Ball screw

Abstract

To provide a ball spring capable of connecting circulation raceways of a circulation groove three-dimensionally formed so that a tangential direction is substantially continuous in a spiral raceway.SOLUTION: A ball screw 1 is equipped with a screw shaft 2 having a spiral groove 2a, a nut 3 having a spiral groove, and a plurality of balls 4 disposed between the spiral groove 2a of the screw shaft 2 and the spiral groove of the nut 3. The nut 3 is provided with a circulation groove that is connected to one end and the other end of the spiral groove of the nut 3 and circulates the balls 4. A circulation raceway 8 of the circulation groove is formed on the basis of a groove cross section raceway curve showing a raceway for circulating the balls 4 on a groove cross section of the screw shaft 2, and a longitudinal raceway curve showing a raceway for circulating the balls 4 on a virtual plane with an H-axis as a trajectory length ω of the groove cross section raceway curve and a V-axis as a spiral raceway length Fv(ω).SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a ball screw.

Background Art

[0002] A ball screw is used to convert a rotational motion into a linear motion and vice versa. A ball screw includes a screw shaft having a spiral groove, a nut having a spiral groove, and a plurality of balls disposed between the spiral groove of the screw shaft and the spiral groove of the nut. In order to circulate the balls, the nut is provided with a return path connected to one end and the other end of the nut spiral groove.

[0003] Examples of the return path include a return pipe type and a deflector type. In a deflector type ball screw, a deflector (also called a bobbin) is attached to the nut, and a circulation groove for circulating the balls through the deflector is formed as the return path (see Patent Document 1).

[0004] As shown in FIG. 14, in a conventional deflector type ball screw, the circulation orbit 36 of the balls moving in the circulation groove (see FIG. 14(c)) was formed based on the axial horizontal plane orbit curve 31 (see FIG. 14(a)) and the axial cross-sectional orbit curve 32 (see FIG. 14(b)). The axial horizontal plane orbit curve 31 shown in FIG. 14(a) is a curve showing the orbit in which the balls circulate in the axial horizontal plane and is, for example, substantially S-shaped. The axial cross-sectional orbit curve 32 shown in FIG. 14(b) is a curve showing the orbit in which the balls circulate in a cross-sectional plane perpendicular to the axis of the screw shaft 30 and is, for example, substantially inverted U-shaped.

[0005] Then, as shown in FIG. 14(c), the substantially S-shaped axial horizontal plane orbit curve 31 is swept (pushed out) in the vertical direction to form a curved surface 34, and the substantially inverted U-shaped axial cross-sectional orbit curve 32 is swept in the axial direction to form a curved surface 35, and the line where the curved surface 34 and the curved surface 35 intersect is used as the circulation orbit 36 of the circulation groove. The dashed-dotted line in FIGS. 14(a) and (b) is the spiral orbit 33 (the spiral orbit of the balls moving between the spiral groove of the screw shaft and the spiral groove of the nut).

Prior Art Documents

Patent Document

[0006]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] However, as shown in the enlarged view of FIG. 14(d), there is a problem that the circulation orbit 36 of the conventional circulation groove is not connected so that the tangential direction is continuous with the spiral orbit 33. For example, as shown in FIG. 14(a), the axial horizontal plane orbit curve 31 is connected in the axial horizontal plane so that the tangential direction is continuous with the spiral orbit 33, and as shown in FIG. 14(b), the axial cross-section orbit curve 32 is connected in the axial cross-section perpendicular to the axis so that the tangential direction is continuous with the spiral orbit 33. However, as shown in FIGS. 14(c) and (d), the three-dimensionally formed circulation orbit 36 is not connected so that the tangential direction is continuous with the spiral orbit 33. For this reason, there is a problem that the circulation orbit is not such that the ball moves smoothly.

[0008] The present invention has been made in view of the above problems, and an object thereof is to provide a ball screw capable of connecting a circulation orbit of a three-dimensionally formed circulation groove so that the tangential direction is substantially continuous with a spiral orbit.

