Jade Axle

Abstract

To provide a ball bearing for a wave reduction gear capable of suppressing generation of excessive stress on a retainer.SOLUTION: In a retainer 324, 0.05≤K10 / D2≤0.15 ... (1) is satisfied, when a minimum dimension of a clearance in an I direction represented by a difference between a distance between pole portions 324B adjacent to each other in the I direction and a diameter of a ball 323 in a pocket 324p in a state that a center of the pocket 324p and a center of the ball 323 in the pocket 324p are agreed with each other, is K10 and a diameter of the ball 323 is D2.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present disclosure relates to a ball bearing, and more particularly to a ball bearing for a strain wave gear reducer. [Background technology]

[0002] For example, Japanese Patent Application Laid-Open Publication No. 2018-200112 (Patent Document 1) discloses a ball bearing for a strain wave gear reducer. In Japanese Patent Application Laid-Open Publication No. 2018-200112, the inner surface of a pocket formed in the cage that can come into contact with the balls is a surface that extends linearly in the radial direction. The ball bearing of Japanese Patent Application Laid-Open Publication No. 2018-200112 is characterized in that the circumferential gap between the inner surface of the cage pocket and the balls is smaller than the radial gap in the annular space formed between the non-circularly deformed raceway rings (outer ring and inner ring) and the cage. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2018-200112 Summary of the Invention [Problem to be solved by the invention]

[0004] JP 2018-200112 A describes that the inner surface of the retainer that can come into contact with the balls extends linearly in the radial direction, making the retainer less susceptible to interference from multiple balls that are arranged in a non-circular manner, and preventing localized stress in the retainer.

[0005] However, the shape obtained by connecting the centers of multiple balls is non-circular, while the cage is circular. For this reason, if the circumferential gap between the inner surface of the pocket and the ball is smaller than a certain value, the cage pocket and the ball will interfere strongly on part of the cage's inner surface. This results in excessive stress being generated in the cage and increased power loss in the cage. This is a phenomenon caused by the difference in rotational speed, or running speed (running difference), between the balls and the cage. If the shape obtained by connecting the centers of the balls is an ellipse, the difference in curvature between the curve on the major axis and the curve on the minor axis of the ellipse will cause a running difference between the balls and the cage.

[0006] The present disclosure has been made in view of the above-mentioned problems, and has an object to provide a ball bearing for a strain wave gear reducer that can suppress the generation of excessive stress on the cage. [Means for solving the problem]

[0007] A ball bearing according to the present disclosure is used in a strain wave gear reducer and comprises an outer ring, an inner ring, balls, and a cage. The outer ring is capable of elastic deformation. The inner ring is disposed inside the outer ring and is capable of elastic deformation. The balls are disposed between the outer ring and the inner ring. The cage has pockets for accommodating the balls formed on its inner surface. The cage includes an annular portion and bar portions extending axially from the annular portion. When the center of the pocket coincides with the center of the ball accommodated in the pocket, the cage has a minimum circumferential gap expressed by the difference between the distance between circumferentially adjacent bar portions that form the pocket and the diameter of the ball accommodated in the pocket, where K10 is the minimum dimension, and the diameter of the ball is D2, 0.05≦K10 / D2≦0.15…(1) holds true. [Effects of the Invention]

[0008] According to the present disclosure, it is possible to provide a ball bearing for a strain wave gear reducer that can suppress the occurrence of excessive stress on the cage. [Brief explanation of the drawings]

[0009] [Figure 1]1 is a schematic plan view showing a strain wave gear reducer according to a first embodiment as viewed from an axial direction. FIG. [Figure 2] FIG. 2 is a schematic cross-sectional view taken along line II-II in FIG. [Figure 3] 3 is a schematic enlarged cross-sectional view of the ball bearing of FIG. 2 and the adjacent parts. [Figure 4] 3 is a schematic diagram showing a state in which half of the circumference of the cage provided in the ball bearing according to the first embodiment is viewed in plan from the r direction. FIG. [Figure 5] 10 is an enlarged schematic view showing a part in which balls are held in one pocket formed in the cage of the first embodiment, viewed in a plan view from the r direction. FIG. [Figure 6] FIG. 6 is a schematic cross-sectional view taken along line VI-VI in FIG. 5. [Figure 7] FIG. 7 is a schematic diagram showing a first step of the method for calculating the minimum dimension K10 of FIGS. 5 and 6. [Figure 8] FIG. 7 is a schematic diagram showing a second step of the method for calculating the minimum dimension K10 in FIGS. 5 and 6. [Figure 9] 1 is a schematic diagram showing the difference in ball position when the ball rolls along an inner ring that has been elastically deformed into a non-circular shape by a cam, and when the ball rolls along an inner ring that does not elastically deform. [Figure 10] FIG. 10 is a schematic plan view showing a strain wave gear reducer according to a second embodiment as viewed from the axial direction. [Figure 11] FIG. 11 is a schematic cross-sectional view taken along line XI-XI in FIG. [Figure 12] 10 is an enlarged schematic view showing a part in which balls are held in one pocket formed in the cage of embodiment 2, viewed in a plan view from the r direction. FIG. [Figure 13] FIG. 13 is a schematic cross-sectional view taken along line XIII-XIII in FIG. [Figure 14] 11 is an enlarged schematic view showing a part in which balls are held in one pocket formed in a cage of embodiment 3, viewed in a plan view from the r direction. FIG. [Figure 15] 10 is an enlarged schematic view showing a part in which balls are held in one pocket formed in a cage of embodiment 4, viewed in a plan view from the r direction. FIG. DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, the present embodiment will be described with reference to the drawings, in which r, l, and a directions are introduced for the sake of convenience.

