JP2005057945A - Sintered ring magnet - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a ring magnet easy in magnetization after the assembling of a rotor, allowed in anisotropic orientation and reducible in the irregularity of torque such as cogging torque and a torque ripple by reducing the distortion of magnetized distribution in a rotative direction. <P>SOLUTION: In the sintered ring magnet formed by integrally stacking anisotropically orientated annular rings by sintering, the ring 2 in which axially extending grooved recesses 2a are periodically formed in its circumferential direction, and the ring 3 without the recesses are stacked. By this constitution, the irregularity of the torque such as the cogging torque and the torque ripple is suppressed. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to an anisotropically oriented sintered ring magnet used for an inner rotor of a permanent magnet motor.

  Radially oriented ring magnets used in the inner rotor of permanent magnet motors often perform skew magnetization in which magnetic poles are formed obliquely with respect to the axial direction in order to reduce rotational unevenness such as cogging torque. However, since the radially oriented ring magnet has a rectangular magnetomotive force, when this magnet is used in the inner rotor of a permanent magnet motor, it contains many high-order components and the cogging torque is sufficient with skew magnetization alone. In many cases, the effect of reducing the above cannot be obtained.

  Therefore, in the resin magnet, there is a method of forming irregularities on the outer periphery of the ring magnet and further skewing the irregularities in the axial direction. According to this method, it is possible to reduce the cogging torque due to the skew of the concavo-convex portion while reducing the distortion of the magnetomotive force in the rotation direction (see, for example, Patent Document 1).

  Magnets used for the inner rotor of the permanent magnet motor include polar-oriented polar anisotropic magnets in addition to the above-described radial-oriented magnets. According to the polar orientation, the magnetomotive force distribution approaches a sine wave, the distortion is reduced, and the cogging torque is reduced. Furthermore, if skew magnetization is possible, the cogging torque can be further reduced. However, the polar anisotropic magnet is oriented so that the magnetic flux passes from the magnet outer circumference to the outer circumference again through the inside of the magnet. I can't.

  Therefore, a magnet is disclosed in which a polar anisotropic magnet is divided into two or more in the axial direction, and the divided polar anisotropic magnet is shifted in the circumferential direction and skewed by a half cycle of an angle determined by cogging torque or more. (For example, refer to Patent Document 2).

JP-A-9-35933 (page 3-6, FIGS. 1 to 4) JP 2001-314050 A (page 4-5, FIG. 5)

  The above conventional resin magnet requires a special extrusion molding machine, and since a magnetic field cannot be applied during molding, anisotropic orientation cannot be achieved, and a small, high output motor that requires a strong magnet is required. There is a problem that it cannot be applied.

  Further, the polar anisotropic magnet has a problem in that it is necessary to fix a plurality of ring magnets to the rotor shaft with a predetermined skew angle with high accuracy, and the motor manufacturing process becomes complicated.

  In addition, since the polar anisotropic magnet cannot be magnetized after the rotor is assembled, when the magnetized ring magnets are fixed to the rotor shaft, they are determined due to the attractive force and repulsive force of the magnets. There are problems that it is difficult to accurately arrange the skew angle and the motor manufacturing process is complicated.

  The present invention is a ring magnet that can be easily magnetized after rotor assembly and can be anisotropically oriented, and reduces torque unevenness such as cogging torque and torque ripple by reducing distortion of magnetization distribution in the rotational direction. The object is to provide a ring magnet that can be used.

  The ring magnet according to the present invention is a sintered ring magnet in which ring-shaped anisotropically oriented rings are stacked in the axial direction and integrated by sintering. At least one of the rings is formed on an outer peripheral surface thereof. The groove-like recesses extending in the direction of the axis are periodically provided in the circumferential direction.

  According to the ring magnet of the present invention, in the sintered ring magnet in which ring-shaped anisotropically oriented rings are stacked in the axial direction and integrated by sintering, at least one of the rings has an outer periphery. Since the groove-like recesses extending in the direction of the axis are periodically provided on the surface in the circumferential direction, torque unevenness such as cogging torque and torque ripple is suppressed.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. The present invention uses a structure in which rings are stacked as a basic component, and the following description shows an example in which two to three rings are stacked. However, the present invention is not limited to this, and a ring in which a plurality of rings are stacked is shown. Applicable to magnets. Moreover, although the case where the number of magnetic poles of the ring magnet is 4 and 6 is described, the present invention is not limited to this, and can be applied to a ring magnet having 2 m magnetic poles (m is an integer). Is.

