JP2002250426A - Nut for ball screw and method of manufacturing the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of manufacturing a nut which will not bring about cutting of metal flow, by forming a ball-rolling groove in a nut for a ball screw, being independent of cutting, and eliminates the need for finishing the ball-rolling grooves. SOLUTION: In the nut for ball screw, in which a ball-rolling groove for balls to roll is spirally formed in the inner circumferential surface of the center hole thereof, the ball-rolling groove is formed by subjecting a nut material having a hole punched beforehand to cold forging, while a relative rotational force around an axis and a relative push-in force towards the axis are exerted simultaneously on a punch having a spiral path. After the cold forging, the surface of the ball rolling groove is subjected to hardening, without finishing grinding.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a nut for a ball screw in which a spiral ball rolling groove for rolling or rolling a ball is formed, and a method for manufacturing the same.

[0002]

2. Description of the Related Art A ball screw includes a shaft provided with a spiral ball rolling groove on the outer surface of a cylinder, a nut provided with a spiral ball rolling groove on the inner surface of a cylinder, and two opposing ball rolling grooves. It is a mechanical element that consists of a plurality of rolling balls and converts the rotation of a shaft or a nut into translation (or vice versa).

Conventionally, a nut for a ball screw is generally manufactured through seven steps as shown in FIG. First, (P01) a substantially cylindrical material is obtained by hot or cold forging. (P02) In the center of the columnar material,
For example, a through hole is formed by a drill. (P03) Finish the outer surface of the material and the inner peripheral surface of the center hole with a cutting tool. (P04) A spiral ball rolling groove is formed (cut) on the inner surface side of the center hole of the material using a cutting tool or a milling tool. (P05) The material is subjected to heat treatment, for example, carburizing and quenching. (P06) Finish the ball rolling groove, for example, grinding or lapping. (P07) The material is subjected to surface treatment, for example, rust prevention treatment.

[0004]

The following problems arise when such a conventional manufacturing method is used.

[0005] The surface roughness of the (P04) ball rolling groove formed by cutting is too rough for use as a ball rolling surface without finishing. For this reason,
Surface finishing (P06) is required.

2 When a through hole is made at the center of a columnar material by, for example, a drill (P02), and the inner peripheral surface of the center hole of the material is finished with a cutting tool (P0).
3) Sometimes, since the holes are relatively deep, it is difficult to discharge chips from the center hole.

[0007] For this reason, it takes time to drill and process the inner peripheral surface of the center hole.

[0010] Further, when the inner peripheral surface of the center hole of the material is finished with a cutting tool (P03), a small cutting tool must be used so as to be able to be inserted into the hole. Since a small cutting bit has low strength, it cannot be cut with a large depth of cut, resulting in poor work efficiency.

[0009] 5 It is possible to use a helical broach instead of a cutting tool. However, the manufacture and maintenance of the helical broach is cumbersome and expensive.

6 Since the cutting tool is worn or chipped, stable machining cannot be performed. In addition, defective products are easily generated. The above problems 2 to 4 become more pronounced as the diameter of the center hole becomes smaller.

[0011] When the ball rolling groove is formed by cutting, the metal flow is cut. Cutting the metal flow reduces its surface strength. Therefore, the durability of the nut and the ball screw using the nut is low.

In view of the above various problems, the present invention does not cause cutting of metal flow by forming a ball rolling groove in a nut for a ball screw without cutting.
It is another object of the present invention to provide a manufacturing method which eliminates the need for finishing a ball rolling groove in some cases and a nut for a ball screw according to the manufacturing method.

[0013]

The above object can be attained by the following means. That is, a first aspect of the present invention is a ball screw nut in which a spiral ball rolling groove for rolling a ball is formed on an inner peripheral surface of a center hole of the ball screw nut. The running groove is a ball rolling groove formed by cold forging and the surface thereof is quenched after the cold forging, and the cold forging is performed by expanding an outer surface of a nut material that is pre-drilled. In a constrained state, relative movement between a punch having a spiral ridge and the nut material, which is performed by a motion that simultaneously provides a translational motion in the central axis direction of the hole and a rotational motion about the central axis. Cold forging.

According to a second aspect of the present invention, in the ball screw nut of the first aspect, the surface of the ball rolling groove is further finished by grinding after the quenching. .

