Ball screw

Abstract

The invention provides a ball screw capable of connecting a circulation track of a three-dimensionally formed circulation groove and a spiral track in a manner of being substantially continuous in the tangential direction. A ball screw (1) is provided 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 ball (4). A circulation track (8) of the circulation groove is formed on the basis of a groove cross-section track curve representing a track for circulating the balls (4) in a groove cross-section of the screw shaft (2), and a length track curve representing a track for circulating the balls (4) in an imaginary plane in which the track length (omega) of the groove cross-section track curve is the H axis and the spiral track length (Fv (omega)) is the V axis.

Description

Technical Field

[0001] The invention relates to a ball screw. Background Art

[0002] The ball screw is used to convert rotational motion into linear motion and vice versa. The ball screw comprises: a screw shaft having a spiral groove; a nut having a spiral groove; and a plurality of balls arranged between the spiral groove of the screw shaft and the spiral groove of the nut. In order to circulate the balls, a return path connected to one end and the other end of the spiral groove of the nut is provided in the nut.

[0003] The return path includes a return pipe type, a deflector type, etc. In a deflector type ball screw, a deflector (also called a gyro) is mounted on the nut, and a circulation groove for circulating the balls is formed in the deflector as a return path (see Patent Document 1).

[0004] like Fig.14 As shown in the figure, in the conventional reverser type ball screw, the circulating track 36 (refer to Fig.14 (c)) based on the axis horizontal plane track curve 31 (reference Fig.14 (a)) and the axis section track curve 32 (refer to Fig.14 (b) is formed. Fig.14 The axis-horizontal plane track curve 31 shown in (a) is a curve showing a track along which the balls circulate in the axis-horizontal plane, and is, for example, substantially S-shaped. Fig.14 The axial cross-section track curve 32 shown in (b) is a curve showing a track along which the balls circulate in a cross section perpendicular to the axis of the screw shaft 30 , and has a substantially inverted U shape, for example.

[0005] And, if Fig.14 As shown in (c), the approximately S-shaped axial horizontal plane track curve 31 is swept (extruded) in the up-down direction to form a curved surface 34, and the approximately inverted U-shaped axial cross-sectional track 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 set as the circulating track 36 of the circulating groove. It should be noted that Fig.14 The one-dot chain line in (a) and (b) is a spiral track 33 (a spiral track of a ball moving between the spiral groove of the screw shaft and the spiral groove of the nut).

[0006] Prior art literature

[0007] Patent Literature

[0008] Patent Document 1: Japanese Patent Application Laid-Open No. 2006-132689 Summary of the invention

[0009] Problems to be solved by the invention

[0010] However, if Fig.14 As shown in the enlarged view of (d), the circulation track 36 of the conventional circulation groove has a problem that it is not connected to the spiral track 33 in a continuous manner in the tangential direction. Fig.14 As shown in (a), the axis-horizontal plane track curve 31 and the spiral track 33 are connected in a tangentially continuous manner in the axis-horizontal plane, and as shown in Fig.14 As shown in (b), the axis section track curve 32 and the spiral track 33 are connected in a continuous manner in the tangential direction in the axis vertical section, such as Fig.14 As shown in (c) and (d) of FIG. 1 , the three-dimensionally formed circulating track 36 is not connected to the spiral track 33 in a continuous manner in the tangential direction. Therefore, there is a problem that the circulating track that allows the ball to move smoothly cannot be formed.

[0011] The present invention has been made in view of the above-mentioned problems, and an object of the present invention is to provide a ball screw capable of connecting a circulation track of a circulation groove formed three-dimensionally and a spiral track in a manner that is substantially continuous in the tangential direction.