[0011] (Embodiment 1) <Structure of a strain wave gear reducer> FIG. 1 is a schematic plan view showing the strain wave gear reducer according to the first embodiment as viewed from the axial direction. However, part of the cage is not shown in FIG. 1. Also, the axial plan view means that the line of sight (the line connecting the eye and the object) is along the axial direction. FIG. 2 is a schematic cross-sectional view taken along line II-II in FIG. 1. Referring to FIGS. 1 and 2, the strain wave gear reducer 100 of this embodiment has a circular shape with a radius (diameter) extending in the r direction and a circumference extending in the l direction. In other words, the r direction indicates the radial direction of the strain wave gear reducer 100, and the l direction indicates the circumferential direction of the strain wave gear reducer 100. The strain wave gear reducer 100 includes a circular spline 10, a flexspline 20, and a wave generator 30.

[0012] The circular spline 10 is disposed at the outermost position in the r direction of the strain wave gear reducer 100 and has an annular shape. The outer peripheral surface of the circular spline 10 is a circle (a perfect circle) centered on the circular axis C of the strain wave gear reducer 100. The circular spline 10 has internal teeth 11 on its inner peripheral surface. The circular spline 10 is fixed to a casing of the strain wave gear reducer 100 (not shown). The circular spline 10 is formed from a highly rigid metal member.

[0013] The flexspline 20 is provided inside the circular spline 10 in the r direction. The flexspline 20 has external teeth 21 on its outer circumferential surface. The number of teeth of the external teeth 21 of the flexspline 20 is, for example, two fewer than the number of teeth of the internal teeth 11 of the circular spline 10. However, the difference in the number of teeth between the external teeth 21 and the internal teeth 11 is not limited to this. In FIG. 2, the left-right direction of the strain wave gear reducer 100 in the figure is the a direction, i.e., the axial direction extending perpendicularly through the center of the circular shape in FIG. 1. As shown in FIG. 2, in addition to the external teeth 21, the flexspline 20 has a cylindrical portion 22 and a bottom portion 23. The cylindrical portion 22 is located at approximately the same position as the circular spline 10 and the external teeth 21 in the a direction, and is provided on the inner circumferential surface of the external teeth 21. Furthermore, the cylindrical portion 22 extends from this position along the a direction and has a portion separated from the external teeth 21. 2, the cylindrical portion 22 bends in the direction a from a portion away from the external teeth 21, and the bottom portion 23 is formed so as to bend toward the cylindrical portion 22. In other words, the bottom portion 23 is disposed at a position away from the circular spline 10 and the external teeth 21 in the direction a. The flexspline 20 is a thin-walled cup-shaped member made up of the cylindrical portion 22 as a side portion and the bottom portion 23 at the bottom of the cylindrical portion 22.

[0014] The flexspline 20 is made of an elastic metal. Therefore, when pressed by a cam (described later), the flexspline 20 is elastically deformed, and the planar shape of FIG. 1 can bend into a non-circular shape (for example, an ellipse). The flexspline 20 and the external teeth 21 are, for example, elliptical with a major axis in the up-down direction in FIG. 1. On the other hand, the circular spline 10 and the internal teeth 11 provided on the outer side of the flexspline 20 in the r direction are circular. As a result, the internal teeth 11 partially mesh with the external teeth 21 at a pair of portions S1, indicated by arrows in FIG. 1, that are 180° apart from the axis C and located in the major axis direction of the ellipse of the flexspline 20. On the other hand, the internal teeth 11 do not mesh with the external teeth 21 at a pair of portions S2, indicated by arrows in FIG. 1, that are 180° apart from the axis C and located in the minor axis direction of the ellipse of the flexspline 20.

[0015] The wave generator 30 is provided on the inside of the flexspline 20, particularly the cylindrical portion 22, in the r direction. In other words, the wave generator 30 is disposed in approximately the same position as the circular spline 10 and the external teeth 21 in the a direction. The wave generator 30 has a cam 31 and a ball bearing 32. The cam 31 is non-circular, and in FIG. 1, for example, is elliptical with its major axis in the up-down direction. The ball bearing 32 is provided on the outside of the cam 31 in the r direction. In other words, the outer peripheral surface of the ball bearing 32 faces the inner peripheral surface of the cylindrical portion 22 of the flexspline 20 in the r direction.

[0016] <Ball bearing configuration> FIG. 3 is a schematic enlarged cross-sectional view of the ball bearing of FIG. 2 and adjacent parts. With reference to FIGS. 1, 2, and 3, ball bearing 32 has an outer ring 321, an inner ring 322, balls 323, and a cage 324. The outer ring 321 is a thin-walled raceway ring located on the outer side of ball bearing 32 in the r direction. The outer ring 321 is fixed to the inside of cylindrical portion 22 of flexspline 20 in the r direction. The outer ring 321 can rotate integrally with flexspline 20. The inner ring 322 is a thin-walled raceway ring located on the inner side of ball bearing 32 in the r direction, i.e., inside outer ring 321. The inner ring 322 is fixed to the outside of cam 31 in the r direction. The inner ring 322 can rotate integrally with cam 31. A raceway groove 321g is formed in the inner peripheral surface of outer ring 321, and a raceway groove 322g is formed in the outer peripheral surface of inner ring 322. Raceway grooves 321g, 322g have an arc-shaped cross section and run in the l direction along the annular shapes of outer ring 321 and inner ring 322. A plurality of balls 323 (for example, 24 in FIG. 1) are arranged so as to be sandwiched between raceway grooves 321g, 322g in the r direction. This allows the plurality of balls 323 and cage 324 to roll around axis C, running along raceway grooves 321g, 322g (outer ring 321 and inner ring 322).

