TWI568955B - Ball screw - Google Patents

Description

Ball screw

The present invention relates to a ball screw having a reciprocating member having a tongue (a component forming a ball return passage).

The ball screw has a screw shaft, a nut and a plurality of balls. The screw shaft extends through the nut, and a spiral groove formed on a peripheral surface of the screw shaft and a spiral groove formed on an inner peripheral surface of the nut form a raceway in which the ball rolls under load. The nut has a ball return passage in which the ball returns from the end of the raceway to the starting point. The balls are disposed in a circulation path formed by the raceway and the ball return passage. The nut is relatively moved with the screw shaft through the ball that is circulated in the circulation path.

As a component (recycling component) that forms a ball return passage, a component (a metal return pipe and a display ball) that is used for inserting a leg into a hole penetrating from the outer peripheral surface of the nut to the inner peripheral surface can be exemplified. The synthetic resin-made circulating component formed by the two divided bodies of the line-dividing in the moving direction) is an end deflector that communicates with the hole passing through the axial direction of the nut.

These components have the ball drawn from the raceway to the end of the raceway The ball return path and guide the ball from the ball return path to the tongue for the raceway at the starting point. In the state in which the components are mounted, the end faces of the tongues are at least opposed to the spiral grooves of the shaft. That is, the end face of the tongue has a spiral groove of the screw shaft and a groove bottom opposing line at the deepest position (hereinafter referred to as "slot bottom").

A conventional example of a ball screw having a metal return pipe is shown in Fig. 5. This figure is a partial cross-sectional view of a portion of the return pipe 40 in which the ball screw is disposed, along the screw shaft 1 and the spiral grooves 11, 21 of the nut 2 (the rolling path 31 of the ball 3). A flat portion 2a is formed on the outer peripheral surface of the nut 2, and a through hole 22 penetrating from the flat portion 2a to the inner peripheral surface is formed.

The front end of the leg portion of the return pipe 40 is in the range of more than half of the direction around the circle of the pipe cross section, and is an end face 410 along the bottom line perpendicular to the pipe axis direction, and the other portion is a tongue projecting from the bottom line in a tongue shape. 420. The leg portion of the return pipe 40 is inserted into the through hole 22 of the nut 2, and the tongue piece 420 is disposed in the rolling path 31 such that the end face M of the tongue piece 420 faces the spiral groove 11 of the screw shaft 1. The balls 3 in the rolling path 31 collide with the tongue piece 420 to be drawn, and are introduced into the return pipe 40.

In the conventional ball screw shown in Fig. 6, the groove bottom opposite line L of the end surface of the tongue piece 420 is an arc of a circle C10 concentric with the circle of the groove bottom 110 which becomes the screw shaft. In other words, in the conventional ball screw, the gap S between the groove bottom line of the tongue piece 420 and the groove bottom 110 of the screw shaft is the same from the front end side to the base end side of the tongue piece 420.

Furthermore, Fig. 6 is a view showing that the thickness of the return pipe 40 is only thickened and formed. The thickness of the portion of the tongue 420. As can be seen from Fig. 6, in the front end portion (corner portion on the side of the guide ball 3) 420a of the tongue piece 420, the angle formed by the inner peripheral surface of the return passage 40 and the groove bottom line L is an acute angle, and the base end portion is formed. In 420b, the angle formed by the peripheral surface of the return passage 40 and the groove bottom line L is an obtuse angle.

In the above-described method of setting the groove bottom opposing line L, the smaller the gap S is, the longer the curvature radius of the groove bottom relative to the line L is, the longer the tongue piece 420 can be formed, but the front end portion (the acute angle portion) of the tongue piece 420 is formed. The thickness of 420a will become thinner. The larger the gap S is, the larger the radius of curvature of the groove bottom relative to the line L is, so that the front end portion (the acute angle portion) 420a of the tongue piece 420 is thickened, but the length of the tongue piece 420 is shortened when the gap S is increased.

Fig. 7 is a view similar to Fig. 6 showing a case where the gap S is larger than that of Fig. 6.

The longer the tongue 420, the smoother the ball 3 can be toward the ball return passage 45. That is, the method of setting the groove bottom line L of the conventional tongue piece 420 (the method of making the groove bottom opposing line L follow a circle concentric with the circle which becomes the groove bottom of the screw shaft), in order to make the ball 3 smooth It is preferable to set the ball return passage 45 to have a small gap S. However, the larger the gap S, the easier the balls 3 enter the gap S from the tongue 420 toward the ball return passage 45.