[0012] Solutions to Solve Problems

[0013] In order to solve the above-mentioned problems, one scheme of the present invention is a ball screw, which comprises: a screw shaft, which has a spiral groove; a nut, which has a spiral groove; and a plurality of balls, which are arranged between the spiral groove of the screw shaft and the spiral groove of the nut, and the nut is provided with a circulation groove connected to one end and the other end of the spiral groove of the nut and allows the balls to circulate, wherein a circulation track of the circulation groove is formed based on a groove cross-section track curve and a length track curve, the groove cross-section track curve represents the track for circulating the balls in the groove cross-section of the screw shaft, and the length track curve represents the track length ω of the groove cross-section track curve as the H axis and the spiral track length F v (ω) is the orbital path for the ball to circulate in the virtual plane of the V axis, and the spiral orbital length F of the length orbital curve from the starting point of the rotation is v (ω) is set to the spiral track length F of the circulating track of the circulating groove from the rotation starting point v (ω), the main normal direction coordinate F of the groove section track curve n (ω) is set to the spiral track length F relative to the circulating track of the circulating groove v (ω) is the principal normal direction coordinate F n (ω), the binormal direction coordinate F of the groove section track curve b (ω) is set to the spiral track length F relative to the circulating track of the circulating groove v(ω)'s binormal direction coordinate F b (ω).

[0014] Effects of the Invention

[0015] According to one aspect of the present invention, the three-dimensional circulation track and the spiral track of the circulation groove can be connected in a substantially continuous manner in the tangential direction. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a perspective view of a ball screw according to one embodiment of the present invention.

[0017] Figure 2 It is a front view of the ball screw according to this embodiment.

[0018] Figure 3 It is a side view of the ball screw according to this embodiment.

[0019] Figure 4 is a diagram showing a cross-sectional track curve.

[0020] Figure 5 is a diagram showing a length track curve.

[0021] Figure 6 is the spiral track length F v (ω) diagram (vertical cross-sectional view of the screw shaft).

[0022] Figure 7 is a conceptual diagram of an imaginary plane ( Figure 7 (a) (b) shows a stereoscopic view of the screw shaft, Figure 7 (c) shows a top view of the screw shaft).

[0023] Figure 8 : is a diagram showing the XYZ coordinate system of the ball screw according to the present embodiment ( Figure 8 (a) shows the XY plane of the ball screw, Figure 8 (b) shows the XZ plane of the ball screw).

[0024] Fig. 9 This is a conceptual diagram showing a state in which a virtual plane is curled.

[0025] Fig.10 It is a perspective view showing the circulating track of the ball screw according to the present embodiment.

[0026] Fig.11 It is a diagram showing a groove cross-section track curve of an embodiment.

[0027] Fig.12 2 is a diagram showing a length track curve of an embodiment.

[0028] Fig.13is a diagram showing a circulating track of an embodiment ( Fig.13 (a) shows the XY plane of the ball screw, Fig.13 (b) shows the YZ plane of the ball screw, Fig.13 (c) shows the XYZ coordinates of the ball screw).

[0029] Fig.14 : is a diagram for explaining a circulating track of a conventional ball screw ( Fig.14 (a) shows the axis horizontal plane, Fig.14 (b) shows a cross section perpendicular to the axis, Fig.14 (c) shows a perspective view of the screw shaft, Fig.14 (d) shows Fig.14 (c) is an enlarged view of a portion of FIG. DETAILED DESCRIPTION

[0030] Hereinafter, the ball screw of the embodiment of the present invention is described in detail with reference to the accompanying drawings. However, the ball screw of the present invention can be embodied in various ways and is not limited to the embodiment described in the specification. This embodiment is provided for the purpose of enabling those skilled in the art to fully understand the intention of the invention by making the specification fully disclosed.

[0031] (Ball Screw)

[0032] Figure 1 A perspective view showing a ball screw 1 according to an embodiment of the present invention. Figure 2 Shows a front view of the ball screw 1, Figure 3 A side view of the ball screw 1 is shown.

[0033] like Figure 1 As shown in the figure, the ball screw 1 comprises: a screw shaft 2 having a spiral groove 2a; a nut 3 having a spiral groove 3a (see Figure 2 ); and a plurality of balls 4, which are arranged between the spiral groove 2a of the screw shaft 2 and the spiral groove 3a of the nut 3. The spiral groove 2a of the screw shaft 2 is formed on the outer peripheral surface of the screw shaft 2. The spiral groove 2a of the screw shaft 2 is in the shape of a pointed arch. The nut 3 is formed with an insertion hole for inserting the screw shaft 2. The spiral groove 3a of the nut 3 (refer to Figure 2 ) is formed on the inner peripheral surface of the nut 3. The spiral groove 3a of the nut 3 (refer to Figure 2 ) is in the shape of an arch. The nut 3 has a flange 3c.