[0017] The outer ring 321 and the inner ring 322 are made of a metal such as bearing steel and have an annular shape, but are thin-walled and therefore can elastically deform in the r direction. Because the inner ring 322 is fixed to the outside of the elliptical cam 31, when the inner ring 322 elastically deforms, it assumes an elliptical planar shape that conforms to the elliptical shape of the cam 31. The balls 323 are spherical members disposed between the outer ring 321 and the inner ring 322 and are made of a metal such as bearing steel. Therefore, when the inner ring 322 elastically deforms and assumes an elliptical shape, the figure obtained by connecting the centers of the multiple balls 323 will also be elliptical, just like the inner ring 322. Furthermore, when the outer ring 321 and the cylindrical portion 22 elastically deform via the balls 323, they will also assume an elliptical planar shape.

[0018] The cage 324 is a member that maintains the state in which the plurality of balls 323 are arranged in an annular shape between the outer ring 321 and the inner ring 322 at intervals in the l direction. The cage 324 has an annular (crown) shape. The cage 324 is made of resin, and is preferably made of, for example, nylon 66.

[0019] Fig. 4 is a schematic diagram showing a half-circumferential portion of the cage provided in the ball bearing according to the first embodiment, viewed from the r direction in a plan view. Referring to Figs. 1, 2, 3, and 4, cage 324 includes annular portion 324A and pillar portions 324B. Annular portion 324A is an annular-shaped portion provided at one end of cage 324 in the a direction (the right side in Fig. 4). In other words, annular portion 324A is formed so as to go around ball bearing 32 once. Pillar portions 324B extend from annular portion 324A in the a direction. Plural pillar portions 324B are formed at equal intervals in the l direction and are arranged to separate a pair of balls 323 adjacent to each other in the l direction. The width of the column portion 324B in the direction intersecting the extending direction (direction a) may not be constant, but may be thin at the tip, thick in the region adjacent to the tip, and then thin again on the opposite side of the tip (the annular portion 324A side) as shown in FIG.

[0020] The cage 324 is formed with pockets 324p that accommodate each of the multiple balls 323. Each pocket 324p is formed as a space surrounded by an annular portion 324A and a pair of pillar portions 324B adjacent to each other in the l direction. Therefore, like the pillar portions 324B, multiple pockets 324p are formed at equal intervals in the l direction. The number of pockets 324p is equal to the number of pillar portions 324B. Therefore, in the example of FIG. 1, 24 pockets 324p are formed. One ball 323 can be accommodated in one pocket 324p. In FIG. 4, one ball 323 accommodated in the central pocket 324p in the l direction is shown by a dotted line.

[0021] 3, annular portion 324A goes around the entire circumference (one circumference) in the direction l perpendicular to the paper surface, while pillar portion 324B is shown as only one extending in the area behind ball 323. To indicate this, annular portion 324A is shaded, and the area behind ball 323 of pillar portion 324B is shown by dotted lines.

[0022] FIG. 5 is an enlarged schematic diagram showing a portion of the cage according to the first embodiment in which balls are held in one pocket, as viewed from the r direction. FIG. 6 is a schematic cross-sectional view taken along line VI-VI in FIG. 5. Note that FIGS. 5 and 6 are schematic views for ease of explanation and may differ slightly from the actual shape. Referring to FIGS. 5, 6, and 4, pocket 324p is a space formed by the wall surfaces of annular portion 324A and columnar portion 324B that surround pocket 324p. An inner surface 324s, which forms a boundary of pocket 324p, has a first surface 324s1 and a second surface 324s2. The first surface 324s1 is a region that serves as an end surface of columnar portion 324B of cage 324. The second surface 324s2 is a region that serves as an end surface of annular portion 324A of cage 324 in the a direction. 4 and 5, the first surface 324s1 and the second surface 324s2 are continuous, and the combined single inner surface 324s forms a single curved pocket 324p. In other words, the pocket 324p in FIGS. 4 and 5 is formed as part of a single curved surface. The first surface 324s1 and the second surface 324s2 face the ball 323 in the pocket 324p formed by them and are surfaces that can come into contact with the ball 323. The boundary between the first surface 324s1 and the second surface 324s2 in FIGS. 4 and 5 can be determined as appropriate. For example, the boundary may be a position where the phase with respect to the a direction is ±45° in a plan view from the r direction in FIG. 5.

[0023] As shown in FIG. 6, the first surface 324s1 that forms the pocket 324p and faces the balls 323 extends linearly in the r direction. In other words, the first surface 324s1 of the pocket 324p has a shape that follows the cylindrical surface of a cylinder whose centerline extends in the r direction (the side surface extending along the r direction on the inside of the cylindrical shape). This reduces the possibility that the cage 324 will come into contact with and be interfered with by the multiple balls 323 that are arranged in a non-circular (elliptical) shape. In other words, the cage 324 tries to maintain its original annular shape, reducing the possibility that localized stress will occur in the cage 324. As a result, stress occurring in the cage 324 can be reduced.

[0024] 5 and 6, the center of pocket 324p and the center of ball 323 contained in pocket 324p coincide with each other. Here, the center of pocket 324p refers to the center of the portion surrounded by the cylindrical surface that constitutes inner side surface 324s of pocket 324p. Therefore, the center of pocket 324p is defined as the center of the circle that constitutes inner side surface 324s in a plan view from the r direction (if a portion is missing, the circle is obtained by filling in that portion, and is also the center in the r direction along which the cylindrical surface extends).

