Ball screw

Abstract

Provided is a ball screw capable of reducing quadrant glitch error and torque resistance. Each of a thread groove of a nut (13) and a thread groove of a screw shaft (12) is formed to be a Gothic arch groove having two flank surfaces (13a1, 13a2) (or 12a1, 12a2). A preload causes the ball (14) to come into two-point contact with a flank surface (13a1) on the load side of the thread groove of the nut (13) and a flank surface (12a1) on the load side of the thread groove of the screw shaft (12). The thread groove of the nut (13) is formed so that the ball (14) does not come into contact with the flank surface (13a2) on the non-load side of the nut (13) even if the ball (14), during forward operation, moves toward biting into the flank surface (13a2) on the non-load side of the nut (13) in a direction perpendicular to the revolution direction. The thread groove of the screw shaft (12) is formed so that the ball (14) does not come into contact with the flank surface (12a2) on the non-load side of the screw shaft (12) even if the ball (14), during reverse operation, moves toward biting into the flank surface (12a2) on the non-load side of the screw shaft (12) in a direction perpendicular to the revolution direction.

Description

Ball screw

[0001] This invention relates to a ball screw that converts rotational motion into linear motion.

[0002] Production machinery such as machine tools and semiconductor / LCD manufacturing equipment often uses linear feed systems that combine ball screws and servo motors. Normally, ball screws are preloaded to eliminate backlash. However, even with preloaded ball screws, it is known that when the drive direction reverses, a change in the contact state between the balls and screw grooves occurs, causing unstable torque resistance.

[0003] As shown in Figure 1, for example, even if servo motors 2 and 3 are controlled on an XY table so that tool 1 moves in a circular motion along workpiece 8, quadrant protrusion errors occur when transitioning between quadrants, and position deviation fluctuations occur during arc motion, resulting in a difference between the ideal circular motion trajectory and the trajectory during machining.

[0004] Quadrant protrusion errors are caused by changes in the contact state between the ball, nut, and screw shaft. As shown in Figure 2, when the ball screw 4 is rotating in reverse (A), the ball 5 is in contact with the nut at one point and with the screw shaft at two points, for a total of three points. When the rotation switches from reverse to forward (B), the ball 5 is in contact with the nut at one point and with the screw shaft at one point, for a total of two points. When rotating in forward (C), the ball 5 is in contact with the nut at two points and with the screw shaft at one point, for a total of three points. Thus, when the driving direction is reversed, the contact state between the ball 5 and the nut and screw shaft changes from three points, two points, and three points.

[0005] Recent geometrical analyses of ball screws have revealed that changes in the contact state between the ball 5 and the nut and screw shaft are due to the ball 5 sinking in when the driving direction of the ball screw 4 is reversed. Because the ball screw 4 has a lead, the sinking of the ball 5 occurs due to the geometry of the helical trajectory. As shown in Figure 2, when reversing (A), the ball 5 attempts to sink in and move toward the screw shaft in a direction perpendicular to the direction of revolution (the direction of the white arrow in the figure). As a result, the ball 5 makes contact with the nut at one point and with the screw shaft at two points, for a total of three points. On the other hand, when rotating forward (C), when the driving direction of the ball screw 4 is reversed, the direction of sinking also reverses, and the ball 5 attempts to move toward the nut in a direction perpendicular to the direction of revolution (the direction of the white arrow in the figure). As a result, the ball 5 makes contact with the screw shaft at one point and with the nut at two points, for a total of three points. When switching from reverse to forward rotation (B), the ball 5 is momentarily stationary, so the preload causes the ball 5 to make contact with the nut at one point and with the screw shaft at one point, for a total of two points.

[0006] The change in contact state when reversing the drive direction (three-point contact → two-point contact → three-point contact) causes quadrant protrusion errors. To reduce quadrant protrusion errors, Patent Document 1 proposes a ball screw that maintains a three-point contact state of the balls. Specifically, Patent Document 1 proposes a ball screw that maintains the contact state as three-point contact → three-point contact → three-point contact when reversing the drive direction.

[0007] Patent No. 7556267

[0008] However, the ball screw described in Patent Document 1 has the problem that the friction torque of the ball screw increases because it maintains a three-point contact state. When the friction torque increases, the torque resistance when driving the ball screw increases, and the position deviation fluctuation shown in Figure 1 also increases.

[0009] This invention was made in view of the above problems, and aims to provide a ball screw that can reduce quadrant projection errors and torque resistance.

[0010] To solve the above problems, one aspect of the present invention provides a ball screw comprising a screw shaft, a nut, and a plurality of balls disposed between the screw groove of the screw shaft and the screw groove of the nut, wherein the ball screw is preloaded, the screw groove of the nut and the screw groove of the screw shaft are each formed as a Gothic arch groove having two flank surfaces, the preload causes the balls to make two-point contact with the load-side flank surface of the screw groove of the nut and the load-side flank surface of the screw groove of the screw shaft, the screw groove of the nut is formed so that even when the balls bite into and move toward the unload-side flank surface of the nut in a direction perpendicular to the direction of revolution during forward operation, they do not come into contact with the unload-side flank surface of the nut, and the screw groove of the screw shaft is formed so that even when the balls bite into and move toward the unload-side flank surface of the screw shaft in a direction perpendicular to the direction of revolution during reverse operation, they do not come into contact with the unload-side flank surface of the screw shaft.