According to a third aspect of the present invention, there is provided a method of manufacturing a nut for a ball screw, wherein a helical ball rolling groove for rolling a ball is formed on an inner peripheral surface of a center hole thereof. In this manufacturing method, a step of preparing a pre-drilled nut material, a step of constraining the expansion of the outer surface of the nut material, and a state in which the expansion of the outer surface of the nut material is constrained, a spiral ridge Performing cold forging by a relative motion between the punch having the hole and the nut material, wherein the translational motion in the central axis direction of the hole and the rotational motion around the central axis are simultaneously performed; and A quenching step of quenching the surface of the rolling groove.

[0016]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 2 is a longitudinal sectional view showing an example of the nut 1 for a ball screw according to the present invention. Nut 1 is hole 1e
At its center, and this hole 1e has three cylindrical hole portions 1
f, 1g and 1h. A spiral ball rolling groove 1d is formed on the inner peripheral surface 1c of the central cylindrical hole portion 1g. The nut 1 further includes a cylindrical outer peripheral portion 1b and a flange portion 1a.

FIG. 3 is a schematic explanatory view of a die unit for carrying out the method of manufacturing a nut for a ball screw according to the present invention. 4, 5, 6, 7, 8, and 9 are:
FIG. 4 is an enlarged view of a main part of FIG. 3, which sequentially shows the position and state of each member in the process of manufacturing the nut of the present invention.

The die unit 100 includes the lower unit 10
1 and the upper unit 102, and the upper unit 10
Reference numeral 2 is supported by a frame (not shown) extending from the lower unit 101 so as to be vertically movable. Lower unit 1
Reference numeral 01 includes a lower base 10, a holder 8, a cylinder 7, and a piston 6. The lower unit 101 is a lower base 1
0 to a press bed (not shown). The holder 8 and the cylinder 7 are each provided with appropriate fixing means,
For example, it is fixed to the lower base 10 and the holder 8 by bolts. A cylindrical portion 8b protrudes from the holder 8, and a piston 6 is fitted in a space defined by an outer peripheral surface of the cylindrical portion 8b and an inner peripheral surface of the cylinder 7. This piston 6
Oil passage 7a in each of the two spaces separated by
And 7b are connected, and the oil passages 7a and 7b are connected to a hydraulic source (not shown).

The piston 6 has an annular cross section, and is provided with a piston upper plate 6a at an upper portion thereof. A hole is formed in the center of the piston upper plate 6a, and the blank 2 and a punch 3 described later can pass through this hole. In addition, an annular wedge 5 is attached downward at the edge of the hole of the piston upper plate 6a. Wedge 5
Has a hole, and the inner periphery of the hole is formed in a tapered surface 5a that spreads downward. The restraining die 4 is fitted to the wedge 5. A wedge 5 is placed outside the restraining die 4.
Taper surface 4 which can be closely adhered to and is almost complementary to the tapered surface 5a
a is formed. The restraining die 4 is further provided with a through hole, and the blank 2 is placed in the through hole.

The through-hole of the constraining die 4 is made slightly larger than the outer diameter of the blank 2 so that the blank 2 can be loaded and discharged therefrom. It has become. Further, not only this, but also during the cold forging, that is, when the punch 3 described later enters the blank 2, the blank 2 is removed from the outside so that the blank 2 does not expand outward due to the force received from the inside. Restrain with strong force. The meaning of this will be described later.

The constraining die 4 can have a thin body or a structure in which a plurality of axial slits are formed in the main body so that the diameter can be reduced. It is necessary to have sufficient hardness or strength to prevent deformation. Also, blank 2
Since the restraining die 4 is backed up by the cylindrical portion 8b through the annular wedge 5, the cylindrical portion 8b must have a more robust structure by increasing the thickness of its wall.

Although an example in which the cylinder 7 is used to grip and restrain the blank 2 has been described above, a clamp mechanism using a toggle mechanism may be employed. In short, it suffices if a firm constraint for preventing the blank 2 from expanding during the gripping and the cold forging of the blank 2 is realized.

The knockout pins 9 are provided in a pressing device (not shown). After the cold forging, the blanks 2 are discharged from below at appropriate timing in order to discharge the blanks 2 from the constraining dies 4. Thrust up.

