Ball screw designing method and ball screw

Abstract

Provided are a ball screw designing method and a ball screw capable of ensuring smooth movement of balls and of accommodating an increase in speed. This ball screw designing method involves, in a case where a straight line exists between two curves having equal radii as the center line of a circulation path, setting the value of L so as to satisfy formulae (1) and (2) where Da represents the ball diameter, L represents the length of the straight line between the two curves, θb represents the ball pitch angle on the curves, θr represents the center angle of the curves, and the angle ratio of the curves is defined as θr / θb, when (A) θr / θb ≈ n+0.25 (n is an arbitrarily-defined integer) is satisfied or (B) θr / θb ≈ n+0.25 is not satisfied.　(1): L / Da+θr / θb ≈ n+ 0.5 (n is an integer) (2): L ≈ (n+0.5-(θr / θb))×Da

Description

Ball screw design method and ball screw

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

[0002] A ball screw is a device that includes a nut with a female screw groove formed on its inner peripheral surface, a screw shaft with a male screw groove formed on its outer peripheral surface, balls arranged in a rolling path formed by the female screw groove of the nut and the male screw groove of the screw shaft, and a circulation path that returns the balls from the end point of the raceway to the start point, and the nut moves relative to the screw shaft as the balls roll in the rolling path. A return tube type is sometimes used as the circulation path for ball screws because of its advantages such as ease of assembly.

[0003] Patent Document 1 discloses an example of a return tube type ball screw. In this ball screw, the tip end of the return tube, which serves as a circulation component, is composed of an end face along a baseline perpendicular to the tube axis and a tongue that protrudes like a tongue from the baseline. The tongue protrudes into the raceway and functions to scoop up balls from the raceway into the return tube.

[0004] Japanese Patent Application Publication No. 2003-329099

[0005] When spheres are lined up and moved along a curved path formed by a groove, cylinder, or the like, such as a return tube, a phenomenon occurs in which the total length of the sphere train varies depending on the position of the spheres along the curved path. For example, even if the same spheres SP are loaded along the same curved path CP, as shown in Figures 1 and 2, if the position of the spheres SP relative to the curved path CP is different, the total length L0 of the sphere train (the distance between the leading and trailing ends of the sphere train in the direction of travel of a sphere train consisting of multiple spheres SP) will vary slightly. This is because when the straight line N connecting the centers of adjacent spheres SP deviates from the center line C of the curved path CP and takes a shortcut, the amount of shortcut varies depending on the position of the spheres SP.

[0006] In other words, as the train of spheres passes through the curved path CP, its total length L0 expands and contracts. Here, if the train of spheres is relatively short, this phenomenon does not pose any particular problem. However, if an infinite train of spheres passes through the curved path CP, the spheres SP in front of and behind the sphere SP in the direction of travel will act as resistance, so the total length L0 will remain almost constant, and instead the spheres SP themselves will elastically deform to cancel out the expansion. In this case, the spheres SP will push against each other, which can cause a problem of preventing smooth passage through the curved path CP. However, because the amount of expansion and contraction of the total length of the train of spheres varies depending on the radius of curvature of the curved path CP and the length of the curve, if the curve shape that reduces the amount of expansion and contraction is identified, smooth passage of the spheres SP can be achieved by taking into account the geometric dimensions of each part.

[0007] When the row of spheres expands or contracts, the amount of spheres SP that enter the entrance and the amount that come out at the exit of the curved path CP will differ by the amount of expansion or contraction. Here, this phenomenon is called "entrance and exit fluctuation," and the amount of expansion or contraction is called "entrance and exit fluctuation amount." If this entrance and exit fluctuation is large, it may cause the ball screws to compete with each other, hindering the speed increase of the ball screws.

[0008] 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 design method and a ball screw that can ensure smooth ball movement and accommodate higher speeds.

[0009] The ball screw of the present invention comprises: a screw shaft having an outer peripheral spiral groove; a nut having an inner peripheral spiral groove; a plurality of balls housed in a rolling path formed by the opposing outer peripheral spiral groove and inner peripheral spiral groove; and a circulation part that returns the balls from one end of the rolling path to the other end, wherein the center line of the circulation path in the circulation part is constituted by a curve of a single radius and straight lines connected before and after the curve, wherein the ball diameter is Da, the length of the straight line between the two curves is L, the ball pitch angle on the curve is θb, and the central angle of the curve is θr, the angle ratio of the curve is defined as θr / θb, and (A) θr / θb ≈ n + 0.25 (n is an arbitrary integer), or (B) when θr / θb is not ≈ n + 0.25, the value of L is set so as to satisfy the following formulas (1) and (2). L / Da+θr / θb≒n+0.5 (n is an integer) (1) L≒(n+0.5-(θr / θb))×Da (2)

[0010] According to the present invention, it is possible to provide a ball screw design method and a ball screw that can ensure smooth ball movement and accommodate higher speeds.