[0011] A preferred embodiment of the present invention is characterized in that the thread groove of the nut and the thread groove of the screw shaft satisfy equations (1) and (2). 0 < C Ｂ / Da<0.1...(1) 0.01<δ ｓ / Da...(2) Here, Da is the diameter of the ball, C Ｂ δ is the distance between the centers of the Gothic arch grooves. ｓ This is the shift amount.

[0012] A more preferred embodiment of the present invention is characterized in that the thread groove of the nut and the thread groove of the screw shaft satisfy equation (3). Here, α is the contact angle and r is the groove radius of the Gothic arch groove.

[0013] A more preferred embodiment of the present invention is characterized in that the nut is a single nut and the ball screw is subjected to an offset preload.

[0014] A more preferred embodiment of the present invention is characterized in that the thread groove of the nut and the thread groove of the screw shaft satisfy equation (4). 0.04 < δ ｓ / Da...(4)

[0015] A more preferred embodiment of the present invention is characterized in that the groove r ratio when assuming no nut clearance is more than 0.50 and less than 0.54. Here, the groove r ratio when assuming no nut clearance is r / Da ０ which is represented by. r is the groove radius of the Gothic arch groove, and Da ０ is the ball diameter of the virtual ball that makes four-point contact with the thread groove of the screw shaft and the thread groove of the nut with the phases aligned.

[0016] A more preferred embodiment of the present invention is characterized in that the groove r ratio when assuming no nut clearance is more than 0.50 and less than 0.52.

[0017] According to one embodiment of the present invention, when reversing the driving direction, the contact state of the balls can be maintained in a two-point contact state (that is, maintained as two-point contact → two-point contact → two-point contact). Therefore, the quadrant protrusion error can be reduced. Also, since the number of contact points is reduced from three to two, the frictional torque of the ball screw can be reduced, and the torque resistance can also be reduced.

[0018] According to a preferred embodiment of the present invention, compared with a conventional ball screw, the thread grooves of the nut and the screw shaft are arranged outside with respect to the balls, in other words, the thread grooves are widened left and right (that is, 0 < C Ｂ / Da < 0.1... satisfying equation (1)), and the shift amount is increased (that is, 0.01 < δ ｓ / Da... satisfying equation (2)), so that the non-loaded side flank surfaces of the nut and the screw shaft can be separated from the balls, and even if the balls move in the biting direction, the balls can be prevented from contacting the non-loaded side flank surface of the nut and the non-loaded side flank surface of the screw shaft.

[0019] According to a more preferred embodiment of the present invention, since equation (3) is further satisfied, it is possible to prevent the load capacity and rigidity of the ball screw from decreasing.

[0020] According to a more preferred embodiment of the present invention, the nut is a single nut, and a preload of the offset preload method is applied to the ball screw, so that a predetermined C Ｂ and δ ｓThis allows for the precise formation of screw grooves with the specified characteristics. Therefore, even when the balls move in the engagement direction, the balls can be prevented from contacting the nut and the unloaded flank surface of the screw shaft.

[0021] In a more preferred embodiment of the present invention, by satisfying equation (4), the gap between the ball and the nut and the flank surface on the unloaded side of the screw shaft becomes larger, so that three-point contact can be prevented even if manufacturing errors occur or if a high load is applied to the ball screw during use. Furthermore, by satisfying equation (4), the contact angle α can be prevented from falling below 40°, so that the load capacity and rigidity of the ball screw can be prevented from decreasing.

[0022] According to a more preferred embodiment of the present invention, since the groove r ratio is greater than 0.50 and less than 0.54 when it is assumed that there is no nut gap, it is possible to use balls with the same diameter as those of existing ball screws, and to ensure the same load capacity and rigidity as existing ball screws.

[0023] According to a more preferred embodiment of the present invention, since the groove r ratio is greater than 0.50 and less than 0.52 when it is assumed that there is no nut gap, it is possible to use balls with the same diameter as those of existing ball screws, and to ensure the same load capacity and rigidity as existing ball screws.