On the other hand, when the ball 3 and the tongue 420 collide and the tongue 420 is deformed, it can be seen from the comparison of the sixth (b) and the seventh (b) that the gap S is small (Fig. 6). The front end portion (an acute angle portion) 420a of the tongue piece 420 easily comes into contact with the groove bottom 110. When the gap S is large (7th) In the figure, the tongue piece 420 does not have the excessive tongue deformation, and the front end portion (the acute angle portion) 420a of the tongue piece 420 does not come into contact with the groove bottom 110.

In particular, the cyclic components made of synthetic resin have lower mechanical strength than the metal cyclic components, and therefore the gap S is too small to cause damage to the tongue. Further, even when the gap S is small, the base end portion (obtuse angle portion) of the tongue piece is difficult to contact the groove bottom of the screw shaft when the ball collides with the tongue piece.

Patent Document 1 discloses a ball screw for preventing the damage of the tongue of the circulating component (the component forming the ball return path), and the minimum clearance between the groove bottom of the screw shaft and the tongue is 1% of the diameter of the ball. Within 15% range. The ball screw described in Patent Document 1 is the same as the conventional method, and the groove bottom line of the tongue is also a circle concentric with a circle which is a groove bottom of the screw shaft.

Patent Document 2 discloses a ball screw for suppressing early damage of a tongue by an end diverter, and a circular curvature radius R formed at a tip end portion (an acute angle portion) of the tongue is set to a diameter Dw of the ball. The relationship satisfies R/Dw≧0.015.

[Previous Technical Literature] [Patent Document]

[Patent Document 1] Japanese Patent Laid-Open Publication No. 2007-107613

[Patent Document 2] Japanese Patent Laid-Open Publication No. 2004-278551

[Summary of the Invention]

As described above, in the conventional method of setting the groove bottom line of the tongue (the method of making the groove bottom line follow the circle which is a concentric circle of the groove bottom of the screw shaft), it is impossible to make the ball smoothly flow toward the ball. The front end of the tongue and the tongue are in difficulty in contact with the groove bottom of the screw shaft and the mechanical strength of the front end portion of the tongue is high.

An object of the present invention is to provide a ball screw having a tongue piece having a circulating component (a component forming a ball return path), and by appropriately setting the groove bottom line of the tongue, the ball can be smoothly flowed toward the ball. The front end of the tongue and the tongue are in difficulty in contact with the groove bottom of the screw shaft and the front end portion of the tongue has high mechanical strength.

In order to solve the above problems, the ball screw of the same state of the present invention has the following constituent elements (1) to (4).

(1) It has a screw shaft, a nut and a plurality of balls. The screw shaft extends through the nut, and a spiral groove formed on a peripheral surface of the screw shaft and a spiral groove formed in a peripheral surface of the nut form a rolling path in which the ball rolls under load. The nut includes a ball return passage that returns the ball from the end of the rolling path to the starting point. The balls are disposed in a circulation path formed by the rolling path and the ball return passage. The nut is relatively moved with the screw shaft through the ball that is circulated in the circulation path.

(2) a component forming the above ball return passage has the above ball Draw the tongue into the ball return runner.

(3) The end surface of the tongue piece (at least the surface facing the spiral groove of the screw shaft) is a cross section of the groove bottom at the deepest position of the spiral groove of the screw shaft, and has a circle that passes through the groove bottom and faces the gap The bottom of the groove is opposite to the line.

(4) The groove bottom line is provided such that the gap becomes smaller from the front end side toward the base end side of the tongue piece.

According to the present invention, the ball screw having the cycle piece of the tongue piece can provide both the ball smoothly facing the ball return path, and the front end portion of the tongue piece is difficult to contact with the groove bottom of the screw shaft and the front end portion of the tongue piece has high mechanical strength. Strength ball screw.

