JP6744607B2 - Angle detector - Google Patents

Description

The present invention relates to an angle detection device including a back yoke.

As an angle detection device that can detect angles with high sensitivity in a very simple assembly process without requiring complicated processing, it is formed of a disk body made of a magnetic material having uniaxial magnetic anisotropy. The plate body is arranged in a disk having a substantially same outer shape facing one plate surface of the rotor, which is rotated in the disk plane about the center point, and is divided into a plurality of fan-shaped areas on the outer periphery of the divided area. A stator around which an exciting coil or a detection coil is wound, and a back yoke that is disposed on the opposite side of the surface on which the rotor is disposed with the stator sandwiched between the stator and the disk body of the stator having substantially the same outer shape. An angle detection device including and is known (for example, see Patent Document 1).

FIG. 1 is an angle detection device described in Patent Document 1, which is formed of a disk body made of a magnetic material having uniaxial magnetic anisotropy, and rotates within a disk surface around a center point 5a to which a pivot 6 is joined. The rotor 5 (FIG. 1(C)) and the stator 3 (FIG. 1(B)) having substantially the same outer shape, which is disposed so as to face one disc surface of the rotor 5 in a non-contact state, A magnetic thin plate that does not have (isotropic) is formed with substantially the same outer shape as that of the stator 3, and is disposed so as to face the surface opposite to the surface on which the rotor 5 is disposed in contact or non-contact with the stator 3. And a back yoke 2 (FIG. 1A). The stator 3 is divided into semicircles (3a, 3b), and the detection coil 4a (denoted as S1) and the exciting coil 4b (denoted as P1) are wound around the side surfaces of the respective regions 3a, 3b. ing. The rotor 5 is formed of a magnetic plate or a magnetic composite plate having a uniaxial magnetic anisotropy (direction indicated by an arrow in FIG. 1C) in its surface direction, and is joined with the central point 5 a coaxial with the pivot 6. There is.

In a magnetic body having uniaxial magnetic anisotropy, there are an easy axis direction in which the magnetic body is easily magnetized and a difficult axis direction in which it is difficult to magnetize in a direction orthogonal to the easy axis direction. In the case of FIG. 1, the vertical direction in the figure is the easy axis direction, and the left and right directions are the difficult axis directions. Here, the magnetic permeability in the easy axis direction is large, and in the hard axis direction orthogonal thereto, the magnetic permeability is a fraction of the magnetic permeability in the easy axis direction to about one tenth, or when it is smaller, it is about the same as vacuum. Become.

In this structure, when the rotor 5 rotates, the easy axis direction of the magnetic anisotropy changes accordingly. The rotation angle can be detected by utilizing the change of the magnetic anisotropy in the easy axis direction. The principle of detecting the rotation angle will be described below with reference to FIG.

First, the exciting coil 4b is connected to the AC power supply 40 and is supplied with an AC current. When an alternating current is supplied to the exciting coil 4b, the magnetic field is generated in a direction orthogonal to the plane direction when the entire region 3b of the stator 3 is viewed on average, but this magnetic field is in the vicinity of the coil copper wire, especially immediately below it. Then, it occurs in a direction parallel to the plane and orthogonal to the coil copper wire, and its strength is far stronger than the magnetic field in other places (for example, the magnetic field in the middle of the region 3b). That is, a strong magnetic field is generated in the region 30 where the detection coil 4a and the exciting coil 4b are adjacent to each other. A voltage corresponding to the magnetic field is generated in the detection coil 4a by the magnetic field excited by the excitation coil 4b, and the voltage is detected by the synchronous detection circuit 41 connected to the detection coil 4b.

Here, when the rotor 5 rotates, the above-mentioned easy axis direction changes. An induced voltage due to the magnetic force generated by the exciting coil 4b is generated in the detection coil 4a, but the magnetic field generated by the exciting coil 4b is affected by the magnetic force generated by the exciting coil 4b in the easy axis direction. 5 is affected by the easy axis direction. That is, the voltage value generated in the detection coil 4a changes depending on the angular position of the rotor 5. According to this principle, the angular position of the rotor 5 (the rotation angle from the reference angular position) can be known from the voltage generated in the detection coil 4a.

