Ball screw device

Abstract

A ball screw device according to the present disclosure comprises a screw shaft, a nut, and a plurality of balls. The outer circumferential surface of the screw shaft is provided with an S-shaped groove surface, and the screw shaft has a corner portion where the outer circumferential surface, and an outer circumferential raceway surface and the S-shaped groove surface, intersect. The ball screw device satisfies expression (1), where Dw is the diameter of the balls, Rn is the radius of a circular arc forming a groove-perpendicular cross section of an inner circumferential raceway surface of the nut, α is the contact angle of the balls with respect to the inner circumferential raceway surface of the nut, θ1 is an angle within the groove-perpendicular cross section representing an effective range of the inner circumferential raceway surface of the nut, Dm is the diameter of a circle joining the centers of the plurality of balls disposed in the raceway, Ds is the diameter of the outer circumferential surface of the screw shaft, Q is the radial-direction distance between the outer circumferential surface of the screw shaft and a portion of the corner part positioned most on the inside in the radial direction if the vertex of the corner part of the screw shaft is shaved, and k (k>1) is a correction coefficient.

Description

Ball screw device

[0001] The present disclosure relates to a ball screw device.

[0002] A ball screw device is a device that converts rotational motion into linear motion and linear motion into rotational motion. The ball screw device includes a screw shaft, a nut inserted through the screw shaft, multiple balls disposed between the screw shaft and the nut, and a circulation unit for circulating the balls. An example of the circulation unit is a ball return roller that returns the balls approximately one lead. In the following Patent Document 1, a mounting hole is formed on the outer peripheral surface of the screw shaft, and a ball is inserted into the mounting hole. An S-shaped groove surface is formed on the radially outer surface of the ball, connecting one end of the outer peripheral raceway surface to the other end. The ball also has a tang for scooping up the balls. In addition to the above-mentioned ball, the circulation unit can also be an S-shaped groove surface formed directly on the outer peripheral surface of the screw shaft.

[0003] Japanese Utility Model Application Publication No. 58-52359

[0004] 2. Description of the Related Art Conventionally, it has been desired in ball screw devices to be able to reliably scoop up balls even when the device does not have a tang.

[0005] The present disclosure has been made in view of the above, and aims to provide a ball screw device that can reliably scoop up balls even without a tang.

[0006] In order to achieve the above object, a ball screw device according to one aspect of the present disclosure includes a screw shaft having an outer peripheral raceway surface formed on its outer peripheral surface, a nut having an inner peripheral raceway surface formed on its inner peripheral surface and inserted onto the screw shaft, and a plurality of balls arranged in a raceway formed between the outer peripheral raceway surface and the inner peripheral raceway surface. An S-shaped groove surface for circulating the balls is directly formed on the outer peripheral surface of the screw shaft. A corner that intersects with the outer peripheral raceway surface or the S-shaped groove surface is formed on the outer peripheral surface of the screw shaft. The diameter of the balls is defined as Dw. The radius of the arc forming a cross section perpendicular to the groove of the inner peripheral raceway surface of the nut is defined as Rn. The contact angle of the ball with respect to the inner peripheral raceway surface of the nut is defined as α. The angle on the cross section perpendicular to the groove that indicates the effective range of the inner peripheral raceway surface of the nut is defined as θ1. The diameter of a circle connecting the centers of the plurality of balls arranged in the raceway is defined as Dm. The diameter of the outer peripheral surface of the screw shaft is defined as Ds. When the apex of the corner of the screw shaft is ground off, the radial distance between the radially innermost part of the corner and the outer circumferential surface of the screw shaft is defined as Q. A correction coefficient is defined as k (k>1). The ball screw device satisfies the following formula (1).

[0007]

[0008] According to the present disclosure, equation (1) includes a correction coefficient k, which takes into account the centrifugal force acting on the ball. Therefore, even if centrifugal force acts on the ball (even if a radially outward load due to centrifugal force acts on the ball), the ball can be reliably scooped up radially inward. In other words, a tang is not required.

[0009] In the ball screw device, the correction coefficient k may be greater than 1.3.

[0010] In the ball screw device, the S-groove surface may be formed directly on the outer circumferential surface of the screw shaft.

[0011] In the ball screw device, the surface hardness of the S-shaped groove surface is preferably 56 HRC or more, or the S-shaped groove surface is preferably subjected to induction hardening, or the S-shaped groove surface is preferably subjected to carburizing hardening.

[0012] According to the above configuration, the S-shaped groove surface is less likely to be damaged.

[0013] In the ball screw device, a mounting hole recessed radially inward is formed on the outer peripheral surface of the screw shaft, and a top is attached to the mounting hole. The S-shaped groove surface may be formed on the radially outer surface of the top.

[0014] In the ball screw device described above, a direction parallel to the central axis of the screw shaft is referred to as the axial direction. A first virtual line is a virtual line that is perpendicular to the central axis and connects the central axis to one end of the S-shaped groove surface. A second virtual line is a virtual line that is perpendicular to the central axis and connects the central axis to the other end of the S-shaped groove surface. Here, when the diameter of the outer circumferential surface of the screw shaft is 25 mm or less, the angle formed between the first virtual line and the second virtual line when viewed from the axial direction is preferably 50° or more and 120° or less. Alternatively, when the diameter of the outer circumferential surface of the screw shaft is greater than 25 mm, the angle formed between the first virtual line and the second virtual line when viewed from the axial direction is preferably 30° or more and 90° or less.

[0015] According to this configuration, the bending angle of the ball when moving between the outer circumferential raceway surface and the S-shaped groove surface is relatively small, which allows the ball to move smoothly between the outer circumferential raceway surface and the S-shaped groove surface.

[0016] In the ball screw device, the S-shaped groove surface extends linearly when viewed from the outside in the radial direction and has a pair of end portions connected to both end portions of the outer circumferential raceway surface, and an intermediate portion connecting the pair of end portions. The intermediate portion extends arcuately when viewed from the outside in the radial direction and has a pair of R portions connected to the end portions. When the radius of curvature of a center line passing through the center of the R portions in the groove width direction is R7, it is preferable that the following formula (2) be satisfied.

[0017]

[0018] According to this configuration, the balls are scooped up near both ends of the S-shaped groove surface, which allows the balls to move smoothly between the outer circumferential raceway surface and the S-shaped groove surface.

[0019] In the ball screw device, the depth of the outer circumferential raceway surface may be greater than the depth of the inner circumferential raceway surface.

[0020] In the ball screw device, it is preferable that an initial contact angle between the outer peripheral raceway surface and the ball is larger than an initial contact angle between the inner peripheral raceway surface and the ball, or that a radius of curvature of an arc forming a cross section of the outer peripheral raceway surface perpendicular to the groove is smaller than a radius of curvature of an arc forming a cross section of the inner peripheral raceway surface perpendicular to the groove.

[0021] According to the above configuration, the load (surface pressure) per unit area acting from the balls on the outer circumferential raceway surface is reduced.

[0022] In the above-described ball screw device, when the diameter of the inner peripheral surface of the nut is Dn, it is preferable that the following formulas (3) and (4) be satisfied.

[0023]

[0024]

[0025] According to the above configuration, the outer peripheral surface (groove shoulder) of the screw shaft is located near Dm (the diameter of a circle connecting the centers of multiple balls arranged in the raceway), and the depth of the outer peripheral raceway surface is relatively large. Therefore, the balls are less likely to ride up onto the groove shoulder of the screw shaft. On the other hand, the inner peripheral surface of the nut is located away from Dm, and the depth of the inner peripheral raceway surface is relatively small. Therefore, the balls rolling on the S-shaped groove surface are less likely to come into contact with the threads of the nut, and the balls move smoothly.