Embodiment 1 FIG.
FIG. 1 is a plan view (a) and a side view (b) showing a first embodiment of a sintered ring magnet according to the present invention, and shows an example of a four-pole magnet. As shown in the figure, the ring magnet 1 is formed by stacking two rings 2 and 3 in the axial direction and integrating them by sintering. The ring 2 is periodically formed in four concave portions 2a ( 1st recessed part) is provided and the ring 3 is a cylindrical shape without a recessed part. The concave portion 2a has a groove shape extending in the axial direction. The concave portion 2a serves as a boundary portion of the magnetic pole, and a magnetic pole is formed by magnetization or the like so that an intermediate portion between the concave portions 2a becomes a magnetic pole.

  FIG. 2 is a view for explaining the magnetomotive force distribution in the rotation direction when magnetic poles are formed on the ring magnet of this embodiment. In the figure, only the range in which the central angle of the magnet axis is 180 ° (angle region for two poles) is shown.

  FIG. 2A shows the thickness A of the ring 3 in which no concave portion is formed. As shown in FIG. 2B, the ring 3 has a magnetomotive force distribution with a constant strength, and a rectangular wave. Distribution B is obtained. Therefore, the fifth harmonic C is included. 3rd and 7th harmonics are also included, and these harmonics cause torque unevenness such as cogging torque and torque ripple, but only show 5th harmonics that have a significant effect on cogging torque. ing.

  FIG. 2 (c) shows the thickness D of the ring 2 in which the concave portion is formed. As shown in FIG. 2 (d), the ring 2 corresponds to one cycle of the fifth harmonic at the boundary of the magnetic pole. Since the concave portion 2a having the groove width to be formed is formed, the magnetomotive force distribution at the boundary portion is weakened like the magnetization distribution E. Therefore, the fifth harmonic component becomes F in FIG. 2D, and FIG. The phase of the second harmonic C is 180 ° out of phase with each other, cancel each other, and the fifth harmonic component is greatly reduced, thereby suppressing torque unevenness such as cogging torque and torque ripple.

  The ring magnet 1 according to this embodiment is, for example, a neodymium sintered ring magnet with a large maximum energy product, a step of vacuum casting Nd, Fe, B, etc. at a predetermined composition ratio, a pulverized powder by pulverizing a cast alloy Is manufactured through a step of forming a magnetic field, a step of magnetically forming finely pulverized powder into a predetermined ring shape, a sintering / heat treatment step, an outer shape processing step and the like.

  In the magnetic field forming step, a finely pulverized powder is filled in a die having a predetermined ring shape, and the filled finely pulverized powder is pressed with a punch having the same cross-sectional shape as that of the die at a predetermined density as shown in FIG. In addition, the molded body having the shape of the rings 2 and 3 is subjected to orientation treatment by applying an orientation magnetic field to the shaped body. The orientation magnetic field is oriented in the radial direction as the radial direction of the ring.

  The two shaped bodies subjected to the orientation treatment are stacked in the axial direction, pressed in the axial direction as necessary, and then sintered and heat-treated to produce the ring magnet of this embodiment.

Embodiment 2. FIG.
FIG. 3 is a plan view (a) and a side view (b) showing a second embodiment of the sintered ring magnet according to the present invention, and shows an example of a quadrupole magnet. In the figure, the same reference numerals as those in the first embodiment denote the same or corresponding parts.

  In this embodiment, as shown in FIG. 3, the ring magnet 1 is integrated by sintering by stacking the ring 4 in the axial direction in addition to the two rings 2 and 3 in the axial direction. Are provided with four groove-shaped recesses 4a (third recesses) extending in the axial direction periodically in the circumferential direction. The recess 4a determines the width of the groove so as to cancel the seventh harmonic.