[0011] FIG. 1 is a schematic diagram showing a sphere passing through a curved path. FIG. 2 is a schematic diagram showing a sphere passing through a curved path. FIG. 3 is a plan view showing the configuration of a ball screw according to an embodiment of the present invention. FIG. 4 is a diagram showing the configuration of a ball screw, where (a) is a partial cross-sectional view as viewed from the axial direction and (b) is a partial cross-sectional view as viewed from the side. FIG. 5 is a graph showing the change in the overall length of a row of spheres passing through a portion of a circulating part. FIG. 6 is a schematic diagram showing the center line of a path connecting a curved portion and a straight portion. FIG. 7 is a schematic diagram showing balls passing in a line along a curved portion. FIG. 8 is a graph showing the amount of ingress / egress fluctuation on the vertical axis and (central angle θr / pitch angle θb) on the horizontal axis under the condition that the central angle θr is constant. FIG. 9 is a graph showing the amount of ingress / egress fluctuation on the vertical axis and (central angle θr / pitch angle θb) on the horizontal axis under the condition that the pitch angle θb is constant. FIG. 10 is a graph showing the change in the total length of a ball train, with the vertical axis representing the change in total length and the horizontal axis representing (ball movement distance / ball diameter). FIG. 11 is a schematic diagram showing balls passing through a circulation path in a circulating component. FIG. 12 is a graph showing the change in the total length of a ball train, with the vertical axis representing the change in total length and the horizontal axis representing (ball movement distance / ball diameter). FIG. 13 is a schematic diagram showing a bend in two straight lines sandwiching a curve. FIG. 14 is a graph showing the bend angle on the vertical axis and the ball diameter on the horizontal axis. FIG. 15 is a graph showing the change in the total length of a ball train, with the vertical axis representing the change in total length and the horizontal axis representing (ball movement distance / ball diameter). FIG. 16 is a schematic diagram showing an example of a circulation path having two curved sections and three straight sections connected to the curved sections. FIG. 17 is a schematic diagram showing an example of a circulation path having two bends, two curved portions, and three straight portions connected to the curved portions.

[0012] Hereinafter, an embodiment of a ball screw according to the present invention will be described with reference to the drawings. Fig. 3 is a plan view showing the configuration of a certain aspect of the ball screw. Fig. 4 is a view showing the configuration of a certain aspect of the ball screw, where (a) is a partial cross-sectional view as seen from the axial direction, and (b) is a partial cross-sectional view as seen from the side.

[0013] 3 and 4 , the ball screw 1 of this embodiment includes a screw shaft 10 having a spiral groove (outer spiral groove) 11 formed on its outer peripheral surface, a nut 20 having a spiral groove (inner spiral groove) 24 formed on its inner peripheral surface, balls SP as rolling elements, and a circulation part 30 which is a U-shaped return tube. The circulation part 30 is fixed to the nut 20 by an attachment part 40. The balls are arranged to be able to roll in a raceway formed by the spiral groove 11 of the screw shaft 10 and the spiral groove 24 of the nut 20, and in a circulation path formed by the circulation part 30.

[0014] 3 and 4, a portion of the outer periphery of the nut 20 is formed as a recess 21, the bottom of which forms an outer flat surface 22 to which the circulation component 30 is attached. A pair of through holes (circulation holes) 23, 23 are formed in the outer flat surface 22 of the nut 20.

[0015] The circulation component 30 comprises a main body 31 machined from a metal (stainless steel, brass, carbon, etc.) and a pair of legs 32 attached to both ends of the main body 31. The circulation component 30 is formed by bending a long cylindrical body into a U-shape, and the ends of the two legs 32, 32 are connected to both ends of the main body 31, which is formed by cutting a short cylindrical body.

[0016] When installing the circulation part 30 in the through hole 23 provided in the outer flat surface 22 of the nut 20, the leg 32 inserted into the through hole 23 is inserted in a direction intersecting the axial direction of the nut 20 relative to the through hole 23, and in this state the circulation part 30 is fixed to the nut 20 by the mounting part 40.

[0017] Furthermore, a tongue portion 32c is formed at the tip 32b of the leg portion 32 for scooping up a spherical ball SP in the tangential direction.

