this structure, since the corrugated fins 82 are self-supporting, the heat resistance is relatively large.
Furthermore, in such a structure, when the fin pitch is narrowed and the radiating area is increased while the fin thickness remains the same, the pressure loss of the cooling air passing between the fins increases. there were.
Further, when the fin pitch is reduced by reducing the fin thickness, there is a problem that the fin efficiency, that is, the cooling efficiency is reduced.
In addition, the fin height can be increased, or the fins can be stacked in several layers, but in this case, the heat conduction distance in the fin height direction becomes too long, which does not bring up the performance and increases the pressure loss. There was a problem. .
[0006]
In order to improve the fin efficiency, as shown in FIG. 9, parallel plate members 92 are erected on the surface of the base portion 91 and brazed. A configuration in which the corrugated fins 93 are provided is also possible, but in this case, there are problems that the number of members is increased and that positioning and assembling and joining of the fins 93 to the plate material 92 become difficult.
[0007]
This is because when the base portion 91 and the plate member 92 are integrally formed and the fins 93 are inserted between the plate members 92 to join them, the distance W0 between the plate members 92 and the width of the fins 93 are different. If the accuracy is not sufficient, there is a problem that a bonding failure occurs.
This is because it is difficult to secure such dimensional accuracy at the time of joining the base portion 91 and the plate member 92 or at the time of manufacturing the fins 93, that is, when the interval between the plate members 92 is equal to or smaller than the width of the fins 93, This is because insertion becomes impossible, and if it is too large, the fins 93 are too loose to be tightly fixed between the plate members 92, so that close bonding by brazing cannot be performed. As a result, there has been a problem that they cannot be connected to such an extent that necessary thermal conductivity can be obtained.
[0008]
In order to solve this problem, when the base 91 and the plate 92 are separated from each other, and the plate 92 and the fins 93 are joined to the base 91 at the same time, the base 91 and the plate 92 are joined together. At the attachment portion, thermal conductivity is lower than that using an extruded material or a die-cast material, so that there is a problem that sufficient cooling performance and fin efficiency cannot be obtained.
[0009]
The present invention has been made in view of the above circumstances, and has as its object to provide an easy-to-manufacture heat sink while maintaining a desired fin efficiency.
[0010]
[Means for Solving the Problems]
The method for manufacturing a heat sink according to the present invention includes a comb-shaped member having a plurality of teeth having a predetermined thickness at predetermined intervals, and a plurality of corrugates having a predetermined height and corrugated between the respective teeth. A method of manufacturing a heat sink in which fins are disposed and a comb-shaped member and a corrugated fin are integrally joined by brazing,
The corrugated fins are divided into a plurality of portions between the tooth portions, and the corrugated fins are subjected to a heat treatment in a state where a spacer for pressing the corrugated fins against the tooth portions is inserted between the corrugated fins. The above problem was solved by brazing corrugated fins.
A heat sink according to the present invention is a comb-shaped member having a plurality of teeth having a predetermined thickness at predetermined intervals, and a plurality of corrugates having a predetermined height and being corrugated and disposed between the teeth. And the corrugated fin is divided into a plurality of portions between the tooth portion and the tooth portion, and a spacer for pressing the corrugated fin against the tooth portion is provided between the corrugated fins. The above problem has been solved.
A heat sink according to the present invention is a comb-shaped member having a plurality of teeth having a predetermined thickness at predetermined intervals, and a plurality of corrugates having a predetermined height and being corrugated and disposed between the teeth. Preferably, the corrugated fin is divided into two portions between the tooth portions, and the corrugated fins are preferably separated from each other.
Further, in the present invention, in the comb-shaped member, a means in which the tip portions of the adjacent tooth portions are integrally connected to each other may be adopted.
[0011]
In the method for manufacturing a heat sink according to the present invention, the corrugated fin is divided into two (a plurality of parts) between the teeth and the teeth, and a spacer is inserted between the corrugated fins. When heat treatment is performed with the fin pressed against the teeth, the comb-shaped member and the corrugated fin can be sufficiently joined by brazing, and thereby, sufficient heat conduction can be obtained without joint failure, The desired fin efficiency can be maintained.