[0034] The ball screw 1 has, for example, two circulation paths 5. Each circulation path 5 includes a load path A between the spiral groove 2a of the screw shaft 2 and the spiral groove 3a of the nut 3, and a return path B connected to one end and the other end of the load path A. A circulation groove 3b connected to one end and the other end of the spiral groove 3a is formed on the inner circumferential surface of the nut 3 as the return path B (see Figure 2). The return path B includes a circulation groove 3b (refer to Figure 2 ) and the portion of the outer peripheral surface of the screw shaft 2 that is opposite to the annular groove 3b.

[0035] When one of the screw shaft 2 and the nut 3 is rotated relative to the other, the ball 4 rolls in the load path A and moves from the rotation starting point (1) (refer to Figure 2 ) enters the circulation groove 3b of the nut 3. In the circulation groove 3b, the ball 4 passes over the thread teeth 2b of the screw shaft 2 (refer to Figure 3 ), moves to the adjacent spiral groove 2a, and from the rotation end point (2) (refer to Figure 2 ) enters the load path A again. Along with this, the other of the screw shaft 2 and the nut 3 moves axially relative to one another.

[0036] like Figure 1 As shown, the orbit of the center of the ball 4 moving in the load path A is the spiral orbit 7. The orbit of the center of the ball 4 moving in the circulation groove 3b is the circulation orbit 8.

[0037] It should be noted that, in the ball screw 1 of the present embodiment, the circulation groove 3b is directly formed on the nut 3 in a manner continuous with the spiral groove 3a, but the circulation groove 3b may also be formed on a deflector (also called a gyro) mounted on the nut 3. In addition, a relief portion 3d for a machining tool having the circulation groove 3b formed on the inner diameter portion of the nut 3 (see Figure 2 ), but as long as the circulation groove 3b can be processed, the avoidance portion 3d may not be formed.

[0038] The circulation track 8 of the circulation groove 3b is based on Figure 4 The groove section track curve 11 and Figure 5 The length track curve 12 shown is formed.

[0039] (Track section track curve)

[0040] like Figure 4 As shown, the groove section track curve 11 is a curve representing the track (actual track) for the ball 4 to circulate in the groove section of the screw shaft 2. Specifically, it is a curve representing the track for the ball 4 to move over the thread 2b of the screw shaft 2 to the adjacent spiral groove 2a. (1) is the rotation starting point of the groove section track curve 11, and (2) is the rotation end point of the groove section track curve 11. The groove section track curve 11 is roughly inverted U-shaped.

[0041] When the track length (curve length) ω is set as a variable, the coordinates of the groove section track curve 11 are given by (F b (ω), F n (ω) indicates. n (ω) is the coordinate in the direction of the principal normal (N axis), F b(ω) is the coordinate in the binormal direction (B-axis direction). The total length of the groove section track curve 11 (the length of the groove section track curve 11 from the turning start point (1) to the turning end point (2)) is α.

[0042] The groove cross section (BN plane) of the screw shaft 2 depicted by the groove cross section track curve 11 is a cross section perpendicular to the spiral groove 2a of the screw shaft 2 (groove vertical cross section) and is relative to the cross section along the axis of the screw shaft 2 ( Figure 1 However, the shape of the spiral groove 2a of the screw shaft 2 in the groove cross section (BN plane) is different from Figure 1 The difference in the shape of the spiral groove 2a of the screw shaft 2 in the YZ plane is small, so the groove cross section of the screw shaft 2 can also be used. Figure 1 It should be noted that in the YZ plane Figure 1 In the diagram, the axial direction of the ball screw 1 is set as the Y axis, the height direction is set as the Z axis, and the horizontal direction is set as the X axis.