The upper unit 102 includes the punch holder 1
1, the punch housing 14, the upper base 21, and the motor 17 are generally constituted. The punch housing 14 is fixed to the upper base 21 by appropriate means. The punch holder 11 is rotatably supported in the punch housing 14 via a bearing. The punch 3 is fixed to a lower end of the punch holder 11 by an appropriate fixing structure such as a punch mounting plate 12.

A pulley 15 on the holder side is fixed above the punch holder 11, and a pulley 15 a on the motor side is fixed to the output shaft of the motor 17. Since the belt 16 is wound around the holder-side pulley 15 and the motor-side pulley 15a, the punch 17 and the punch 3 fixed thereto can be rotated by the motor 17 fixed to the upper base 21. Has become.

The rack bar 18 is further fixed to the upper base 21. On the other hand, the lower base 10 is provided with an encoder support member 10a. An encoder 20 is attached to the distal end side of the encoder support member 10a, and a pinion 19 is fixed to an input shaft of the encoder 20 and meshes with rack teeth of a rack bar 18. With this configuration, the amount of vertical movement of the upper base 21 can be detected by the encoder 20.

The amount of rotation of the motor 17 is controlled in accordance with the amount of movement of the upper base 21 detected by the encoder 20. Therefore, as the press moves up and down, the punch translates (moves in the axial direction) and rotates at the same time. The relationship between the rotation and the translation is set to a relationship corresponding to a spiral locus drawn by a ridge provided on the outer periphery of the punch 3. That is, the relationship between the rotation and the vertical movement of the press is set so as to correspond to the advance angle of the ball groove of the ball screw.

Such a relationship between rotation and translation can be realized by another configuration. For example, because of the relative relationship between the movement of the punch 3 and the motion of the blank 2, the blank 2 may be rotated instead of rotating the punch 3. Further, it is possible to adopt a configuration in which the vertical movement of the press is directly converted into the rotation of the punch 3 or the blank 2 by a mechanical transmission mechanism such as a rack-pinion mechanism without using the encoder 20. Further, another position measuring means such as a linear scale can be used instead of the encoder 20.

Each process executed by the above-described die unit 100 will be described with reference to FIGS. During these processes, the blank 2 is not externally heated.

FIG. 4 shows the state of the die unit 100 before processing. The piston 6 is raised by sending high-pressure hydraulic oil to the oil passage 7a of the cylinder 7, so that the wedge 5 is also raised, and the tapered surface 5 on the inner side of the wedge 5 is raised.
a and the tapered surface 4a on the outer surface side of the constraining die 4 are separated from each other, and the inner surface side of the constraining dice 4 is shaped like a voice heard in the radial direction. The punch 3 is on standby in a state of being separated above the restraining die 4.

The punch 3 and the restraining die 4 are maintained such that their axes are aligned. In this state, the blank 2 is inserted into the restraining die 4. At this time, restraint die 4
Since is open, the blank 2 can be easily inserted into the restraining die 4. Blank 2 inserted
Stabilizes and stops in a state where the flange portion 2a is in contact with the upper surface of the restraining die 4. In addition, FIG. 2 shows a nut as a product after forging, and in order to distinguish it from the above, in FIG. 3 and subsequent figures, the blank and its reference numerals are 2 regardless of before, during, or after forging. Represented by its suffix.

After the blank 2 is inserted into the restraining die, the piston 6 is lowered by sending hydraulic oil to the oil passage 7b of the cylinder 7, and the wedge 5 is lowered accordingly.
The tapered surface 5a of the wedge 5 is the tapered surface 4a of the restraining die 4.
And the diameter of the constraining die 4 is reduced. The blank 2 is gripped by the diameter reduction of the restraining die 4. This state is shown in FIG. At this time, since the blank 2 is held concentric by the restraining die 4, the blank 2 and the punch 3 are also concentric.

When the ram of the press starts descending, the punch 3 waiting upward enters the inner surface of the blank 2 while rotating. At this time, the rotation of the motor 17 is controlled by the encoder 20 shown in FIG.
Is axially proportional to the amount of its rotational movement. For this reason, the punch 3 enters the inner surface of the blank 2 while rotating and moving in the axial direction corresponding to the advance angle of the spiral ridge (projection) 3a. Punch 3 keeps rotating while blank 2
Keep going inside. By this operation, the shape of the ridges (projections) 3 a of the punch 3 is transferred to the inner surface of the blank 2. FIG. 6 shows the final state of this operation.