Means for Solving the Problems

[0009] In order to solve the above problems, one aspect of the present invention includes a screw shaft having a spiral groove, a nut having a spiral groove, and a plurality of balls disposed between the spiral groove of the screw shaft and the spiral groove of the nut. In the ball screw provided with a circulation groove that is connected to one end and the other end of the spiral groove of the nut and circulates the balls, a groove cross-section orbit curve showing an orbit for circulating the balls in the groove cross-section of the screw shaft, and an orbit length ω of the groove cross-section orbit curve are set as the H axis, and a spiral orbit length F vBased on the longitudinal orbital curve showing the orbit for circulating the ball in a virtual plane with V-axis as (ω), form the circulation orbit of the circulation groove, and the spiral orbital length F from the turn start point of the longitudinal orbital curve v (ω) is the spiral orbital length F from the turn start point of the circulation orbit of the circulation groove v Set to (ω), and the principal normal direction coordinate F of the groove cross-sectional orbital curve n (ω) is the spiral orbital length F of the circulation orbit of the circulation groove v The principal normal direction coordinate F with respect to (ω) n Set to (ω), and the binormal direction coordinate F of the groove cross-sectional orbital curve b (ω) is the spiral orbital length F of the circulation orbit of the circulation groove v The binormal direction coordinate F with respect to (ω) b It is a ball screw set to (ω).

Effect of the Invention

[0010] According to one aspect of the present invention, the three-dimensional circulation orbit of the circulation groove can be connected such that the tangential direction is substantially continuous to the spiral orbit.

Brief Description of the Drawings

[0011] [Figure 1] It is a perspective view of a ball screw according to an embodiment of the present invention. [Figure 2] It is a front view of the ball screw of this embodiment. [Figure 3] It is a side view of the ball screw of this embodiment. [Figure 4] It is a diagram showing a cross-sectional orbital curve. [Figure 5] It is a diagram showing a longitudinal orbital curve. [Figure 6] It is a diagram (a cross-sectional view perpendicular to the screw axis) showing the spiral orbital length Fv(ω). [Figure 7] It is a conceptual diagram of a virtual plane (Figs. 7(a)(b) show a perspective view of the screw axis, and Fig. 7(c) shows a plan view of the screw axis). [Figure 8] It is a diagram showing the XYZ coordinate system of the ball screw of this embodiment (Fig. 8(a) shows the XY plane of the ball screw, and Fig. 8(b) shows the XZ plane of the ball screw). [Figure 9] This is a conceptual diagram showing a virtual plane in a rolled-up state. [Figure 10] This is a perspective view showing the circulating trajectory of the ball screw in this embodiment. [Figure 11] This figure shows the groove cross-sectional trajectory curve of the embodiment. [Figure 12] This figure shows the longitudinal trajectory curve of the embodiment. [Figure 13] This figure shows the circulating trajectory of the embodiment (Figure 13(a) shows the XY plane of the ball screw, Figure 13(b) shows the YZ plane of the ball screw, and Figure 13(c) shows the XYZ coordinates of the ball screw). [Figure 14] This diagram illustrates the circulating trajectory of a conventional ball screw (Figure 14(a) shows the axial horizontal plane, Figure 14(b) shows the cross-section perpendicular to the axis, Figure 14(c) shows a perspective view of the screw axis, and Figure 14(d) shows an enlarged view of a part of Figure 14(c)). [Modes for carrying out the invention]

[0012] Hereinafter, an embodiment of the ball screw of the present invention will be described in detail with reference to the attached drawings. However, the ball screw of the present invention can be embodied in various forms and is not limited to the embodiments described in this specification. This embodiment is provided with the intention that those skilled in the art will be able to fully understand the invention by making full disclosures in this specification. (Ball screw)

[0013] Figure 1 shows a perspective view of a ball screw 1 according to one embodiment of the present invention. Figure 2 shows a front view of the ball screw 1, and Figure 3 shows a side view of the ball screw 1.

[0014] As shown in Figure 1, the ball screw 1 comprises a screw shaft 2 having a helical groove 2a, a nut 3 having a helical groove 3a (see Figure 2), and a plurality of balls 4 positioned between the helical groove 2a of the screw shaft 2 and the helical groove 3a of the nut 3. The helical groove 2a of the screw shaft 2 is formed on the outer circumferential surface of the screw shaft 2. The helical groove 2a of the screw shaft 2 is in the shape of a Gothic arch. The nut 3 has an insertion hole into which the screw shaft 2 is inserted. The helical groove 3a (see Figure 2) of the nut 3 is formed on the inner circumferential surface of the nut 3. The helical groove 3a (see Figure 2) of the nut 3 is in the shape of a Gothic arch. The nut 3 has a flange 3c.