[0025] When the center of a pocket 324p of the cage 324 is aligned with the center of a ball 323 housed therein, the minimum dimension K10 of the gap in the l direction, which is expressed as the difference between the distance between a pair of adjacent pillars 324B forming the pocket 324p in the l direction and the diameter of the ball 323 housed in the pocket 324p, is calculated as follows: Note that the minimum dimension K10 of the gap is the dimension along the l direction. For example, in FIG. 5, there are two gaps K5 between the first surface 324s1 at the center in the a direction of the cylindrical inner surface 324s (including the missing portion that needs to be filled in to make it a complete cylindrical surface) and the surface of the ball 323, one on one side of the ball 323 in the l direction, and the other on the other side. The sum of these gaps K5 is the minimum dimension K10. If the distance between the first surface 324s1 and the surface of the ball 323 varies depending on the position in the a direction, the smallest distance (for example, the distance at the center in the a direction) is the distance K5, and the sum of the two distances K5 is the minimum dimension K10. In other words, the minimum dimension K10 of the gap is the difference between the diameter D1 of the cylindrical surface of the inner surface 324s (which is circular in plan view and includes missing portions that need to be filled in to make it circular) and the diameter D2 of the ball 323. The diameter D1 is, for example, the dimension of the inner surface 324s (which is circular in plan view and includes missing portions that need to be filled in to make it circular). A method for calculating the minimum dimension K10 in FIGS. 5 and 6 will be described below with reference to FIGS. 7 and 8.

[0026] FIG. 7 is a schematic diagram showing the first step of the method for calculating the minimum dimension K10 shown in FIGS. 5 and 6. However, FIG. 7 illustrates only the left half of a pitch ellipse, which will be described later, and only a portion of the ball centers. Referring to FIG. 7, when at least one of the outer ring 321 and the inner ring 322 (at least the inner ring 322) is fitted onto the cam 31 and elastically deforms, the figure connecting the centers O of the multiple balls 323 becomes an ellipse similar to the cam 31. The ellipse obtained by connecting the centers O of the balls 323 is called a pitch ellipse 41. The multiple balls 323 are arranged on the circumference of the pitch ellipse 41 at equal intervals a. In other words, the circumferential length of the pitch ellipse 41 divided by the number of balls 323 is the interval a. The intervals a between the centers O of adjacent balls 323 arranged on the circumference of the pitch ellipse 41 are all equal. In Figure 7, only the centers O of four balls 323 are shown, and the others are omitted from the illustration. In reality, the balls 323 are arranged at equal intervals around the entire circumference of the pitch ellipse 41, with the distance between the centers O all equal to a.

[0027] Next, lines are found that connect the axis C of the entire strain wave gear reducer 100 (the center of the ball bearings 32), which is the center of the pitch ellipse 41, with the center O of each of the multiple balls 323, and extend radially from the center of the pitch ellipse 41. The angle between line 51 extending in the vertical direction in FIG. 7 and line 52 connecting the axis C and the center O adjacent to the line 51 on the left side is defined as A. Similarly, the angle between line 52 in FIG. 7 and line 53 connecting the axis C and the center O adjacent to the line 52 on the left side is defined as B. The angle between line 53 in FIG. 7 and line 54 connecting the axis C and the center O adjacent to the line 52 on the left side is defined as C.

[0028] FIG. 8 is a schematic diagram showing the second step of the method for calculating the minimum dimension K10 shown in FIGS. 5 and 6. Like FIG. 7, FIG. 8 also omits some parts. Referring to FIG. 8, a virtual circle 42 is calculated, having a center at the same position as the center (axis center C) of the pitch ellipse 41 and having a diameter equal to the length of the major axis of the pitch ellipse 41. The length of the major axis of the pitch ellipse 41 is equal to twice the distance between the center O and the axis center C on the line 51. The virtual circle 42 intersects with each of the radially extending lines 51 to 54 shown in FIG. 7, thereby dividing the circumference of the virtual circle 42 into a plurality of arcs. For example, in FIG. 8, the lines 51 and 52 divide the circumference of the virtual circle 42 into an arc 61. The lines 52 and 53 divide the circumference of the virtual circle 42 into an arc 62. The lines 53 and 54 divide the circumference of the virtual circle 42 into an arc 63. Then, the length x of arc 61, the length y of arc 62, and the length z of arc 63 are found. The lengths of arcs 61, 62, and 63 are found within the area of ​​ball 323 that receives load from the raceways (outer race 321 and inner race 322). The area of ​​ball 323 that receives load from the raceways is the area of ​​one circumference where ball 323 is arranged in the l direction in Figure 1, and this area is called the load zone.

[0029] Finally, the difference between the maximum and minimum lengths of the multiple arcs found within the load zone is doubled, which is the calculated value to be found, and is the minimum gap dimension K10 to be found. For example, in Figure 8, without taking into account parts not shown, let the length of the maximum arc 63 of the multiple arcs found be z and the length of the minimum arc 61 be x. In this case, the value of the minimum dimension K10 is found as 2(zx).

[0030] <Action and effect> Next, the effects of this embodiment will be described with reference to Fig. 9. Note that some of the details of the effects may overlap with those of the configuration described above.

[0031] 9 is a schematic diagram showing the difference in ball position between when a ball rolls along an inner ring that has been elastically deformed into a non-circular shape by a cam and when a ball rolls along an inner ring that has not been elastically deformed. Referring to FIG. 9, when inner ring 322 of strain wave gear reducer 100 of this embodiment is not elastically deformed and has a circular shape, dotted lines indicate raceway surface 322A of inner ring 322 and imaginary balls 323A rolling thereon. Furthermore, when inner ring 322 of strain wave gear reducer 100 of this embodiment is elastically deformed by non-circular cam 31 and has become elliptical, solid lines indicate raceway surface 322B of inner ring 322 and imaginary balls 323B rolling thereon.

[0032] When the cam 31 rotates counterclockwise about the axis C, i.e., in the direction R indicated by the arrow in the figure, connecting the centers of the multiple balls 323B rolling on the raceway surface 322B results in an ellipse, similar to the shape of the cam 31 and the raceway surface 322B. The figure obtained by connecting the centers of such multiple balls 323B is an ellipse (pitch ellipse 41: see Figures 1, 7, and 8). On the other hand, the cage 324 maintains its annular shape even when the inner ring 322 elastically deforms into an ellipse like the raceway surface 322B. This is because the cage 324 is not subjected to large stresses from the outer ring 321, the inner ring 322, and the balls 323. Therefore, connecting the centers of the multiple pockets 324p formed in the cage 324 results in a circle.