[0018] 3 and 4, when the nut 20 and the screw shaft 10 move relative to each other, the ball SP moves within the rolling path, rotates around the screw shaft 10 multiple times, and reaches the end point of the rolling path (the intersection of the rolling path and the circulation path), where it is scooped up into the circulation part 30 from one end (opening) of the circulation part 30 via the tongue portion 32c. Furthermore, the ball SP that has passed through the circulation part 30 is returned into the rolling path by the tongue portion 32c on the opposite side.

[0019] (Ball screw design method) Figure 5 is a diagram showing the change in the overall length of a row of balls passing through a portion of the circulating component 30, with the vertical axis representing the change in overall length and the horizontal axis representing (ball movement distance / ball diameter). In the change in overall length, when a ball moves by its diameter, it returns to its original length. Because this is repeated periodically, only the period during which it moves by the diameter is considered. By determining the change in overall length as shown in Figure 5, the difference Δ between its maximum and minimum values ​​can be calculated. If this difference Δ is large, the overall length of the row of balls will change significantly. Here, this difference Δ is referred to as the "in / out fluctuation amount." By suppressing the in / out fluctuation amount, it is possible to suppress balls fighting, etc.

[0020] Below, we consider a method for suppressing inflow and outflow fluctuations in the circulation path, which can be used as an example of a ball screw design method. The circulation path of the circulation part 30, which is the return tube, is often composed of single-radius curves, straight lines, and bends. For example, the circulation path of the circulation part 30 is composed of two bends, a curved line, and three straight lines. Furthermore, a ball screw with a tangential scooping method has no bends and is composed only of multiple curved lines and straight lines.

[0021] Such fluctuations in the flow of circulating parts 30 occur at curved and bent sections. As a result of extensive research, the inventors have derived a method for reducing the path fluctuations throughout the entire circulation path by calculating the path fluctuations that occur at these two sections. This method is described below.

[0022] First, we model a path consisting of a single-radius curved section and straight sections connected to both ends of the curved section. Here, we assume that the center line of the circulation path within the circulating part is composed of a single-radius curved section and straight sections connected before and after the curved section. Figure 6 shows the center line CL of the path connecting the curved section and the straight section. We then determine the characteristics of the inflow and outflow fluctuations that occur in the train of balls passing through this path.

[0023] In Fig. 6, the radius of the curved portion of the center line CL is R, the central angle is θr, and the length of the straight portion is Da, which is equal to the ball diameter. Also in Fig. 7, the pitch angle of adjacent balls SP lined up on the curved portion is θb. Fig. 8 shows the amount of in-out fluctuation when the radius R is changed while the central angle θr is constant, and Fig. 9 shows the amount of in-out fluctuation when the central angle θr is changed while the radius R is constant. Here, θr / θb is called the angle ratio.

[0024] 8 and 9, it is clear that in both cases the minimum value is reached when θr / θb = n + 0.25. From this result, it can be inferred that no matter what the value of the curve radius R or central angle θr, the amount of inflow and outflow fluctuation will be small if θr / θb is near n + 0.25 (n is an arbitrary integer) (i.e., θr / θb ≈ n + 0.25 (n is an arbitrary integer)).

[0025] However, there are cases where θr / θb = n + 0.25 cannot be achieved due to limitations on the dimensions of each part of the ball screw, etc. In such cases, a method can be applied to cancel out the two in-and-out fluctuations. This method will be explained below. If the amount of change in the total length of the row of balls passing through the path shown in Figure 6 is not near θr / θb = n + 0.25, it will have a waveform as shown in Figure 10, with one cycle being the movement of the diameter of the ball.

[0026] Normally, the circulation path within the circulable part 30 has a symmetrical shape, so there are two curves CV of the same shape on the center line of the circulation path, as shown in Figure 11. Therefore, if the phases of the changes in the total length of the ball row on the two curves CV are opposite, the changes will cancel each other out, and the overall amount of inflow and outflow fluctuation can be reduced. To achieve this, as shown in Figure 11, the positions of the balls SP at the entrances E of the two curves CV must be offset by half the ball diameter. Here, the entrance E of the curves CV is the tip of the curve on the side where the balls SP enter the circulable part 30.

