Ball screw device

Abstract

The present invention provides a ball screw device that facilitates the processing of nut components while also enabling smooth circulation of balls at the connection point between the load track and the return passage. [Solution] A ball screw device of the type in which a pair of circulating members are attached to both axial ends of a nut member to construct a return passage that connects the end of a load track on which the ball rolls under load to the end of a return through hole on which the ball rolls under no load, wherein a state transition groove opposite to the rolling groove of the screw shaft is formed at the connection end of the return passage to the load track, and at the connection portion between the load track and the return passage, the center of curvature of the arc-shaped cross section of the state transition groove is displaced radially inward of the nut member than the center of the ball rolling in the load rolling groove.

Description

Technical Field

[0001] The present invention relates to a ball screw device capable of mutually converting rotational motion and linear motion.

Background Art

[0002] A ball screw device is a mechanical element capable of mutually converting rotational motion and linear motion, and is widely used in various machine tools, conveying devices, industrial robots and the like for the purpose of converting rotational motion generated by a servo motor into linear motion. In the ball screw device, a screw shaft and a cylindrical nut member are screwed together via a large number of balls, and a spiral rolling groove for the balls to roll is formed on the outer peripheral surface of the screw shaft with a predetermined lead. Further, a spiral loaded rolling groove facing the rolling groove of the screw shaft is formed on the inner peripheral surface of the nut member, and the rolling groove and the loaded rolling groove face each other to form a spiral loaded track in which the balls roll while bearing a load.

[0003] The nut member is provided with a circulation passage that connects both ends of the loaded track to circulate the balls, and various structures of the circulation passage are known. As one of them, there is known a structure in which end deflectors (end circulation pieces) are attached to both axial end faces of the nut member to provide a ball circulation passage. In this end deflector type ball screw, return through holes along the axial direction are provided in the nut member, a pair of end deflectors are respectively attached to both end faces of the nut member, and the end of the loaded track and the end of the return through hole are connected by return passages formed in the end deflectors.

[0004] As mentioned above, the balls rolling within the load track are subjected to a load and are slightly compressed by elastic compression. On the other hand, once a ball enters the return passage from the load track, it is released from the load and returns to its original spherical shape. For this reason, the return passage has a larger inner diameter than the load track, and a step is created at the connection point between the load rolling groove of the nut member and the return passage. This caused vibration and noise when the balls passed through this connection point.

[0005] In conventional ball screw devices, crowning was applied to both ends of the load rolling groove of the nut member, gradually widening the diameter of the load track at the connection point with the return passage, reducing the step difference at the connection point between the load track and the return passage, and also gradually reducing the load acting on the ball as it enters the return passage from the load track (see Patent Document 1). [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2005-127402 [Overview of the project] [Problems that the invention aims to solve]

[0007] However, since the crowning process on the load rolling groove is performed by grinding with an abrasive wheel, the process is time-consuming and contributes to increased processing costs for the nut component. Furthermore, even if crowning is performed on the end of the load rolling groove, it is not possible to completely eliminate the step at the connection point between the load rolling groove and the return passage, and therefore it is not possible to completely prevent the generation of vibrations and noise associated with the circulation of the balls. [Means for solving the problem]

[0008] This invention has been made in view of these problems, and its objective is to provide a ball screw device that facilitates the processing of nut members while also facilitating the circulation of balls at the connection point between the load track and the return passage.

[0009] In other words, the present invention comprises a number of balls, a screw shaft having a spiral rolling groove on its outer circumference on which the number of balls roll, and the cross-section of the rolling groove having a Gothic arch shape where a pair of ball rolling surfaces intersect, a nut member having a through hole into which the screw shaft is loosely fitted, and having a spiral load rolling groove on the inner circumference of the through hole that forms a load trajectory for the balls opposite to the rolling groove of the screw shaft, and the cross-section of the load rolling groove having the same Gothic arch shape as the rolling groove, and a ball provided parallel to the through hole relative to the nut member A ball screw device comprising a return through-hole and a pair of circulating members attached to both axial ends of the nut member to construct a return passage connecting the end of the load track and the end of the return through-hole, wherein a state transition groove opposite to the rolling groove of the screw shaft is formed at the connection end of the return passage to the load track, and at the connection portion of the load track and the return passage, the center of curvature of the arc-shaped cross section of the state transition groove is displaced radially inward of the nut member than the center of the ball rolling in the load rolling groove. [Effects of the Invention]