[0026] According to the ball screw device of the present disclosure, the ball can be reliably scooped up even without a tang.

[0027] FIG. 1 is a schematic diagram of a ball screw device according to an embodiment cut in the axial direction. FIG. 2 is an enlarged view of an S-groove surface according to an embodiment. FIG. 3 is a cross-sectional view of a ball screw device according to an embodiment (a ball screw device in which corners are not cut) cut along line VIII-VIII in FIG. 2. FIG. 4 is a schematic diagram of the vicinity of the center of the ball in FIG. 3. FIG. 5 is a cross-sectional view of a ball screw device according to a comparative example. FIG. 6 is a cross-sectional view of a rounded corner according to an embodiment. FIG. 7 is a cross-sectional view of a C-chamfered corner according to an embodiment. FIG. 8 is a cross-sectional view of a ball screw device according to an embodiment (a ball screw device in which corners are cut) cut along line VIII-VIII in FIG. 2. FIG. 9 is a side view of the screw shaft of a ball screw device according to a first modification, viewed from the radial outside. FIG. 10 is a cross-sectional view of a ball screw device according to a second modification, cut along the S-groove surface and the outer circumferential raceway surface, viewed from the axial direction. FIG. 11A is an enlarged view of the S-groove surface and its vicinity according to the second modification. 11B is an enlarged view of the S-shaped groove surface and its vicinity in Comparative Example 1. FIG. 12 is a view of the S-shaped groove surface of a ball screw device of Modified Example 3 viewed from the radial outside. FIG. 13 is a view of the S-shaped groove surface of Comparative Example 2 viewed from the radial outside. FIG. 14A is a schematic view of a ball screw device of Modified Example 3, where the outer peripheral raceway surface and the S-shaped groove surface are cut at the center in the groove width direction, and the cross section is viewed from the axial direction. FIG. 14B is a schematic view of a ball screw device of Comparative Example 2, where the outer peripheral raceway surface and the S-shaped groove surface are cut at the center in the groove width direction, and the cross section is viewed from the axial direction. FIG. 15 is a cross-sectional view of the outer peripheral raceway surface and the inner peripheral raceway surface of a ball screw device of Modified Example 4, where the outer peripheral raceway surface and the inner peripheral raceway surface are cut at the center in the groove width direction. FIG. 16 is a cross-sectional view of the outer peripheral raceway surface and the inner peripheral raceway surface of a ball screw device of Modified Example 5, where the outer peripheral raceway surface and the inner peripheral raceway surface are cut at the center in the groove width direction. FIG. 17 is a cross-sectional view of the outer peripheral raceway surface and the inner peripheral raceway surface of a ball screw device of Modified Example 6, where the outer peripheral raceway surface and the inner peripheral raceway surface are cut at the center in the groove width direction. FIG. 18 is an enlarged view of a cross section perpendicular to the grooves of the outer peripheral raceway surface and the inner peripheral raceway surface of the ball screw device of the seventh modification.

[0028] The ball screw device of the present disclosure will be described in detail below with reference to the drawings. Note that the present disclosure is not limited to the following modes for carrying out the invention (hereinafter referred to as embodiments). Furthermore, the components in the following embodiments include those that can be easily imagined by a person skilled in the art, those that are substantially the same, and those that are within the so-called equivalent range. Furthermore, the components disclosed in the following embodiments can be combined as appropriate.

[0029] (Embodiment) FIG. 1 is a schematic diagram of a ball screw device of an embodiment cut in the axial direction. The ball screw device 100 is a device that converts rotational motion into linear motion, or linear motion into rotational motion. As shown in FIG. 1, the ball screw device 100 includes a screw shaft 1, a nut 2, and a plurality of balls 3 (not shown in FIG. 1; see FIG. 3). The screw shaft 1 also has an S-shaped groove surface 4 formed as a circulation portion. Hereinafter, a direction parallel to the central axis X of the screw shaft 1 will be referred to as the axial direction. One side of the axial direction will be referred to as the first direction X1, and the direction opposite to the first direction X1 will be referred to as the second direction X2. A direction perpendicular to the central axis X will be referred to as the radial direction.

[0030] The nut 2 is formed in a cylindrical shape centered on the central axis X. An inner circumferential surface 21 extending in a spiral direction is formed on an inner circumferential surface 20 of the nut 2. The inner circumferential surface 21 is formed over the entire axial direction of the inner circumferential surface 20. In other words, the inner circumferential surface 21 is continuous from the end of the inner circumferential surface 20 in the first direction X1 to the end of the inner circumferential surface 20 in the second direction X2. Although not particularly shown, the nut 2 of this embodiment is supported by other components such as a housing so as to be non-rotatable around the central axis X and so as to be freely movable in the axial direction.

[0031] The screw shaft 1 includes a screw shaft main body 10 and a shank 11. The shank 11 is disposed in a first direction X1 relative to the screw shaft main body 10. The shank 11 is rotatably supported by other components such as a bearing device (not shown). Torque generated by a motor (not shown) is input to the shank 11.

[0032] The screw shaft body 10 is formed in a cylindrical shape centered on the central axis X. Four outer peripheral raceway surfaces 13 and four S-shaped groove surfaces 4 (one of which is not shown in FIG. 1 ) are formed directly on the outer peripheral surface 12 of the screw shaft body 10. The outer peripheral raceway surfaces 13 and the S-shaped groove surfaces 4 are each formed by cutting the outer peripheral surface 12 of the screw shaft body 10. In addition, the screw shaft body 10 has a corner portion 15 where the groove surfaces (the outer peripheral raceway surfaces 13 and the S-shaped groove surfaces 4) and the outer peripheral surface 12 intersect.

[0033] The outer circumferential raceway surface 13 extends in the same spiral direction as the inner circumferential raceway surface 21. The length of the outer circumferential raceway surface 13 is approximately one lead. The outer circumferential raceway surface 13 faces the inner circumferential raceway surface 21 in the radial direction. The space between the outer circumferential raceway surface 13 and the inner circumferential raceway surface 21 forms a raceway. A plurality of balls 3 are arranged in the raceway. Each ball 3 is in contact with the inner circumferential raceway surface 21 and the outer circumferential raceway surface 13, respectively, and is subjected to a load.

[0034] Fig. 2 is an enlarged view of the S-shaped groove surface of the embodiment. As shown in Fig. 2, the S-shaped groove surface 4 has a pair of end portions 5 connected to one end 13a and the other end 13b of the outer circumferential raceway surface 13, and an intermediate portion 6 connected to the pair of end portions 5. The end portions 5 are formed in a straight line. The intermediate portion 6 is formed in a curved line. The depth of the intermediate portion 6 is greater than the depth of the end portions 5. As a result, the balls 3 rolling in the intermediate portion 6 do not come into contact with the threads of the nut 2.

[0035] According to the ball screw device 100 described above, when torque is transmitted to the screw shaft 1, the screw shaft 1 rotates and the nut 2 moves in the axial direction. Each ball 3 moves along the track and enters the S-shaped groove surface 4 from one end of the track. The balls 3 are then scooped up radially inward at the boundary between the end portion 5 and the intermediate portion 6 of the S-shaped groove surface 4 (see dashed lines B1 and B2 in FIG. 2 ). The mechanism for scooping up the balls 3 will be described later. As a result, the balls 3 move along the intermediate portion 6 and climb over the threads of the nut 2. After passing the intermediate portion 6, the balls 3 circulate from the end portion 5 of the S-shaped groove surface 4 to the other end of the track. While the present embodiment illustrates an example in which torque is transmitted to the screw shaft 1 and the nut 2 moves in the axial direction, the present disclosure may also be configured such that torque is transmitted to the nut 2 and the screw shaft 1 moves in the axial direction.