WO2012/002126 A1 publication

The back yoke 2 is arranged so that the coil current can efficiently generate the magnetic flux and prevents the leakage of the magnetic flux. The presence of the back yoke 2 improves the output characteristics such as an increase in the output voltage. It is desirable that the back yoke has isotropic magnetic characteristics so that it does not affect the angle information. By the way, when a rolled magnetic plate is used for such a back yoke, the magnetic properties of the back yoke must be directional because the rolling process has directionality even if the material properties of the plate are isotropic. become. For this reason, there is a slight difference between the magnetic permeability in the rolling direction and the magnetic permeability in the direction orthogonal to the rolling direction, and as a result, magnetic characteristics vary depending on the direction. The higher magnetic permeability corresponds to the easy axis of magnetization, and the other corresponds to the hard axis of magnetization. If the easy axis of magnetization is present in the back yoke in this way, the magnetic flux will easily pass in a specific direction, and as a result, the action of the rotor will not be reflected correctly, offset will occur in the two-phase output of the detection coil, and the angle detection There is a problem that the value error becomes large.

The present invention has been made to solve the above problem, and by providing a back yoke to improve output characteristics, the offset included in the output of the detection coil is improved and the angle detection accuracy is improved. It is an object of the present invention to provide an angle detection device that can perform such an operation.

An angle detection device of the present invention has a stator provided with an excitation coil and a detection coil, a rotor having a directional property arranged on one side of the stator, and a directional property arranged on the other side of the stator. An angle detector including a back yoke, wherein the back yoke has a magnetic characteristic in one direction that is an easy axis of magnetization and a magnetic characteristic in a direction orthogonal to the one direction. The adjustment of the magnetic characteristics is performed by adjusting the ratio of the cross-sectional area in the one direction and the cross-sectional area in the direction orthogonal to the one direction. The cross-sectional area for one direction is the area of the cross section along the direction crossing the one direction, and the cross-sectional area for the direction orthogonal to the one direction is the cross section along the direction crossing the direction orthogonal to the one direction. The cross-sectional area.

Further, the angle detecting device of the present invention includes a stator including an exciting coil and a detecting coil, a directional rotor disposed on one side of the stator, and a directional characteristic disposed on the other side of the stator. And a back yoke having a back yoke, the magnetic characteristic in one direction being the easy axis of magnetization of the back yoke and the magnetic characteristic in a direction orthogonal to the one direction being equalized to each other. The magnetic characteristic is adjusted, and the means for adjusting the magnetic characteristic is characterized in that a modifying layer for changing the magnetic characteristic is formed in the back yoke. Examples of the modified layer of the present invention include a hardened layer that can be formed by dents or laser irradiation.

In the present invention, the directional back yoke includes a plate material obtained by rolling or a plate material obtained by a liquid quenching method. In the case of a rolled plate material, directionality is imparted in the rolling direction. Examples of the plate material obtained by the liquid quenching method include a magnetic ribbon made of an amorphous alloy having a thickness of about 20 μm. In the liquid quenching method, melted magnetic metal is injected onto a rotating roll and rapidly cooled to produce long ribbon-like ones. This is because magnetic anisotropy occurs in the plane perpendicular to it. The invention also includes a mode in which the magnetic property is magnetic permeability.

In the present invention for adjusting the cross-sectional area, specifically, the cross-sectional area for the one direction (the rolling direction in the case of being rolled) is provided by providing the cut portion on the back yoke. Means for reducing the cross-sectional area in the direction orthogonal to the direction .mu.roll, the magnetic permeability in the direction orthogonal to the one direction .mu.cross, the cross-sectional area in the direction orthogonal to the direction Sroll, the one direction A means for reducing at least the cross-sectional area in the one direction is preferably adopted so that when the cross-sectional area in the direction orthogonal to the direction is Scross, μroll×Sroll≈μcross×Scross.

According to the present invention, by providing the back yoke, the output characteristic is improved, and the offset included in the output of the detection coil is improved, so that the angle detection accuracy can be improved.