[0010] According to the present invention, it is possible to prevent as much as possible the occurrence of steps in the ball rolling trajectory at the connection between the load trajectory and the return passage without performing special processing such as cornealing on the ends of the load rolling groove of the nut member, thereby simplifying the processing of the nut member while facilitating the circulation of balls at the connection between the load trajectory and the return passage. [Brief explanation of the drawing]

[0011] [Figure 1] This is a perspective view showing an example of a ball screw device to which the present invention is applied. [Figure 2] Figure 1 is a schematic diagram showing a side view of the ball screw device. [Figure 3] This is a perspective view showing a nut member to which a circulating member has been attached. [Figure 4] This is a perspective view showing the circulating components. [Figure 5] This is a side view showing the circulating components. [Figure 6] This is an enlarged view showing the connection between the load rolling groove and the state transition groove in the nut member. [Figure 7] This is a cross-sectional view showing the positional relationship between the state transition groove and the load rolling groove at the connection point between the load track and the return passage. [Figure 8] This is a cross-sectional view showing the change in the contact state of the balls between the nut member and the screw shaft. [Modes for carrying out the invention]

[0012] The ball screw device of the present invention will be described in detail below with reference to the attached drawings.

[0013] Figures 1 and 2 show an example of a ball screw device to which the present invention is applied. This ball screw device 1 consists of a screw shaft 2 with ball rolling grooves 20 formed spirally on its outer circumferential surface, and a cylindrical nut member 3 that screws around the screw shaft 20 via a number of balls 4. By rotating the screw shaft 2 relative to the nut member 3, the nut member 3 moves in the axial direction of the screw shaft 2, or by rotating the nut member 3 relative to the screw shaft 2, the screw shaft 2 moves in the axial direction of the nut member 3.

[0014] A single rolling groove 20 is formed on the outer circumferential surface of the screw shaft 2 with a predetermined lead, and the rolling grooves 20 are present at a constant pitch along the axial direction of the screw shaft 2. Furthermore, the space between adjacent rolling grooves 20 is a threaded portion 21, and this threaded portion 21 represents the outer diameter of the screw shaft 2. The rolling groove 20 is formed by a pair of ball rolling surfaces intersecting at an angle of approximately 90 degrees, and its cross-section is a so-called Gothic arch shape. It should be noted that, for example, two or more rolling grooves 20 may be formed on the outer circumferential surface of the screw shaft 2.

[0015] Said nut member 3 is formed in a substantially cylindrical shape having a through-hole 22, said through-hole 22 has an inner diameter slightly larger than the outer diameter of said screw shaft 2, and said screw shaft 2 is inserted thereinto. At one axial end of the outer peripheral surface of said nut member 3, a flange portion 30 for fixing said nut member 3 to a mechanical device is provided, and a plurality of mounting holes 31 for fixing bolts are formed in this flange portion 30. Incidentally, said flange portion is not an essential component of the ball screw device of the present invention.

[0016] On the other hand, on the inner peripheral surface of said nut member 3, a spiral loaded rolling groove having the same lead as the rolling groove 20 of said screw shaft 2 is formed. The rolling groove 20 of said screw shaft 2 and the loaded rolling groove of said nut member 3 face each other to form a loaded raceway 60 for said balls 4, and said balls 4 rolling in this loaded raceway 60 bear a load between said screw shaft 2 and said nut member 3. Similar to the rolling groove 20 of said screw shaft 2, said loaded rolling groove is formed by a pair of ball rolling surfaces intersecting at an angle of approximately 90 degrees, and its cross section has a so-called gothic arch shape.

[0017] Incidentally, depending on the preloading method applied to said balls 4, said balls 4 may be loaded while in contact with each of the rolling groove 20 of said screw shaft 2 and the loaded rolling groove of said nut member 3 at two points, or may be loaded while in contact with each of the rolling groove 20 of said screw shaft 2 and the loaded rolling groove of said nut member 3 at one point.

[0018] Further, said nut member 3 is provided with an infinite circulation path for said balls 4. This infinite circulation path is composed of said loaded raceway 60 and unloaded raceways 61 connecting both ends thereof. Said unloaded raceways 61 are composed of linear ball return holes 32 penetrating said nut member 3 in the axial direction, and return passages 50 connecting the ends of said loaded raceway 60 and said ball return holes 32.