[0012]
FIG. 1 shows an example of a heat sink structure of the present invention, and FIGS. 2 to 4 show members of a brazed heat sink which is a means of FIG. 1. Specifically, the heat sink of the present invention is shown in FIG. As shown in the figure, the structure comprises a comb-shaped material 10 of an extruded material or a die-cast material, a corrugated fin 17, and a spacer 19. As shown in FIG. 2, the comb-shaped member 10 has a shape in which a plurality of flat-plate-shaped teeth 12 are arranged in parallel to a single base portion (heat receiving portion) 11. As shown in FIG. 3, the corrugated fins 17 are a plurality of thin-walled panels subjected to corrugation, and the width dimension W2 of the corrugated fins 17 is the distance between the teeth 12, 12, and the corrugated fins 17 are provided between the teeth 12, 12. It is set to be smaller than the value divided by the number 17. As shown in FIG. 4, the spacer 19 has a plate shape bent in a V-shape, and is elastically deformable so that the thickness expands in the direction of arrow A.
[0013]
When manufacturing such a heat sink, two corrugated fins 17 are inserted into the gaps 14 between the respective tooth portions 12, 12 of the comb-shaped member 10, and are parallel to the tooth portions 12 between the corrugated fins 17, 17. The plate-like spacer 19 is inserted in the state.
Then, as shown by an arrow A in FIG. 4, the corrugated fin 17 is pressed against the tooth portion 12 by the spacer 19. The core thus assembled is brazed in a brazing furnace in an integrated manner to form an integral heat sink structure.
[0014]
Further, since the comb-shaped extruded material 10 is made of aluminum or an aluminum alloy having good heat conductivity and the base portion 11 and the tooth portion 12 are integrated, a heat source is provided on the surface of the base portion 11 to perform cooling. In this case, good heat conduction from the base portion 11 to the tooth portion 12 is maintained and the cost is low. In addition, the heat treatment is performed in a state where the corrugated fin 17 is pressed against the tooth portion 12 by the spacer 19 and is in contact therewith. Therefore, the corrugated fins 17 and the tooth portions 12 are sufficiently brazed, and the occurrence of poor joining can be prevented. As a result, a fin-efficient heat sink can be provided.
[0015]
In the integrated brazing structure of the present invention, a heating element such as a semiconductor element is mounted on a flat portion outside the base portion 11 and used as a radiator. Heat is efficiently transmitted to the thin corrugated fins 17 brazed to the teeth 12 and transmitted to the portion of the teeth 12 having the area, and finally the heat is released to the air passing through the corrugated fins 17. Will be.
In the integrated brazing structure of the present invention, the thickness of the base portion 11, the thickness of the tooth portion 12, the thickness of the fins 17, the pitch of the fins 17, the fin through-holes, the cutout of the looper, and the like can be widened as necessary. Various combinations are possible.
[0016]
In the prior art, in the heat sink 70, the diameter or the thickness of the fin 71 for transmitting heat to the air, the frame or the lattice of the extruded profile is difficult to be 1.0 mm or less, and the heights of the pins and the fins are limited. Yes, there are technical limitations. In the heat sink 80, a thin fin similar to the present invention can be used, but a portion corresponding to the tooth portion 12 of the present invention for efficiently transmitting heat from the base portion is missing, and the fin 82 is free standing. Therefore, it is difficult to increase the height of the fins 82, and it is difficult to apply the fins 82 other than as a compact heat sink.
[0017]
In the present invention, the interval between the teeth 12 of the comb 10 is designed to be slightly smaller than the width of the corrugated fin 17 + the width of the spacer, as shown in FIG. The corrugated fins 17 can be easily inserted into W1 between the portions 12, and thereafter, the spacers 19 are inserted between the corrugated fins 17 and 17, and the elasticity of the spacers 19 causes the corrugated fins 17 to be inserted from the mountain direction. If the comb-shaped extruded material 10 and the corrugated fin 17 are lightly pressed, the close contact between the tooth portion 12 and the corrugated fin 17 is completed. By performing the heat treatment in this state, it is possible to join the fins and the tooth portions 12 without poor joining.
[0018]
The spacers 19 inserted between the corrugated fins 17 are made of an aluminum plate or an aluminum alloy plate, and can be joined to the corrugated fins 17 by a heat treatment. In this case, it is possible to transfer heat from the base portion 11 to the corrugated fins 17 by contacting the base portion 11 and to have a rectifying effect on cooling air passing between the corrugated fins 17.
[0019]
Alternatively, as shown in FIG. 5, the spacer 19 may be made of a SUS plate or the like and removed after the heat treatment, so that a gap 14 exists between the corrugated fins 17.
This gap 14 can also be used as an air passage when used as a radiator during brazing in a furnace. In this case, the flow velocity of the air inside the gap 14 is faster than the flow velocity of the air between the corrugated fins 17, so that the warmed air between the corrugated fins 17 is sucked out to the gap 14 side, thereby further cooling effect. Can be provided.