[0036] The ball screw device 100 of this embodiment satisfies the following formula (5).

[0037]

[0038] Dw in equation (5) is the diameter of the ball 3. Rn in equation (5) is the radius of the arc 22 (see FIG. 3 ) forming the groove-perpendicular cross section of the inner circumferential raceway surface 21 of the nut 2. The groove-perpendicular cross section is a cross section obtained by cutting the inner circumferential raceway surface 21 along a plane perpendicular (orthogonal) to the spiral direction in which the inner circumferential raceway surface 21 extends. α in equation (5) is the contact angle of the ball 3 with the inner circumferential raceway surface 21 of the nut 2. θ1 in equation (5) is the angle in the groove-perpendicular cross section that indicates the effective range of the inner circumferential raceway surface 21 of the nut 2. Dm in equation (5) is the diameter of a circle connecting the centers O of the multiple balls 3 arranged in the raceway. Dm is sometimes called BCD (Ball Center Diameter). Ds in equation (5) is the diameter of the outer circumferential surface 12 of the screw shaft 1 (screw shaft main body 10). In the formula (5), Q is the radial distance between the radially innermost portion of the corner 15 of the screw shaft 1 when the apex of the corner 15 is ground off and the outer circumferential surface of the screw shaft 1. In the formula (5), k (k>1) is a correction coefficient.

[0039] Next, a method for deriving the above-mentioned formula (5) will be described with reference to the drawings.

[0040] Figure 3 is a cross-sectional view of a ball screw device according to an embodiment (a ball screw device in which the corners have not been cut) taken along line VIII-VIII in Figure 2. First, an example will be given in which the corners 15 have not been cut. Note that the case in which the corners 15 have not been cut refers to a state in which, as shown in Figure 3, the corners 15 are angled at approximately 90° when viewed in cross section, and a vertex is present.

[0041] As shown in Figure 3, a straight line extending radially from the central axis X and passing through the axial center of the inner circumferential raceway surface 21 is designated as M1. The inner circumferential raceway surface 21 of the nut 2 is formed symmetrically with respect to the straight line M1. The inner circumferential raceway surface 21 of this embodiment has a Gothic arc shape and is composed of two arcs 22. Note that the present disclosure may also be directed to an inner circumferential raceway surface having a circular arc shape. The center of the arcs 22 is designated as e. A straight line passing through the center e and parallel to the straight line M1 is designated as M2.

[0042] A straight line extending in the axial direction and passing through the center O of the ball 3 is defined as auxiliary line T1. A straight line passing through the center e of the arc 22 and parallel to auxiliary line T1 is defined as auxiliary line T2. The contact point between the ball 3 and the arc 22 is defined as h. A straight line passing through the contact point h and the center e of the arc 22 is defined as auxiliary line T3. Note that since the ball 3 is in contact at the contact point h, auxiliary line T3 passes through the center O of the ball 3. The contact angle between the ball 3 and the arc 22 is defined as α.

[0043] Figure 4 is a schematic diagram illustrating the vicinity of the center of the ball in Figure 3. As shown in Figure 4, the distance between the center O of the ball 3 and the center e of the arc 22 is designated as Z. The center O of the ball 3 and the center e of the arc 22 are on the auxiliary line T3, and the following equation (6) is obtained.

[0044]

[0045] As shown in Figure 4, the radial distance between the center O of the ball 3 and the center e of the arc 22 (the distance between the auxiliary lines T1 and T2) is b. Using trigonometric functions, the distance b can be calculated using the following formula (7-1). Furthermore, rearranging formula (7-1) gives formula (7-2).

[0046]

[0047] Then, equation (8) can be obtained from equation (6) and equation (7-2).

[0048]

[0049] As shown in Figure 3, in the nut 2, the corner between the inner peripheral surface 20 and the inner peripheral raceway surface 21 is chamfered to form a chamfered portion 23. The boundary position between this chamfered portion 23 and the inner peripheral raceway surface 21 is designated as point f. A straight line that passes through point f and is parallel to the auxiliary line T1 is designated as auxiliary line T4. Furthermore, the intersection of the straight line M2 and the auxiliary line T4 is designated as U1.

[0050] The radial distance between the center O of the ball 3 and the auxiliary line T4 (the distance between the auxiliary lines T1 and T4) is defined as c. Furthermore, in a triangle having the center e, point U1, and point f as vertices, the distance b+c is the same as the length of the side connecting point U1 and the center e. Therefore, the following equation (9-1) can be obtained from the trigonometric functions of the triangle having the vertices at the center e, point U1, and point f. Furthermore, rearranging equation (9-1) yields equation (9-2).

[0051]

[0052] A straight line passing through point f and center e is designated as auxiliary line T5. Auxiliary line T5 intersects with the outline of ball 3 twice, and the intersection point farther from point f is designated as g. A straight line passing through point g and parallel to line M1 is designated as line M3. Furthermore, the intersection point between line M3 and auxiliary line T4 is designated as U2.

[0053] Furthermore, the angle at which the straight line M3 and the auxiliary line T5 intersect is θ3. The radial distance between the auxiliary line T1 and point g is d. The triangle with point f, center e, and point U1 as vertices and the triangle with point f, point g, and point U2 as vertices are right-angled triangles with the auxiliary line T5 as their common hypotenuse, so θ3 = θ1.

[0054] The distance between points f and g on auxiliary line T5 is defined as y. The following equation (10-1) can be determined from the trigonometric functions of a triangle with vertices at points f, g, and U2. Furthermore, since θ3 = θ1 and the distance y between points g and f is approximately equal to the diameter Dw of ball 3 (y ≒ Dw), equation (10-1) can be replaced with equation (10-2). Then, rearranging equation (10-2) yields the following equation (10-3).

[0055]

[0056] Then, by substituting c in equation (10-3) with the right side of equation (10-2), the following equation (11) is obtained.

[0057]

[0058] Next, substituting b in equation (11) with the right side of equation (8) gives equation (12) below.

[0059]

[0060] If the corner 15 is not cut, the vertex of the corner 15 becomes the scooping contact point a. The line passing through this scooping contact point a and the center e is defined as L. The radial distance between the auxiliary line T1 and the scooping contact point a is defined as P.

[0061] Here, when ball 3 enters S-shaped groove surface 4, ball 3 comes into contact with scooping contact point a at the boundary of S-shaped groove surface 4 (see dashed lines B1 and B2 in FIG. 2 ). Then, ball 3 is pushed to the right side of FIG. 3 within S-shaped groove surface 4. As a result, the contact angle α between ball 3 and arc 22 becomes θ1 (contact point h overlaps point f. Also, center O of ball 3 moves and overlaps auxiliary line T5). As ball 3 moves further, it is sandwiched between scooping contact points a and f. Therefore, ball 3 is subjected to load F1 directed from point f to center O and load F2 directed from scooping contact point a to center O. Then, ball 3 moves toward load F3, which is the combination of loads F1 and F2.