[0024] This is a schematic plan view of a conventional XY table. This is a schematic diagram showing the contact state between the ball, nut and screw shaft when the drive direction is reversed (prior art). This is a cross-sectional view along the center line of a ball screw according to an embodiment of the present invention. This is a schematic cross-sectional view of the nut and screw shaft. This is a diagram showing the contact angle in a stationary state. This is a diagram showing the ball's engagement movement during forward operation. This is a diagram showing the ball's engagement movement during reverse operation. This is a schematic diagram showing the contact state between the ball, nut and screw shaft when the drive direction is reversed (this embodiment). This is a graph showing the relationship between Fa / Ca and friction torque in a ball screw according to this embodiment. Here, Fa is the axial load and Ca is the basic dynamic load rating in the axial direction. This is a graph showing the ranges of equations (1), (2), and (3). This is a graph showing the ranges of equations (1), (2), and (4). This is a schematic diagram illustrating the groove r ratio assuming no nut gap. Figure 12(a) schematically shows a cross-sectional view perpendicular to the screw groove when a virtual ball with no nut gap is placed in the screw groove of the screw shaft and the screw groove of the nut with aligned phases. Figure 12(b) schematically shows a cross-sectional view perpendicular to the screw groove when the screw shaft and nut are moved axially by the amount of the actual gap between the ball and the screw groove. This is a schematic cross-sectional view of the nut and screw shaft in an example where the screw groove of the nut is formed as a Gothic arch expansion groove. This is a cross-sectional view perpendicular to the groove in an example where a relief groove is added to the screw groove of the screw shaft and nut. This diagram shows the positions of the ball center and the center of curvature of the screw groove of the screw shaft and nut when the ball screw is operated in the forward and reverse directions. Figure 15(a) shows the case when it is operated in the forward direction (forward feed), and Figure 15(b) shows the case when it is operated in the reverse direction (backward feed). This is a graph comparing the friction torque of the ball screw of the actual product and the ball screw of an existing product.

[0025] 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.

[0026] Figure 3 shows a cross-sectional view along the centerline of a ball screw 11 according to an embodiment of the present invention. The ball screw 11 comprises a screw shaft 12, a nut 13, and a plurality of balls 14 arranged between the screw groove 12a of the screw shaft 12 and the screw groove 13a of the nut 13. The nut 13 is provided with, for example, two return pipes 15 for circulating the balls 14.

[0027] A helical screw groove 12a is formed on the outer circumferential surface of the screw shaft 12. A through hole is formed in the nut 13 into which the screw shaft 12 is inserted. A helical screw groove 13a is formed on the inner circumferential surface of the through hole. As shown in Figure 4, the screw groove 13a of the nut 13 is formed in a Gothic arch groove having two flank surfaces 13a1 and 13a2. Each flank surface 13a1 and 13a2 has a circular arc cross-section. Reference numeral 13a1 denotes the flank surface on the load side, and reference numeral 13a2 denotes the flank surface on the unloaded side.

[0028] Similarly, the thread groove 12a of the screw shaft 12 is formed as a Gothic arch groove having two flank surfaces 12a1 and 12a2. Each of the flank surfaces 12a1 and 12a2 of the screw shaft 12 has a circular arc cross-section. Reference numeral 12a1 indicates the flank surface on the load side, and reference numeral 12a2 indicates the flank surface on the unloaded side. Note that in Figure 4, the thread groove 13a of the nut 13 and the thread groove 12a of the screw shaft 12 are shown in a cross-section perpendicular to the lead (cross-section perpendicular to the groove).

[0029] In Figure 4, the lead L+δ of the thread groove in the central part including the boundary W of the nut 13. ｓ The shift amount δ is greater than the lead L of other parts. ｓ It is only larger (see also Figure 3). On the other hand, the lead L of the screw shaft 12 is constant in the central part and in other parts. Therefore, as shown in Figure 4, the screw groove 13a of the nut 13 presses the balls 14 so that the balls 14, which are arranged on both sides with the offset point as the boundary W, are separated. A preload (=axial load) Fa acts on the nut 13 with the offset point as the boundary W. Shift amount δ ｓ This is the lead L + δ of the nut 13 when the ball 14 is not present. ｓ This is the difference between the screw shaft 12 and the lead L. Figure 4 C ＢThis is the distance between the centers of the Gothic arch grooves (the distance between the center of curvature of the thread groove on the load-side flank surface 12a1 of the screw shaft 12 and the center of curvature of the thread groove on the unload-side flank surface 12a2, and the distance between the center of curvature of the thread groove on the load-side flank surface 13a1 of the nut 13 and the center of curvature of the thread groove on the unload-side flank surface 13a2). C Ｂ is the same for nut 13 and screw shaft 12. r is the groove radius of the Gothic arch groove. r is the same for nut 13 and screw shaft 12. m ｓ This represents the center of the ball. Note that C is the distance between the centers of the Gothic arch grooves. Ｂ This can be determined from the geometric shapes of the screw grooves 12a and 13a of the screw shaft 12 and nut 13. It can also be determined from the groove radius r, ball diameter, and contact angle α of the screw grooves 12a and 13a of the screw shaft 12 and nut 13.