[0020]
In the present invention, as shown in FIG. 6, in the comb-shaped member 10, the tip portions of the adjacent tooth portions 12 are integrally connected to each other to form a second base portion 13. By arranging a heat source on the front surface and the back surface of the portion 11 and the base portion 13, both surfaces can be cooled.
[0021]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, a first embodiment of a heat sink manufacturing method and a heat sink according to the present invention will be described with reference to the drawings.
[0022]
FIG. 1 is a front view (a) and a bottom view (b) showing the heat sink of the present embodiment, and FIGS. 2 to 4 are front views showing members of the heat sink in FIG. 1, respectively.
[0023]
The heat sink according to the present embodiment is configured to include the comb-shaped member 10, the corrugated fin 17, and the spacer 19.
[0024]
As shown in FIG. 2, the comb-shaped member 10 has a shape in which a plurality of flat-plate-shaped teeth 12 are arranged in parallel and suspended from a single base portion (heat receiving portion) 11. 12 is an integral member made of an extruded material or a die-cast material.
A not-shown heat source (cooled portion) is arranged on a flat portion on the outer surface of the base portion (heat receiving portion) 11. As the heat source, a power module (power device element) such as a MOSFET (Metal Oxide Silicon Effect Transistor), an IGBT (Insulated Gate Bipolar Transistor), an IPM (Intelligent Power Module) or the like can be applied.
The dimensions of the base 11 in plan view are set substantially equal to the contour dimensions of these power modules.
The dimension between the tooth portions 12, 12 is set as shown by W1 in FIG.
[0025]
As shown in FIG. 3, the corrugated fins 17 are formed of a plurality of thin panels formed by corrugating an aluminum plate or an aluminum alloy plate into a corrugated shape by roller forming or pressing, and have a width dimension W2 corresponding to the tooth portion 12. , 12 are set to be smaller than 1/2 of the interval W1. The corrugated fins 17 are obtained by heat-treating a brazing sheet having an aluminum brazing material provided on its surface at a thickness of about 10% and brazing the teeth 12. As the brazing material on the surface of the corrugated fin 17, an Al-Si alloy, another Al-eutectic alloy, or the like can be used.
[0026]
As shown in FIG. 4, the spacer 19 has a plate shape obtained by bending an aluminum plate or an aluminum alloy plate into a V-shape, and is elastically deformable so that the thickness expands in the direction of arrow A. Is done. The spacer 19 is an aluminum plate or an aluminum alloy plate having the same material and structure as the corrugated fins 17, and the surface is provided with the brazing material as described above, or even if the brazing material is provided. Good.
The thickness dimension of the spacer 19 is set to be larger than the interval W4 between the corrugated fins 17, 17 when the corrugated fins 17, 17 are joined to the tooth portions 12, 12 without the spacer 19.
[0027]
When such a corrugated fin is manufactured, two corrugated fins 17, 17 are inserted into the gap 14 between the respective tooth portions 12, 12 in the comb-shaped member 10, and the toothed portions are interposed between the corrugated fins 17, 17. A plate-like spacer 19 is inserted in a state parallel to 12. Then, as shown by an arrow A in FIG. 4, the corrugated fin 17 is pressed against the tooth portion 12 by the spacer 19.
Here, at least the corrugated fin 17 is made of an aluminum plate or an aluminum alloy plate, and is provided with an Al-based brazing material on the surface in contact with the tooth portion 12 and the spacer 19. Since the brazing filler metal can be provided, the tooth portions 12, the corrugated fins 17, and the spacers 19 are joined by the heat treatment.
The core thus assembled is brazed in a brazing furnace in an integrated manner to form an integral heat sink structure.
[0028]
Further, since the comb-shaped extruded material 10 is made of aluminum or an aluminum alloy having good heat conductivity and the base portion 11 and the tooth portion 12 are integrated, a heat source is provided on the surface of the base portion 11 to perform cooling. In this case, the corrugated fins 17 are heated by the spacers 19 in contact with the teeth 12 while maintaining good heat conduction from the base 11 to the teeth 12. The fins 17 and the teeth 12 are sufficiently brazed to prevent poor joints from occurring.
In the heat sink having the integral brazing structure of the present embodiment, a heating element such as a power module is mounted on a flat portion outside the base portion 11 and used as a radiator. Is transferred to the tooth portion 12 having an appropriate heat transfer cross-sectional area, and is further efficiently transferred to the thin corrugated fins 17 brazed to the tooth portion 12, and finally the corrugated fins 17 are removed. The heat will be dissipated to the passing air. At this time, the heat is transmitted from the base portion 11 to the corrugated fins 17 even through the spacers 19 made of aluminum, and the spacers 19 can have a rectifying action for adjusting the direction of the cooling air in the heat sink. Thus, the flow of the cooling air is stabilized, and the cooling efficiency can be improved. Thereby, a desired cooling efficiency can be obtained, so that the heat sink can be reduced in size and space can be saved.