1‧‧‧Screw shaft

11‧‧‧Spiral groove of screw shaft

110‧‧‧Slot bottom of the screw shaft (the deepest position of the spiral groove)

2‧‧‧ nuts

2a‧‧‧ Flat part of the outer surface of the nut

21‧‧‧Spiral groove of the nut

22‧‧‧through holes (mounting holes for return pipes)

3‧‧‧ balls

31‧‧‧Rolling track of the ball

4‧‧‧Return pipe (forming the components of the ball return runner)

40‧‧‧Return pipe

4A‧‧‧End steering gear (forming the components of the ball return runner)

4B‧‧‧Recycling components made of synthetic resin (components forming ball return runners)

41‧‧‧ End face of the foot of the return pipe

410‧‧‧End of the foot of the return tube

42‧‧‧Parts forming the components of the ball return runner

42a‧‧‧ front end of the tongue

42b‧‧‧ base end

420‧‧‧ tongues of the return pipe

45‧‧‧Rollback runner

The center of C1‧‧‧ is different from the circle that becomes the bottom of the groove of the screw shaft

C10‧‧‧ center with the same circle as the circle at the bottom of the screw shaft

L‧‧‧The end face of the tongue has a groove bottom line

M‧‧‧ end face of the tongue

S‧‧‧The gap between the groove bottom line and the circle that becomes the groove bottom of the screw shaft

Fig. 1 is a view showing the relationship between the return pipe of the ball screw of the first embodiment, the ball and the deepest position (slot bottom) of the spiral groove of the screw shaft.

Fig. 2 is a cross-sectional view showing the relationship between the tongue of the ball return passage forming component of the ball screw constituting the embodiment and the groove bottom of the screw shaft, and the thickness of the ball return runner forming component is only formed by the tongue. Part is thicker.

Figure 3 is a view showing the end turn of the ball screw constituting the second embodiment. Diagram of the relationship between the deepest position (slot bottom) of the spiral groove of the ball, the ball and the screw shaft.

Fig. 4 is a view showing the relationship between the synthetic resin cycle components, the end diverter, and the deepest position (groove bottom) of the spiral groove of the ball and the screw shaft which constitute the ball screw of the third embodiment.

Fig. 5 is a cross-sectional view showing a conventional example of a ball screw.

Fig. 6 is a view for explaining the relationship between the tongue of the ball returning passage forming member of the ball screw of the conventional example and the groove bottom of the screw shaft, and showing that the thickness of the return pipe is thick only by the portion forming the tongue.

Fig. 7 is a view for explaining the relationship between the tongue forming the ball returning passage of the ball screw of the conventional example and the groove bottom of the screw shaft, and showing that the thickness of the return pipe is thick only by the portion forming the tongue.

Fig. 8 is a view for explaining the gaps Sa, Sb and the test method, showing a section of the ball returning passage forming the tongue of the component and the groove bottom of the screw shaft.

Fig. 9 is a graph showing the relationship between the contact surface pressure ratio and the gap ratio (Sa/Sb).

Hereinafter, the embodiments of the present invention will be described, but the present invention is not limited to the following embodiments.

[First Embodiment]

The ball screw of this embodiment has the same screw shaft 1, nut 2, and ball 3 as the conventional ball screw shown in Fig. 5, and only Fig. 6 The return pipe 40 has a return pipe 4 having a different shape from the end face of the tongue.

As shown in FIGS. 1 and 2, the end surface of the tongue piece 42 of the return pipe 4 has a circle which is the deepest position (slot bottom) 110 of the spiral groove of the screw shaft, and a groove bottom opposing line L where the transmission gap S faces. The groove bottom opposing line L is an arc of a circle C1 having a center different from the circle which becomes the groove bottom 110 of the screw shaft, and as shown in Fig. 2(a), the gap S is provided from the front end portion 42a side of the tongue piece 42. It becomes smaller toward the proximal end portion 42b side. Further, the gap S on the tip end portion 42a side of the tongue piece 42 is set to an appropriate size (a size larger than the base end 42b side but not easily accessible to the balls 3).

Therefore, in the case of the ball screw according to the embodiment, when the ball 3 collides with the tongue piece 42 to deform the tongue piece 42, for example, the state shown in Fig. 2(b) is obtained. That is, compared with the state shown in Figs. 6(b) and 7(b), the groove bottom of the tongue piece 42 on the base end portion (obtuse angle portion) 42b side of the tongue piece 42 is opposite to the groove L of the screw shaft. The distance of the bottom 110 becomes smaller.