It is a figure which decomposes|disassembles and shows the structure of the conventional angle detection apparatus. It is a side view which shows the resolver which concerns on one Embodiment of this invention. It is a top view of the 1st and 2nd stator which constitutes a stator. It is a top view which shows the stator of another form. It is a figure which shows the element for adjusting the magnetic characteristic of a back yoke. It is a figure which decomposes|disassembles and shows the structure of the resolver of embodiment which equipped the back yoke which carried out D cut as adjustment of a magnetic characteristic. It is a figure which decomposes|disassembles and shows the structure of the resolver of embodiment which provided the back yoke which formed the slit as adjustment of a magnetic characteristic. It is a figure which shows another form of the excision part formed in a back yoke, (A) shows another form of D cut, (B)-(D) shows another form of a slit. FIG. 4 is a cross-sectional view of the back yoke in which the modified layer is formed in the rolling direction. It is an output waveform of the resolver of the embodiment in which the back yoke is D-cut. It is an output waveform of the resolver of the embodiment in which a slit is formed in the back yoke. 8 is an output waveform of a resolver of a comparative example using a back yoke without adjusting magnetic characteristics. 7 is an output waveform of a resolver of a comparative example that does not include a back yoke.

Hereinafter, a resolver (angle detection device) according to an embodiment to which the present invention is applied will be described with reference to the drawings.

[1] Configuration of Resolver FIG. 2 shows the configuration of the resolver 100 according to the embodiment of the present invention. The resolver 100 is an axial resolver and detects information on the angle of the shaft (rotational axis) 60 of the motor 200. The resolver 100 has a stator 30, a rotor 50, and a back yoke 20.

The stator 30 is fixed to a housing (not shown) of the resolver 100. The stator 30 has a substantially circular disc shape when viewed from the axial direction (extending direction of the shaft 60). An opening is provided in the center of the stator 30 so that the shaft 60 can rotate therethrough. The stator 30 is composed of a first stator 31 and a second stator 32 laminated on the surface of the first stator 31 on the rotor 50 side.

FIG. 3 shows a state in which the first stator 31 and the second stator 32 that form the stator 30 are viewed from the axial direction. The first stator 31 and the second stator 32 are the same, and are laminated and bonded in a state in which the phases of the coils are at angular positions deviated from each other by 45° about the axis. Since the first stator 31 and the second stator 32 are the same, the first stator 31 will be described here.

The first stator 31 has a disk-shaped PCB substrate as a base material, and has four coils of the same fan shape opened at 90° on the surface thereof. Each coil has an inner circumference 1/4 circumference along the inner circumference, an outer circumference 1/4 circumference along the outer circumference, and an inner circumference 1/4 circumference and an outer circumference 1/4. It is composed of two straight portions which connect both ends of the four circumferential portions and extend in the radial direction. The four coils are two exciting coils P11 and P12 and two detecting coils S11 and S12, and the exciting coils and the detecting coils are alternately arranged in the circumferential direction.

Like the first stator 31, the second stator 32 has two exciting coils P21 and P22 and two detecting coils S21 and S22. In each of the stators 31 and 32, a hole is provided in the PCB substrate as the above-mentioned opening in the center portion inside the quarter circumference portion on the inner circumferential side of each of the four coils, and the shaft 60 is rotatable in the hole. It penetrates in the state.

In this example, the exciting coil P1 (P11, P12) of the first stator 31 receives, for example, a sinω ₁ t exciting current, and the exciting coil P2 (P21, P22) of the second stator 32 is input. A current for excitation of sin ω ₂ t, for example, is input to the system. Here, ω ₁ and ω ₂ must not be equal to each other, and the frequency of one is 1.1 to 1.9 times that of the other. At this time, sin ω ₁ t of the P1 system and sin ω ₂ t of the P2 system are separated by synchronous detection so as not to interfere with each other. Thereby, the angle information of the rotor 30 is obtained from the detection signals of the detection coils S11, S12, S21, S22. The details of this technique are described in the above "WO2012/002126 A1".

The back yoke 20 has a disk shape similar to that of the stator 30, and is arranged coaxially with the stator 30 on the back side of the second stator 32, which is the side opposite to the rotor 50. Although the back yoke 20 is bonded to the lower surface of the stator 32 in the illustrated example, a certain gap may be formed between the back yoke 20 and the stator 32.

The back yoke 20 is a disc-shaped thin plate having a predetermined thickness (for example, 0.3 mm) obtained by rolling a non-directional material (for example, a non-oriented silicon steel plate). As shown in FIG. 5, a hole 201 is formed in the center of the back yoke 20 so that the shaft 60 can rotate in the same manner as the stator 30. The back yoke 20 has a directionality due to the rolling process, the rolling direction is an easy axis of relatively high magnetic permeability, and the direction orthogonal to the rolling direction is relatively low in magnetic permeability. It is the axis.