[0033] When the elliptical cam 31 rotates around the axis C as indicated by the arrow R, the multiple balls 323B on the raceway surface 322B roll along the pitch ellipse 41. At this time, the angular velocity of the revolution of the balls 323 varies depending on the position (phase) of the balls 323 on the raceway surface 322B. This is because the diameter of the pitch ellipse formed by the balls 323 (the distance between the axis C and the pitch ellipse 41) varies depending on the position (phase) on the pitch ellipse 41. Because the angular velocity of the rotational motion changes depending on the position, the balls 323B on the pitch ellipse 41 move forward and backward in rotation (travel) relative to the balls 323A that roll along a circle obtained by connecting the centers of the pockets 324p of the cage 324, resulting in a difference in traveling speed (travel difference). As a result, compared to balls 323A running on raceway surface 322A, balls 323B running on raceway surface 322B advance ahead in the right half of the region in Fig. 9, but lag behind in the left half of the region in Fig. 9. This difference in running distance causes interference between pillars 324B of retainer 324 and multiple balls 323B, which can restrain retainer 324 by balls 323B and cause localized stress in retainer 324.

[0034] Therefore, the ball bearing 32 according to the present disclosure is used in the strain wave gear reducer 100 and includes an outer ring 321, an inner ring 322, balls 323, and a cage 324. The outer ring 321 is capable of elastic deformation. The inner ring 322 is disposed inside the outer ring 321 and is also capable of elastic deformation. The balls 323 are disposed between the outer ring 321 and the inner ring 322. The cage 324 has pockets 324p formed by an inner surface 324s for accommodating the balls 323. The cage 324 includes an annular portion 324A and pillar portions 324B extending axially (direction a) from the annular portion 324A. When the center of a pocket 324p of the cage 324 is aligned with the center of a ball 323 housed in the pocket 324p, the minimum dimension K10 of the circumferential gap (in the l direction) represented by the difference between the distance between adjacent column portions 324B in the l direction that form the pocket 324p and the diameter of the ball 323 housed in the pocket 324p is calculated as follows: i) The balls 323 are arranged at equal intervals on the circumference of a pitch ellipse 41 obtained by connecting the centers of the balls 323 when at least one of the outer ring 321 and the inner ring 322 is elastically deformed. ii) Straight lines 51 to 54 extending radially from the center of the pitch ellipse 41 are determined by connecting the center (axis center C) of the pitch ellipse 41 with the center O of the ball 323. iii) The lengths of the multiple arcs 61-63 obtained by dividing an imaginary circle 42, which has its center at the same position as the center (axis center C) of pitch ellipse 41 and has a diameter equal to the length of the major axis of pitch ellipse 41, by intersecting with radially extending straight lines 51-54, are determined. iv) The above calculated value is obtained by doubling the difference between the maximum length z and the minimum length x of the multiple arcs 61-63 determined within the area (load zone) of ball 323 receiving load from outer ring 321 and inner ring 322.

[0035] This creates a sufficiently large circumferential gap between the pockets 324p (inner surfaces 324s) of the cage 324 and the balls 323. Therefore, even if the balls 323 form pitch ellipses 41 while the cage 324 maintains an annular shape, and the difference between the shapes of the two becomes large, strong interference due to contact between the pockets 324p and the balls 323 can be suppressed, and the generation of excessive stress on the cage 324 can be suppressed.

[0036] Furthermore, this configuration suppresses strong interference with the pockets 324p due to contact between the balls 323 and the pockets 324p, even if the difference in the running of the pitch ellipse 41 of the balls 323 is greater than when the centers of the balls 323 form a circle. This suppresses excessive stress on the cage 324. zx indicates the amount of rotational delay (see FIG. 9) of the centers O of the balls 323, which are evenly spaced on the pitch ellipse 41, compared to when the centers O of the balls 323 are arranged circumferentially. zx is the maximum difference in the left half of the axis C shown in FIGS. 7 and 8, i.e., the region where ball 323B is delayed. However, the same arc length and maximum difference also appear in the right half of FIGS. 7 and 8. In other words, the amount of rotational advance in the region to the right of center O, not shown in FIG. 9, is the same as above, zx. Therefore, by doubling the amount of delay, the difference between the maximum advance and maximum delay of the rotation can be calculated. This maximum difference is the maximum running difference of the balls relative to the cage. Therefore, the maximum running difference of the balls is used as the calculated value for the minimum dimension K10 of the circumferential gap, which is expressed as the difference between the distance between a pair of circumferentially adjacent pillar portions 324B of pocket 324p and the diameter of ball 323. By making the circumferential gap dimension equal to or greater than the calculated value, it is possible to suppress significant interference caused by contact between the pocket 324p (inner surface 324s) of cage 324 and the surface of ball 323, which is caused by ball 323 deforming into the shape of pitch ellipse 41.

[0037] More specifically, the ball bearing 32 according to the present disclosure is used in the strain wave gear reducer 100 and includes an outer ring 321, an inner ring 322, balls 323, and a cage 324. The outer ring 321 is elastically deformable. The inner ring 322 is disposed inside the outer ring 321 and is elastically deformable. The balls 323 are disposed between the outer ring 321 and the inner ring 322. The cage 324 has pockets 324p formed by an inner surface 324s for accommodating the balls 323. The cage 324 includes an annular portion 324A and pillar portions 324B extending axially (direction a) from the annular portion 324A. When the center of the pocket 324p of the cage 324 is aligned with the center of the ball 323 housed in the pocket 324p, and the minimum dimension of the circumferential (l direction) gap, which is expressed by the difference between the distance between the pillar portions 324B adjacent in the l direction forming the pocket 324p and the diameter of the ball 323 housed in the pocket 324p, is K10, and the diameter of the ball 323 is D2 (see FIG. 5 ), 0.05≦K10 / D2≦0.15…(1) This makes it possible to prevent excessive stress from being generated in the cage 324. A ball bearing having this characteristic may be one in which the minimum dimension K110 is determined by the above calculation method, for example.