Further, since the gap S on the side of the tip end portion (an acute angle portion) 42a of the tongue piece 42 is set to an appropriate size, the ball 3 can be smoothly faced toward the ball return passage 45, and the front end portion 42a of the tongue piece 42 is not easily fitted. The groove bottom 110 of the screw shaft is in contact.

Further, in the case where the tongue piece 42 comes into contact with the groove bottom 110 of the screw shaft, not only the front end portion 42a of the tongue piece 42 but also the base end portion 42b is also in contact, whereby the groove bottom is opposed to the line L and the groove bottom 110 of the screw shaft. Not only is it a little touch, but it is easy to form a line contact. Therefore, compared with the state shown in FIGS. 6(b) and 7(b), the front end of the tongue 42 can be relaxed. 42a stress.

Therefore, the ball screw of this embodiment is appropriately set by the groove bottom line L of the tongue piece 42 of the return pipe 4, and can simultaneously make the ball 3 smoothly face the ball return path 45, and the tip end portion 42a of the tongue piece 42 and The groove bottom 110 of the screw shaft is difficult to contact and the front end portion 42a of the tongue 42 has high mechanical strength.

[Second embodiment]

The ball screw of this embodiment is shown in Fig. 3, and has an end deflector 4A made of synthetic resin as a component formed in the ball return passage 45. The tongue 42 of the end diverter 4A and the groove bottom 110 of the screw shaft have the relationship shown in Fig. 2.

That is, the groove bottom opposing line L of the tongue piece 42 is an arc of a circle C1 different from the center of the groove bottom 110 which becomes the screw shaft, as shown in the second (a) diagram, and the gap S is set from the tongue piece. The front end portion 42a side of the 42 becomes smaller toward the proximal end portion 42b side. Further, the gap S on the tip end portion 42a side of the tongue piece 42 is set to an appropriate size (a size larger than the base end 42b side but not easily accessible to the balls 3).

Therefore, in the case of the ball screw according to the embodiment, when the ball 3 collides with the tongue piece 42 to deform the tongue piece 42, for example, the state shown in Fig. 2(b) is obtained. That is, compared with the state shown in Figs. 6(b) and 7(b), the groove bottom of the tongue piece 42 on the base end portion (obtuse angle portion) 42b side of the tongue piece 42 is opposite to the groove L of the screw shaft. The distance of the bottom 110 becomes smaller.

Further, since the gap S on the side of the tip end portion (an acute angle portion) 42a of the tongue piece 42 is set to an appropriate size, the ball 3 can be smoothly faced toward the ball return passage 45, and the front end portion 42a of the tongue piece 42 is not easily fitted. The groove bottom 110 of the screw shaft is in contact.

Further, in the case where the tongue piece 42 is in contact with the groove bottom 110 of the screw shaft, not only the front end portion 42a of the tongue piece 42 but also the base end portion 42b is also in contact, whereby the groove bottom opposing line L and the groove bottom 110 of the shaft are not only It is a little contact and is easily formed into a line contact. Therefore, the stress generated at the front end portion 42a of the tongue piece 42 can be alleviated as compared with the state shown in Figs. 6(b) and 7(b).

Therefore, the ball screw of this embodiment is appropriately set to the groove bottom opposing line L of the tongue piece 42 of the deflector 4A, and can simultaneously make the ball 3 smoothly face the ball return path 45, and the tip end portion 42a of the tongue piece 42. Contact with the groove bottom 110 of the screw shaft is difficult and the front end portion 42a of the tongue 42 has high mechanical strength.

[Third embodiment]

The ball screw of this embodiment is a component formed on the ball return passage 45 as shown in Fig. 4, and has a cycle member 4B made of synthetic resin. The circulating component 4B made of synthetic resin is composed of a divided body divided into two along a line indicating the direction in which the balls move. Each of the divided bodies is formed by injection molding of a synthetic resin, and is assembled into a circulating component 4B in combination with the divided bodies. The tongue piece 42 of the cycle component 4B and the groove bottom 110 of the screw shaft have the relationship shown in Fig. 2.

That is, the groove bottom opposing line L of the tongue piece 42 is an arc of a circle C1 different from the center of the groove bottom 110 which becomes the screw shaft, as shown in the second (a) diagram, and the gap S is set from the tongue piece. The front end portion 42a side of the 42 becomes smaller toward the proximal end portion 42b side. Further, the gap S on the tip end portion 42a side of the tongue piece 42 is set to an appropriate size (a size larger than the base end 42b side but not easily accessible to the balls 3).