The rotor 50 has a disk shape similar to that of the stator 30, and is coaxially arranged with respect to the stator 30 with a predetermined gap. The rotor 50 is fixed in a state where a shaft 60, which is a drive shaft of the motor 200, penetrates through the center of the rotor 50, and rotates together with the shaft 60. The rotor 50 has a plate thickness of about 0.3 mm and is made of a disk-shaped grain-oriented silicon steel plate having a uniaxial anisotropy as a whole in magnetic permeability.

[2] Basic Function of Resolver In the resolver 100, when the motor 200 rotates, the rotor 50 fixed to the shaft 60 rotates. When the rotor 50 rotates, the magnetic fields generated by the exciting coils P11, P12, P21, P22 of the first stator 31 and the second stator 32 are modulated according to the rotation angle of the rotor 50 having uniaxial magnetic anisotropy. The influence appears in the voltage induced in each of the detection coils S11, S12, S21, S22 of the first stator 31 and the second stator 32. That is, the voltages induced in the respective detection coils S11, S12, S21, S22 of the first stator 31 and the second stator 32 are modulated by the angular position of the rotor 50. Specifically, the detection coils S11, S12, S21, S22 are periodic signals containing the angle information of the rotor 50, and the rotor 50 is processed by processing the detection signals of these detection coils S11, S12, S21, S22. The rotation angle of is obtained.

[3] Alternative Embodiment [3-1] Stator The stator 30 has a two-layer structure, but the stator is configured by the exciting coils P1 and P2 and the detecting coils S1 and S2 shown in FIG. It may be. The stator 30B is divided into four first to fourth fan-shaped bodies 3a, 3b, 3c, 3d having substantially the same outer shape, and two sets of fan-shaped bodies ((( 3a, 3c) and (3b, 3d)), the coil wound around the outer circumference of each of the groups of the first fan-shaped body 3a and the third fan-shaped body 3c is the detection coil 4a, 4c (referred to as S1 and S2), and the coils wound along the outer circumference of each set of the second fan-shaped body 3b and the fourth fan-shaped body 3d are exciting coils 4b and 4d (P1). , P2). Each coil 4a, 4b, 4c, 4d is wound around the outer circumference of each fan-shaped body 3a, 3b, 3c, 3d for about 100 turns, and the height of the coil is about 2 mm.

The exciting coils P1 and P2 are wound such that the directions of the magnetic fluxes in the directions orthogonal to the surface direction of the stator 30B are opposite to each other (when one is the N pole, the other is the S pole). The detection coils S1 and S2 are connected and connected so that the winding directions are opposite to each other. By doing so, when the rotation angle of the rotor 5 is 0 degree, the detection coil S1 and the excitation coil P1, and the detection coil S2 and the excitation coil P2 are located in the easy axis direction of the magnetic anisotropy of the rotor 5. Because of this, it will bond strongly. On the contrary, since the detection coil S1 and the exciting coil P2, and the detection coil S2 and the exciting coil P1 are located in the hard axis direction of the magnetic anisotropy of the rotor 5, the coupling becomes almost zero. The resolver shown in FIGS. 6 and 7 described later employs the stator 30B shown in FIG.

[3-2] Back Yoke The back yoke 20 has a disc shape, but the back yoke 20 does not rotate, and therefore is not limited to the disc shape, and may have another shape.

[4] Adjustment of magnetic characteristics of back yoke The back yoke 20 is a disk-shaped magnetic thin plate obtained by rolling a non-directional material, but has directionality by rolling. In such a back yoke 20, there is a difference in the magnetic characteristics (permeability) between the rolling direction and the direction orthogonal to the rolling direction. Therefore, an offset occurs in the two-phase output of the detection coil and the angle detection value The large error is as described above. Therefore, adjustment for equalizing the magnetic characteristics generated between the rolling direction of the back yoke 20 and the direction orthogonal to the rolling direction and minimizing the difference (referred to as “adjustment of magnetic characteristics” in the following description). Is applied to the back yoke 20. Hereinafter, examples of means for adjusting magnetic characteristics will be described.