In order to cancel the fifth harmonic, when the width of the groove is defined as a central angle with the axis as the center, the groove angle is the central angle with respect to the axis corresponding to the width of one pole, that is, the concave portion. In order to cancel the 7th harmonic by setting 2/5 of the central angle from the center of 4a to the center of the adjacent recess 4a (one cycle of the 5th harmonic), the width of the groove is also the width of one pole. In order to cancel the third-order harmonic by setting the center angle to 2/7 (one cycle of the seventh-order harmonic), the groove width is similarly set to 2/3 of the center angle corresponding to the width of one pole. (One cycle of the third harmonic). As shown in FIG. 3, in the case of four poles, the groove width of the recess 2a that cancels the fifth harmonic is set to a center angle of about 36 ° centering on the axis, and the groove width of the recess 4a that cancels the seventh harmonic. Is a central angle of about 25.7 °. In order to cancel the third harmonic, the groove width of the recess 4a is set to about 60 ° central angle.
Thus, by setting the groove width to 2/3, 2/5, and 2/7 of the central angle corresponding to the width of one pole, the third-order, fifth-order, and seventh-order harmonics are canceled and cogging is performed. Torque can be eliminated.
Further, by setting the groove width to 2/3 to 2/7 of the center angle corresponding to the width of one pole, the third-order, fifth-order and seventh-order harmonics can be reduced, and the cogging torque can be reduced. it can.

  In addition, a ring magnet may be configured with three rings that cancel third-order, fifth-order, and seventh-order harmonics, and further, it is configured with three or more rings to cancel n-th order (n is an odd number) harmonic. You may do it.

Embodiment 3 FIG.
FIG. 4 is a plan view (a) and a side view (b) showing a third embodiment of the sintered ring magnet according to the present invention, showing an example of a quadrupole magnet. In the figure, the same reference numerals as those in the first embodiment denote the same or corresponding parts.

  In this embodiment, as shown in FIG. 4, in addition to the recess 2a, a recess 2b (second recess) is provided in the magnetic pole between the boundary portions.

  As in the second embodiment, the recess 2a at the boundary of the magnetic pole has a groove width of about one cycle of the fifth harmonic, and the recess 2b has a groove width of about a half cycle of the fifth harmonic. Do it. As shown in FIG. 4, in the case of four poles, the groove width of the recess 2a is set to a center angle of about 36 ° around the axis, and the groove width of the recess 2b is set to a center angle of about 18 °.

  For the reduction of the seventh harmonic other than the fifth harmonic, etc., the groove width of the recess may be determined in the same manner.

  According to this embodiment, the effect of suppressing the influence of harmonics including the fifth harmonic is further increased.

Embodiment 4 FIG.
FIG. 5 is a plan view (a) and a side view (b) showing a fourth embodiment of a sintered ring magnet according to the present invention, and FIG. 6 is a plan view showing an enlarged groove shape of FIG. An example of a quadrupole magnet is shown. In the figure, the same reference numerals as those in the first embodiment denote the same or corresponding parts.

In this embodiment, as shown in FIGS. 5 and 6, the groove shape of the recess 2a at the boundary between the magnetic poles is an arc.
Since the cogging torque is generated by the harmonic component of the magnetomotive force distribution as described above, in order to accurately define the width W and the depth d of the groove constituting the recess 2a, the magnetomotive force distribution is set to the rotation angle. On the other hand, it is necessary to evaluate the amplitude of each component obtained by frequency conversion by Fourier transform, but even the actual groove width and depth do not cause a large error.

  The same effect can be obtained even if the groove shape of the recess 2a is a curve such as a parabola or a combination of straight lines.

  For the seventh harmonic other than the fifth harmonic, the actual depth d and width w of the groove may be about one cycle of the harmonic.

Embodiment 5 FIG.
FIG. 7: is the top view (a) and side view (b) which show Embodiment 5 of the sintered ring magnet based on this invention, and has shown the example of the 6 pole magnet. In the figure, the same reference numerals as those in the first embodiment denote the same or corresponding parts.

  In the first to fourth embodiments, the case where the magnetic pole has four poles has been described. However, the same effect can be obtained when the magnetic pole has six poles as in this embodiment.

  When the number of magnetic poles is six, the central angle of the groove width of the recess 2a may be 24 ° with respect to the fifth harmonic.

Embodiment 6 FIG.
FIG. 8 is a diagram for explaining the relationship between the thickness of the concavo-convex part and the harmonic suppression in the ring having the concave part 2a.

  As shown in FIG. 8, the thickness of the ring 2 in the recess 2a is mb, and the thickness of the ring 2 between the recesses 2a is mr. The axial length of the ring 2 having the recess 2a is Lb, and the axial length of the ring 3 having no recess is Lc.