[0043] The groove cross-section track curve 11 is symmetrical about the center point (3). The solid line indicates the turning start point (1) side of the groove cross-section track curve 11, and the dotted line indicates the turning end point (2) side. The circulation track 8 of the circulation groove 3b (see Fig.10 ) is symmetrical with respect to the center point (3), so if the groove cross-section track curve 11 on the side of the rotation starting point (1) is drawn, the circulating track 8 of the circulating groove 3b can be formed. The groove cross-section track curve 11 is, for example, a single arc, multiple arcs with different curvatures, an ellipse, a clothoid curve, a spline curve, etc., or a curve formed by connecting them with a straight line, and is a curve continuous in the tangent direction.

[0044] (Length track curve)

[0045] like Figure 5 As shown in the figure, the length track curve 12 is a curve obtained by setting the track length ω of the groove section track curve 11 to the H axis and the spiral track length F v (ω) is a curve of the orbit of the ball 4 in the imaginary plane (VH plane) of the V axis. Specifically, it is a curve showing the orbit of the ball 4 moving from the spiral groove 2a of the screw shaft 2 to the adjacent spiral groove 2a from the rotation start point (1) to the rotation end point (2). The length track curve 12 is generally S-shaped.

[0046] The imaginary plane (VH plane) is similar to the axial horizontal plane of the ball screw 1, but is different from the axial horizontal plane of the ball screw 1. The variable ω of the H axis of the imaginary plane is not the length of the ball screw 1 in the Y-axis direction, but the track length ω of the groove section track curve 11 from the rotation starting point (1).

[0047] F of the V axis of the imaginary plane v(ω) is not the length of the ball screw 1 in the X-axis direction, but Figure 6 The length F of the spiral track 7 from the rotation starting point (1) is shown as v (ω). Figure 6 In the vertical cross-sectional view of the screw shaft 2, the spiral track 7 is a circle on the BCD (Ball Center Diameter). Figure 6 β is the length of the spiral track F v The total length of (ω) is the length of the spiral track 7 from the rotation start point (1) to the rotation end point (2) (indicated by the double-dashed line in the figure). θ is the circulation range, and d is the shaft diameter of the screw shaft 2. The spiral track length F v (ω) ratio Figure 6 The length of the arc on the BCD shown is the amount of lead angle. However, the spiral track length F v The difference between (ω) and the length of the arc on BCD is small, so it is taken as the length of the spiral track F v (ω) can also be used Figure 6 The length of the arc on BCD shown.

[0048] like Figure 5 As shown, the coordinates of the length track curve 12 are given by a function of ω, namely (F v (ω), ω). ω is the track length of the cross-sectional track curve, F v (ω) is the spiral track length. The rotation track width α in the H-axis direction of the length track curve 12 (the length of the length track curve 12 in the H-axis direction from the rotation start point (1) to the rotation end point (2)) and the total length α of the groove section track curve 11 (refer to Figure 4 The V-axis width β of the length track curve 12 (the length of the length track curve 12 from the rotation start point (1) to the rotation end point (2) in the V-axis direction) is consistent with the spiral track length F v (ω) total length β (refer to Figure 6 ) are consistent.

[0049] The length track curve 12 is symmetrical about the center point (3). The solid line indicates the rotation start point (1) side of the length track curve 12, and the dotted line indicates the rotation end point (2) side. The circulation track 8 of the circulation groove 3b (see Fig.10 ) is symmetrical about the center point (3), so if a length track curve 12 is drawn on the side of the rotation starting point (1), a circulation track 8 of the circulation groove 3b can be formed. The length track curve 12 is, for example, a single arc, multiple arcs with different curvatures, an ellipse, a clothoid curve, a spline curve, etc., or a curve formed by connecting them with a straight line, and is a curve continuous in the tangent direction.

[0050] The tangent direction of the length track curve 12 at the turning start point (1) is substantially consistent with the V-axis direction of the imaginary plane. In addition, the tangent direction of the length track curve 12 at the turning end point (2) is consistent with the V-axis direction of the imaginary plane. It is desirable that the tangent directions of both the turning start point (1) and the turning end point (2) of the length track curve 12 are substantially consistent with the V-axis direction of the imaginary plane, but only one of them may be consistent.