[0030] The preload is not limited to the single-nut offset method described above; a double-nut method with a spacer between the two nuts is also acceptable. The direction of the load due to the preload can be either tensile or compressive. Tensile preload refers to pressing the balls 14 so that they are separated from each other, with the offset point as the boundary W as described above. Compressive preload refers to pressing the balls 14 so that they are brought closer together, with the offset point as the boundary. Furthermore, the ball circulation method is not limited to the return pipe method; a deflector method, an end cap method, an end deflector method, or a side deflector method is also acceptable.

[0031] Figure 5 shows the contact angle in a stationary state. As shown in Figure 4, the screw groove 13a of the nut 13 is shifted by a amount δ ｓWhen the nut 13 is shifted by this amount, an axial load Fa acts on it, which is a preload, with the offset point as the boundary W. As a result, the ball 14 makes two-point contact with the load-side flank surface 13a1 of the thread groove 13a of the nut 13 and the load-side flank surface 12a1 of the thread groove 12a of the screw shaft 12. The contact angle is α. The axial load Fa, which is a preload, is basically set to be between 3% and 10% of the same rated load Ca. Furthermore, even though it is a point contact, the ball 14 is elastically deformed at the contact point, and the ball 14 and the load-side flank surface 13a1 make contact in a contact ellipse, and the ball 14 and the load-side flank surface 12a1 make contact in a contact ellipse.

[0032] Consider the case where a ball screw 11 subjected to an axial load Fa, as shown in Figure 5, is driven to operate in the forward direction while constraining the rotation of the nut 13. Forward operation is an operating state in which the direction of movement of the nut 13 (direction of the white arrow in the figure) is opposite to the direction of the axial load Fa. Reverse operation is an operating state in which the direction of movement of the nut 13 is in the direction of the axial load Fa.

[0033] As shown in Figure 6, during forward operation, the ball 14 attempts to bite into the flank surface 13a2 on the unloaded side of the nut 13 in a direction perpendicular to the direction of revolution (indicated by the white arrow in the figure). As the ball 14 moves towards a narrow space, the resistance to biting in increases, and when this resistance exceeds the frictional force between the ball 14 and the screw grooves 12a and 13a, the biting reaches a saturation state. At this time, the ball 14 revolves with steady sliding. The center m of the ball 14 when the ball screw 11 is at rest. ｓ And the center m of ball 14 when the penetration is saturated Ｗ The distance to this point is the indentation displacement ε.

[0034] In Figure 6, where the engagement is saturated, the ball 14 is penetrated by the nut 13 and P ＭＷ A load is applied, and from the screw shaft 12 to P ＢＷ The force acts upon it. The contact angle on the nut 13 side at this time is α ＭＷ Therefore, the contact angle on the screw shaft 12 side is α ＢＷFurthermore, since the ball 14 slides against the screw groove 12a of the screw shaft 12, P ＢＷ Frictional force μP perpendicular to the curve ＢＷ The following forces act upon the ball 14 and the screw shaft 12. μ is the coefficient of friction between the ball 14 and the screw shaft 12. The insertion displacement ε can be determined from the balance of these loads in the vertical and horizontal directions. The method for determining the insertion displacement ε will be described later.

[0035] Figure 7 shows the case when operating in the reverse direction. When the driving direction of the ball screw 11 is reversed, the direction of engagement is also reversed, and the ball 14 attempts to engage and move toward the flank surface 12a2 on the unloaded side of the screw shaft 12 in a direction perpendicular to the direction of revolution (the direction of the white arrow in the figure). The engagement displacement ε can be determined from the balance of the vertical and horizontal loads in Figure 7, where the engagement is in a saturated state. The method for determining the engagement displacement ε will be described later.

[0036] As shown in Figure 6, the screw groove 13a of the nut 13 is formed so that even when the ball 14 bites into the flank surface 13a2 of the nut 13 in a direction perpendicular to the orbital direction during forward operation, it does not come into contact with the flank surface 13a2 of the nut 13 on the unloaded side. Similarly, as shown in Figure 7, the screw groove 12a of the screw shaft 12 is formed so that even when the ball 14 bites into the flank surface 12a2 of the screw shaft 12 in a direction perpendicular to the orbital direction during reverse operation, it does not come into contact with the flank surface 13a2 of the nut 13 on the unloaded side. It is desirable that the positions of the flank surface 13a2 of the nut 13 and the flank surface 12a2 of the screw shaft 12 be set considering the bite displacement ε, the machining accuracy of the screw grooves 12a and 13a, and the distance between the ball 14 and the flank surfaces 12a2 and 13a2 in the bite direction.

[0037] As shown in Figure 8, the ball screw 11 of this embodiment can maintain a constant two-point contact state of the balls 14 when reversing the drive direction (i.e., maintain a two-point contact → two-point contact → two-point contact state). Therefore, quadrant projection errors can be reduced and torque resistance immediately after reversal can be stabilized.

[0038] Furthermore, according to the ball screw 11 of this embodiment, the number of contact points can be reduced from three to two, so as shown in Figure 9, the friction torque of the ball screw 11 under the same preload load can be reduced by, for example, 55%. As a result, the torque resistance of the ball screw 11 is also reduced, and the amount of heat generated is also reduced.