[0062] Figure 5 is a cross-sectional view of a ball screw device of a comparative example. The contact angle of the ball 3 with respect to the screw shaft 1 is θ2. Here, as shown in Figure 5, if θ2 < θ1, when the load F1 acting on the ball 3 from point f and the load F2 acting on the ball 3 from the scooping contact point a are combined, the direction of the load F3 is radially outward. In other words, the ball 3 cannot be scooped up. From the above, in order to scoop up the ball 3, in other words, to ensure that the load F3, which is the combined loads F1 and F2, faces radially inward as shown in Figure 3, it is essential that θ2 > θ1.

[0063] As shown in Figure 3, when θ2 = θ1, the auxiliary line T5 passes through the scooping contact point a, and d = P. Therefore, when θ2 > θ1, d > P. Therefore, when d > P is substituted into equation (12), the following equation (13-1) is obtained. Furthermore, rearranging equation (13-1) below yields equation (13-2).

[0064]

[0065] The diameter of the circle connecting the centers of the multiple balls 3 in the raceway is Dm. The diameter of the outer peripheral surface 12 of the screw shaft 1 is Ds. Then, P = (Dm - Ds) / 2. Applying this to equation (13-2), it can be replaced with the following equation (14).

[0066]

[0067] The above are the basic requirements for scooping up the ball 3.

[0068] FIG. 6 is a cross-sectional view of a rounded corner in an embodiment. FIG. 7 is a cross-sectional view of a C-chamfered corner in an embodiment. However, the above description applies to a case where the apex of the corner 15 of the screw shaft 1 is the scooping contact point a. As shown in FIG. 6, the corner 15 may be rounded by R-chamfering during the manufacture of the screw shaft 1. In this case, the corner 15 has no apex, and is arc-shaped when viewed in cross section. Alternatively, as shown in FIG. 7, the corner 15 may be C-chamfered during the manufacture of the screw shaft 1, resulting in a slope. In addition, the corner 15 may not be chamfered during the manufacture of the screw shaft 1, and may have a apex, but may become rounded due to deterioration over time. In this way, the corner 15 may be ground down and have no apex.

[0069] When the corner 15 is cut in this way, the scooping contact point a is the radially innermost part of the cut portion, as shown in Figures 6 and 7. Therefore, the radial distance P from the auxiliary line T1 (center O of the ball 3) to the scooping contact point a described above does not take this into consideration. For this reason, it is necessary to slightly modify the above-mentioned P = (Dm - Ds) / 2.

[0070] Figure 8 is a cross-sectional view of a ball screw device (a ball screw device in which a corner portion is cut) according to an embodiment, taken along line VIII-VIII in Figure 2. Specifically, as shown in Figure 8, the radial distance from the outer peripheral surface 12 of the screw shaft 1 to the scooping contact point a is designated as Q. When considering the case in which the corner portion 15 is cut, the radial distance P from the auxiliary line T1 to the scooping contact point a is given by the following equation (15).

[0071]

[0072] Then, when equation (15) is substituted with equation (13-2), the following equation (16) is obtained.

[0073]

[0074] In addition, if the corner portion 15 is not cut, the radial distance Q from the outer peripheral surface 12 of the screw shaft 1 to the scooping contact point a1 in equation (16) becomes zero, which is the same as equation (14).

[0075] In addition, when the ball screw device 100 is driven, the ball 3 moves along the orbit, and therefore a centrifugal force (see arrow F4 in FIG. 8 ) acts radially outward. Therefore, even if the design satisfies equation (16), there is a possibility that the ball 3 will not be scooped up. For this reason, in this embodiment, the left side of equation (16) (the radial distance P from the auxiliary line T1 to the scooping contact point a) is multiplied by a correction coefficient k that takes centrifugal force into consideration, to derive the following equation (17).

[0076]

[0077] This equation (17) is the above-mentioned equation (5). Regarding the correction coefficient k, when k=1, the value of the distance P does not increase (the scooping contact point a is not corrected to move radially inward). In other words, the centrifugal force acting on the ball 3 is not taken into consideration. Therefore, k does not include 1 and takes a value greater than 1 (k>1).

[0078] As described above, the ball screw device 100 of the embodiment can reliably scoop up the balls 3 radially inward. Also, it is possible to grasp the critical angle of the angle θ1 of the effective range of the nut 2. In other words, it is possible to avoid a situation in which the angle θ1 of the effective range of the nut 2 is set smaller than necessary in order to reliably scoop up the balls 3, causing the balls 3 to ride up onto the groove shoulder of the nut 2.

[0079] Although the embodiment has been described above, in the present disclosure, the value of the correction coefficient k may be set appropriately depending on the centrifugal force acting on the ball 3. The larger the value of the correction coefficient k, the more reliably the ball can be scooped up. For example, the value of the correction coefficient k is preferably greater than 1.3 (k>1.3), and more preferably greater than 1.6 (k>1.6).

[0080] Furthermore, with regard to the S-shaped groove surface 4 provided on the outer peripheral surface 12 of the screw shaft 1, in the embodiment, it is formed directly on the outer peripheral surface 12 of the screw shaft 1, but in the present disclosure, the S-shaped groove surface may be formed on a top. Below, a first modification using a top will be described. Furthermore, the following explanation will focus on the differences from the embodiment.

[0081] (Variation 1) Figure 9 is a side view of the screw shaft of a ball screw device of Variation 1, viewed from the radial outside. A mounting hole 16 recessed radially inward is formed in the outer peripheral surface 12 of the screw shaft 1 of a ball screw device 100A of Variation 1. A top 17 is attached to the mounting hole 16. An S-shaped groove surface 4 is formed on the radially outer surface of the top 17. The top 17 does not have a tang. In Variation 1, as in the embodiment, the balls 3 are reliably scooped up.

[0082] In the present disclosure, there are no particular limitations on the material or manufacturing method of the top 17. For example, a top 17 made of resin manufactured by injection molding may be used. Alternatively, a top 17 manufactured by metal powder injection molding may be used. Alternatively, a top 17 manufactured by cutting a metal material may be used.

[0083] Additionally, according to Modification 1, the outer circumferential raceway surface 13 of the screw shaft 1 is formed over the entire axial direction of the outer circumferential surface 12. In other words, the outer circumferential raceway surface 13 is continuous from the end of the outer circumferential surface 12 in the first direction X1 to the end of the outer circumferential surface 12 in the second direction X2.

[0084] The above describes Modification Example 1. The present disclosure may also utilize a screw shaft 1 whose outer peripheral surface 12 has been heat-treated. A common heat treatment method is to harden the outer peripheral surface 12 of the screw shaft 1 and then temper it. By performing such heat treatment, the outer peripheral surface 12 (outer peripheral raceway surface 13) of the screw shaft 1 can obtain the desired hardness and toughness.

[0085] In the present disclosure, carburizing and quenching may be performed. The quenching method may be induction hardening. In the present disclosure, the heat treatment method may be other than the above-mentioned method, and is not particularly limited. Furthermore, when the S-shaped groove surface 4 is formed directly on the outer peripheral surface 12 of the screw shaft 1 as in the embodiment, the S-shaped groove surface 4 may also be heat-treated. This suppresses damage to the S-shaped groove surface 4. The surface hardness of the S-shaped groove surface 4 is preferably HRC 56 or higher.

[0086] Next, another modified example will be described.