  FIG. 9 is a diagram showing the fundamental wave of the magnetomotive force distribution and the amplitudes of the third, fifth, and seventh harmonics in relation to mb / mr. As for the amplitude, the amplitude of the harmonic in the ring 3 having no recess is set to 1. When mb / mr is 1, it corresponds to a ring having no recess, and when mb / mr is 0, it means that the thickness of the ring in the recess 2a is 0.

  In FIG. 9, when mb / mr = 1, the amplitude of the fundamental wave that contributes to the rotation of the motor is large, and the amplitudes of the third, fifth, and seventh harmonics are also large, 0.42, 0.25, and 0.18. Torque unevenness such as cogging torque occurs. FIG. 9 corresponds to Lc = 0.

  Here, for example, when mb / mr = 0.3 is selected, the amplitude of the fifth harmonic is about −0.1. In the figure, the fact that the amplitude is negative indicates that the phase is shifted by 180 ° with respect to the positive amplitude. Therefore, if the lengths Lb and Lc of the rings 2 and 3 are the same, the amplitude 0.25 of the fifth harmonic generated in the ring 3 is canceled by 0.1 amplitude, and becomes 0.15. Furthermore, if the ratio of Lb to Lc is 2.5: 1, the fifth harmonic generated in the ring 3 is canceled out.

When the relationship with respect to the fifth harmonic is expressed by an equation,
Lc / Lb = 1−2 × (mb / mr)
Therefore, the fifth harmonic generated in the ring 3 is canceled out.

In more detailed terms,
(Lc / Lb) × (1-α) ≦ 1-2 × (mb / mr) + α
(Lc / Lb) × (1 + α) ≧ 1-2 × (mb / mr) −α
It becomes. Here, (1-α) indicates the rate at which the fifth harmonic is attenuated.
Here, when α = 0.3, the following equation (1) is obtained.
1.9-2.9 × (mb / mr) ≧ (Lc / Lb)
≧ 0.54-1.5 × (mb / mr) (1)
The fifth harmonic is 0.3 times and the cogging torque is squared by the condition of the expression (1), and can be reduced to 0.1, that is, 10%.

Embodiment 7 FIG.
FIG. 10 is a diagram for explaining the relationship between the thickness of the concavo-convex part and the harmonic suppression in the ring having the concave part. In the sixth embodiment, the case where the groove-like concave part 2b is provided in the magnetic pole will be described. Is.

  As shown in FIG. 10, the thickness of the ring 2 in the recess 2a is mb, and the thickness of the ring 2 between the recesses 2a is mr. The axial length of the ring 2 having the recess 2a is Lb, and the axial length of the ring 3 having no recess is Lc.

  FIG. 11 is a diagram showing the fundamental wave of the magnetomotive force distribution and the amplitudes of the third, fifth, and seventh harmonics in relation to mb / mr. As for the amplitude, the amplitude of the harmonic in the ring 3 having no recess is set to 1. When mb / mr is 1, it corresponds to a ring having no recess, and when mb / mr is 0, it means that the thickness of the ring in the recess 2a is 0.

  In this embodiment, the fifth harmonic can be attenuated even when the depth of the recess 2a is shallower than in the case of the sixth embodiment.

  For example, with respect to the amplitude 0.25 of the fifth harmonic at mb / mr = 1, the amplitude of the fifth harmonic is about −0 by selecting mb / mr = 0.3 in the sixth embodiment. In this embodiment, mb / mr = 0.4 is selected, while the ratio of Lb to Lc is 2.5: 1 in order to cancel the amplitude 0.25 of the fifth harmonic. By doing so, the amplitude of the fifth harmonic becomes about −0.2, and the ratio of Lb to Lc may be set to 5: 4 in order to cancel the amplitude 0.25 of the fifth harmonic.

When the relationship with respect to the fifth harmonic is expressed by an equation,
Lc / Lb = 2-3 × (mb / mr)
Therefore, the fifth harmonic generated in the ring 3 is canceled out.