Therefore, in the case of the ball screw according to the embodiment, when the ball 3 collides with the tongue piece 42 to deform the tongue piece 42, for example, the state shown in Fig. 2(b) is obtained. That is, compared with the state shown in Figs. 6(b) and 7(b), the groove bottom of the tongue piece 42 on the base end portion (obtuse angle portion) 42b side of the tongue piece 42 is opposite to the groove L of the screw shaft. The distance of the bottom 110 becomes smaller.

Further, since the gap S on the side of the tip end portion (an acute angle portion) 42a of the tongue piece 42 is set to an appropriate size, the ball 3 can be smoothly faced toward the ball return passage 45, and the front end portion 42a of the tongue piece 42 is not easily fitted. The groove bottom 110 of the screw shaft is in contact.

Further, in the case where the tongue piece 42 is in contact with the groove bottom 110 of the screw shaft, not only the front end portion 42a of the tongue piece 42 but also the base end portion 42b is also in contact, whereby the groove bottom opposing line L and the groove bottom 110 of the shaft are not only It is a little contact and is easily formed into a line contact. Therefore, the stress generated at the front end portion 42a of the tongue piece 42 can be alleviated as compared with the state shown in Figs. 6(b) and 7(b).

Therefore, the ball screw of this embodiment is appropriately set with respect to the groove bottom line L of the tongue piece 42 of the synthetic resin-made circulating component 4B. In addition, the ball 3 can be made to face the ball return path 45 smoothly, and the tip end portion 42a of the tongue piece 42 is difficult to contact with the groove bottom 110 of the screw shaft, and the tip end portion 42a of the tongue piece 42 has high mechanical strength.

That is, according to the method of setting the groove bottom line of the tongue according to each of the above embodiments, the mechanical strength of the tip end portion of the tongue is not reduced, the risk of contact between the screw shaft and the tongue is reduced, and the mobility and acoustic characteristics of the ball screw are improved. .

[Explanation of the action of the ball screw in the same state of the present invention]

In the ball screw of the same state of the present invention, the groove bottom line of the tongue is disposed between the circle formed at the groove bottom which is the deepest position of the spiral groove of the screw shaft which is the groove bottom opposite line of the tongue. The gap) becomes smaller from the front end side of the tongue toward the base end side. Therefore, when the ball collides with the tongue to deform the tongue, the ball screw of the same state is compared with the ball screw in which the gap is opposite to the groove bottom, and the end face of the tongue on the proximal end side of the tongue and the screw shaft The distance from the bottom of the groove becomes smaller.

Therefore, in the same state, the ball screw sets the gap on the front end side of the tongue to an appropriate size (although the base end side is larger, but the ball is less likely to enter), so that the ball can smoothly face the ball return path, and The front end portion of the tongue piece is difficult to contact with the groove bottom of the screw shaft.

Further, in the case of the ball screw of the same state, in the case where the tongue piece comes into contact with the groove bottom of the screw shaft, not only the front end portion of the tongue piece but also the base end portion side may be in contact with each other. Thereby, the groove bottom opposing line and the groove bottom of the screw shaft are not only in contact with each other but are easily formed in a plurality of points of contact or line contact, so that stress generated at the front end portion (an acute angle portion) of the tongue piece can be alleviated.

The ball screw of the same state is a circular arc having a circle different from a circle having a groove bottom at the center of the screw shaft.

Further, when the components forming the ball return passage are made of synthetic resin, the mechanical strength is lower than that of the case of metal, and thus the ball screw of the same state can be applied.

The ball screw of the same state is the distance from the center of the cross-sectional circle of the groove bottom and the farthest point (Sa) of the groove bottom from the groove bottom line with respect to the center of the cross-sectional circle of the groove bottom and from the groove bottom The ratio (Sa/Sb) of the distance (Sb) closest to the groove bottom of the opposite line is preferably in accordance with the following formula (1).

1.2≦Sa/Sb≦2.6...(1)

[for (1) formula]

A plurality of return pipes 4 having different groove bottoms with respect to the line L of the tongue piece 42 are prepared. The tongue piece 42 of the return pipe 4 is a value which is a ratio (Sa/Sb) of the gap Sa and the gap Sb shown in Fig. 8. Fig. 8 is a magnifying glass view corresponding to Fig. 2(a).