At the time of this cold forging, the blank 2 is
Receives a strong rotational force from the
, The blank 2 does not rotate. Further, since the axis of the punch 3 and the axis of the blank 2 coincide with each other, the formed spiral groove is accurately formed with respect to the axis of the blank 2.

The punch 3 must be forcedly rotated. In particular, when the pitch of the ball screw is small (the lead angle is small), the thread groove cannot be formed without forced rotation. That is, in the case where there is no forced rotation, the frictional force generated between the punch 3 and the blank 2 is larger than the rotational force generated by the component of the axial force, so that a so-called self-lock state is established, and the punch 3 It does not rotate naturally. Therefore, no thread groove is formed.

On the other hand, in the case of a large lead angle, the punch 3 can be spontaneously rotated (rotated along with the mating member) without applying any forced rotation, and a thread groove can be formed. However, a nut obtained by a cold forging method that entrusts the natural rotation of the punch 3 cannot be used as a ball screw component (nut) because the lead error is inevitably increased. For this reason, in the present invention, it is required to provide relative rotation and translation between the punch 3 and the blank 2.

At the end of the stroke of the ram of the press, the movement of the punch 3 stops, and then the punch 3 rises while rotating in the reverse direction. At this time, the rotation of the punch 3 is also the punch 3.
The punch 3 and the blank 2 can come out without interference and can be separated smoothly because they rotate in reverse at an angle commensurate with the angle of the spiral ridge (projected ridge) 3a. This state is shown in FIG.

After the punch 3 is raised, the working oil is sent to the oil passage 7a of the cylinder 7, whereby the piston 6 and the wedge 5 are raised. 4 is released. This state is shown in FIG.

Thereafter, the blank 2 is lifted above the restraining die 4 by raising the knockout pin 9. This state is shown in FIG. Here, the blank 2 that has been forged is discharged out of the unit. After that, the knockout pin 9 descends, the next blank 2 is inserted,
It returns to the initial state (the state of FIG. 4).

After the forging is completed, the blank 2 is subjected to a heat treatment (carburizing and quenching), and is sent to an assembling process through a rust prevention treatment (in the case of a general ball screw). FIG. 10 shows a processing step of a nut for a general (general) ball screw according to the present invention. Process P11
Steps P13 to P13 are the same as those described above with reference to FIG. 1, P01 to P03. A spiral groove is formed on the inner surface of the center hole of the blank (P13) in which the outer surface and the inner peripheral surface of the center hole are finished with a cutting tool by the cold forging described above (P14). The formed spiral groove is heat-treated (carburized and quenched) (P15). The finishing (grinding or lapping) of the ball rolling groove, which has been performed with the nut for conventional (general-purpose) ball screws, has been omitted for the following reasons. (P1
6) It becomes a nut of the product.

The surface roughness of the forming surface (spiral ridges, ridges) of the cold forging punch 3 is transferred to the blank. Therefore, when the surface roughness is good, the processed ball rolling groove has a sufficiently good surface roughness to be used as a nut for a general ball screw. And even if the ball rolling groove is heat-treated to increase the surface hardness,
The dimensional accuracy required for general ball screws can be maintained almost as it is. Therefore, when the ball rolling groove of the blank is processed by the cold forging method, the ball rolling groove can be used as it is as a rolling surface of a nut for a general ball screw without grinding and finishing the ball rolling groove. This makes it possible to reduce the manufacturing cost of the nut.

In the case of a high-precision ball screw, it is necessary to remove the irregularity in precision caused by heat-treating the ball rolling groove after cold forging, and therefore, a grinding (or lapping) finish is performed. In this case, the effect that the grinding finish can be omitted cannot be expected. Can be expected.

When the processing conditions are poor, galling and seizure may occur between the blank 2 and the punch 3 during cold forging. This can be prevented to some extent by supplying sufficient lubricating oil, but if this is still insufficient,
It is necessary to devise the shape of the punch 3. The following is an example of this ingenuity.