[0039] As shown in Figure 4, in the ball screw 11 of this embodiment, compared to a conventional ball screw, the thread grooves 13a and 12a of the nut 13 and screw shaft 12 are positioned outward relative to the ball, in other words, the thread grooves 13a and 12a of the nut 13 and screw shaft 12 are widened to the left and right (i.e., 0 < C Ｂ / Da < 0.1 ... (satisfying equation (1)), and increase the shift amount (i.e., 0.01 < δ) ｓ / Da... (satisfies equation (2)). Here, Da is the diameter of ball 14, C Ｂ δ is the distance between the centers of the Gothic arch grooves. ｓ This is the shift amount.

[0040] This allows the unloaded flank surface 13a2 of the nut 13 and the unloaded flank surface 12a2 of the screw shaft 12 to be separated from the ball 14, preventing the ball 14 from contacting the unloaded flank surface 13a2 of the nut 13 during forward movement. Furthermore, it prevents the ball 14 from contacting the unloaded flank surface 12a2 of the screw shaft 12 during reverse movement.

[0041] Furthermore, in the ball screw 11 of this embodiment, the screw grooves 13a and 12a of the nut 13 and screw shaft 12 satisfy equation (3). Here, α is the contact angle and r is the groove radius of the Gothic arch groove. This prevents a decrease in the load capacity and rigidity of the ball screw 11.

[0042] Figure 10 is a graph showing the ranges of equations (1), (2), and (3). The horizontal axis is C Ｂ The equation is / Da, and the vertical axis is δ ｓ / Da. The range threshold C represents the lower limit of equation (1), and the range threshold E represents the upper limit of equation (1). 0 = C ＢIf / Da is used, the screw grooves 13a and 12a become circular arc grooves, making it difficult to control the machining accuracy of the screw grooves 13a and 12a, such as the pitch and BCD. Therefore, 0 < C Ｂ Set to / Da. Also, 0.1 ≤ C Ｂ If the value is / Da, it becomes difficult to obtain the same load capacity and rigidity as the existing ball screw 11. Therefore, C Ｂ / Da < 0.1, preferably C Ｂ Set / Da < 0.07.

[0043] The range threshold D represents the lower limit of equation (2). δ ｓ If / Da ≤ 0.01, the ball 14 makes three-point contact with the nut 13 and the screw shaft 12, similar to existing ball screws. × in the figure indicates an existing ball screw. Therefore, 0.01 < δ ｓ Set to / Da. As shown in the graph in Figure 10, δ ｓ The upper limit of / Da is 0.27. Also, δ ｓ If / Da falls below 0.012, sufficient preload cannot be applied. Therefore, 0.012 ≤ δ ｓ / Da is preferable.

[0044] The threshold ranges A and B are represented by equation (3). As in equation (3), C Ｂ / Da and δ ｓ By balancing / Da, the groove radius r of the Gothic arch groove can be set to 0.52Da < r < 0.58Da, and the contact angle α can be set to 30° < α < 60°, thereby ensuring load capacity and rigidity equivalent to existing ball screws.

[0045] Figure 11 shows 0.04 < δ ｓ / Da...This is a graph showing the range of equation (4). The ranges of equations (1) and (2) are the same as those shown in the graph in Figure 10. By satisfying equation (4), the gap between the ball 14 and the flank surfaces 12a2 and 13a2 on the unloaded side of the screw shaft 12 and nut 13 becomes larger, thus preventing three-point contact from occurring when manufacturing errors occur or when a high load is applied to the ball screw 11. Also, by satisfying equation (4), it is possible to prevent the contact angle α from falling below 40°, thus preventing a decrease in the load capacity and rigidity of the ball screw 11.

[0046] The graphs in Figures 10 and 11 hold true regardless of the ball diameter Da. While the typical ball diameter is set to 40% to 80% of the lead of the screw shaft 12, the ball diameter may also be set to a smaller diameter of 20% to 50% of the lead of the screw shaft 12. A smaller ball diameter allows for lower torque fluctuations and higher rigidity.

[0047] In the ball screw 11 according to this embodiment, assuming there is no nut gap, the groove r ratio is preferably greater than 0.50 and less than 0.54, and more preferably greater than 0.50 and less than 0.52. In Figure 12(a), the ball 21 drawn with a dashed line is a virtual ball 21 assuming there is no nut gap. Ball diameter Da of the virtual ball 21 ０ The virtual ball 21 is larger than the actual ball diameter Da of the ball 14. The virtual ball 21 makes contact with zero load at two locations each of the screw groove 12a of the screw shaft 12 and the screw groove 13a of the nut 13, which are aligned in phase, for a total of four locations where it makes contact with zero load. Contact angle α Ｖ０ The range is 35° to 55°.