[0087] (Variation 2) Figure 10 is a cross-sectional view of a ball screw device of Variation 2 taken along the S-shaped groove surface and the outer peripheral raceway surface, viewed from the axial direction. Hereinafter, the portions of the S-shaped groove surface 4 that are both ends in the longitudinal direction and located at the groove bottom (the center in the groove width direction) will be referred to as one end 4a and the other end 4b. Note that the one end 4a or the other end 4b is located at the boundary between the S-shaped groove surface 4 and the outer peripheral raceway surface 13. Furthermore, the portion of the S-shaped groove surface 4 that is the center in the longitudinal direction and located at the groove bottom (the center in the groove width direction) will be referred to as the center point 4c. The ball 3 located at the center point 4c of the S-shaped groove surface 4 will be referred to as a bottom ball 3A.

[0088] Furthermore, in Modification 2, a virtual line that is perpendicular to the central axis X and connects the central axis X to one end 4a of the S-shaped groove surface 4 is referred to as a first virtual line M11. A virtual line that is perpendicular to the central axis X and connects the central axis X to the other end 4b of the S-shaped groove surface 4 is referred to as a second virtual line M12. A virtual line that is perpendicular to the central axis X and connects the central axis X to the center point 4c of the S-shaped groove surface 4 is referred to as a third virtual line M13. A direction parallel to the third virtual line M13 and in which the central axis X is disposed as viewed from the S-shaped groove surface 4 is referred to as a depth direction M14. A direction perpendicular to each of the axial direction (central axis X) and the depth direction M14 (third virtual line M13) is referred to as a cross direction M15.

[0089] As shown in Fig. 10, in the ball screw device 100B of Modification 2, the angle θ10 between the first virtual line M11 and the second virtual line M12 is 30° or more and 90° or less when viewed from the axial direction. The diameter Ds of the outer peripheral surface 12 of the screw shaft 1 is greater than 25 mm. This allows the balls 3 to be smoothly scooped up. The effects of Modification 2 will be described in comparison with Comparative Example 1.

[0090] FIG. 11A is a schematic diagram showing an enlargement of the S-shaped groove surface and its vicinity in Modification 2. FIG. 11B is a schematic diagram showing an enlargement of the S-shaped groove surface and its vicinity in Comparative Example 1. Note that the angle θ10 in Modification 2 shown in FIG. 11A is 30°. On the other hand, in Comparative Example 1 shown in FIG. 11B, the angle θ10 of the S-shaped groove surface 1004 is approximately 15°, which does not satisfy the requirement of Modification 2 (angle θ10 of 30° to 90°). Furthermore, the configuration of Comparative Example 1 is the same as that of the ball screw device 100B of Modification 2, except for the S-shaped groove surface 1004.

[0091] 11A and 11B is a circle (curve) connecting the centers O of the balls 3 rolling on the raceway (outer peripheral raceway surface 13). In this description, the balls 3 attempting to enter the S-shaped groove surface 4 from the outer peripheral raceway surface 13 are referred to as scooped balls 3B, 1003B (see ball 3B in FIG. 11A and ball 1003B in FIG. 11B).

[0092] As shown in Fig. 11A, the balls 3 arranged on the S-shaped groove surface 4 move under the load of the scooping balls 3B. As a result, the scooping balls 3B receive a reaction force F25 (see Fig. 11A) from the balls 3 arranged on the S-shaped groove surface 4. The scooping balls 3B are also pressed by the balls 3 rolling on the outer circumferential raceway surface 13, and receive a load F26 (see Fig. 11A). The resultant force F27, which is a combination of the reaction force F25 and the load F26, becomes a load that moves toward the nut 2, as shown in Fig. 11A. The angle formed by the reaction force F25 and the load F26 is θ11.

[0093] 11B , similarly in Comparative Example 1, the scooping ball 1003B receives a reaction force F1025 (see FIG. 11B ) from the balls 1003 arranged on the S-groove surface 1004. The scooping ball 1003B also receives a load F1026 (see FIG. 11B ) from the balls 1003 arranged on the outer circumferential raceway surface 13. Therefore, a resultant force F1027 (see FIG. 11B ) combining the reaction force F1025 and the load F1026 also acts on the scooping ball 1003B of Comparative Example 1. The angle formed by the reaction force F1025 and the load F1026 is θ1011.

[0094] As described in the embodiment, a load F3 (see FIG. 5) is applied to the scooping balls 3B, 1003B, which is a combination of the load F1 (see FIG. 5) received from the nut 2 and the load F2 (see FIG. 5) received from the screw shaft 1. If the resultant forces F27A, F1027A described above become larger than the load F3, the scooping balls 3B, 1003B will move toward the inner circumferential raceway surface 21 of the nut 2, preventing smooth scooping of the balls 3B, 1003B.

[0095] Comparing the angle θ11 of Modification 2 with the angle θ1011 of Comparative Example 1, the angle θ11 of Modification 2 is greater than the angle θ1011 of Comparative Example 1. In other words, the amount of load that the reaction force F25 and the load F26 cancel out when they oppose each other is greater than the amount of load that the reaction force F1025 and the load F1026 cancel out when they oppose each other. Therefore, the resultant force F27 is smaller than the resultant force F1027. From the above, according to Modification 2, the ball 3 can be scooped up more smoothly than in Comparative Example 1.

[0096] The above describes Modification 2. Note that although the diameter Ds (see FIG. 3 ) of the outer peripheral surface 12 of the screw shaft 1 in Modification 2 is greater than 25 mm, in the present disclosure, the diameter Ds of the screw shaft 1 may be 25 mm or less. In this case, the angle θ10 (see FIG. 10 ) formed between the first virtual line M11 and the second virtual line M12 needs to be greater than or equal to 50° and less than or equal to 120°.

[0097] (Modification 3) Fig. 12 is a view of the S-shaped groove surface of a ball screw device of Modification 3 as viewed from the radial outside. As shown in Fig. 12, the S-shaped groove surface 4 of the ball screw device 100C of Modification 3 is the same as that of the embodiment, and has a pair of end portions 5 and an intermediate portion 6 (see also Fig. 2). As described in the embodiment, the end portions 5 are formed linearly when viewed from the radial outside. Therefore, the center line N5 passing through the center of the end portion 5 in the groove width direction is also linear.

[0098] As described in the embodiment, the intermediate portion 6 is formed in a curved shape. More specifically, the intermediate portion 6 is composed of a pair of R portions 7. The R portions 7 are formed in an R-shape (arc-like) when viewed from the radially outer side. Therefore, the center line N7 passing through the center of the R portions 7 in the groove width direction is also arc-shaped. The center line N7 is part of a virtual circle N6 centered at point N7a. The virtual circle N6 (center line N7) has a curvature radius R7 and is tangent to the center line N5 at a tangent point N1. Furthermore, one virtual circle N6 of the pair of R portions 7 is tangent to the other virtual circle N6 at point N2. In Modification 3, the curvature radius R7 of the center line N7 of the R portions 7 satisfies the following formula (18).

[0099]

[0100] The effect of the ball screw device 100C of the third modified example will be described in comparison with the S-shaped groove surface 2004 of the second comparative example.

[0101] Fig. 13 is a view of the S-shaped groove surface of Comparative Example 2 as viewed from the radially outer side. As shown in Fig. 13, the S-shaped groove surface 2004 of Comparative Example 2 differs from Modification Example 3 in that it has an intermediate portion 2006 instead of the intermediate portion 6. The intermediate portion 2006 has a pair of R portions 2007 and a straight portion 2008 disposed between the pair of R portions 2007. Note that dashed lines B2001 and B2002 in Fig. 13 are boundaries between the end portion 5 and the intermediate portion 2006 of the S-shaped groove surface 2004. In Fig. 13, boundaries B1 and B2 of Modification Example 3 are also shown to make it easier to understand the difference from boundary B2001 of Comparative Example 2.