[0051] (Imaginary plane)

[0052] The concept of the imaginary plane is explained below. Figure 7 (a) schematically shows a curved surface 21 drawn on the screw shaft 2. The short side 21a of the curved surface 21 represents the cross-sectional track curve 11, and the long side 21b of the curved surface 21 represents the spiral track length F. v The length of the short side 21a of the curved surface 21 is consistent with the total length α of the cross-sectional track curve 11, and the length of the long side 21b of the curved surface 21 is consistent with the spiral track length F v The total length β of (ω) is consistent. Figure 7 As shown in (b), the imaginary plane 22 is obtained by unfolding the curved surface 21 into a plane. The length of the short side 22a of the imaginary plane 22 is consistent with the total length α of the axial section track curve 11, and the length of the long side 22b of the imaginary plane 22 is consistent with the spiral track length F v The total length β of (ω) is consistent. Figure 7 As shown in (c) of FIG. 2 , when the screw shaft 2 is viewed from above, the imaginary plane is inclined at the lead angle.

[0053] Figure 7 The imaginary plane 22 shown in (c) is equivalent to Figure 5 The imaginary plane (VH plane) shown. Figure 7 12 of (c) is a length track curve drawn on the virtual plane 22. As described above, the tangent direction of the rotation starting point (1) of the length track curve 12 is substantially consistent with the V-axis direction of the virtual plane 22 (refer to Figure 7 (c) The part enclosed by the ellipse).

[0054] (Conversion to XYZ coordinates of ball screw)

[0055] The principal normal direction coordinate F of the groove section track curve 11 is converted into the coordinate F of the groove section track curve 11 by using the Frent-Serret frame composed of a set of three unit vectors T, N, and B indicating the tangent direction, the principal normal direction, and the binormal direction relative to the spiral track 7. n (ω), the binormal direction coordinate F of the groove section track curve 11 b (ω), length track curve 12 spiral track length F v (ω) is transformed into the XYZ coordinates of the ball screw 1.

[0056] First, Figure 5 The length track curve 12 shown has a spiral track length F v (ω) Figure 8 The spiral track length F of the circulating track 8 from the rotation starting point (1) is set as shown in the XZ plane of the ball screw 1 in (b). v (ω), find the length of the spiral track from the starting point (1) to become F v Here, the length of the spiral track from the starting point (1) along the spiral is calculated to be F v (ω) of point P1.

[0057] And, Figure 4 The main normal direction coordinate F of the groove section track curve 11 is shown n (ω) Figure 8 The ball screw 1 is set to have a spiral track length F relative to the circulating track 8 as shown in the XZ plane of (b). v (ω) is the principal normal direction coordinate F n (ω), calculate the distance F from point P1 on the spiral track 7 to the principal normal direction (N direction) n (ω) after point P2.

[0058] And, Figure 4 The binormal direction coordinate F of the groove section track curve 11 is shown b (ω) Figure 8 The XY plane of the ball screw 1 is set as shown in (a) with respect to the spiral track length F v (ω)'s binormal direction coordinate F b (ω), calculate the distance F from point P1 on the spiral track 7 to the binormal direction (direction B) b (ω) after point P3.

[0059] Loop Track 8 Figure 8 The ball screw 1 shown in (b) is located at point P2 in the XZ plane. Figure 8 Since the ball screw 1 shown in (a) is located at point P3 in the XY plane, the circulating orbit 8 can be obtained from point P2 and point P3.

[0060] The groove section track curve 11 and the length track curve 12 are a collection of points, so let ω be changed to ω1, ω2, ω3..., and find (F v (ω1), F n (ω1), F b (ω1)), (F v (ω2), F n (ω2), F b(ω2)), (F v (ω3), F n (ω3), F b (ω3)) ..., and transform them into the XYZ coordinates of the ball screw 1 to obtain the points P1, P2, and P3. If point P2 is connected and point P3 is connected, it can be formed Fig.10 The three-dimensional circulating track 8 is shown.