[0019] Furthermore, a circulation member 5 is mounted on each of the axial end faces of the nut member 3, and the return passage 50 is constructed in the nut member 3 by the mounting of the circulation member 5. That is, when a pair of circulation members 5 are mounted to the nut member 3, a no-load raceway 61 composed of the ball return hole 32 and the return passage is completed, and accordingly, an infinite circulation path for the balls 4 composed of the loaded raceway 60 and the no-load raceway 61 is completed.

[0020] Figure 3 is a perspective view showing the nut member 3, and shows a state where the circulation member 5 is mounted on the end face of the nut member 3. A spiral loaded rolling groove 33 is formed on the inner peripheral surface of the through hole 22 of the nut member 3. As described above, this loaded rolling groove 33 faces the spiral rolling groove 20 formed on the outer peripheral surface of the screw shaft 2 to constitute the loaded raceway 60. Therefore, in a state where the screw shaft 2 is inserted into the through hole 22 of the nut member 3, the balls 4 rolling in the loaded rolling groove 33 are in contact with both the loaded rolling groove 33 and the rolling groove 20 of the screw shaft 2, and roll while bearing a load between the screw shaft 2 and the nut member 3.

[0021] The circulation member 5 is provided with a part of the return passage 50 that transfers the balls 4 between the loaded raceway 60 and the ball return hole 32. The balls 4 that have rolled along the loaded raceway 60 while bearing a load are gradually released from the load when reaching the return passage 50, and after separating from the rolling groove 20 of the screw shaft 2, enter a no-load state and are fed from the return passage 50 into the ball return hole 32.

[0022] The return passage 50 includes a state transition groove 50a formed at the connection end with the load track 60, and a tunnel-shaped direction change passage 50b connecting the state transition groove 50a and the ball return hole 32 of the nut member 3. The state transition groove 50a gradually transitions the ball 4 that has entered the return passage 50 from a loaded state to an unloaded state, and after detaching from the rolling groove 20 of the screw shaft 2, sends it to the direction change passage 50b. When the ball 4 rolls from the unloaded track 61 to the loaded track 60, that is, when it enters the return passage 50 from the ball return hole 32, the reverse occurs, and the ball 4 that has entered the state transition groove 50a via the direction change passage 50b enters the rolling groove 20 of the screw shaft 2, and as it progresses through the state transition groove 50a, it gradually becomes loaded as it enters the load track 60.

[0023] Figures 4 and 5 are perspective views showing the circulating member 5. The circulating member 5 comprises a main body portion 5a on which the direction change path 50b is formed, and a connecting portion 5b that is continuous with the main body portion 5a and has a part of the state transition groove 50a formed on its surface. As shown in Figure 3, a retaining groove 35 is formed on the opening edge of the ball return hole 32 of the nut member 3, and the main body portion 5a fits into the retaining groove 35. The retaining groove 35 has a pair of fixed surfaces that face each other, and the main body portion 5a of the circulating member 5 fitted into the retaining groove 35 contacts the pair of fixed surfaces, thereby preventing the circulating member 5 from shifting position when attached to the nut member 3. Furthermore, when the circulating member 5 is attached to the nut member 3, the connecting portion 5b fits into a recess provided on the inner circumferential surface of the through hole 22 of the nut member 3 and is positioned to extend tangentially to the through hole 22. In Figures 4 and 5, reference numeral 51 denotes a scooping piece that loosely fits into the rolling groove 20 of the screw shaft 2. This scooping piece 51 is located at the connection point between the state transition groove 50a and the direction change path 50b, ensuring that the ball 4, which is in an unloaded state in the state transition groove 50a, detaches from the rolling groove 20 of the screw shaft 2 and enters the direction change path 50b.

[0024] Figure 6 is an enlarged view showing the connection between the state transition groove 50a in the return passage 50 and the load rolling groove 33 in the load track 60.

[0025] As described above, the load rolling groove 33 formed in the nut member 3 has a Gothic arch-shaped cross section consisting of a pair of ball rolling surfaces 33a and 33b. Since this load rolling groove 33 needs to be formed with high precision, the pair of ball rolling surfaces 33a and 33b that constitute it are formed simultaneously by grinding using a grinding wheel. The state transition groove 50a of the return passage 50 that connects to this load rolling groove 33 consists of an inner connecting surface 34 and an outer connecting surface 52 that correspond to the pair of ball rolling surfaces 33a and 33b of the load rolling groove 33. The inner connecting surface 34 is formed in the nut member 3 and is continuous with one of the ball rolling surfaces 33a that constitute the load rolling groove 33. In contrast, the outer connecting surface 52 is formed in the connecting portion 5b of the circulation member 5 and comes into contact with the end of the other ball rolling surface 33b that constitutes the load rolling groove 33 when the circulation member 5 is attached to the nut member 3. Therefore, when the circulation member 5 is attached to the nut member 3, a state transition groove 50a, which is part of the return passage 50, is completed at the connection point with the load rolling groove 33, making it possible to transfer the ball 4 between the load rolling groove 33 and the return passage 50.