[4-1] Decrease the cross-sectional area in the rolling direction In adjusting the magnetic characteristics, first, the magnetic permeability in each of the rolling direction of the back yoke 20 and the direction orthogonal to the rolling direction is measured. As shown in FIG. 5, the magnetic permeability in the rolling direction of the back yoke 20 is μroll, the magnetic permeability in the direction orthogonal thereto is μcross, and the cross-sectional area of the diameter passing through the center of the back yoke 20 with respect to the rolling direction (the area of the XX cross section). ) Is Sroll, the cross-sectional area (the area of the YY cross section) of the diameter with respect to the direction orthogonal thereto is Scross, the diameter of the back yoke 20 is D, the central hole diameter for shaft insertion is d, and the plate thickness is t. With respect to Sroll=(D−d)×t, and the cross-sectional area Scross=(D−d)×t in the direction orthogonal to the rolling direction.

Generally, the magnetomotive force is proportional to the exciting current, and the magnetic flux resulting therefrom is given by the magnetomotive force/magnetic resistance. Here, magnetic resistance=magnetic path length/(cross-sectional area through which magnetic flux passes×permeability). The magnetic path length is determined by the shape of the stator coil, the size of the gap between the stator coil and the rotor, and the size of the gap between the stator coil and the back yoke. If this magnetic resistance is equalized in the rolling direction of the back yoke and the direction orthogonal thereto, it is possible to suppress the occurrence of the difference in magnetic characteristics in those directions. That is, for that purpose, Sroll may be reduced with respect to Scross and the ratio of Sroll:Scross may be adjusted so that Sroll×μroll≈Scross×μcross.

In FIG. 6, in the case of μroll:μcross=1.2:1, the D-cut (removed portion) 202 that cuts the outer peripheral portion of the back yoke 20 linearly along the rolling direction is formed to reduce the Sroll. Then, Sroll×μroll≈Scross×μcross. The D cut 202 is orthogonal to XX in FIG. Although the D-cut portion is formed only on one end side in FIG. 6, both sides may be D-cut as shown in FIG. 8(A).

In FIG. 7, slits (cutting portions) 203 extending in the direction orthogonal to the rolling direction are formed on both sides of the central hole 201 in a state along XX of FIG. 5 to reduce the Sroll. The width of the slit 203 is, for example, about 1 to 2 mm in order to increase the magnetic resistance. In FIG. 7, the slit 203 communicates with the central hole 201 and is formed on both sides, but it may be formed only on one side of the hole 201 as shown in FIG. 8B. Further, the slits 203 may be formed between the outer peripheral edge and the inner peripheral edge on both sides of the hole 201 as shown in FIG. 8C, and further on both sides of the hole 201 as shown in FIG. 8D. You may form in the state opened to the outer peripheral edge.

The magnetic characteristics can be adjusted by reducing the cross-sectional area with respect to the rolling direction, in addition to the above D-cuts and slits, cutouts such as through holes and dents can be formed on XX.

[4-2] Formation of Modified Layer As shown in FIG. 9, a modified layer 210 is formed inside the back yoke 20 so that the magnetic flux in the rolling direction does not easily pass therethrough and the magnetic permeability can be reduced. Thus, the magnetic characteristics can be adjusted. The reformed layer 210 is preferably formed at a location on the XX cross section of FIG. 5, and the reformed layer 210 substantially reduces the Sroll. The modified layer 210 that lowers the magnetic permeability can be formed by, for example, increasing the residual stress, and specifically, a hardened layer formed by dents, laser irradiation, or the like is effective.

[5] Effects According to the above-described embodiment, since the back yoke 20 is provided, the coil current can efficiently generate the magnetic flux and the leakage of the magnetic flux can be suppressed, so that the output characteristics can be improved. On the other hand, the back yoke 20 formed by rolling has a directional property, and such a back yoke conventionally has a demerit that it causes an offset in the output of the detection signal. However, in the present embodiment, by adjusting the magnetic characteristics as described above, the magnetic permeability in the rolling direction of the back yoke 20 and the magnetic permeability in the direction orthogonal to the rolling direction can be made equal to each other. Therefore, it is possible to suppress the difference in magnetic permeability between the directions. Therefore, it is possible to suppress the occurrence of offset in the two-phase output of the detection coil while providing the directional back yoke 20, and as a result, it is possible to improve the angle detection accuracy.