[0038] The reason why the establishment of the above formula (1) can suppress the occurrence of excessive stress on the cage 324 will now be explained using an example. Six types of samples were prepared by changing the ratio K10 / D2 of the minimum dimension K10 of the gap in the l direction, which is expressed as the difference between the distance between the pillar portions 324B in the l direction obtained using the above calculation method and the diameter of the balls 323 housed in the pockets 324p, to the diameter D2 of the balls 323. Each sample was assigned a number from sample No. 1 to sample No. 6. The presence or absence of contact between the pockets 324p and the balls 323 and the condition of the cage were examined for each sample, and the results are shown in the table below.

[0039] [Table 1]

[0040] The cage condition in the table above is as follows: A indicates that the cage is in good condition. B indicates that the cage is not in poor condition. C indicates that the cage is in poor condition. From Table 1 above, if K10 / D2 is less than 0.05, as in samples No. 1 and 2, the gap is small and the pocket 324p and ball 323 come into strong contact, causing excessive stress on the cage 324. For this reason, the cage condition of samples No. 1 and 2 is rated C. Also, if K10 / D2 exceeds 0.15, as in sample No. 6, the gap is large and the column portion 324B of the cage 324 is thin, weakening the strength of the cage 324. For this reason, the cage condition of sample No. 6 is also rated C. On the other hand, the cage condition of samples No. 3 and 4 is rated A, and that of sample No. 5 is rated B.

[0041] For the above reasons, it is preferable to set the numerical range of formula (1), that is, K10 / D2 to be 0.05 or more and 0.15 or less, as in samples Nos. 3, 4, and 5. This prevents excessive stress on the retainer 324 and increases the strength of the retainer 324. From the perspective of further increasing the strength of the retainer 324, it is more preferable to set K10 / D2 to be 0.05 or more and 0.14 or less, as in samples Nos. 3 and 4.

[0042] In the above, the wave gear reducer 100 includes a wave generator 30, a flexspline 20, and a circular spline 10. The wave generator 30 has a non-circular (e.g., elliptical) cam 31 and a ball bearing 32. The flexspline 20 is provided on the outside of the wave generator 30, has external teeth 21, and is capable of being deflected in a non-circular (elliptical) shape by the cam 31. The circular spline 10 is provided on the outside of the flexspline 20, has an annular shape, and has internal teeth 11 that partially mesh with the external teeth 21. The outer ring 321 is rotatable integrally with the flexspline 20. The inner ring 322 is rotatable integrally with the cam 31. The cam 31 causes the ball bearing 32 to elastically deform in a non-circular shape, and the outer ring 321 of the ball bearing 32 is deflected in a non-circular shape similar to the flexspline 20. As a result, even if the maximum difference in ball running relative to the retainer occurs as described above, by setting the maximum difference in ball running as the minimum dimension K10 of the gap, it is possible to suppress large interference caused by contact from the surface of ball 323 with pocket 324p (inner surface 324s) of retainer 324, which is caused by ball 323 deforming into the shape of pitch ellipse 41.

[0043] (Embodiment 2) <Ball bearing configuration> FIG. 10 is a schematic plan view showing the strain wave gear reducer according to the second embodiment as viewed from the axial direction. However, part of the cage is not shown in FIG. 10. FIG. 11 is a schematic cross-sectional view taken along line XI-XI in FIG. 10. FIG. 12 is an enlarged schematic view showing a portion of the cage according to the second embodiment, in which balls are held in one pocket, as viewed from the r direction. FIG. 13 is a schematic cross-sectional view taken along line XIII-XIII in FIG. 11. Note that FIG. 13 is a schematic view for simplicity of explanation, and may differ slightly from the actual shape. Referring to FIGS. 10 to 13, the strain wave gear reducer 100 and ball bearing 32 according to this embodiment have basically the same configuration as the strain wave gear reducer 100 and ball bearing 32 according to the first embodiment. Generally, FIG. 10 corresponds to FIG. 1, FIG. 11 corresponds to FIG. 3, FIG. 12 corresponds to FIG. 5, and FIG. 13 corresponds to FIG. 6. 10 to 13, parts that are the same as or correspond to those in the first embodiment are given the same reference numerals, and unless particularly necessary, description thereof will not be repeated.

[0044] 10, 12, and 13, in ball bearing 32 of this embodiment, first surface 324s1 facing balls 323 in pocket 324p is a curved surface extending in a curved line in the r direction. In this respect, this embodiment is structurally different from Embodiment 1, in which first surface 324s1 is a cylindrical surface extending linearly in the r direction. Also, as shown in FIG. 11, second surface 324s2 facing balls 323 in pocket 324p is a curved surface extending in a curved line in the r direction, similar to first surface 324s1.

[0045] In this embodiment, the center in the a and l directions of the portion surrounded by the first surface 324s1 and the second surface 324s2 (the portion missing due to the surrounding area is supplemented by the second surface 324s2 so that it is point-symmetric with the existing portion) is defined as the center of the pocket 324p.