[0027] For the above condition to be met, the length of the straight line LN between the two curves CV is L, the ball pitch angle on the curve CV (the angle formed by the line from the center of the curve CV to the center of the two balls SP when adjacent balls SP are in contact with each other without any gaps on the curve) is θb, and the angle of the curve CV is θr. Therefore, the value of L is set so that the following equations (1) and (2) are met. Note that throughout this specification, "≒" means that the difference between the value on the left side and the value on the right side is within ±10%. L / Da + θr / θb ≒ n + 0.5 (n is an integer) (1) L ≒ (n + 0.5 - (θr / θb)) × Da (2)

[0028] If another free curve (including a straight line with an infinite radius of curvature) exists between two curves CV, the free curve between the curves CV is approximated by a plurality of infinitesimal curves, the total length of the infinitesimal curves is defined as L, the angle ratio of each infinitesimal curve is defined as θri / θbi, and formula (2) is replaced with formula (3) below: L ≒ (n + 0.5 - (θr / θb) - Σ (θri / θbi)) × Da (i = 1, 2, 3, ...) (3)

[0029] On the other hand, for the curve near θr / θb=n+0.25, the waveform has a period of 0.5 equal to the ball diameter, as shown in Figure 12. Therefore, if the number of balls between the first curve CV and the straight line LN is n±0.25, the change in the total length can be cancelled out. In other words, it can be seen that it is sufficient to satisfy equation (4). L ≒ (n+0.25-(θr / θb)-Σ(θri / θbi)) × Da (i=1, 2, 3...) (4)

[0030] Next, consider the inward / outward fluctuation at the bend of the two straight lines LN that sandwich the curve. If the bend angle is the crossing angle θ of the two straight lines LN as shown in Figure 13, the inward / outward fluctuation amount changes depending on the crossing angle θ and the ball diameter Da. The smaller the ball diameter Da and the crossing angle θ, the smaller the fluctuation amount.

[0031] 14 is a graph showing the results of calculating the combination of the crossing angle θ and the ball diameter Da when the amount of inward / outward fluctuation is 0.05 mm and 0.1 mm. From FIG. 14, it can be seen that in order to keep the amount of inward / outward fluctuation to 0.05 mm or less, the following formula (5) should be satisfied: θ≦36.55 Da －０．５１ (5)

[0032] The change in the total length of the ball train at a bent portion also forms a waveform with one cycle being the movement of one ball diameter, as shown in Figure 15. To cancel out the change in the total length of the ball train in a path with two bent portions, it is necessary to set the number of balls between the bent portions to (n + 0.5).

[0033] That is, the length of the straight line between the two bent portions is defined as L, and the curves are defined as θri and θbi as described above, so that the following equation (6) is satisfied: L ≈ (n + 0.5 - Σ (θri / θbi)) × Da (i = 1, 2, 3, ...) (6)

[0034] Since the change in the overall length of the path of the bent portion is mountain-shaped as shown in Figure 15, even if the phases are opposite, the amount of inward / outward fluctuation is only 1 / 2. Therefore, in order to limit the amount of inward / outward fluctuation of two bent portions to 0.05 mm or less as a guideline, the amount of inward / outward fluctuation of one bent portion must be 0.1 mm or less. In that case, the crossing angle θ from Figure 10 must satisfy the following equation (7): θ≦50.25 × Da- ０．４９ (7)

[0035] The present invention can be applied to ball screws having a circulation path (for example, a return tube type, an end deflector type, an end cap type, etc.) that is made up of a single-radius curve, a straight line, and a bent section.

[0036] In particular, the ball screws having return tube-type circulation paths shown in Figures 3 and 4 have two curved portions CV and three straight portions LN connected to the curved portions CV on the center line of the circulation path as shown in Figure 16, or have two bent portions FL, two curved portions CV, and a straight portion LN connecting the bent portions FL and the curved portions CV, and a straight portion LN connecting the curved portions CV together on the center line of the circulation path as shown in Figure 17. In the example of Figure 17, the circulation path is set so that the bent portion FL and the two curved portions CV satisfy equations (2) and (6), respectively.

[0037] The method of reducing the in-and-out fluctuation of the present invention is even more effective when retainer pieces are inserted between the balls. In a normal ball screw, when the balls are fully loaded, several balls are removed to ensure a gap. In contrast, when retainer pieces are inserted, the balls are adjusted to a nearly fully loaded state so that no large gaps are formed between them, in order to prevent the pieces from falling out.

[0038] In such a case, if there is a movement fluctuation in and out of the ball row when the ball row is tightly packed with no gaps, the balls will push against each other when the ball row tries to extend, causing a deterioration in the operation of the ball screw. Therefore, the present invention is particularly effective when a retainer piece is used or when the balls are nearly fully loaded (when a maximum of m balls can be loaded in one circuit, a state in which (m-1) balls are loaded in that circuit).