In more detailed terms,
(Lc / Lb) × (1-α) ≦ 2−3 × (mb / mr) + α
(Lc / Lb) × (1 + α) ≧ 2−3 × (mb / mr) −α
It becomes. Here, (1-α) indicates the rate at which the fifth harmonic is attenuated.
Here, when α = 0.3, the following equation (2) is obtained.
3.3-4.3 × (mb / mr) ≧ (Lc / Lb)
≧ 1.3-2.3 × (mb / mr) (2)
According to the condition of the formula (2), the fifth harmonic is 0.3 times and the cogging torque is the square of the fifth, so that it can be reduced to 0.1, that is, 10%.

Embodiment 8 FIG.
FIG. 12 is a plan view (a) and a side view (b) showing an eighth embodiment of the sintered ring magnet according to the present invention.

  In the first to seventh embodiments, the rings having the recesses are stacked and integrated so as to cancel the third, fifth, and seventh harmonics generated by the ring having no recess.

  In this embodiment, as shown in FIG. 12, by selectively determining the shape of the concave portion 11a of the ring 11, the generated third-order, fifth-order and seventh-order harmonics are reduced. The ring 11 is stacked in accordance with the position.

  For example, as can be seen from FIG. 9, by setting mb / mr to 0.5, that is, the thickness of the ring 11 in the recess 11a is set to ½ of the thickness between the recesses 11a, the fifth harmonic is reduced to almost zero. can do. However, in this case, the mechanical strength of the ring magnet is not maintained, and breakage easily occurs.

  By setting mb / mr to 0.75, that is, the thickness of the ring 11 in the recess 11a is set to 75% of the thickness between the recesses 11a, the fifth harmonic can be reduced to ½. In FIG. 12, the dotted line indicates that the ring magnet is formed by stacking two rings 11.

Embodiment 9 FIG.
FIG. 13 is a plan view (a) and a side view (b) showing a ninth embodiment of the sintered ring magnet according to the present invention.

  In the eighth embodiment, the ring 11 is stacked with the position of the recess 11a being aligned, but in this embodiment, the ring 11 is stacked with the position of the recess 11a being shifted.

  When mb / mr is 0.75 as in the eighth embodiment, the fifth harmonic remains, but the cogging torque generated by the remaining fifth harmonic cancels out as in this embodiment. Thus, the cogging torque can be greatly reduced by rotating the recesses 11a of the upper and lower rings 11 around the axis and shifting them.

  As shown in FIG. 13, in the case of a 4-pole rotor and the number of stator slots is 6, cogging torque is generated in 12 cycles per one revolution of the motor, so the displacement angle due to the rotation of the recesses 11a of the upper and lower rings 11 is By setting the mechanical angle to around 15 °, the cogging torque generated by the remaining fifth harmonic can be canceled out.

Embodiment 10 FIG.
FIG. 14 is a plan view (a) and a side view (b) showing an embodiment 10 of the sintered ring magnet according to the present invention.

  In the said Embodiment 8 and 9, the ring 11 which has the recessed part 11a with the same groove shape was piled up.

  In this embodiment, the ring 11 and the ring 12 having the recesses 11a and 12a having different widths in the groove shape are stacked and integrated in the axial direction.

  The width of the concave portion is, for example, by setting the width of the concave portion 11a to a central angle of 36 ° centering on the axis and the width of the concave portion 12a to the vicinity of the central angle of 25.7 ° (5/7 of the central angle of the concave portion 11a). The fifth harmonic and the seventh harmonic can be reduced, and the cogging torque due to the harmonic can be reduced.

  The ratio of the thickness (mb) between the recesses 11a and 12a and the thickness (mr) between the recesses 11a and 12a is selected according to FIG.

  In the first to ninth embodiments, the dimensional accuracy of the groove width need not be strict. FIG. 15 is a diagram illustrating a result of calculating the fifth harmonic component based on the magnetomotive force distribution due to the shape of the ring magnet. In the figure, the horizontal axis represents the groove width normalized by the ideal groove width (ratio to the ideal groove width), and the vertical axis represents the ratio to the fifth-order harmonic component without the groove. As shown in the figure, in the case of an ideal groove width, the fifth harmonic is eliminated, so that it becomes zero. In an error range of about 15% with respect to the ideal groove width, the fifth harmonic is less than 10% with respect to no groove, and an error with respect to the ideal groove width is acceptable.

  It can be used for an inner rotor of a rotating electrical machine such as a permanent magnet motor.