[0015] The ball screw 1 has, for example, two circulation paths 5. Each circulation path 5 consists of a load path A between the helical groove 2a of the screw shaft 2 and the helical groove 3a of the nut 3, and a return path B connected to one end and the other end of the load path A. On the inner circumferential surface of the nut 3, a circulation groove 3b (see Figure 2) is formed as the return path B, connected to one end and the other end of the helical groove 3a. The return path B consists of the circulation groove 3b of the nut 3 (see Figure 2) and the portion of the outer circumferential surface of the screw shaft 2 that faces the circulation groove 3b.

[0016] When one of the screw shaft 2 and nut 3 is rotated relative to the other, the ball 4 rolls along the load path A and enters the circulation groove 3b of the nut 3 from the turn starting point (1) (see Figure 2). In the circulation groove 3b, the ball 4 overcomes the threads 2b of the screw shaft 2 (see Figure 3), moves to the adjacent helical groove 2a, and re-enters the load path A from the turn ending point (2) (see Figure 2). Consequently, the other of the screw shaft 2 and nut 3 moves axially relative to the other.

[0017] As shown in Figure 1, the central trajectory of ball 4 moving along load path A is a spiral trajectory 7. The central trajectory of ball 4 moving along circulation groove 3b is a circulation trajectory 8.

[0018] In this embodiment of the ball screw 1, the circulation groove 3b is formed directly in the nut 3 so as to be continuous with the helical groove 3a, but the circulation groove 3b may also be formed in a deflector (also called a spool) attached to the nut 3. Furthermore, although a relief 3d (see Figure 2) for the machining tool of the circulation groove 3b is formed in the inner diameter of the nut 3, the relief 3d does not need to be formed if the circulation groove 3b can be machined.

[0019] The circulation track 8 of the circulation groove 3b is formed based on the groove cross-sectional track curve 11 shown in Figure 4 and the longitudinal track curve 12 shown in Figure 5. (Groove cross section trajectory curve)

[0020] As shown in Figure 4, the groove cross-section trajectory curve 11 is a curve that shows the trajectory (actual trajectory) of the ball 4 circulating in the groove cross-section of the screw shaft 2. Specifically, it is a curve that shows the trajectory of the ball 4 moving over the screw threads 2b of the screw shaft 2 to the adjacent helical groove 2a. (1) is the starting point of the turn of the groove cross-section trajectory curve 11, and (2) is the ending point of the turn of the groove cross-section trajectory curve 11. The groove cross-section trajectory curve 11 is roughly in the shape of an inverted U.

[0021] The coordinates of the groove cross-section track curve 11 are given by (F) when the track length (curve length) ω is a variable. b (ω),F n It is represented by (ω). n (ω) is the principal normal direction (N axis direction) coordinate, F b (ω) is the coordinate in the binormal direction (B-axis direction). The total length of the groove cross-section trajectory curve 11 (the length of the groove cross-section trajectory curve 11 from the turn start point (1) to the turn end point (2)) is α.

[0022] The groove cross-section (BN plane) of the screw shaft 2 on which the groove cross-section trajectory curve 11 is drawn is a cross-section perpendicular to the helical groove 2a of the screw shaft 2 (groove-perpendicular cross-section), and is tilted by a lead angle with respect to the cross-section along the axis of the screw shaft 2 (YZ plane in Figure 1). However, since the difference between the shape of the helical groove 2a of the screw shaft 2 in the groove cross-section (BN plane) and the shape of the helical groove 2a of the screw shaft 2 in the YZ plane in Figure 1 is slight, the YZ plane in Figure 1 may be used as the groove cross-section of the screw shaft 2. Note that in Figure 1, the axial direction of the ball screw 1 is the Y axis, the height direction is the Z axis, and the horizontal direction is the X axis.