[0061] As mentioned above, F v (ω)F n (ω)F b Transforming (ω) into the XYZ coordinates of the ball screw 1 means that, Fig. 9 As shown, the imaginary plane 22 is curved to return to the original curved surface 21. By curving the imaginary plane 22, the long track curve 12 (indicated by the dotted line in the figure) drawn on the imaginary plane 22 becomes three-dimensional, and a three-dimensional circulating track 8 can be formed.

[0062] like Figure 7 As shown in (c), the tangent direction of the rotation starting point (1) of the length track curve 12 in the virtual plane 22 is substantially consistent with the V-axis direction of the virtual plane 22. Fig. 9 As shown in the figure, even in the curved surface 21 where the imaginary plane 22 is curled, it is possible to ensure that the tangent direction of the rotation starting point (1) of the length track curve 12 is substantially consistent with the V-axis direction of the curved surface 21, which can ensure Fig.10 The three-dimensional circulating track 8 shown is substantially continuous with the spiral track 7 in the tangential direction at the turning starting point (1).

[0063] If formed Fig.10 As for the circulation track 8 shown in the figure, the balls 4 are arranged along the circulation track 8, and the circulation groove 3b is formed in such a way that the balls 4 move along the circulation track 8. Specifically, in the middle part of the length direction of the circulation groove 3b (on the thread 2b of the screw shaft 2), the balls 4 move in a no-load state, and there is a small clearance around the balls 4. Therefore, in the middle part of the length direction of the circulation groove 3b, the circulation groove 3b is formed in such a way that the center of the clearance of the balls 4 becomes the circulation track 8. On the other hand, in the raised parts at both ends of the length direction of the circulation groove 3b, the balls 4 are clamped by the circulation groove 3b of the nut 3 and the spiral groove 2a of the screw shaft 2 and are lifted. At the raised part, the circulation groove 3b is formed in such a way that the track of the balls 4 clamped by the circulation groove 3b of the nut 3 and the spiral groove 2a of the screw shaft 2 becomes the circulation track 8.

[0064] However, sometimes the circulation track 8 is corrected in order to smoothly lift the ball 4, and sometimes there are processing errors in the circulation groove 3b of the nut 3 and the spiral groove 2a of the screw shaft 2. The tangent direction of the circulation track 8 and the spiral track 7 is "substantially" continuous, which also includes such a situation. In addition, the tangent direction of the rotation starting point and / or rotation end point of the length track curve 12 in the imaginary plane is "substantially" consistent with the V-axis direction of the imaginary plane, which also includes such a situation.

[0065] (Effect)

[0066] The structure of the ball screw 1 according to the present embodiment has been described above. According to the ball screw according to the present embodiment, the following effects are achieved.

[0067] The circulating track 8 of the circulating groove 3b is formed based on the groove cross-section track curve 11 and the length track curve 12, so that the three-dimensional circulating track 8 of the circulating groove 3b can be connected to the spiral track 7 in a substantially continuous manner in the tangential direction.

[0068] The tangent direction of the starting point and / or end point of the length track curve 12 in the imaginary plane is substantially consistent with the V-axis direction of the imaginary plane, thereby ensuring that the tangent direction of the circulating track 8 and the spiral track 7 at the starting point and / or end point of the three-dimensional circulating track 8 is substantially continuous.

[0069] In the imaginary plane, the rotation track width of the length track curve 12 in the H-axis direction is consistent with the total length α of the groove section track curve 11, and the rotation track width of the length track curve 12 in the V-axis direction is consistent with the spiral track length F v Since the total length β of (ω) is consistent, the circulation track 8 of the circulation groove 3 b can be smoothly formed within the total length.

[0070] Example

[0071] (Track section track curve)

[0072] like Fig.11 As shown, in the groove section (BN plane) of the screw shaft 2, a single arc of radius R1 and a straight line are used to draw the groove section track curve 11. (1) is the rotation starting point, (3) is the symmetrical middle point of the groove section track curve 11, (5) is the curvature change point, α is the total length of the groove section track curve 11 (mm), R1 is the groove section track radius (mm), θ1 is the rotation start angle (rad), and ω is the variable (0→α).

[0073] The coordinates of the groove section track curve 11 (F B (ω), F N (ω)) is expressed as follows.