It is the top view (a) and side view (b) which show Embodiment 1 of the sintered ring magnet which concerns on this invention. It is a figure for demonstrating the magnetization distribution of the rotation direction when a magnetic pole is formed in the ring magnet of the first embodiment. It is the top view (a) and side view (b) which show Embodiment 2 of the sintered ring magnet which concerns on this invention. It is the top view (a) and side view (b) which show Embodiment 3 of the sintered ring magnet which concerns on this invention. It is the top view (a) and side view (b) which show Embodiment 4 of the sintered ring magnet which concerns on this invention. It is a top view which expands and shows the groove shape of FIG. It is the top view (a) and side view (b) which show Embodiment 5 of the sintered ring magnet which concerns on this invention. It is a figure for demonstrating the relationship between the thickness of the uneven | corrugated | grooved part in a ring which has a recessed part, and harmonic suppression. It is the figure which showed the amplitude of the fundamental wave of magnetomotive force distribution, the 3rd harmonic, the 5th harmonic, and the 7th harmonic in relation to mb / mr. It is a figure for demonstrating the relationship between the thickness of the uneven | corrugated | grooved part in a ring which has a recessed part, and harmonic suppression. It is the figure which showed the amplitude of the fundamental wave of magnetomotive force distribution, the 3rd harmonic, the 5th harmonic, and the 7th harmonic in relation to mb / mr. It is the top view (a) and side view (b) which show Embodiment 8 of the sintered ring magnet which concerns on this invention. It is the top view (a) and side view (b) which show Embodiment 9 of the sintered ring magnet which concerns on this invention. It is the top view (a) and side view (b) which show Embodiment 10 of the sintered ring magnet which concerns on this invention. It is a figure which shows the result of having calculated the component of the 5th harmonic based on the magnetomotive force distribution by the shape of a ring magnet.

Explanation of symbols

1 ring magnet, 2, 3, 4, 11, 12 ring,
2a, 2b, 4a, 11a, 12a Recess.

Claims (11)

In a sintered ring magnet in which anisotropically oriented rings are stacked in the axial direction and integrated by sintering, at least one of the rings has a groove shape extending in the axial direction on the outer peripheral surface thereof. A sintered ring magnet characterized in that the first recesses are periodically provided in the circumferential direction. The sintered ring magnet according to claim 1, wherein at least one of the rings has a cylindrical shape having no concave portion on an outer peripheral surface. The sintered ring magnet according to claim 1 or 2, wherein a magnetic pole is formed in an intermediate portion between the concave portions, and the first concave portion is used as a boundary portion of the magnetic pole. The sintered ring magnet according to claim 3, wherein the magnetic pole is provided with a groove-like second recess extending in the direction of the axis. 5. The sintered ring magnet according to claim 4, wherein the width of the groove in the second recess provided in the magnetic pole is ½ of the width of the groove in the first recess. The width of the groove in the first concave portion is about 2/3 to 2/7 of the central angle between the centers of the adjacent boundary portions when expressed by a central angle centered on the axis. The sintered ring magnet according to claim 2. In addition to the ring provided with the first recess, another ring provided with a third recess is provided so that the circumferential positions of the first recess and the third recess overlap. The sintered ring magnet according to claim 1 or 2, characterized in that The sintered ring magnet according to claim 7, wherein the groove width in the third recess is 5/7 of the groove width in the first recess. The sintered ring magnet according to claim 1, wherein the ring provided with the first recess is stacked in two stages, and the recess in the upper ring and the recess in the lower ring are shifted in the circumferential direction. The ring thickness in the first recess is mb, the ring thickness between the first recesses is mr, the axial length of the ring having the first recess is Lb, and the ring without the recess is The sintered ring magnet according to claim 2, wherein the following formula (1) is established when the axial length is Lc.
1.9-2.9 × (mb / mr) ≧ (Lc / Lb)
≧ 0.54-1.5 × (mb / mr) (1) A cylindrical ring having no recess on the outer periphery, the thickness of the ring in the first recess is mb, the thickness of the ring between the first recesses is mr, and the axis of the ring having the first recess The sintered ring magnet according to claim 4, wherein the following formula (2) is established, where Lb is a length in the direction and Lc is an axial length of the ring having no recess.
3.3-4.3 × (mb / mr) ≧ (Lc / Lb)
≧ 1.3-2.3 × (mb / mr) (2)

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