The gap Sa is a gap of the front end portion 42a of the tongue piece 42, and is a cross section shown in Fig. 8, which is the distance from the center of the cross-sectional circle of the groove bottom 100 of the screw shaft to the farthest point of the groove bottom 110 of the groove bottom line L. The gap Sb is a gap of the base end portion 42b of the tongue piece 42, and is a cross section shown in Fig. 8, and the center of the cross-sectional circle of the groove bottom 100 is the closest to the groove bottom 110 of the groove bottom line L.

Using the ball screw after assembling each of the return pipes 4, the tongue 42 is The force F shown in Fig. 8 is pressed toward the groove bottom 110 of the screw shaft, and the area A of the contact portion which is formed on the opposite surface of the groove bottom of the tongue piece 42 at this time is calculated. Then, the ratio of the area A when Sa/Sb=1.6 is set to 1 is calculated. This ratio corresponds to the contact area ratio. The relationship between the obtained contact surface pressure ratio and the contact gap ratio Sa/Sb is shown in a graph in FIG.

When the gap ratio (Sa/Sb) satisfies the range of 1.2 or more and 2.6 or less, the contact surface pressure ratio is 1.5 or less, and when the range of 1.3 or more and 2.2 or less is satisfied, the contact surface pressure ratio is 1.4 or less. .

That is, the groove bottom line L of the tongue piece 42 is set such that the gap ratio (Sa/Sb) satisfies the range of 1.2 or more and 2.6 or less, whereby the low contact which is generated when the tongue piece 42 is pressed toward the groove bottom 110 of the screw shaft can be obtained. The surface pressure is pressed, and the front end portion 42a of the tongue piece 42 is less likely to be damaged. The groove bottom line L of the tongue piece 42 is set so that the gap ratio (Sa/Sb) is in the range of 1.3 or more and 2.2 or less, and the effect of not easily damaging the tip end portion 42a of the tongue piece 42 is further increased.

3‧‧‧ balls

4‧‧‧Return pipe (forming the components of the ball return runner)

4A‧‧‧End steering gear (forming the components of the ball return runner)

4B‧‧‧Recycling components made of synthetic resin (components forming ball return runners)

42‧‧‧Parts forming the components of the ball return runner

42a‧‧‧ front end of the tongue

42b‧‧‧ base end

45‧‧‧Rollback runner

110‧‧‧Slot bottom of the screw shaft (the deepest position of the spiral groove)

The center of C1‧‧‧ is different from the circle that becomes the bottom of the groove of the screw shaft

L‧‧‧The end face of the tongue has a groove bottom line

S‧‧‧ gap

Claims (4)

A ball screw having a screw shaft, a nut and a plurality of balls, wherein the screw shaft penetrates the nut, and the spiral groove formed on a peripheral surface of the screw shaft and a spiral groove formed on a peripheral surface of the nut form the above a rolling path in which the ball rolls in a load state, the nut having a ball returning path for returning the ball from an end point of the rolling path to a starting point, wherein the ball is disposed in a circulation path formed by the rolling path and the ball returning path, The component forming the ball return passage has a tongue for drawing the ball into the ball return passage, and an end surface of the tongue is a cross section of a groove bottom at a deepest position of the spiral groove of the screw shaft, and the transmission is the above a groove bottom line opposite to the gap, wherein the groove bottom line is provided such that the gap is reduced from the front end side toward the base end side of the tongue piece, and the ball is circulated through the circulation path to make the nut Moving relative to the screw shaft described above. The ball screw according to claim 1, wherein the groove bottom line is an arc of a circle having a circle different from a circle at the center of the groove of the screw shaft. For example, the ball screw as described in item 1 or 2 of the patent application scope A rod in which the components forming the ball return passage are made of synthetic resin. The ball screw according to claim 1 or 2, wherein a distance (Sa) of a center of a cross-sectional circle of the groove bottom and a farthest point from the groove bottom line of the groove bottom is opposite to the groove The ratio (Sa/Sb) of the distance from the center of the cross-sectional circle of the bottom to the closest point to the groove bottom of the groove bottom line satisfies the following formula (1) 1.2 ≦ Sa / Sb ≦ 2.6 (1).