[0048] As shown in Figure 12(a), there is a gap (ΔDa) between the ball 14 and the screw grooves 12a and 13a of the screw shaft 12 and nut 13. If the screw shaft 12 and nut 13 are moved axially by the amount of the gap (ΔDa), the ball 14 will make two-point contact with the screw grooves 12a and 13a of the screw shaft 12 and nut 13 with zero load. Subsequently, if an axial load Fa, which is a preload, is applied, the ball 14 will make two-point contact with the screw grooves 12a and 13a of the screw shaft 12 and nut 13 with a contact angle α, as shown in Figure 12(b). The state in Figure 12(b) is the same as the state in Figure 5.

[0049] Assuming there is no nut gap, the groove r ratio is r / Da ０This is represented by the following: r is the groove radius of the screw grooves (Gothic arch grooves) 12a and 13a of the screw shaft 12 and nut 13. By setting the groove r ratio to be greater than 0.50 and less than 0.54, assuming no nut clearance, it is possible to use balls 14 with the same diameter as the balls of existing ball screws, and to ensure the same load capacity and rigidity as existing ball screws. If the groove r ratio exceeds 0.54, the load capacity and rigidity of the ball screw 11 will decrease compared to existing ball screws. If the groove r ratio is 0.50 or less, the balls 14 and the screw grooves 12a and 13a will not make proper contact. The preferred range for the groove r ratio is greater than 0.50 and less than 0.54, and more preferably greater than 0.50 and less than 0.52.

[0050] Figure 13 shows an example in which the thread groove 13a of the nut 13 is formed as an expanded Gothic arch groove 13a', which is an expanded Gothic arch groove having two flank surfaces 13a1 and 13a2. As shown in Figure 4, the ball 14 does not come into contact with the flank surface 13a2 on the non-load side of the nut 13. For this reason, in the ball screw shown in Figure 13, the thread groove 13a of the nut 13 can be formed as an expanded Gothic arch groove 13a', which is an expanded Gothic arch groove with the flank surface 13a1 on the load side extended. The expanded Gothic arch groove 13a' is, for example, a circular arc groove having the same radius of curvature as the flank surface 13a1 on the load side of the nut 13.

[0051] Even when the thread groove 13a of the nut 13 is formed as a Gothic arch expanded groove 13a', the thread grooves 12a and 13a of the thread shaft 12 and the Gothic arch groove of the nut 13 remain 0 < C Ｂ / Da < 0.1 ... satisfies equation (1) and 0.01 < δ ｓ / Da...(2) is satisfied. Therefore, two-point contact can be achieved at all times, similar to the ball screw 11 shown in Figure 4. Note that the Gothic arch expansion groove 13a' only needs to be further away from the ball 14 than the flank surface 13a2 on the unloaded side of the nut 13 shown by the dashed line, and does not have to be a circular arc groove. Alternatively, instead of forming the screw groove 13a of the nut 13 as a Gothic arch expansion groove 13a', the screw groove 12a of the screw shaft 12 may be formed as a Gothic arch expansion groove.

[0052] Figure 14 shows an example in which relief grooves 15 and 16 are added to the bottom of the screw grooves 12a and 13a of the screw shaft 12 and nut 13. The relief grooves 15 and 16 are formed during rough machining (cutting). By forming the relief grooves 15 and 16, the top of the grinding wheel can be avoided by not touching the bottom of the screw grooves 12a and 13a during finishing (grinding), and the top of the grinding wheel can be moved away from the bottom of the screw grooves 12a and 13a. This improves the machining accuracy of the screw grooves 12a and 13a and reduces grinding costs.

[0053] The method for calculating the indentation displacement ε is described below. The following calculation method is known for calculating the indentation displacement ε.

[0054] Figure 15 shows the positions of the ball center and the center of curvature of the screw groove of the screw shaft 12 and nut 13 when the ball screw 11 is operated in the forward and reverse directions, respectively. Figure 15(a) shows the case when the ball screw is operated in the forward direction (forward feed), and Figure 15(b) shows the case when the ball screw is operated in the reverse direction (backward feed).

[0055] C ＭＷ , C Ｍ０ , and C ＭＳ This is the fixed position of the center of the thread groove curvature on the load-side flank surface 13a1 of the nut 13. ０ This is the initial position of the ball's center. Ｂ０ This is the initial position of the center of the screw groove curvature on the load-side flank surface 12a1 of the screw shaft 12. Ｓ This is the resting position of the ball's center when no indentation occurs. ＢＳ This is the resting position of the center of the screw groove curvature of the screw shaft 12 when no cutting occurs. Ｗ and C ＢＷ This is the final position when the food infeeding is saturated.

[0056] When the ball 14 is in contact with the screw grooves 12a and 13a of the screw shaft 12 and nut 13 with zero load, the distance between the centers of curvature of the screw grooves of the screw shaft 12 and nut 13 is the distance from the center of the ball m ０ and screw groove curvature center C Ｂ０ and C Ｍ０ distance λ between ｂ Therefore, the distance between the centers of the screw grooves of the screw shaft 12 and the nut 13 is given by equation (5). Here, f ｐ represents the thread groove fitment, and Da represents the ball diameter.