[0046] However, the curvature in the r direction of the first surface 324s1 and the second surface 324s2, which are portions of the inner surface 324s of the pocket 324p in FIGS. 10 to 13 that can come into contact with the ball 323 (facing the ball 323), is equal to or less than the curvature of the surface of the ball 323. Therefore, this embodiment also includes a case where the inner surface 324s extends linearly in the r direction, as in the first embodiment, i.e., a case where the curvature of the inner surface 324s in the r direction is zero. Also, in FIGS. 10 to 13, the first surface 324s1 (inner surface 324s) is formed so that the dimension in the l direction is smaller at the center in the r direction than at the ends. However, this is not limiting, and the first surface 324s1 (inner surface 324s) may be formed so that the dimension in the l direction is smaller at the center in the r direction than at the ends.

[0047] <Action and effect> In this embodiment, as in the first embodiment, the minimum dimension K10 of the gap in the l direction between the balls 323 housed in the pockets 324p and the column portions 324B is at least twice the difference between z and x in FIG. 8. By providing a sufficient gap in this manner, it is not necessary to make the first surfaces 324s1 and the like straight in the r direction as in the first embodiment. By making the curvature relatively small, at least equal to or less than the curvature of the curved surface of the balls 323, it is possible to suppress significant interference of the balls 323 with the cage 324 (the generation of excessive stress), as in the first embodiment.

[0048] Furthermore, if the column portions 324B of the cage 324 are thin in the l direction, the strength of the cage 324 against the external load in the l direction received from the balls 323 is significantly reduced. Therefore, by making the first surfaces 324s1 and the like curved in the r direction as in the present embodiment, the cross-sectional area of ​​the column portions 324B shown in FIG. 13 can be made larger than in the first embodiment, which has a straight shape. This is because the cross-sectional area of ​​the column portions 324B shown in FIG. 13 is increased by the amount that the curved portions of the first surfaces 324s1 of the column portions 324B protrude outward in the circumferential direction. As a result, the strength of the column portions 324B of the cage 324 can be made higher than in the first embodiment.

[0049] (Embodiment 3) <Ball bearing configuration> Fig. 14 is an enlarged schematic diagram showing a portion of the cage of embodiment 3 in which balls are held in one pocket, as viewed from the r direction. Referring to Fig. 14, the strain wave gear reducer 100 and ball bearing 32 of this embodiment have basically the same configuration as the strain wave gear reducer 100 and ball bearing 32 of embodiment 1. Fig. 14 generally corresponds to Fig. 5. In Fig. 14, parts that are the same as or correspond to those of embodiment 1 are given the same reference numerals, and unless particularly necessary, their description will not be repeated.

[0050] In FIG. 14, the shape of the cage 324 of the first embodiment is indicated by a dotted line for comparison. As shown in FIG. 14, in the cage 324 of the present embodiment, the inner surface 324s of the pocket 324p has a shape that is a part of a curved surface in which the dimension in the l direction is larger than the dimension in the a direction, when viewed from the r direction. More specifically, the cage 324 of FIG. 14 has a first surface 324s1 and a second surface 324s2 as the inner surface 324s of the pocket 324p. As in the first embodiment, the first surface 324s1 has an arc shape in plan view as a part of a cylindrical surface with a diameter D1. In contrast, the second surface 324s2 has a shape that is a part of a cylindrical surface with a smaller curvature (larger radius) of the arc shape in plan view than the first surface 324s1. In this case, as in the first embodiment, the minimum dimension K10 can be calculated as the sum of the values ​​of two intervals K5 at the same position as the center of the first surface 324s1 (the center of the ball 323) in the a direction. Alternatively, the minimum dimension K10 can be determined as the difference between the diameter D1 (see Figures 5 and 6) of the cylindrical surface (which is circular when viewed from a plane in the r direction and is a complete circle with missing portions filled in) that forms the first surface 324s1 and the diameter D2 (see Figures 5 and 6) of the ball 323.

[0051] In this embodiment, the center of pocket 324p refers to the center of the portion surrounded by the cylindrical surface that constitutes first surface 324s1. Therefore, when viewed from the r direction, first surface 324s1 is actually present in the region where second surface 324s2 is formed and in the missing portion, and assuming that first surface 324s1 is arranged as a complete cylindrical surface, the center of the circle that constitutes the cylindrical surface defined by first surface 324s1 and the center in the r direction along which the cylindrical surface extends is defined as the center of pocket 324p.

[0052] 14, the inner surface 324s of the cage 324 may be part of an ellipse having a major axis in the l direction and a minor axis in the a direction in a plan view from the r direction. In this case, the second surface 324s2 (the minor axis side) has a smaller curvature than the first surface 324s1 (the major axis side). In other words, the inner surface 324s may be a curved surface that is partially missing on the left side in the a direction in FIG. 14, and that becomes an ellipse when viewed from the r direction by filling in the missing portion.

[0053] <Action and effect> In this embodiment, the inner surface 324s of the pocket 324p has a first surface 324s1 as an end surface of the column portion 324B of the cage 324 and a second surface 324s2 as an end surface of the annular portion 324A of the cage 324. The first surface 324s1 has a planar shape (shape when viewed from the r direction) as a part of a circle. The second surface 324s2 has a planar shape (shape when viewed from the r direction) as a part of a circle with a smaller curvature than the first surface 324s1. This makes the dimension in the a direction of the inner surface 324s forming the pocket 324p smaller than the dimension in the l direction. Therefore, the thickness of the annular portion 324A adjacent to the pocket 324p in the a direction is greater in the a direction than in the case where the second surface 324s2 is a circle with the same curvature as the first surface 324s1 as shown by the dotted line in FIG. 14 . This increases the strength of the cage 324.

[0054] (Fourth embodiment) <Ball bearing configuration> Fig. 15 is an enlarged schematic diagram showing a portion of the cage of embodiment 4 in which balls are held in one pocket, as viewed from the r direction. Referring to Fig. 15, the strain wave gear reducer 100 and ball bearing 32 of this embodiment have basically the same configuration as the strain wave gear reducer 100 and ball bearing 32 of embodiment 1. Fig. 15 generally corresponds to Fig. 5. In Fig. 15, parts that are the same as or correspond to those of embodiment 1 are given the same reference numerals, and unless particularly necessary, their description will not be repeated.