[0026] Figure 7 shows the positional relationship between the state transition groove 50a and the load rolling groove 33 at the connection point between the load track 60 and the return passage 50, with the cross-sections of the load rolling groove 33 and the state transition groove 50a superimposed. As mentioned above, the load rolling groove 33 is formed in a Gothic arch shape composed of a pair of rolling surfaces 33a and 33b, and the balls 4 rolling on the load track 60 are in contact with each of these rolling surfaces 33a and 33b that constitute the load rolling groove 33. In addition, the balls 4 rolling on the load track 60 are also in contact with the rolling groove 20 of the screw shaft 2. In Figure 7, the center of the balls 4 rolling on the load track 60 is denoted as O, and the radius of the balls 4 rolling on the load rolling groove 33 is indicated by a solid arrow.

[0027] On the other hand, the cross-section of the state transition groove 50a is basically formed as a circular arc with a constant curvature, and this radius of curvature is set to be slightly larger than the radius of the ball 4. As a result, the ball 4 that enters the return passage 50 from the load track 60 transitions to an unloaded state. In Figure 7, the state transition groove 50a is shown as a dashed line, and the cross-section of the state transition groove 50a is a circular arc with a constant radius from the center of curvature P. As mentioned above, the state transition groove 50a is composed of an outer connecting surface 52 and an inner connecting surface 34, and the cross-sections of the outer connecting surface 52 and the inner connecting surface 34 are circular arcs with a radius of curvature slightly larger than the radius of the ball 4.

[0028] In order to facilitate the entry of the ball 4 from the load rolling groove 33 into the state transition groove 50a, at the connection between the load rolling groove 33 and the state transition groove 50a, the center of curvature P of the state transition groove 50a is set radially inward from the nut member 3 compared to the center O of the ball 4 that is in contact with the load rolling groove 33. That is, the center of curvature P of the state transition groove 50a is set closer to the axis of the screw shaft 2 than the center O of the ball 4 that rolls along the load trajectory 60.

[0029] In this way, by displacing the center of curvature P of the state transition groove 50a radially inward of the nut member 3 with respect to the center O of the ball 4 just before it exits the load track 60, the step difference when the ball 4 rolling on the pair of rolling surfaces 33a and 33b of the load rolling groove 33 moves onto the state transition groove 50a can be minimized, and the rolling of the ball 4 entering the return passage 50 from the load track 60 can be made smoother.

[0030] Furthermore, from the viewpoint of eliminating the step when the ball 4, which is rolling on the pair of rolling surfaces 33a and 33b of the load rolling groove 33, moves onto the state transition groove 50a, the displacement σ between the center O of the ball and the center of curvature P of the state transition groove 50a shown in Figure 7 can be expressed by the following formula, where d is the diameter of the ball 4, h is the inner diameter of the return through hole 32, and Θ is the contact angle of the ball 4 with respect to the load rolling groove 33.

[0031]

number

[0032] If the curvature center P of the state transition groove 50a is displaced by a distance σ radially inward from the center O of the ball 4 just before it exits the load track 60, the step difference that occurs when the ball 4, which is rolling on the pair of rolling surfaces 33a and 33b of the load rolling groove 33, moves onto the state transition groove 50a can be eliminated, and the rolling of the ball 4 as it enters the return passage 50 from the load track 60 can be made smoother.

[0033] On the other hand, as mentioned above, the cross-sectional shape of the load rolling groove 33 and the cross-sectional shape of the state transition groove 50a are different. Therefore, even if the step difference when the ball 4 moves from the load rolling groove 33 to the state transition groove 50a of the return passage 50 can be minimized in design by displacing the center of curvature P of the state transition groove 50a radially inward of the nut member 3, it is necessary to machine the load rolling groove 33 and the state transition groove 50a with high precision in order to completely eliminate the step difference.