[0030]
In the present embodiment, the interval W1 between the teeth 12, 12 of the comb-shaped member 10 is set to be slightly smaller than twice the width W2 of the corrugated fin 17 + the width of the spacer, and as shown in FIG. The corrugated fins 17 are easily inserted into W1 between the teeth 12 of the comb-shaped extruded material 10, and the spacers 19 are inserted between the corrugated fins 17 and 17 thereafter. Thus, if the comb-shaped extruded material 10 and the corrugated fin 17 are lightly pressed from the crest direction of the corrugated fin 17, the close contact between the tooth portion 12 and the corrugated fin 17 is completed. By performing the heat treatment in this state, it is possible to join the fins and the tooth portions 12 without poor joining.
[0031]
Hereinafter, a heat sink manufacturing method and a heat sink according to a second embodiment of the present invention will be described with reference to the drawings.
FIG. 5 is a front view showing the heat sink of the present embodiment.
[0032]
This embodiment is different from the above-described first embodiment in that the heat sink does not include the spacer 19. The other corresponding components have the same reference characters allotted, and description thereof will not be repeated.
[0033]
In the method of manufacturing the heat sink according to the present embodiment, for example, instead of the aluminum spacer 19 shown in FIG. As shown in b), it is possible to use a spacer 21 having a taper surface in the thickness direction and comprising opposing spacer members 21a, 21a.
These SUS spacers 19 and 21 have their surfaces coated with BN (boron nitride).
[0034]
As a result, the corrugated fins 17, 17 are inserted between the teeth 12, 12, and the SUS spacer 19 or the spacer 21 is inserted. After the spacer 21 is inserted between the teeth 12, the spacer members 21 a move in the direction of arrow B shown in FIG. 4. Thereby, the thickness dimension of the spacer 21 increases in the direction of the arrow A, and the corrugated fin 17 can be pressed against the tooth portion 12 and brought into close contact with the tooth portion 12, similarly to the spacer 19 described above. In this state, a heat treatment is performed. Similarly, the corrugated fins 17 and the teeth 12 are joined by brazing.
[0035]
After brazing by heat treatment, the spacers 19 and 21 made of SUS are removed. At this time, since the SUS does not react with the aluminum, the SUS spacers 19 and 21 can be easily removed. Further, the BN applied to the surface makes it possible to more easily remove the BN. Thereby, the gap 14 exists between the corrugated fins 17.
[0036]
Further, in the present embodiment, the same effects as those of the first embodiment can be obtained, and a gap 14 exists between the corrugated fins 17 as shown in FIG. 14 can be used as an air passage when used as a radiator. In this case, the flow velocity of the air inside the gap 14 is faster than the flow velocity of the air between the corrugated fins 17. A further cooling effect can be obtained by the so-called eject effect in which the warmed air in the air is sucked out to the gap 14 side.
[0037]
Hereinafter, a third embodiment of a heat sink manufacturing method and a heat sink according to the present invention will be described with reference to the drawings.
FIG. 6 is a front view showing the heat sink of the present embodiment.
[0038]
The present embodiment is different from the above-described first embodiment in that the tips of the teeth 12 are connected to form a second base 13. The other corresponding components have the same reference characters allotted, and description thereof will not be repeated.
As shown in FIG. 6, the heat sink of the present embodiment has a configuration in which, in the comb-shaped member 10, the tip portions of the adjacent tooth portions 12 are integrally connected to each other to form a second base portion 13. I have.
[0039]
In the present embodiment, the same effects as those of the first embodiment can be obtained, and a power device for inverter control is disposed on a flat portion on the outer surface of the base portion 11. A voltage converter (converter) is arranged on the flat portion on the back surface, whereby heat sources can be arranged on the front surface and the back surface of the base portion 11 and the base portion 13 to cool both surfaces.
[0040]
Next, examples of the present invention will be described in detail together with comparative examples.
[0041]
<Example>
As an example, a heat sink was manufactured with the member configuration shown in FIG. 1 and the heat transfer characteristics were evaluated. That is, as shown in FIG.
Material: Pure aluminum A1050-F
Base size: 150mm x 120mm
Base part thickness: 10mm
Tooth height: 40mm
Tooth thickness: 5mm
Tooth spacing: 24mm
Number of teeth = 6 The shaped material having the above cross section was extruded to a length of 10 m, and was cut into a width of 120 mm immediately after setting.