[0055] In FIG. 15, the shape of the cage 324 of the first embodiment is shown by a dotted line for comparison. As shown in FIG. 15, in the cage 324 of the present embodiment, the inner surface 324s of the pocket 324p has a first surface 324s1 and a planar second surface 324s2. The first surface 324s1 is an end surface of the column portion 324B in the l direction. The first surface 324s1 may be a planar surface that is not curved (the curvature of the curve is negligibly small). However, the first surface 324s1 may be a cylindrical surface as in the first embodiment. Alternatively, the first surface 324s1 may be a curved surface with a curvature in the r direction equal to or smaller than the curvature of the surface of the ball 323 as in the second embodiment. The second surface 324s2 is an end surface of the annular portion 324A in the a direction. The second surface 324s2 is a planar surface that is not curved (the curvature of the curve is negligibly small). The first surface 324s1 and the second surface 324s2 intersect (for example, perpendicular to) each other. In this embodiment, the minimum dimension K10 is the difference between the distance between a pair of first surfaces 324s1 that are adjacent in the l direction and face each other in parallel, and the diameter of the ball 323. The minimum dimension K10 is also the sum of the two dimensions K5 in FIG. 15.

[0056] In this embodiment, the center in the a and l directions of the portion surrounded by the first surface 324s1 and the second surface 324s2 (the portion missing due to the surrounding area is supplemented by the second surface 324s2 so that it is point-symmetric with the existing portion) is defined as the center of the pocket 324p.

[0057] <Action and effect> In this embodiment, the inner surface 324s of the pocket 324p has a first surface 324s1 as an end surface of the column portion 324B of the cage 324, and a planar second surface 324s2 that intersects with the first surface 324s1 and is an end surface of the annular portion 324A of the cage 324. In this way, by positioning the second surface 324s2 and the balls 323 as far to the left side of the drawing (the tip end side of the column portion 324B in the a direction) as possible as shown in FIG. 15 , the dimension in the a direction of the inner surface 324s that forms the pocket 324p is smaller than the dimension in the l direction, compared to the first embodiment shown by the dotted line in FIG. 15 . Therefore, in the a direction, the thickness of the annular portion 324A adjacent to the pocket 324p in the a direction is increased. This increases the strength of the cage 324.

[0058] The features described in each of the above-described embodiments (each example included therein) may be applied in an appropriate combination within the scope of technical compatibility.

[0059] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of the present invention is defined by the claims, not by the above description, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0060] 10 circular spline, 11 internal teeth, 20 flexspline, 21 external teeth, 22 cylindrical portion, 23 bottom portion, 30 wave generator, 31 cam, 32 ball bearing, 41 pitch ellipse, 42 virtual circle, 51, 52, 53, 54 straight line, 61, 62, 63 arc, 100 strain wave gear reducer, 321 outer ring, 321g, 322g raceway groove, 322 inner ring, 322A, 322B raceway surface, 323 ball, 324 cage, 324A annular portion, 324B column portion, 324p pocket, 324s inner surface, 324s1 first surface, 324s2 second surface, C axis center, O center.

Claims

1. A ball bearing used in a strain wave gear reducer, an outer ring capable of elastic deformation; an inner ring that is arranged inside the outer ring and is elastically deformable; a ball disposed between the outer ring and the inner ring; a cage having an inner surface defining a pocket for accommodating the balls; the cage includes an annular portion and a column portion extending in the axial direction from the annular portion, When the minimum dimension of the circumferential gap of the cage is K10, which is expressed by the difference between the distance between circumferentially adjacent pillar portions forming the pocket and the diameter of the ball accommodated in the pocket when the center of the pocket and the center of the ball accommodated in the pocket are aligned, and the diameter of the ball is D2, 0.05≦K10 / D2≦0.15 (1) is established, the inner surface of the pocket has a first surface as an end surface of the column portion of the cage and a second surface as an end surface of the annular portion of the cage, the first surface has a planar shape as a part of a circle, the second surface has a planar shape as part of a circle with a smaller curvature than the first surface, i) the balls are arranged at equal intervals on the circumference of a pitch ellipse obtained by connecting the centers of the balls when at least one of the outer ring and the inner ring is elastically deformed, ii) determining a straight line extending radially from the center of the pitch ellipse by connecting the center of the pitch ellipse with the center of the ball; iii) calculating the lengths of a plurality of arcs obtained by dividing an imaginary circle having a center at the same position as the center of the pitch ellipse and having a diameter equal to the length of the major axis of the pitch ellipse by intersecting the radially extending straight lines; iv) determining a calculated value by doubling the difference between the maximum length and the minimum length of the lengths of the plurality of circular arcs determined within the load zone of the ball receiving the load from the outer ring and the inner ring; A ball bearing, wherein the calculated value obtained based on i) to iv) is K10.

2. 2. The ball bearing according to claim 1, wherein a curvature of a portion of the inner surface of the pocket that can come into contact with the ball in the radial direction of the cage is equal to or smaller than a curvature of a surface of the ball.

3. The ball bearing according to claim 1 or 2, wherein the second surface has a planar shape that intersects with the first surface.

4. The strain wave gear reducer comprises: a wave generator having a non-circular cam and the ball bearing; a flexspline provided on the outside of the wave generator, having external teeth, and capable of being deflected non-circularly by the cam; a circular spline provided on the outside of the flexspline, having an annular shape, and having internal teeth that partially mesh with the external teeth; the outer ring is rotatable integrally with the flexspline, 4. The ball bearing according to claim 1, wherein the inner ring is rotatable integrally with the cam.

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