[0074]

[0075] (Length track curve)

[0076] like Fig.12 As shown, in the imaginary plane (VH plane), a single arc with a radius R3 and a straight line are used to draw the length track curve 12. At the rotation starting point (1), the tangent direction of the length track curve 12 is consistent with the V axis direction. (1) is the rotation starting point, (2) is F V (ω) is the end point, (3) is the middle point of the length track symmetry, (6) is the curvature change point, β is the total length of the spiral track (mm), R3 is the radius of the length track (mm), θ2 is the arc position of the length track (rad), θ3 is the arc range of the length track (rad), θ4 is the inclination angle of the length track (rad), and L1 is the straight-line distance of the length track (mm).

[0077] Length of track curve 12 when variable ω is F V (ω) is expressed as follows.

[0078]

[0079] (loop track of loop groove)

[0080] F V (ω)F N (ω)F B (ω) is transformed into the XYZ coordinates of the ball screw 1. That is, by changing ω to ω1, ω2, ω3, etc., we can find (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)…, transform them into the XYZ coordinates of the ball screw 1 and find the points P1, P2, and P3, connect point P2 and point P3, and find Fig.13 (c) shows the three-dimensional cyclic orbit 8.

[0081] exist Fig.13 In (a)(b)(c), (1) is the starting point of the rotation, (2) is F V (ω) is the end point, (3) is the middle point of the symmetry of the loop track 8, and (4) takes the rotation starting point (1) as the starting point and becomes the length F V(ω) is the point on the spiral track 7. R2 is the radius of the spiral track on the axial section (mm). TNB are the tangent direction (T), normal direction (N), and binormal direction (B) based on point (4).

[0082] The obtained circulating track 8 is connected to the spiral track 7 in a continuous manner in the tangential direction at the rotation starting point (1), and the circulating track 8 itself is also smooth.

[0083] This specification is based on Japanese Patent Application No. 2022-149823 filed on September 21, 2022. The entire contents are incorporated herein.

[0084] Description of Reference Numerals

[0085] 1: ball screw, 2: screw shaft, 2a: spiral groove of screw shaft, 3: nut, 3a: spiral groove of nut, 3b: circulating groove, 4: ball, 7: spiral track, 8: circulating track, 11: groove section track curve, 12: length track curve, 22: imaginary plane, (1): starting point of rotation, (2) end point of rotation.

Claims

1. A ball screw, wherein: The ball screw has: a screw shaft having a spiral groove; a nut having a spiral groove; and a plurality of balls arranged between the spiral groove of the screw shaft and the spiral groove of the nut, The nut is provided with a circulation groove connected to one end and the other end of the spiral groove of the nut and allowing the ball to circulate. in, The circulation track of the circulation groove is formed based on the groove section track curve and the length track curve. The groove section track curve represents the track for circulating the ball in the groove section of the screw shaft, and the length track curve represents the track length ω of the groove section track curve as the H axis and the spiral track length F v (ω) is the orbital path of the ball in the imaginary plane of the V axis, The spiral track length F of the track curve from the starting point of the rotation v (ω) is set to the spiral track length F of the circulating track of the circulating groove from the rotation starting point v (ω), The principal normal direction coordinate F of the groove section track curve n (ω) is set to the spiral track length F relative to the circulating track of the circulating groove v (ω) is the principal normal direction coordinate F n (ω), The binormal direction coordinate F of the groove section track curve b (ω) is set to the spiral track length F relative to the circulating track of the circulating groove v (ω)'s binormal direction coordinate F b (ω).

2. The ball screw according to claim 1, characterized in that: The tangent direction of the length track curve at the rotation starting point and / or rotation end point in the imaginary plane is substantially consistent with the V-axis direction of the imaginary plane.

3. The ball screw according to claim 1 or 2, characterized in that: The width of the rotation track of the length track curve in the H-axis direction in the imaginary plane is consistent with the total length (α) of the groove section track curve. The width of the rotating track in the V-axis direction of the length track curve is equal to the length F of the spiral track v (ω) and the total length (β) are consistent.

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