[0042]
Corrugated fin: as shown in FIG.
The material is brazing sheet (core material A3003 / skin material BA4343)
Fin material dimensions: 0.10 mm thick x 50 mm wide coil.
Dimensions after corrugated processing;
Fin height: 10mm
Fin pitch: 3.8mm
Fin length: 120mm
Number of mountains: 10 mountains / 40mm
[0043]
Spacer: As shown in FIG.
The material is pure aluminum A1050-P
Dimensions: 40.0 mm width x 20.0 mm length x 1.5 mm thickness plate.
Spacer maximum thickness: 4.5mm
And bent in a V -shape such that
[0044]
The corrugated fins 17 and the spacers 19 are combined and arranged on the comb-shaped extruded material 10 having the above dimensions as shown in FIG. After that, the combined core was brazed in an inert gas atmosphere furnace. As a result, an integrated brazing heat sink having no problems such as brazing integrity and dimensions was obtained.
[0045]
The external dimensions of the heat sink of the embodiment are 150 mm × 120 mm × 50 mm.
Weight: 1.2kg
Heat radiation area: 1.04 mm ²
Heat dissipation performance: 690W
Pressure loss: 70Pa
[0046]
<Comparative example>
As a comparative example, a corrugated fin brazing heat sink shown in FIG. 8 was produced. Dimensions: 150mm x 200mm x 60mm
Weight: 2.5kg
Heat radiation area: 1.05 mm ²
Heat dissipation performance: 660W
Pressure loss: 40Pa
[0047]
As described above, according to the structure of the heat sink of the present invention, the external dimensions can be reduced while maintaining the heat radiation performance (cooling performance) or slightly improving the heat radiation area while the heat radiation area is almost the same. That is, it can be understood that space can be saved.
[0048]
【The invention's effect】
According to the heat sink manufacturing method and the heat sink of the present invention, the corrugated fin is divided into two portions between the teeth and the teeth, and a spacer is inserted between the corrugated fins to thereby form the corrugated fin. When the heat treatment is performed while pressing the teeth against the teeth, the comb-shaped member and the corrugated fin can be sufficiently joined by brazing, whereby it is possible to obtain a sufficient heat conduction without a joining defect, and The fin efficiency can be maintained.
[Brief description of the drawings]
FIG. 1 is a front view (a) and a bottom view (b) showing a first embodiment of a heat sink according to the present invention.
FIG. 2 is a front view showing members of the heat sink in FIG.
FIG. 3 is a front view showing members of the heat sink in FIG. 1;
FIG. 4 is a front view showing members of the heat sink in FIG. 1;
FIG. 5 is a front view showing a second embodiment of the heat sink according to the present invention.
FIG. 6 is a front view showing a third embodiment of the heat sink according to the present invention.
FIG. 7 is a front view showing a conventional heat sink.
FIG. 8 is a front view showing a conventional heat sink.
FIG. 9 is a front view showing a conventional heat sink.
[Explanation of symbols]
Reference Signs 10 Comb 11 Base portion 12 Tooth portion 13 Base portion 14 Gap 17 Corrugated fin 19, 21 Spacer 21a Spacer member

Claims (4)

A comb-shaped member having a plurality of teeth having a predetermined thickness at predetermined intervals, and a plurality of corrugated fins having a predetermined height and subjected to corrugation are disposed between each tooth and a brazing process. A method for manufacturing a heat sink in which a comb member and a corrugated fin are integrally joined by
The corrugated fins are divided into a plurality of portions between the tooth portions, and the corrugated fins are subjected to a heat treatment in a state where a spacer for pressing the corrugated fins against the tooth portions is inserted between the corrugated fins. And a method of manufacturing a heat sink, comprising brazing a corrugated fin. A comb-shaped member having a plurality of teeth having a predetermined thickness at predetermined intervals, and a plurality of corrugated fins having a predetermined height and corrugated disposed between the teeth. A heat sink, wherein the corrugated fin is divided into a plurality of portions between the teeth, and a spacer is provided between the corrugated fins. A comb-shaped member having a plurality of teeth having a predetermined thickness at predetermined intervals, and a plurality of corrugated fins having a predetermined height and corrugated disposed between the teeth. A heat sink, wherein the corrugated fin is divided into two portions between the tooth portions, and the corrugated fins are separated from each other. The heat sink according to claim 2, wherein, in the comb-shaped member, tip portions of the adjacent tooth portions are integrally connected to each other.

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