[0102] The size of the S-shaped groove surface 2004 of Comparative Example 2 in the cross direction M15 is the same as that of the S-shaped groove surface 4 of Modification Example 3. The depth of the S-shaped groove surface 2004 of Comparative Example 2 is also the same as that of the S-shaped groove surface 4 of Modification Example 3 (see FIGS. 14A and 14B ).

[0103] A center line N2007 passing through the center of the R portion 2007 in the groove width direction is part of a virtual circle N2006 centered at point N2007a. The virtual circle N2006 (center line N2007) has a radius of curvature R2007 and is tangent to the center line N5 at point N2001. The radius of curvature R2007 of the center line N2007 of the R portion 2007 is less than the value obtained by multiplying the diameter Dw of the ball 3 by 1.3, and does not satisfy equation (18). Therefore, the center line N2007 has a smaller diameter than the center line N7 of Modification Example 3.

[0104] The straight portion 2008 is formed in a straight line. Therefore, a center line N2008 passing through the center of the straight portion 2008 in the groove width direction is also straight. The center line N2008 is tangent to each of the two imaginary circles N2006 at a point N2002.

[0105] As explained in the embodiment, the ball 3 is scooped up radially inward at the boundaries between the end portion 5 and the middle portion 6 of the S-shaped groove surface 4 (see boundaries B1 and B2 and boundaries B2001 and B2002 in FIG. 13 ). As shown in FIG. 13 , the boundaries B1 and B2 in Modification 3 are located closer to both ends of the S-shaped groove surface 4 than the boundaries B2001 and B2002 in Comparative Example 2. This is because the radius of curvature R7 of the center line N7 is large, and therefore the point of contact N1 with the center line N5 is closer to both ends of the S-shaped groove surface 4. From the above, the ball 3 is scooped up closer to both ends of the S-shaped groove surface 4 in Modification 3 than in Comparative Example 2.

[0106] Fig. 14A is a schematic diagram of a ball screw device of Modification 3, in which the outer circumferential raceway surface and the S-shaped groove surface are cut at the center in the groove width direction, and the cross section is viewed from the axial direction. Fig. 14B is a schematic diagram of a ball screw device of Comparative Example 2, in which the outer circumferential raceway surface and the S-shaped groove surface are cut at the center in the groove width direction, and the cross section is viewed from the axial direction. Balls 3C and 2003C shown in Figs. 14A and 14B are balls scooped up at boundaries B1 and B2001.

[0107] The ball 3 that enters the S-groove surface 4 from the raceway (outer peripheral raceway surface 13) receives a radially inward load at the boundaries B1 and B2001 (see FIGS. 12 and 13 ) and is scooped up radially inward. Therefore, as shown in FIGS. 14A and 14B , before reaching the boundaries B1 and B2001, in other words, the center O of the ball 3 moving along the end 5, roughly coincides with the imaginary line M20.

[0108] 14A , at boundary B1 of Modification Example 3, ball 3C is subjected to load F3 (see FIG. 5), which is a combination of load F1 (see FIG. 5) and load F2 (see FIG. 5), and is directed radially inward. Furthermore, ball 3C is subjected to a resultant force F, which is a combination of reaction force F25 received from balls 3 disposed on S-groove surface 4 and resultant force F27 received from balls 3 disposed on outer circumferential raceway surface 13. Here, the angle formed by reaction force F25 and load F26 is θ12.

[0109] 14B , at boundary B2001 of Comparative Example 2, ball 2003C is similarly subjected to load F3 (see FIG. 5) which is a combination of load F1 (see FIG. 5) and load F2 (see FIG. 5), and moves radially inward. Furthermore, ball 2003C is subjected to resultant force F2027, which is a combination of reaction force F2025 received from ball 2003 disposed on S-groove surface 2004 and load F2026 received from ball 2003 disposed on outer circumferential raceway surface 13. Here, the angle formed by reaction force F2025 and load F2026 is θ2012.

[0110] 14A and 14B, the scooping of ball 3C in Modification 3 occurs closer to both ends of the S-shaped groove surface 4 than the scooping of ball 2003 in Comparative Example 2. Therefore, angle θ12 in Modification 3 is greater than angle θ2012 in Comparative Example 2. In other words, the amount of load that cancels out when reaction force F25 and load F26 oppose each other is greater than the amount of load that cancels out when reaction force F2025 and load F2026 oppose each other. As a result, resultant force F27 in Modification 3 is smaller than resultant force F2027 in Comparative Example 2. From the above, Modification 3 allows ball 3 to be scooped up more smoothly than Comparative Example 2.

[0111] Although Modification 3 has been described above, it is preferable to combine the details of Modification 3 with the details of Modification 2. By combining the details of Modification 2 and Modification 3, the resultant force F27 (see FIG. 11A ) acting on the ball 3 is further reduced, and the ball 3 is scooped up more smoothly. Furthermore, the intermediate portion 6 of the present disclosure may include, in addition to the pair of rounded portions 7, a straight portion 2008 ( FIG. 13 ) disposed between the pair of rounded portions 2007.

[0112] In Modifications 2 and 3, modifications relating to the S-groove surface 4 have been described. Next, modifications relating to the outer circumferential raceway surface 13 and the inner circumferential raceway surface 21 will be described.

[0113] (Modification 4) Fig. 15 is a cross-sectional view perpendicular to the grooves of the outer peripheral raceway surface and the inner peripheral raceway surface of a ball screw device of Modification 4. Note that the cross-sectional view perpendicular to the grooves is a cross-sectional view taken along a plane perpendicular (orthogonal) to the spiral direction in which the outer peripheral raceway surface 13 and the inner peripheral raceway surface 21 extend. Also, the imaginary line N3 shown in Fig. 15 is a straight line perpendicular to the central axis X of the screw shaft 1, connecting the central axis X and the center O of the ball 3. As shown in Fig. 15, in a ball screw device 100D of Modification 4, the depth Δ13 of the outer peripheral raceway surface 13 is greater than the depth Δ21 of the inner peripheral raceway surface 21. Note that the outer peripheral raceway surface 13 and the inner peripheral raceway surface 21 shown in Fig. 15 have the same Gothic arc shape as the embodiment, but in the present disclosure, they may have a circular arc shape.

[0114] To explain the details of Modification 4, in the screw shaft 1 of Modification 4, the depth from the outer peripheral surface 12 to the groove bottom 13c of the outer peripheral raceway surface 13 is Δ13. The groove bottom 13c is the center in the groove width direction of the outer peripheral raceway surface 13, and is the intersection of two circular arcs 113 that constitute the Gothic arc shape.

[0115] In the nut 2 of the fourth modified example, the depth from the inner peripheral surface 20 to the groove bottom 21 a of the inner peripheral raceway surface 21 is Δ21. The groove bottom 21 a is the center of the inner peripheral raceway surface 21 in the groove width direction, and is the intersection of two circular arcs 121 that form the Gothic arc shape.

[0116] Arc 113 and arc 121 have the same radius of curvature, and outer peripheral raceway surface 13 and inner peripheral raceway surface 21 have the same shape in cross section perpendicular to the groove. Therefore, contact angle θ15 between outer peripheral raceway surface 13 and ball 3 is the same as contact angle θ16 between inner peripheral raceway surface 21 and ball 3. Furthermore, distance Δ13A from contact point 13d between outer peripheral raceway surface 13 and ball 3 to groove bottom 13c is the same as distance Δ21A from contact point 21b between inner peripheral raceway surface 21 and ball 3 to groove bottom 21a.