10 and 11 show output waveforms (sin output signal, cos output signal) of the detected current of the resolver of the embodiment of the present invention in which the magnetic characteristics are adjusted on the back yoke obtained by rolling. 10 shows the D cut shown in FIG. 6, and FIG. 11 shows the adjustment by the slit shown in FIG. On the other hand, FIG. 12 shows the output waveform of the detected current of the resolver of the comparative example in which the magnetic characteristics of the back yoke obtained by rolling are not adjusted. Further, FIG. 13 shows the output waveform of the detection current of the resolver not including the back yoke.

The excitation conditions in each resolver are all the same, the rotation speed of the rotor is 1400 rpm, and the excitation coil P1 has a voltage of 2v and f1 (first excitation signal)=14 KHz so that the excitation signals applied to the excitation coils P1 and P2 do not interfere with each other. And a sin signal of voltage 2v, f2 (second excitation signal)=20 KHz was applied to the excitation coil P2. An induced voltage is generated in the detection coils S1 and S2 by the exciting coils P1 and P2. Since the induced voltage contains frequency components f1 and f2, the sin signal component and the cos signal component were extracted by the synchronous detection circuit.

First, as shown in FIG. 13, in the case where the back yoke is not provided, both the sin output signal and the cos output signal have substantially the same positive and negative amplitude values, and it can be seen that no offset occurs in the output waveform. .. However, the output voltage value in the output waveform is low.

Next, as shown in FIG. 12, in the case of using a directional back yoke in which the magnetic characteristics are not adjusted, the back yoke is provided, so that compared to the case of FIG. 13 in which the back yoke is not provided. The output voltage value of the output waveform is large. Looking at the output waveform, the magnitude is different between the positive amplitude and the negative amplitude, and particularly the cos output signal is greatly offset.

On the other hand, according to the embodiment in which the slit is formed in the back yoke shown in FIG. 11, the difference between the positive amplitude and the negative amplitude is reduced as compared with the output waveform shown in FIG. 12, and the offset in the cos output signal is reduced. Has been reduced. In the embodiment in which the back yoke shown in FIG. 10 is D-cut, the difference between the positive amplitude and the negative amplitude is greatly reduced compared to the output waveform shown in FIG. It is decreasing.

The present invention is suitable as a resolver.

100... Resolver (angle detector)
20... Back yoke 202... D cut (removal part)
203... Slit (excision part)
210... Modified layer 30... Stator 50... Rotor P1, P11, P12... Excitation coil S1, S11, S12... Detection coil

Claims (7)

A stator having an exciting coil and a detecting coil;
A directional rotor disposed on one side of the stator;
A directional back yoke disposed on the other side of the stator;
An angle detection device comprising:
The magnetic properties of the back yoke in one direction that is the easy axis direction of magnetization and the magnetic properties in a direction orthogonal to the one direction are adjusted to be equal to each other.
The angle detecting device, wherein the means for adjusting the magnetic characteristics adjusts a ratio of a cross-sectional area in the one direction and a cross-sectional area in a direction orthogonal to the one direction. A stator having an excitation coil and a detection coil;
A directional rotor disposed on one side of the stator,
A directional back yoke disposed on the other side of the stator,
An angle detection device comprising:
The magnetic characteristics of the back yoke are adjusted so as to equalize the magnetic characteristics in one direction that is the easy axis direction and the magnetic characteristics in the direction orthogonal to the one direction.
The angle detecting device, wherein the means for adjusting the magnetic characteristics forms a modified layer for changing the magnetic characteristics in the back yoke. The angle detecting device according to claim 1, wherein the directional back yoke is a plate material obtained by rolling. The angle detecting device according to claim 1 or 2, wherein the directional back yoke is a plate material obtained by a liquid quenching method. The angle detection device according to claim 1, wherein the magnetic characteristic is magnetic permeability. The means for adjusting the magnetic characteristics is a means for reducing the cross-sectional area in the one direction by providing a cutout portion in the back yoke than the cross-sectional area in the direction orthogonal to the one direction,
When the magnetic permeability in the one direction is μroll, the magnetic permeability in the direction orthogonal to the one direction is μcross, the cross-sectional area in the one direction is Sroll, and the cross-sectional area in the direction orthogonal to the one direction is Scross, μroll×Sroll The angle detection device according to claim 1, wherein a cross-sectional area in at least the one direction is reduced so that ≅μcross×Scross. The angle detection device according to claim 2, wherein the modified layer is a hardened layer.

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