[0034] Taking this into consideration, in this embodiment, as shown in Figure 6, an introduction portion 34a is formed in part on the inner connecting surface 34, which is continuous with the ball rolling surface 33a. This introduction portion 34a is formed simultaneously with the ball rolling surface 33a by grinding, and is continuous with the ball rolling surface 33a without any steps. Therefore, when the ball 4 rolling on the ball rolling surface 33a of the load rolling groove 33 enters the return passage 50, it comes into contact with the introduction portion 34a of the inner connecting surface 34a and rolls there. In other words, the contact trajectory of the ball 4 with respect to the introduction portion 34a and the contact trajectory of the ball 4 with respect to the ball rolling surface 33a are continuous, as shown by the dashed line in Figure 5.

[0035] The introduction portion 34a is formed only on a part of the inner connecting surface 34 connected to the ball rolling surface 33a, and the inner connecting surface 34 as a whole has an arc shape with a radius of curvature slightly larger than the radius of the ball 4, as described above. For this reason, the cross-sectional shape of the inner connecting surface 34 changes as it moves away from the connection portion with the ball rolling surface 33a, and in the area on the direction change path 50b side of the introduction portion 34a (the area separated from the introduction portion 34a by a dashed line in Figure 6), it has the same cross-sectional shape as the outer connecting surface 52. The inner connecting surface 34 can be formed by cutting the nut member 3 with a ball end mill, leaving the introduction portion 34a which is continuously ground with the ball rolling surface 33a, and the processing of the nut member 3 is also extremely easy.

[0036] Figure 8 shows an example of the change in the contact state of the ball 4 between the nut member 3 and the screw shaft 2, assuming a case where the ball 4 is subjected to a load while making contact at two points with the rolling groove 20 of the screw shaft 2 and the load rolling groove 33 of the nut member 3. Diagram (a) of Figure 8 shows the ball 4 being subjected to a load between the load rolling groove 33 of the nut member 3 and the rolling groove 20 of the screw shaft 2. At this time, the ball 4 is in contact with each of the pair of ball rolling surfaces 33a and 33b that constitute the load rolling groove 33, while also being in contact with each of the pair of ball rolling surfaces 20a and 20b that constitute the rolling groove 20, and is subjected to a load while being constrained from four directions.

[0037] As shown in Figure 8(b), in the initial stage when the ball 4 enters the state transition groove 50a from the load rolling groove 33, the ball 4 is still in contact with the ball rolling surfaces 20a and 20b that constitute the rolling groove 20 of the screw shaft 2 at two points. On the other hand, the ball 4 is in contact with the introduction portion 34a of the inner connection surface 34 of the state transition groove 50a of the return passage 50, and a small gap is created between the ball 4 and the outer connection surface 52 which is formed with a radius of curvature larger than the radius of the ball 4.

[0038] In other words, once the ball 4 enters the return passage 50, it is released from the constraints on all four directions in the load track 60, and a small gap is created between it and the outer connecting surface 52, allowing it to be gradually released from the load. On the other hand, since the ball 4 is in contact with the screw shaft 2 and the nut member 3 at a total of three points, the behavior of the ball 4 entering the return passage 50 from the load track 60 does not suddenly become unstable. Furthermore, since the introduction portion 34a of the inner connecting surface 34 is smoothly continuous with the ball rolling surface 33a of the load rolling groove 33 without any steps, no impact is applied to the ball 4 as it passes through the connection portion between the load rolling groove 33 and the state transition groove 50a, allowing the ball 4 to smoothly enter the return passage 50 from the load track 60.

[0039] On the other hand, the inner connecting surface 34 and the outer connecting surface 52 that constitute the state transition groove 50a gradually become deeper relative to the inner circumferential surface of the through hole 22 of the nut member 3 as they move away from the load track 60. As a result, as shown in Figure 8(c), the ball 4 is released from the load as it moves through the return passage 50 toward the ball return hole 32 and begins to disengage from the rolling groove 20 of the screw shaft 2.

[0040] As the ball 4 moves further through the return passage 50 toward the ball return hole 32, it passes through the introduction portion 34a provided on the inner connection surface 34 and comes into contact with the inner contact surface 34 provided so as to surround the introduction portion 34a (see Figure 6). The inner connection surface 34, like the outer connection surface 52, has an arc-shaped cross-section with a radius of curvature larger than the radius of the ball 4. Therefore, as shown in subdivision (d) of Figure 8, the outer connection surface 52 and the inner connection surface 34 together constitute the state transition groove 50a, and this state transition groove 50a forms an arc-shaped cross-section with a radius of curvature larger than the radius of the ball 4. The ball 4 rolls through the state transition groove 50a, detaches from the rolling groove 20 of the screw shaft 2, and is housed in the direction change passage 50b.