[0057] When an axial load is applied to a stationary ball screw 11, the ball center m Ｓ Since the ball load lies on the line of action, the distance between the centers of curvature of the screw grooves increases by the amount of contact deformation in the screw grooves 12a and 13a of the screw shaft 12 and the nut 13. However, when a biting phenomenon occurs in the ball screw 11, the contact angles of the screw shaft 12 and the nut 13 change, causing a discontinuity in the line of action of the ball load. In Figures 15(a) and 15(b), if we assume that the center of curvature of the screw groove of the nut 13 is fixed, the center of curvature of the screw groove of the screw shaft 12 moves only horizontally relative to the fixed center of curvature of the screw groove of the nut 13. Furthermore, at this time, the ball center moves due to the difference in contact angles between the screw shaft 12 and the nut 13. If the biting of the balls 14 in the ball screw 11 under axial load occurs uniformly, then for all loaded balls 14, the center of curvature of the screw groove of the fixed nut 13 C ＭＷ And the ball center m when the penetration is saturated Ｗ The distance to is given by the following equation. Similarly, the center of curvature C of the screw groove of the screw shaft 12 ＢＷ and the center of the ball m Ｗ The equation is as follows: Here, δ ＢＷ , δ ＭＷ These represent the normal elastic deformation amounts at the contact between the ball 14 and the screw shaft 12 and the nut 13, respectively.

[0058] Horizontal relative displacement δ between the screw shaft 12 and the nut 13 ｈｓ +δ ｈｗ Using this method, the center of curvature of the screw groove where the nut 12 is fixed is C in all load balls 14. ＭＷ The center of curvature C of the screw groove of the screw shaft 12 ＢＷ The horizontal distance between them is expressed by the following formula. Here, H ０ This is the horizontal groove curvature center C when there is no load. Ｂ０ and C Ｍ０ The distance between, HＳ is the horizontal screw groove curvature center C when the stationary ball 14 is under axial load ＢＳ and C ＭＳ the distance between, α ０ respectively represent the initial contact angles. In Equation (8), the axial displacement δ of the ball screw 11 when the indentation is saturated ａＳ +δ ａＷ Using, the horizontal screw groove curvature center distance H Ｗ is expressed as follows. Here, γ ｍ represents the lead angle. Further, the vertical screw groove curvature center distance V Ｗ is as follows.

[0059] Next, when under axial load, for the distance between the ball center m of the stationary ball screw 11 Ｓ and the ball center M of the ball screw 11 with saturated indentation Ｗ Regarding the vertical and horizontal distances as ε Ｖ , ε ｈ respectively, the vertical distance between the fixed screw groove curvature center C of the nut 13 ＭＷ and the ball center m Ｗ is obtained as follows. O ＶＷ = O ＶＳ + ε Ｖ …(11) Similarly, the horizontal distance is as follows. O ｈＷ = O ｈＳ + ε ｈ …(12)

[0060] Therefore, the displacement of the ball center caused by indentation is expressed by the following equation.

[0061] From the geometric relationships in FIGS. 15(a) and 15(b), the following equation is obtained.

[0062] [[ID=​​

[0063] When the ball screw 11 is operating in the forward and reverse directions, the ball loads for all the load balls 14, viewed in a cross section perpendicular to the screw groove, are as shown in Figures 6 and 7, respectively. According to Hertz theory, the relationship between the ball load in the normal direction and the contact elastic deformation in the normal direction is expressed as follows.

[0064] In Figures 6 and 7, the equilibrium of ball loads in the vertical and horizontal directions is as follows. Furthermore, if we assume that the axial load Fa acting on the screw shaft 12 is equal to the sum of the axial components of the ball load for Z load balls, then the following equation can be derived. Here, μ represents the coefficient of sliding friction between the ball 14 and the screw groove 12a of the screw shaft 12.

[0065] Substituting equations (14) through (17), and equations (20) and (21) into equations (22) through (24), we obtain the following: However, in equations (22) to (27), the up and down signs indicate the case where the ball screw is operating in the forward direction or the reverse direction, respectively.

[0066] Based on the above, δ in the ball screw 11 ａＷ , ε Ｖ , ε ｈ , δ ＢＷ , and δ ＭＷ The solution can be obtained by solving equations (18) and (19), and equations (25) through (27) simultaneously. Furthermore, the Newton-Raphson method is a reasonable approach for numerical analysis of nonlinear systems of linear equations.

[0067] Furthermore, the axial displacement δ between the screw shaft 12 and the nut 13 in a ball screw 11 that is stationary and subjected to an axial load Fa is... ａＳ It can be obtained by the following equation. Here, V Ｓ and H Ｓ It can be expressed as follows:

[0068] A prototype ball screw with the specifications shown in Table 1 was fabricated. Ｂ / Da and δ ｓ / Da is within the range indicated by the shaded area in Figure 11. The friction torque of the ball screw in the test product and the existing ball screw were varied by changing the shift amount, thereby changing the preload Fa from 0%Ca to 30%Ca. The ball screw in the test product is the ball screw with the specifications shown in Table 1. The ball screw in the test product is the same model as the existing ball screw, and its screw shaft outer diameter, lead, ball diameter, and contact angle α are the same as the existing ball screw. The friction torque of the ball screw in the test product and the existing ball screw were measured when the preload Fa was changed. As shown in Figure 16, the friction torque of the ball screw in the test product was reduced by approximately 50% compared to the existing ball screw. This is because two-point contact was always achieved, and there was no third-point contact.

[0069] This specification is based on Japanese Patent Application No. 2024-192232, filed on 31 October 2024, and Japanese Patent Application No. 2025-181025, filed on 27 October 2025. All of this content is included herein.

[0070] 11...Ball screw 12...Screw shaft 12a...Screw groove of screw shaft 12a1...Frank surface on the load side 12a2...Frank surface on the unloaded side 13...Nut 13a...Screw groove of nut 13a1...Frank surface on the load side 13a2...Frank surface on the unloaded side 14...Ball 21...Virtual ball

Claims

1. A ball screw comprising a screw shaft, a nut, and a plurality of balls disposed between the screw groove of the screw shaft and the screw groove of the nut, wherein the ball screw is preloaded, the screw groove of the nut and the screw groove of the screw shaft are each formed as a Gothic arch groove having two flank surfaces, the preload causes the balls to make two-point contact with the load-side flank surface of the screw groove of the nut and the load-side flank surface of the screw groove of the screw shaft, the screw groove of the nut is formed so that when the balls move toward the unload-side flank surface of the nut in a direction perpendicular to the direction of revolution during forward operation, they do not come into contact with the unload-side flank surface of the nut, and the screw groove of the screw shaft is formed so that when the balls move toward the unload-side flank surface of the screw shaft in a direction perpendicular to the direction of revolution during reverse operation, they do not come into contact with the unload-side flank surface of the screw shaft.

2. The ball screw according to claim 1, characterized in that the thread groove of the nut and the thread groove of the screw shaft satisfy equations (1) and (2). 0 < C Ｂ / Da<0.1...(1) 0.01<δ ｓ / Da...(2) Here, Da is the diameter of the ball, C Ｂ δ is the distance between the centers of the Gothic arch grooves. ｓ This is the shift amount.

3. The ball screw according to claim 2, characterized in that the thread groove of the nut and the thread groove of the screw shaft satisfy formula (3). Here, α is the contact angle and r is the groove radius of the Gothic arch groove.

4. The ball screw according to claim 1 or 2, characterized in that the nut is a single nut and the ball screw is subjected to an offset preload.

5. The ball screw according to claim 2 or 3, characterized in that the thread groove of the nut and the thread groove of the screw shaft satisfy formula (4). 0.04 < δ ｓ / Da...(4) 6. The ball screw according to claim 5, characterized in that the groove r ratio, assuming no nut clearance, is greater than 0.50 and less than 0.

54. Here, the groove r ratio, assuming no nut clearance, is r / Da ０ It is represented as follows: r is the groove radius of the Gothic arch groove, and Da ０ This is the ball diameter of a virtual ball that makes four-point contact with the screw groove of the screw shaft and the screw groove of the nut, with their phases aligned.

7. The ball screw according to claim 1 or 2, wherein the groove r ratio when assuming no nut clearance is more than 0.50 and less than 0.

52. Here, the groove r ratio when assuming no nut clearance is r / Da ０ which is represented by. r is the groove radius of the Gothic arch groove, and Da ０ is the ball diameter of the virtual ball that makes four-point contact with the thread groove of the screw shaft with the same phase and the thread groove of the nut.

8. A ball screw comprising a screw shaft, a nut, and a plurality of balls disposed between the screw groove of the screw shaft and the screw groove of the nut, wherein the ball screw is preloaded, and either the screw groove of the screw shaft or the screw groove of the nut is formed as a Gothic arch groove having two flank surfaces, and the other screw groove of the screw shaft or the screw groove of the nut is formed as an expanded Gothic arch groove having two flank surfaces, and the preload causes the balls to make two-point contact with the load-side flank surface of the screw groove of the nut and the load-side flank surface of the screw groove of the screw shaft, and the screw groove of the nut is formed such that, when the balls move toward the unload-side flank surface of the nut in a direction perpendicular to the orbital direction during forward operation, they do not come into contact with the unload-side flank surface of the nut. The screw groove of the screw shaft is formed so that, even when the ball bites into and moves toward the unloaded flank surface of the screw shaft in a direction perpendicular to the orbital direction during reverse operation, it does not come into contact with the unloaded flank surface of the screw shaft.

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