[0039] Furthermore, in ball screws, where balls are packed tightly together in localized areas with no gaps and compete with each other, a condition known as clogging, is likely to occur, and balls are also packed tightly in the circulation path, so they are similarly greatly affected by fluctuations in ball movement.

[0040] For example, ball screws with 90 to 100 balls per circuit consisting of a rolling path and a circulation path, or double-start ball screws with a lead equal to twice the pitch, are known to be prone to clogging. Generally, the cross section of the nut is uneven where the circulation path is formed, making it prone to deformation due to heat treatment and other factors. Double-start ball screws have two circulation paths, which means they are prone to greater deformation, making them more susceptible to ball clogging.

[0041] If the circulating part is made of metal, it is difficult for the deformation of the circulating part to absorb the change in the ball row due to the fluctuation in the ball movement, so it can be said that it is also susceptible to the influence of the fluctuation in the ball movement.Also, even if the circulating part is made of resin, if the entire surface is covered with metal, it is similarly susceptible to the influence of the fluctuation in the ball movement.

[0042] Furthermore, when the friction torque due to the preload is small, the torque fluctuation due to the fluctuation in the movement in and out can be more pronounced. Therefore, the effect of the present invention can be more effectively exhibited in the case of a ball screw with a small lead or a small preload.

[0043] Furthermore, in the case of a ball screw with a tangential scooping system, the amount of movement fluctuation can be minimized because there are no bending points in the tangential scooping system.

[0044] The present invention is not limited to the above-described embodiments. Any of the components of the above-described embodiments can be modified within the scope of the present invention. Furthermore, any of the components can be added or omitted from the above-described embodiments.

[0045] This application is based on a Japanese patent application (Patent Application No. 2024-025753) filed on February 22, 2024, the contents of which are incorporated herein by reference.

[0046] REFERENCE SIGNS LIST 1 ball screw 10 screw shaft 11 spiral groove of screw shaft (outer peripheral spiral groove) 20 nut 21 recess 22 outer flat surface 23 through hole (circulation hole) 24 spiral groove of nut (inner peripheral spiral groove) 30 circulation part 31 main body 32 leg 40 attachment part

Claims

1. A design method for a ball screw comprising: a screw shaft having an outer peripheral spiral groove; a nut having an inner peripheral spiral groove; a plurality of balls housed in a rolling path formed by the opposing outer peripheral spiral groove and inner peripheral spiral groove; and a circulation part that returns the balls from one end of the rolling path to the other, wherein the center line of the circulation path in the circulation part is composed of a curved line with a single radius and straight lines connected before and after the curved line, wherein: Da is the ball diameter, L is the length of the straight line between the two curved lines, θb is the ball pitch angle on the curved line, and θr is the central angle of the curved line; and the angle ratio of the curved line is defined as θr / θb, (A) θr / θb ≒ n + 0.25 (n is an arbitrary integer), or (B) when θr / θb ≒ n + 0.25 is not true, the value of L is set so as to satisfy the following equations (1) and (2): L / Da + θr / θb ≒ n + 0.5 (n is an integer). (1) A method for designing a ball screw, characterized in that: L≈(n+0.5−(θr / θb))×Da (2).

2. When a free curve exists between two of the curves with the same radius, the free curve is approximated by a plurality of infinitesimal curves, the total length of the infinitesimal curves is defined as L, the angle ratio of each infinitesimal curve is defined as θri / θbi, and the value of L is set using equation (3) instead of equation (2): L ≒ (n + 0.5 - (θr / θb) - Σ (θri / θbi)) × Da (i = 1, 2, 3...) (3) A design method for a ball screw as set forth in claim 1, characterized in that 3. When θr / θb≈n+0.25 and a free curve exists between the two curves of equal radius, the free curve is approximated by a plurality of infinitesimal curves, the total length of the infinitesimal curves is defined as L, the angle ratio of each infinitesimal curve is defined as θri / θbi, and the value of L is set so as to satisfy equation (4): L≈(n+0.25-(θr / θb)-Σ(θri / θbi))×Da(i=1, 2, 3,...) (4) The design method for a ball screw as set forth in claim 1, characterized in that 4. A ball screw designed by the ball screw design method described in any one of claims 1 to 3, characterized in that, when a maximum of m balls can be packed into one circuit consisting of the rolling path and the circulation path, (m-1) balls are packed into said circuit.

5. A ball screw designed by the ball screw design method described in any one of claims 1 to 3, characterized in that the number of balls filled in one circuit consisting of the circulation path and the rolling path is 90 or more.

6. A ball screw designed by the ball screw design method according to any one of claims 1 to 3, characterized in that the ball screw is a double-start ball screw.

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