FIG. 11 is a partially enlarged sectional view of the punch 3 and the blank 2 which have been devised. Projection 3a of punch 3
Must be in contact with the surface of the groove 2d of the blank 2 in order to forge, but in this case, there is a gap between the cylindrical inner surface 2c of the blank 2 and the cylindrical outer surface 3d of the punch. δ is formed. As a result, the contact area between the blank 2 and the punch 3 is reduced and the forming load is reduced. Further, since the lubricating oil is supplied between the cylindrical inner surface 2c and the cylindrical outer surface 3d through the gap δ, the forming load is further increased. Can be reduced.

FIG. 12 shows another example in which the shape of the ridges of the punch 3 is devised, and is a cross-sectional view of the punch 3 as viewed from a cut surface indicated by AA in FIG. The punch 3 has a substantially rectangular outer edge when viewed from the axial direction. Therefore, when viewed from the processed portion of the blank 2 during cold forging, the convex portions (high wide portions) 3b and the concave portions (low narrow portions) 3c come alternately. The convex portion 3b performs molding, and the concave portion 3c plays a role of escape of molding. Further, since a gap is formed between the concave portion 3c and the blank 2, lubricating oil is carried by this gap and is supplied to a molding portion. As a result, the molding load can be reduced. Further, the blank 2 and the punch 3 come into contact only with the convex portion 3b, and the contact area between the blank 2 and the punch 3 is reduced, so that the molding load is reduced. The shape of the outer edge can be an appropriate shape such as triangular, pentagonal or hexagonal in addition to the quadrangular shape.

When the punch 3 enters into the hole of the blank 2, a force is generated which causes the punch 2 to expand (expand) from the inside to the outside of the blank 2. If the blank 2 is freely expanded by this force, no matter how precisely the dimensions of the ridges of the punch 3 are created, the blank 2 escapes by the expansion, so that the groove is not accurately processed.

In the present invention, since the restraining die 4 restrains the blank 2 with a strong force from all directions around the blank 2, the blank 2 is prevented from expanding. In the case where the blank 2 is merely gripped partially, such as when a three-jaw chuck is used, the expansion of the blank 2 is inevitable. However, in the present invention, the expansion of the blank 2 is prevented. The rolling grooves can be machined with high precision.

The decrease in precision caused by the expansion of the blank 2 may be caused by the shape of the blank. FIG. 13 is an explanatory diagram for explaining such a decrease in accuracy. FIG. 13A is similar to FIG. 2 and FIG.
FIG. 13 is a graph showing the error (radial error) of the radial position at the bottom of the ball rolling groove of the cold forged blank, and FIG.
FIG. 3C is an exaggerated view of the shape of the inner surface of the constraining die 4.

After the cold forging, the bottom of the ball rolling groove was measured, and as shown in FIG.
The distribution of the radius error Δr according to the height position is recognized. The radius error Δr is large at the central portion C and relatively small at the lower portion L. This is because, in the upper portion H, the amount of expansion (escape) is small due to the effect of the rigidity of the flange portion 1a, and in the lower portion L, the amount of expansion is relatively small due to the effect of the rigidity of the cylindrical portion 1j extending downward. It is considered that the central portion C is not provided with a structure that affects the rigidity.

In the present invention, in order to remove such a radius error Δr, a crowning (bulge) CR corresponding to the radius error is formed on the inner surface side of the constraining die 4. The crowning CR is processed so that the bottoms of the ball rolling grooves are at the same radial position.

The above-mentioned radius error Δr is caused not only by the shape of the blank 2 but also by the combined action of the rigidity with the restraining die 4, the wedge 5, the cylindrical portion 8b and other shapes. And the shape must be determined by trial and error.

In addition, a, the surface roughness of the formed portion of the punch 3 is increased. b, Hard coating such as TiN, TiCN is applied to the surface of the punch 3. (c) The shape and length of the introduction portion of the punch 3 are optimized. d. Devise a lubrication method such as forced lubrication. e. The forming load is reduced by superposing the ultrasonic vibration in the rotating direction on the punch. Such means can be applied alone or in combination as appropriate.