[0117] In the fourth modification, the depth Δ13 of the outer peripheral raceway surface 13 is greater than the depth Δ21 of the inner peripheral raceway surface 21. Therefore, the distance Δ13B from the contact point 13d to the outer peripheral surface 12 of the screw shaft 1 is greater than the distance Δ21B from the contact point 21b to the inner peripheral surface 20 of the nut 2.

[0118] Furthermore, a configuration in which the depth Δ13 of the outer peripheral raceway surface 13 is greater than the depth Δ21 of the inner peripheral raceway surface 21 can be adopted because the present disclosure satisfies the prerequisite that the screw shaft 1 is provided with an S-shaped groove surface 4. Specifically, if the nut 2 is provided with an S-shaped groove surface 4, the balls 3 are scooped radially outward by the S-shaped groove surface 4 and go beyond the threads of the screw shaft 1. If this configuration is further combined with a configuration in which the depth Δ13 of the outer peripheral raceway surface 13 is greater than the depth Δ21 of the inner peripheral raceway surface 21, the balls 3 rolling on the outer peripheral raceway surface 13 need to move a greater amount radially to go beyond the threads of the screw shaft 1. In other words, the balls 3 are likely to get caught on the threads of the screw shaft 1, potentially preventing them from circulating. On the other hand, according to the present disclosure, the screw shaft 1 is provided with an S-shaped groove surface 4. Therefore, even if a configuration in which the depth Δ13 of the outer peripheral raceway surface 13 is larger than the depth Δ21 of the inner peripheral raceway surface 21 is further combined, the disadvantage of the balls 3 becoming more likely to get caught on the threads of the screw shaft 1 does not occur. For this reason, the configuration in which the depth Δ13 of the outer peripheral raceway surface 13 is larger than the depth Δ21 of the inner peripheral raceway surface 21 satisfies the prerequisite that the S-groove surface 4 is provided on the screw shaft 1, and therefore can be adopted.

[0119] Next, Modifications 5 and 6, which are partial modifications of Modification 4, will be described.

[0120] (Modification 5) Fig. 16 is a cross-sectional view perpendicular to the grooves of the outer peripheral raceway surface and the inner peripheral raceway surface of a ball screw device of Modification 5. As shown in Fig. 16, a ball screw device 100E of Modification 5 differs from Modification 4 in that the initial contact angle θ17 between the outer peripheral raceway surface 13 and the ball 3 is larger than the initial contact angle θ18 between the inner peripheral raceway surface 21 and the ball 3. Note that the ball screw device 100E of Modification 5 has in common with Modification 4 the fact that the depth Δ13 of the outer peripheral raceway surface 13 is larger than the depth Δ21 of the inner peripheral raceway surface 21.

[0121] The initial contact angle will now be described. The no-load state of the balls is when the nut 2 is moved axially relative to the screw shaft 1 to bring the balls 3 into contact with the outer peripheral raceway surface 13 and the inner peripheral raceway surface 21, and the load acting on the balls 3 is zero. In this no-load state of the balls, the contact angle between the outer peripheral raceway surface 13 and the balls 3 is an initial contact angle θ17, and the contact angle between the inner peripheral raceway surface 21 and the balls 3 is an initial contact angle θ18.

[0122] Next, the effects of Modification 5 will be described. The effects of Modification 5 will be described in comparison with Comparative Example 3. In Comparative Example 3, the initial contact angle between the outer peripheral raceway surface 13 and the ball 3 is θ19. Furthermore, the initial contact angle θ19 is the same as the initial contact angle θ18 between the inner peripheral raceway surface 21 and the ball 3. Furthermore, contact point 13e shown in Figure 16 is the contact point between the outer peripheral raceway surface 13 and the ball 3 in Comparative Example 3 when the ball is in an unloaded state.

[0123] In Modification 5, when an axial load F21 acts on the nut 2 due to the driving of the ball screw device 100E, a load acts from the ball 3 to the contact point 13d of the outer circumferential raceway surface 13. Therefore, a load F14 is applied to the contact point 13d. When this load F14 is resolved into axial and radial components, the axial component force F14A has the same magnitude as the load F21.

[0124] Similarly, in Comparative Example 3, when an axial load F21 acts on the nut 2 due to the driving of the ball screw device 100E, a load acts from the ball 3 to the contact point 13e of the outer circumferential raceway surface 13. Therefore, a load F16 is applied to the contact point 13e. When this load F16 is resolved into axial and radial components, an axial component force F16A has the same magnitude as the load F21. In other words, the component force F16A has the same magnitude as the component force F14A of Modification Example 5.

[0125] On the other hand, the initial contact angle θ19 of Comparative Example 3 is larger than the initial contact angle θ17 of Modified Example 5. In other words, the radial component force 16B of the load F16 is larger than the radial component force 14B of the load F14. Therefore, the load F16 applied to the outer circumferential raceway surface 13 of Comparative Example 3 is larger than the load F14 applied to the outer circumferential raceway surface 13 of Modified Example 5. As described above, according to Modified Example 5, the load (surface pressure) acting on the outer circumferential raceway surface 13 is reduced.

[0126] Note that the contact point 13d in Modification 5 is located radially outward of the contact point 13e in Comparative Example 3. That is, the possibility that the balls 3 will ride up onto the groove shoulder of the screw shaft 1 increases. However, the depth Δ13 of the outer peripheral raceway surface 13 is greater than the depth Δ21 of the inner peripheral raceway surface 21. Therefore, in Modification 5 as well, the possibility that the balls 3 will ride up onto the groove shoulder of the screw shaft 1 is low.

[0127] (Variation 6) Fig. 17 is a cross-sectional view perpendicular to the grooves of the outer peripheral raceway surface and the inner peripheral raceway surface of a ball screw device of Variation 6. As shown in Fig. 17, a ball screw device 100F of Variation 6 differs from Variation 4 in that the radius of curvature R121 of the arc 121 of the inner peripheral raceway surface 21 is larger. That is, in Variation 6, the radius of curvature R113 of the arc 113 of the outer peripheral raceway surface 13 is smaller than the radius of curvature R121 of the arc 121 of the inner peripheral raceway surface 21. Note that, in common with Variation 4, the depth Δ13 of the outer peripheral raceway surface 13 is larger than the depth Δ21 of the inner peripheral raceway surface 21.

[0128] As shown in Modification 4, if the radius of curvature R113 of the arc 113 and the radius of curvature R121 of the arc 121 are the same, the contact angle θ15 between the outer circumferential raceway surface 13 and the ball 3 and the contact angle θ16 between the inner circumferential raceway surface 21 and the ball 3 will be the same (see FIG. 15 ). On the other hand, if the radius of curvature R121 of the arc 121 increases, the contact point 21b between the arc 121 and the ball 3 will be closer to the imaginary line N3 (groove bottom 13c). In other words, the contact points 21b, 21b on the inner circumferential raceway surface 21 of the nut 2 will be closer to the imaginary line N3 than the contact points 13d, 13d on the outer circumferential raceway surface 13. Therefore, in Modification 6, the contact angle θ20 between the outer circumferential raceway surface 13 (arc 113) and the ball 3 is larger than the contact angle θ21 between the inner circumferential raceway surface 21 (arc 121) and the ball 3. Therefore, according to the sixth modification, the load (surface pressure) acting on the outer circumferential raceway surface 13 is reduced, similarly to the fifth modification.

[0129] In addition, since the contact point 13d in Modification 6 is closer to the groove shoulder, there is a high possibility that the balls 3 will ride up onto the groove shoulder of the screw shaft 1. However, the depth Δ13 of the outer peripheral raceway surface 13 is greater than the depth Δ21 of the inner peripheral raceway surface 21. Therefore, in Modification 6 as well, there is a low possibility that the balls 3 will ride up onto the groove shoulder of the screw shaft 1.

[0130] In addition, in the fifth and sixth modifications, the case where the outer circumferential raceway surface 13 and the inner circumferential raceway surface 21 have a gothic arc shape has been described as an example, but in the present disclosure, the outer circumferential raceway surface 13 and the inner circumferential raceway surface 21 may also have a circular arc shape.

[0131] (Variation 7) Figure 18 is an enlarged view of a cross section perpendicular to the groove of the outer peripheral raceway surface and the inner peripheral raceway surface of a ball screw device of Variation 7. In Figure 18, the imaginary line N30 is a line drawn in the axial direction from a circle connecting the centers of multiple balls 3 in the raceway. In the following, the diameter of the inner peripheral surface 20 of the nut 2 is taken as Dn. The ball screw device 100G of Variation 7 satisfies the following formulas (19) and (20).

[0132]

[0133]

[0134] In equation (19), (Dm-Ds) / 2 represents the distance Dms (see FIG. 18) between the outer peripheral surface 12 of the screw shaft 1 and the imaginary line N30. If this distance Dms is 0.25 mm or less, the outer peripheral surface 12 of the screw shaft 1 is located near the center O of the ball 3. In other words, the distance from the groove bottom 13c (see FIG. 15) of the outer peripheral raceway surface 13 to the outer peripheral surface 12, in other words, the depth of the outer peripheral raceway surface 13, is large. Therefore, the ball 3 is less likely to ride up onto the groove shoulder of the screw shaft 1.

[0135] Furthermore, (Dn-Dm) / 2 in equation (20) represents the distance Dmn (see FIG. 18) from the inner peripheral surface 20 of the nut 2 to the imaginary line N30. The larger this distance Dmn is, the smaller the distance from the groove bottom 21a (see FIG. 15) of the inner peripheral raceway surface 21 to the inner peripheral surface 20 of the nut 2, in other words, the smaller the depth of the inner peripheral raceway surface 21. Therefore, the balls 3 rolling on the S-groove surface 4 are less likely to come into contact with the threads of the nut 2, and the balls 3 move smoothly.

[0136] DESCRIPTION OF SYMBOLS 1 Screw shaft 2 Nut 3, 3B, 3C, 1003, 1003B, 2003C Ball 4, 1004, 2004 S-groove surface 5 End 6, 2006 Middle portion 7, 2007 R portion 10 Screw shaft body 11 Shaft portion 12 Outer peripheral surface 13 Outer peripheral raceway surface 15 Corner portion 16 Mounting hole 17 Link 20 Inner peripheral surface 21 Inner peripheral raceway surface 22, 113, 121 Arc 100, 100A, 100B, 100C, 100D, 100E, 100F, 100G Ball screw device 2008 Straight portion

Claims

1. A screw shaft having an outer raceway surface formed on its outer surface, An inner circumferential raceway surface is formed on the inner circumferential surface, and a nut is inserted into the screw shaft, A plurality of balls arranged in a track formed between the outer circumferential track surface and the inner circumferential track surface, Equipped with, The outer surface of the screw shaft is provided with an S-shaped groove surface for circulating the balls. The screw shaft has a corner where the outer circumferential raceway surface and the S-shaped groove surface intersect with the outer circumferential surface. Let the diameter of the ball be Dw. The radius of the arc forming a cross-section perpendicular to the groove on the inner circumferential raceway surface of the nut is Rn. The contact angle of the ball with respect to the inner circumferential raceway surface of the nut is α. The angle at the cross-section perpendicular to the groove that indicates the effective range of the inner circumferential raceway surface of the nut is θ1, Dm is the diameter of the circle formed by connecting the centers of the multiple balls arranged in the aforementioned orbit. The diameter of the outer surface of the screw shaft is Ds, When the vertex of the corner of the screw shaft is worn down, the radial distance between the part of the corner that is located most radially inward and the outer surface of the screw shaft is Q. The correction factor is k (k > 1), When this is the case, the following equation (1) is satisfied Ball screw device. [Math 1]

2. The correction coefficient k is greater than 1.3 The ball screw device according to claim 1.

3. The S-shaped groove surface is formed directly on the outer circumferential surface of the screw shaft. The ball screw device according to claim 1 or claim 2.

4. The surface hardness of the S-shaped groove surface is HRC 56 or higher. The ball screw device according to claim 3.

5. The aforementioned S-shaped groove surface has been subjected to high-frequency induction hardening treatment. The ball screw device according to claim 3.

6. The aforementioned S-shaped groove surface has undergone carburizing and quenching treatment. The ball screw device according to claim 3.

7. Mounting holes are formed on the outer surface of the screw shaft, recessed radially inward. A saddle is attached to the aforementioned mounting hole. The S-shaped groove surface is formed on the radially outer surface of the aforementioned spool. The ball screw device according to claim 1 or claim 2.

8. The diameter of the outer surface of the screw shaft is 25 mm or less. The direction parallel to the central axis of the screw shaft is referred to as the axial direction. The first imaginary line is an imaginary line perpendicular to the central axis, and the imaginary line connecting the central axis and one end of the S-shaped groove surface is defined as follows: The first virtual line is perpendicular to the central axis, and the second virtual line is a virtual line connecting the central axis to the other end of the S-shaped groove surface. Viewed from the axial direction, the angle between the first virtual line and the second virtual line is between 50° and 120°. The ball screw device according to claim 1.

9. The diameter of the outer surface of the screw shaft is greater than 25 mm. The direction parallel to the central axis of the screw shaft is referred to as the axial direction. The first imaginary line is an imaginary line perpendicular to the central axis, and the imaginary line connecting the central axis and one end of the S-shaped groove surface is defined as follows: The first virtual line is perpendicular to the central axis, and the second virtual line is a virtual line connecting the central axis to the other end of the S-shaped groove surface. Viewed from the axial direction, the angle between the first virtual line and the second virtual line is between 30° and 90°. The ball screw device according to claim 1.

10. The aforementioned S-shaped groove surface is A pair of ends extending linearly when viewed from the radially outer side, and connected to both ends of the outer circumferential raceway surface, An intermediate portion connecting the pair of aforementioned ends, It has, The aforementioned intermediate portion extends in an arc shape when viewed from the radially outer side and has a pair of R-shaped portions that connect to the end portion. When R7 is the radius of curvature of the center line passing through the center of the groove width direction of the R section, the following equation (2) is satisfied. The ball screw device according to claim 8 or claim 9. [Math 2]

11. The depth of the outer circumferential raceway surface is greater than the depth of the inner circumferential raceway surface. The ball screw device according to claim 1 or claim 2.

12. The initial contact angle between the outer circumferential raceway surface and the ball is greater than the initial contact angle between the inner circumferential raceway surface and the ball. The ball screw device according to claim 11.

13. The radius of curvature of the arc forming a cross-section perpendicular to the groove on the outer circumferential raceway surface is smaller than the radius of curvature of the arc forming a cross-section perpendicular to the groove on the inner circumferential raceway surface. The ball screw device according to claim 11.

14. When the diameter of the inner surface of the nut is Dn, the following equations (3) and (4) are satisfied. The ball screw device according to claim 1 or claim 2. [Math 3] [Math 4]

Images