[0041] Furthermore, the introduction portion 34a provided on the inner connecting surface 34 was provided considering the machinability of the nut member when carrying out the present invention, and the introduction portion 34a is not an essential component of the present invention.

[0042] As described above, according to the ball screw device 1 of this embodiment, at the connection between the load rolling groove 33 and the state transition groove 50a, the curvature center P of the state transition groove 50a is set radially inward of the nut member 3 compared to the center O of the ball 4 in contact with the load rolling groove 33. This eliminates the step at the connection between the load rolling groove 33 and the state transition groove 50a, and facilitates the rolling of the ball 4 entering the return passage 50 from the load track 60.

[0043] Conventionally, in order to facilitate the movement of the balls 4 at the connection point between the load track 60 and the return passage 50, a so-called crowning process was performed to form a gently sloping surface on the end of the load rolling groove 33. However, as described above, by displacing the center of curvature P of the state transition groove 50a radially inward by a predetermined distance from the nut member 3, the entry of the balls 4 into the return passage 50 can be facilitated without performing the crowning process, and the processing of the nut member 3 can be made easier accordingly.

[0044] Furthermore, as shown in Figure 6, the inner connecting surface 34, which constitutes a part of the state transition groove 50a, can be formed on the nut member 3. Since the state transition groove 50a can be formed continuously with one of the ball rolling surfaces 33a of the load rolling groove 33, the continuity between the load track 60 and the return passage can be ensured. As a result, the behavior of the ball 4 that enters the return passage 50 from the load track 60 will not suddenly become unstable, and the joint between the nut member 3 and the circulation member 5 will not adversely affect the smooth rolling of the ball 4.

[0045] In other words, the ball screw device of the present invention makes it possible to reduce the production cost of the nut member 3 while facilitating the circulation of the balls 4 at the connection point between the load track 60 and the return passage 50, and consequently, to increase the feed speed in the linear guide section of the machine device. [Explanation of Symbols]

[0046] 1...Ball screw device, 2...Screw shaft, 3...Nut member, 4...Ball, 5...Circulation member, 20...Rolling groove, 33...Load rolling groove, 33a,33b...Ball rolling surface, 34...Inner connection surface, 50a...State transition groove, 52...Outer connection surface

Claims

1. Many balls, A screw shaft having a spiral rolling groove on its outer surface through which the numerous balls roll, and the cross-section of the rolling groove forming a Gothic arch shape where a pair of ball rolling surfaces intersect, The nut member has a through hole into which the screw shaft is loosely fitted, and the inner circumferential surface of the through hole has a helical load rolling groove that forms a load trajectory for the ball opposite the rolling groove of the screw shaft, and the cross section of the load rolling groove is in the same Gothic arch shape as the rolling groove, where a pair of ball rolling surfaces intersect. A ball return hole is provided parallel to the through hole in the nut member, A pair of circulating members are attached to both axial ends of the nut member to form a return passage connecting the end of the load track and the end of the ball return hole, In a ball screw device equipped with, A state transition groove is formed at the connection end of the return passage to the load track, opposite to the rolling groove of the screw shaft. A ball screw device characterized in that, at the connection between the load track and the return passage, the center of curvature of the arc-shaped cross-section of the state transition groove is displaced radially inward from the nut member than the center of the ball rolling in the load rolling groove.

2. The displacement σ between the center of curvature of the arc-shaped cross-section of the state transition groove at the connection between the load track and the return passage and the center of the ball rolling in the load rolling groove is given by d being the ball diameter, h being the inner diameter of the return through hole, and Θ being the contact angle of the ball with respect to the load rolling groove. [Math 1] The ball screw device according to claim 1, characterized by being represented as such.

3. The state transition groove comprises an inner connecting surface adjacent to one of the ball rolling surfaces constituting the load rolling groove, and an outer connecting surface formed in the circulating component and adjacent to the other ball rolling surface constituting the load rolling groove. The ball screw device according to claim 1 or 2, characterized in that the cross-section of the outer connecting surface is formed by a single circular arc with a diameter larger than the diameter of the ball, and the center of curvature of the outer connecting surface is displaced radially inward of the nut member than the groove center of the load rolling groove.

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