[0023] The groove cross-section trajectory curve 11 is symmetrical with respect to the central point (3). The turn start point (1) side of the groove cross-section trajectory curve 11 is shown with a solid line, and the turn end point (2) side is shown with a dashed line. Since the circulating trajectory 8 of the circulating groove 3b (see Figure 10) is symmetrical with respect to the central point (3), the circulating trajectory 8 of the circulating groove 3b can be formed by drawing the groove cross-section trajectory curve 11 on the turn start point (1) side. The groove cross-section trajectory curve 11 is, for example, a single circular arc, multiple circular arcs with different curvatures, an ellipse, a clothoid curve, a spline curve, etc., or a curve formed by connecting these with a straight line, and is a curve in which the tangential direction is continuous. (Longitudinal curve)

[0024] As shown in Figure 5, the longitudinal trajectory curve 12 has the trajectory length ω of the groove cross-section trajectory curve 11 as the H axis, and the helical trajectory length F v This curve shows the trajectory of the ball 4 circulating in a virtual plane (VH plane) with (ω) as the V axis. Specifically, it is a curve that shows the trajectory of the ball 4 moving from the helical groove 2a of the screw shaft 2 to the adjacent helical groove 2a, from the turn start point (1) to the turn end point (2). The longitudinal trajectory curve 12 is roughly S-shaped.

[0025] The virtual plane (VH plane) is similar to the axial horizontal plane of the ball screw 1, but different from the axial horizontal plane of the ball screw 1. The variable ω of the H axis of the virtual plane is not the length in the Y axis direction of the ball screw 1, but the trajectory length ω from the turn starting point (1) of the groove cross-section trajectory curve 11.

[0026] F of the V axis of the virtual plane v(ω) is not the length of the ball screw 1 in the X-axis direction, but rather the length F of the helical trajectory 7 from the turn starting point (1), as shown in Figure 6. v (ω) is the value. In the cross-sectional view perpendicular to the axis of the screw shaft 2 in Figure 6, the helical track 7 is a circle on the BCD (Ball Center Diameter). β in Figure 6 is the helical track length F. v (ω) is the total length of the spiral trajectory 7 from the turn start point (1) to the turn end point (2) (shown as a dashed line in the figure). θ is the circulating range, and d is the shaft diameter of the screw shaft 2. Spiral trajectory length F v (ω) is longer than the arc length on the BCD shown in Figure 6 by the lead angle, where F is the helical trajectory length. v The difference between (ω) and the arc length on the BCD is small, so the helical orbit length F v You may use the arc length on the BCD shown in Figure 6 as (ω).

[0027] As shown in Figure 5, the coordinates of the longitudinal trajectory curve 12 are a function of ω, i.e., (F v It is represented as (ω),ω). ω is the orbital length of the cross-sectional orbital curve, and F v (ω) is the helical trajectory length. The turn trajectory width α in the H-axis direction of the longitudinal trajectory curve 12 (the length in the H-axis direction from the turn start point (1) to the turn end point (2) of the longitudinal trajectory curve 12) is equal to the total length α of the groove cross-section trajectory curve 11 (see Figure 4). The turn trajectory width β in the V-axis direction of the longitudinal trajectory curve 12 (the length in the V-axis direction from the turn start point (1) to the turn end point (2) of the longitudinal trajectory curve 12) is equal to the helical trajectory length F v This coincides with the total length β of (ω) (see Figure 6).

[0028] The longitudinal trajectory curve 12 is symmetrical with respect to the central point (3). The turn start point (1) side of the longitudinal trajectory curve 12 is shown as a solid line, and the turn end point (2) side is shown as a dashed line. Since the circulating trajectory 8 of the circulating groove 3b (see Figure 10) is symmetrical with respect to the central point (3), the circulating trajectory 8 of the circulating groove 3b can be formed by drawing the longitudinal trajectory curve 12 on the turn start point (1) side. The longitudinal trajectory curve 12 is, for example, a single circular arc, multiple circular arcs with different curvatures, an ellipse, a clothoid curve, a spline curve, etc., or a curve formed by connecting these with a straight line, and is a curve in which the tangential direction is continuous.

[0029] The longitudinal trajectory curve 12 has a tangential direction that substantially coincides with the V-axis direction of the virtual plane at the turn start point (1). Similarly, the longitudinal trajectory curve 12 has a tangential direction that coincides with the V-axis direction of the virtual plane at the turn end point (2). It is desirable that the tangential directions of the longitudinal trajectory curve 12 at both the turn start point (1) and the turn end point (2) substantially coincide with the V-axis direction of the virtual plane, but it is acceptable if only one of them coincides. (Virtual plane)

[0030] The concept of a virtual plane is explained below. Figure 7(a) schematically shows a curved surface 21 drawn on the screw axis 2. The shorter side 21a of the curved surface 21 represents the cross-sectional trajectory curve 11, and the longer side 21b of the curved surface 21 represents the helical trajectory length F. v (ω) is represented. The length of the short side 21a of the curved surface 21 coincides with the total length α of the cross-sectional trajectory curve 11, and the length of the long side 21b of the curved surface 21 is the helical trajectory length F. v It coincides with the total length β of (ω). As shown in Figure 7(b), the virtual plane 22 is the curved surface 21 unfolded into a plane. The length of the short side 22a of the virtual plane 22 coincides with the total length α of the axial cross-sectional trajectory curve 11, and the length of the long side 22b of the virtual plane 22 is the helical trajectory length F. v This coincides with the total length β of (ω). As shown in Figure 7(c), in a plan view of the screw shaft 2, the virtual plane is tilted by the lead angle.

[0031] The virtual plane 22 shown in Figure 7(c) corresponds to the virtual plane (VH plane) shown in Figure 5. 12 in Figure 7(c) is the longitudinal trajectory curve drawn on the virtual plane 22. As described above, the tangential direction of the turn starting point (1) of the longitudinal trajectory curve 12 substantially coincides with the V-axis direction of the virtual plane 22 (see the elliptical area in Figure 7(c)). (Conversion of ball screw to XYZ coordinates)

[0032] Using a Freinet-Serret frame consisting of a set of three unit vectors T, N, and B that point in the tangential, principal normal, and binormal directions to the helical track 7, the principal normal coordinate F of the groove cross-section track curve 11 is determined. n (ω), binormal coordinate F of groove cross-section track curve 11 b (ω), spiral orbit length F of longitudinal orbit curve 12 vConvert (ω) to the XYZ coordinates of ball screw 1.

[0033] First, the spiral trajectory length F of the longitudinal trajectory curve 12 shown in Figure 5. v (ω) is the helical trajectory length F from the turn starting point (1) of the circulating trajectory 8, as shown in the XZ plane of the ball screw 1 in Figure 8(b). v Set to (ω), and the spiral trajectory length from the turn starting point (1) is F. v Find point P1 on the spiral trajectory 7 such that (ω). Here, the length of the spiral trajectory from the turn starting point (1) along the spiral is F. v Find the point P1 such that (ω).

[0034] Then, the principal normal coordinate F of the groove cross-section trajectory curve 11 shown in Figure 4. n (ω) is the helical trajectory length F of the circulating trajectory 8, as shown in the XZ plane of the ball screw 1 in Figure 8(b). v Principal normal coordinate F for (ω) n Set to (ω), and from point P1 on spiral trajectory 7, F in the direction of the principal normal (N direction). n Find point P2, which is moved by (ω).

[0035] Then, the binormal coordinate F of the groove cross-section trajectory curve 11 shown in Figure 4. b (ω) is the helical trajectory length F, as shown in the XY plane of the ball screw 1 in Figure 8(a). v Binormal coordinate F for (ω) b Set to (ω), and from point P1 on spiral trajectory 7, move F in the direction of the binormal (direction B). b Find point P3, which is moved by (ω).

[0036] The circulating trajectory 8 is located on point P2 in the XZ plane of the ball screw 1 shown in Figure 8(b), and on point P3 in the XY plane of the ball screw 1 shown in Figure 8(a). Therefore, the circulating trajectory 8 can be determined from points P2 and P3.

[0037] Since the groove cross-sectional trajectory curve 11 and the longitudinal trajectory curve 12 are collections of points, we can change ω to ω1, ω2, ω3... and (F v (ω1),F n (ω1),Fb (ω1)), (F v (ω2),F n (ω2),F b (ω2)), (F v (ω3),F n (ω3),F b By calculating (ω3)..., transforming these into the XYZ coordinates of the ball screw 1 to find points P1, P2, and P3, and then connecting points P2 and P3, a three-dimensional cyclic trajectory 8 can be formed as shown in Figure 10.

[0038] As above F v (ω), F n (ω), F b Converting (ω) to the XYZ coordinates of the ball screw 1 means winding the virtual plane 22 back to the initial curved surface 21, as shown in Figure 9. By winding the virtual plane 22, the longitudinal trajectory curve 12 (shown as a dashed line in the figure) drawn on the virtual plane 22 becomes three-dimensional, and a three-dimensional circulating trajectory 8 can be formed.

[0039] As shown in Figure 7(c), in the virtual plane 22, the tangential direction of the turn starting point (1) of the longitudinal trajectory curve 12 substantially coincides with the V-axis direction of the virtual plane 22. Therefore, as shown in Figure 9, even in the curved surface 21 formed by winding the virtual plane 22, it can be guaranteed that the tangential direction of the turn starting point (1) of the longitudinal trajectory curve 12 substantially coincides with the V-axis direction of the curved surface 21, and it can be guaranteed that the three-dimensional circulating trajectory 8 shown in Figure 10 is substantially continuous with the spiral trajectory 7 in tangential direction at the turn starting point (1).

[0040] Once the circulation track 8 shown in Figure 10 is formed, the balls 4 should be positioned along the circulation track 8, and the circulation groove 3b should be formed so that the balls 4 move along the circulation track 8. Specifically, in the middle of the length of the circulation groove 3b (on the threads 2b of the screw shaft 2), the balls 4 move under no load, and there is a small amount of play around the balls 4. For this reason, in the middle of the length of the circulation groove 3b, the circulation groove 3b should be formed so that the center of the play of the balls 4 is the circulation track 8. On the other hand, in the scooping sections at both ends of the length of the circulation groove 3b, the balls 4 are scooped up by being sandwiched between the circulation groove 3b of the nut 3 and the helical groove 2a of the screw shaft 2. In the scooping sections, the circulation groove 3b should be formed so that the trajectory of the balls 4 sandwiched between the circulation groove 3b of the nut 3 and the helical groove 2a of the screw shaft 2 is the circulation track 8.

[0041] However, the circulation trajectory 8 may be corrected to smoothly scoop up the ball 4, and there may be machining errors in the circulation groove 3b of the nut 3 and the helical groove 2a of the screw shaft 2. "Substantially" continuous tangent directions of the circulation trajectory 8 and the helical trajectory 7 include such cases. Similarly, "substantially" coinciding tangent directions of the turn start and / or turn end points of the longitudinal trajectory curve 12 with the V-axis direction of the virtual plane also includes such cases. (effect)

[0042] The configuration of the ball screw 1 of this embodiment has been described above. The ball screw of this embodiment provides the following advantages.

[0043] Since the circulating track 8 of the circulating groove 3b is formed based on the groove cross-sectional track curve 11 and the longitudinal track curve 12, the three-dimensional circulating track 8 of the circulating groove 3b can be connected to the helical track 7 in a manner that is substantially continuous in the tangential direction.

[0044] Since the tangential direction of the turn start and / or end points of the longitudinal trajectory curve 12 substantially coincides with the V-axis direction of the virtual plane, it is possible to ensure that the tangential directions of the circulating trajectory 8 and the spiral trajectory 7 are substantially continuous at the turn start and / or end points of the three-dimensional circulating trajectory 8.

[0045] In a virtual plane, the turn trajectory width in the H-axis direction of the longitudinal trajectory curve 12 coincides with the total length α of the groove cross-section trajectory curve 11, and the turn trajectory width in the V-axis direction of the longitudinal trajectory curve 12 coincides with the helical trajectory length F. v Since it coincides with the total length β of (ω), the circulation orbital 8 of the circulation groove 3b can be formed smoothly along its entire length. [Examples]

[0046] (Groove cross section trajectory curve) As shown in Figure 11, the groove cross-section (BN plane) of the screw shaft 2 is drawn with a single circular arc of radius R1 and a straight line to create the groove cross-section trajectory curve 11. (1) is the turn starting point, (3) is the midpoint where the groove cross-section trajectory curve 11 is symmetrical, (5) is the curvature change point, α is the total length of the groove cross-section trajectory curve 11 (mm), R1 is the groove cross-section trajectory radius (mm), θ1 is the turn initiation angle (rad), and ω is a variable (0→α).

[0047] Coordinates of groove cross-section trajectory curve 11 (F B (ω),F N (ω)) can be represented as follows: TIFF0007853181000001.tif88130

[0048] (Longitudinal curve) As shown in Figure 12, the longitudinal trajectory curve 12 was drawn in a virtual plane (VH plane) using a single circular arc with radius R3 and a straight line. At the turn starting point (1), the tangent direction of the longitudinal trajectory curve 12 coincided with the V-axis direction. (1) is the turn starting point, (2) is F V (ω) is the endpoint, (3) is the midpoint where the longitudinal orbit is symmetrical, (6) is the point of curvature change, β is the total length of the spiral orbit (mm), R3 is the longitudinal orbit radius (mm), θ2 is the longitudinal orbit arc position (rad), θ3 is the longitudinal orbit arc range (rad), θ4 is the longitudinal orbit inclination angle (rad), and L1 is the longitudinal orbit straight-line distance (mm).

[0049] The spiral orbit length F of the longitudinal orbit curve 12 for variable ω. V (ω) can be represented as follows: TIFF0007853181000002.tif88142

[0050] (Circulation track in the circulation groove) F V (ω), F N (ω), F B (ω) was converted to the XYZ coordinates of ball screw 1. That is, ω was changed to ω1, ω2, ω3... and (F V (ω1), F N (ω1), F B (ω3), (F V (ω2), F N (ω2), F B (ω2), (F V (ω3), F N (ω3), F B (ω3)... was determined, and these were transformed onto the XYZ coordinates of the ball screw 1 to find points P1, P2, and P3. Points P2 and P3 were then connected to form the three-dimensional circulating trajectory 8 shown in Figure 13(c).

[0051] In Figures 13(a), (b), and (c), (1) is the turn starting point, and (2) is F V (ω) is the endpoint, (3) is the midpoint where the circular orbit 8 is symmetrical, and (4) is the turn starting point (1), with length F. V This is a point on the helical orbit 7 where (ω) is the value. R2 is the radius of the helical orbit in the axial cross-section (mm). TNB are the tangential direction (T), normal direction (N), and binormal direction (B) relative to point (4), respectively.

[0052] The resulting circular trajectory 8 connected to the spiral trajectory 7 at the turn starting point (1) in a tangential direction, and the circular trajectory 8 itself was smooth. [Explanation of Symbols]

[0053] 1...Ball screw, 2...Screw shaft, 2a...Screw groove on screw shaft, 3...Nut, 3a...Screw groove on nut, 3b...Circulation groove, 4...Ball, 7...Screw track, 8...Circulation track, 11...Track cross section track curve, 12...Longitudinal track curve, 22...Virtual plane, (1)...Turn start point, (2)Turn end point

Claims

1. A screw shaft having a helical groove, A nut having a spiral groove, It comprises a plurality of balls positioned between the helical groove of the screw shaft and the helical groove of the nut, In a ball screw, the nut is provided with a circulation groove for circulating the balls, which is connected to one end and the other end of the helical groove of the nut, The groove cross-section of the screw shaft shows a groove cross-section trajectory curve that indicates the trajectory in which the ball circulates, and the trajectory length ω of the groove cross-section trajectory curve is defined as the H axis, with the helical trajectory length F ｖ Based on the longitudinal trajectory curve that shows the trajectory of the ball circulating in a virtual plane with (ω) as the V axis, the circulating trajectory of the circulating groove is formed. The spiral trajectory length F from the turn starting point of the aforementioned longitudinal trajectory curve. ｖ (ω) is the helical trajectory length F from the turn starting point of the circulating trajectory of the circulating groove. ｖ Set to (ω), The principal normal coordinate F of the groove cross-section trajectory curve. ｎ (ω) is the helical track length F of the circulation track of the circulation groove. ｖ Principal normal coordinate F relative to (ω) ｎ Set to (ω), The coordinate F in the direction of the normal to the groove cross-sectional orbital curve ｂ (ω) is the coordinate F in the direction of the normal to the spiral orbital length F ｖ (ω) of the circulating orbit of the circulating groove ｂ A ball screw set to (ω).

2. The ball screw according to claim 1, characterized in that, in the virtual plane, the tangential direction at the turn start and / or turn end of the longitudinal trajectory curve substantially coincides with the V-axis direction of the virtual plane.

3. In the aforementioned virtual plane, the turn track width in the H-axis direction of the longitudinal track curve coincides with the total length (α) of the groove cross-section track curve. The turn path width in the V-axis direction of the longitudinal trajectory curve is the helical trajectory length F. ｖ The ball screw according to claim 1 or 2, characterized in that the total length (β) of (ω) matches.

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