[0053]

As described above, according to the present invention, when manufacturing a ball screw nut, the ball rolling groove of the nut is formed by cold forging. In addition, there is an advantage that the grinding finish or the lap finish of the ball rolling groove can be omitted. Also, since the ball rolling grooves are formed without cutting, there is an advantage that troublesome troubles due to cutting can be avoided.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram for explaining a schematic process of manufacturing a conventional nut for a ball screw.

FIG. 2 is a longitudinal sectional view showing one example of a nut for a ball screw of the present invention.

FIG. 3 is a schematic explanatory view of a die unit for carrying out the method of manufacturing a nut for a ball screw according to the present invention.

4 is an enlarged view of a main part of the die unit of FIG. 3, and together with FIGS. 5, 6, 7, 8 and 9, the position and state of each member in the manufacturing process of the nut of the present invention are shown in order. I will show you later.

FIG. 5 is an enlarged view of a main part of the die unit of FIG. 3, as in FIG. 4;

FIG. 6 is an enlarged view of a main part of the die unit of FIG. 3, similarly to FIG. 4;

FIG. 7 is an enlarged view of a main part of the die unit of FIG. 3, as in FIG. 4;

FIG. 8 is an enlarged view of a main part of the die unit of FIG. 3, as in FIG. 4;

FIG. 9 is an enlarged view of a main part of the die unit of FIG. 3, as in FIG. 4;

FIG. 10 is an explanatory diagram for explaining a processing step of the nut for general (general) ball screw according to the present invention.

FIG. 11 is a partially enlarged cross-sectional view of the punch 3 and the blank 2 in which the shape of the punch 3 is devised.

FIG. 12 is a cross-sectional view of a punch 3 showing another example in which the shape of the ridge is devised.

FIG. 13 is an explanatory diagram for explaining a decrease in accuracy;
2 (a) is the same as FIG. 2, FIG. 2 (b) is a graph showing the error (radial error) in the radial position at the bottom of the ball rolling groove of the cold forged blank, and FIG. FIG. 3 is an exaggerated view of the shape of the inner surface of FIG.

[Explanation of symbols]

 Reference Signs List 1 nut 1a, 2a flange portion 1b cylindrical outer peripheral portion 1c inner peripheral surface 1d ball rolling groove 1e hole 1f, 1g cylindrical hole portion 1j cylindrical portion 2 blank 2c cylindrical inner surface 2c cylindrical inner surface 2d groove portion 3 punch 3a protrusion Shaped portion 3b Convex portion 3c Concave portion 3d Cylindrical outer surface 4 Restricted die 5a, 4a Tapered surface 6 Piston 6a Piston upper plate 7 Cylinder 7a, 7b Oil passage 8 Holder 8b Cylindrical portion 9 Knockout pin 10 Lower base 10a Encoder support member 11 Punch Holder 12 Punch mounting plate 14 Punch housing 15 Holder side pulley 15a Motor side pulley 16 Belt 17 Motor 18 Rack bar 19 Pinion 20 Encoder 21 Upper base 100 Die unit 101 Lower unit 102 Upper unit CR crowning

Claims (3)

[Claims] 1. A ball screw nut having a helical ball rolling groove for rolling a ball formed on an inner peripheral surface of a center hole thereof, wherein the ball rolling groove is formed by cold forging. After cold forging, the surface thereof is a ball rolling groove whose surface is quenched, and the cold forging is formed in a spiral shape in a state in which the expansion of the outer surface of a pre-drilled nut material is restrained. Cold forging, which is a relative movement between a punch having a ridge and a nut material, wherein the translational movement in the central axis direction of the hole and the rotational movement around the central axis are simultaneously performed. A ball screw nut characterized by the following. 2. The ball screw nut according to claim 1, wherein the surface of the ball rolling groove is further finished by grinding after the quenching. Nuts. 3. A method of manufacturing a nut for a ball screw, wherein a helical ball rolling groove for rolling a ball is formed on an inner peripheral surface of a center hole thereof. A step of preparing an opened nut material; a step of restraining the expansion of the outer surface of the nut material; and a punch having a spiral ridge and the nut material in a state where the expansion of the outer surface of the nut material is restrained. Performing a cold forging by simultaneous movement of providing a translational movement in the central axis direction of the hole and a rotational movement about the central axis of the hole, and quenching the surface of the ball rolling groove. A method of manufacturing a nut for a ball screw, comprising: