Forging device for crown-shaped helical gear

Crown twist forming teeth (14) are formed on the inside circumferential surface of a finishing die (13) with the thickness of each teeth being thinner in the middle part than toward both ends in the axial direction. The finishing die (13) is fitted for axial sliding in the axial direction in the axially central part of a die holder (11) through taper surfaces (12a, 13a) diminishing from its one end to the other. A half-finished work (35, 35') with its outside circumferential surface having rough-formed twist teeth is brought into screw engagement with the finishing die (13). A first punch (25) for pressing the half-finished work (35, 35') from one axial end toward the other, and a second punch (26) for pressing the finishing die (13) from one axial end toward the other are provided. A rotary device (30) is provided to rotate the die holder (11) in the direction opposite the direction in which the half-finished work (35, 35') is rotated with the finishing die (13) when the first and second punches (25, 26) are working under pressure. This makes it possible to form with a forging device a helical gear having crown-formed twist teeth, with each tooth being thicker in its middle part in its axial direction than on its both ends.

BACKGROUND OF THE INVENTION
 This invention relates to a forging device for forming a helical gear
 having crown-shaped teeth with the tooth thicker in the axial direction
 center of the twisted tooth than at both axial direction ends.
 A prior art is disclosed in JP-B-6-98449. That is, a helical gear forging
 device in which a die having twist forming teeth is fitted for vertical
 sliding in the axially central part of a die holder through downward
 diminishing taper surfaces, a cylindrical material is placed on the die,
 and the device comprises a first and a second punches for pressing the
 material and the die from above, a counter punch in engagement with the
 lower end part of the die to restrict the downward movement of the
 material, and a rotary device for rotating the die holder in the direction
 opposite the direction in which the material is rotated with the die.
 The above-described device of the prior art is the one in which the
 material is forced into the die, and twist teeth are formed on the outside
 circumferential surface of the material. Therefore, the thickness of the
 formed twist tooth is nearly constant over its entire length.
 SUMMARY OF THE INVENTION
 It is therefore, an object of the invention is to provide a novel forging
 device for forming a helical gear having crown-shaped teeth with the tooth
 thicker in the axial direction center of the twist tooth than at both
 axial direction ends.
 This invention is constituted as describe below to accomplish the
 above-mentioned object. That is, the invention is constituted that, for
 forging a crown-shaped gear, crown twist forming teeth are formed on the
 inside circumferential surface of a finishing die with the thickness of
 each tooth being thinner in the middle part than toward both axial
 direction ends, the finishing die is fitted for axial sliding in the axial
 direction in the axially central part of a die holder through taper
 surfaces diminishing from its one end to the other, a half-finished work
 with its outside circumferential surface having rough-formed twist teeth
 is brought into screw engagement with the finishing die, and a first punch
 for pressing the half-finished work from one axial end toward the other, a
 second punch for pressing the finishing die from one axial end toward the
 other, and a rotary device for rotating the die holder in the direction
 opposite the direction in which the half-finished work is rotated with the
 finishing die when the first and second punches are working to press.
 The invention is further constituted as above wherein the taper angle of
 the taper surface of the die holder is made slightly smaller than that of
 the taper surface of the finishing die.
 The invention is still further constituted that the taper angle of the
 taper surface of the die holder is made slightly smaller on the small
 diameter side with respect to an apex in the approximate center in its
 axial direction than the taper angle of the taper surface of the finishing
 die, and is made slightly larger on the larger diameter side than the
 taper angle of the taper surface of the finishing die.
 The invention is yet further constituted that the second punch presses the
 finishing die in the axial direction from one end to the other when the
 half-finished work is located in the middle part in the axial direction of
 the finishing die.
 The invention is in addition constituted that the rotary device is provided
 with the die holder and a punch holder for axially moving together with
 the first and second punches, with one of them being formed with lead
 grooves tilted to the direction of twist of the crown twist forming tooth,
 and with the other of them being provided with guide pins or rollers for
 fitting into the lead grooves.
 The invention is also constituted that a core is fitted to be immovable in
 the axial direction in the axially central part of the finishing die, a
 cylindrical half-finished work having rough-formed twist teeth on its
 outside circumferential surface and an axial hole in its axially central
 part is provided, the half-finished work is fitted between the finishing
 die and the core, and the first and second punches are provided to press
 the half-finished work and the finishing die axially from one end to the
 other.
 The invention is additionally further constituted that a solid cylindrical
 half-finished work with its outside circumferential surface having
 rough-formed twist teeth is brought into screw engagement with the
 finishing die, a first and the second punches are provided to press a
 half-finished work and the finishing die axially from one end to the
 other, a counter punch in engagement with the other end part of the
 finishing die and for restricting the axial movement of the half-finished
 work is provided, and a rotary device is provided to rotate the die holder
 in the direction opposite the direction in which the half-finished work is
 rotated with the finishing die when the first and second punches are
 working to press.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT OF THE INVENTION
 In FIG. 1 the symbol A denotes the finish form-forging device of the first
 embodiment, with the symbol 1 denoting a holding ring secured to a support
 table of the forging device. In the holding ring 1 are stacked in
 succession, a bottom disk 2, three disk-shaped flat bearings 3, and a
 receiving disk 4. Also in the holding ring 1 is fitted a guide ring 5 with
 its inside circumference holding the flat bearing 3 and the receiving disk
 4 coaxial. A die unit 10 is placed on the top surface of the receiving
 disk 4. The die unit 10 comprises a large-diameter die holder 11 in the
 center of which is press-fitted a tightening ring 12 in the axial center
 of which is taper-fitted a finishing die 13.
 That is, the axially central part of the tightening 12 is formed with a
 downward diminishing taper surface (taper hole) 12a, while the outside
 circumferential surface of the finishing die 13 is formed with a downward
 diminishing taper surface 13a, so that the finishing die 13 is vertically
 slidably fitted into the tightening 12 by means of the taper surfaces 12a
 and 13a. Here, the taper angle of the taper surface 12a of the tightening
 12 is made slightly smaller, by a range of less than 1.0 degree for
 example, than the taper surface (outside circumferential surface) 13a of
 the finishing die 13 so that the upper part of the taper surface 13a of
 the finishing die 13 comes into stronger contact with the taper surface
 12a of the tightening ring 12 than its lower part as shown in FIG. 4(a).
 In this way, when a half-finished work 35 is formed, the half-finished
 work 35 may be finished with a high precision over its entire length as
 the deformation amount in the lower part of the finishing die 13 is
 compensated. Furthermore as shown in FIG. 4(a), annular oil grooves 13b
 are formed at specified over-under intervals over the taper surface 13a of
 the finishing die 13 to supply lubrication oil to that surface and permit
 smooth vertical sliding of the finishing die 13 within the tightening ring
 12.
 Here, as shown in FIG. 4(b), the taper angle of the taper surface 12a may
 also be made as follows: When the central part (C) with respect to
 generally axial (vertical) direction of the taper surface is assumed to be
 an apex, the taper angle of the taper surface 12a-1 on the smaller
 diameter (lower) side is made smaller by a range of less than 1.0 degree
 than the taper angle of the taper surface 13a of the finishing die 13. In
 this way, when a half-finished work 35 extending over the entire length of
 the finishing die 13 is formed, the half-finished work 35 may be finished
 with a high precision over its entire length as the deformation amount in
 the middle part of the finishing die 13 is compensated. Incidentally, the
 above-mentioned central part (C) with respect to vertical direction of the
 taper surface may vary in vertical directions depending on the shape,
 thickness, etc. of the half-finished work 35. Also, an apex part of the
 taper surface 12a of the tightening ring 12 corresponding to the vertical
 direction center (C) may have some expansion (for example 5 mm or less) in
 the vertical direction.
 A return spring 17 as a compression coil spring is disposed under the
 tightening ring 12 so that the finishing die 13 is pushed up after its
 forming action by the reactional force of the return spring 17, that a gap
 is produced between the taper surface 13a of the finishing die 13 and the
 taper surface 12a of the tightening 12, and that lubrication oil is
 supplied to the oil grooves 13b. A restraint ring 18 for restraining the
 upward overshoot of the finishing die 13.
 The inside circumferential surface of the finishing die 13 integrally has
 crown twisted forming teeth 14. The crown twisted forming teeth 14 as
 shown in FIG. 5 is formed so that its tooth thickness (thickness in the
 direction crossing at right angles to the longitudinal center line L of
 the crown twisted forming tooth) becomes gradually thicker from the
 vertical (axial) direction center part X toward upper and lower ends
 (axial direction ends) Y and Z. In this example, the tooth thickness in
 the vertical direction center (X) is smaller by about 1/100 mm to 2/100 mm
 than that in upper and lower end parts (Y and Z). The twist angle of the
 crown twist tooth from a vertical direction center is about 18 degrees to
 the left. The crown twisted forming tooth 14 may be alternatively formed
 so that its thickness (thickness in the direction crossing at right angles
 to the longitudinal center line L of the tooth) is approximately constant
 and thin in the vertical (axial) direction central part and gradually
 thicker from both ends of the vertical direction central part toward both
 ends in the vertical (axial) direction ends of the tooth.
 A core 20 is secured upright in the bottom disk 2 with its upper end part
 fitted into the axially central part of the finishing die 13. A knock-out
 21 also serving as a counter punch is fitted over the outside
 circumference of the core 20. The knock-out 21 with its upper end fitted
 to the lower end part of the finishing die 13 restricts the half-finished
 work 35 from moving downward beyond a specified position and, after
 finish-forming the work (helical gear), is moved upward with an ejector
 pin 22 to remove the finished work upward from the finishing die 13.
 A punch holder 24 moved up and down with a ram (not shown) is disposed
 above the die unit 10. A first punch 25 and a second punch 26 of a
 cylindrical shape projecting downward are secured in the axially central
 part of the punch holder 24. The first punch 25 is made to project
 downward by a specified amount from the punch 26 and to be able to, when
 lowered, fit into the gap between the finishing die 13 and the core 20, to
 strike against the upper end of the half-finished work 35 in screw
 engagement with the finishing die 13, and to move the half-finished work
 35 downward so that the work 35 is positioned in the vertically central
 part of the finishing die 13.
 The second punch 26, when the first punch 25 is at its bottom dead point,
 strikes against the top surface of the finishing die 13 to move it
 downward along the taper surface 12a, to reduce the diameter of the
 finishing die 13 by elastic deformation, and to radially compress the
 half-finished work 35.
 A rotary device 30 is provided to rotate the die holder 11 in the direction
 opposite the direction in which the half-finished work 35 is rotated with
 the finishing die 13 when the first and second punches are in operation
 under pressure. The rotary device 30 is constituted as shown in FIGS. 1
 through 3. That is, the upper part of the die holder 11 is fitted over the
 lower outside circumference of the punch holder 24. Lead grooves 31 are
 formed at three circumferential positions in the upper part of the die
 holder 11, with each groove tilting to the same direction as the crown
 twist forming tooth 14 and having approximately the same pitch as that of
 the crown twist forming tooth 14. Those lead grooves 31 are open on their
 upper ends as shown in FIG. 3.
 On the other hand, guide rollers 32 for fitting into the lead grooves 31
 are disposed rotatably at three positions on the lower outside
 circumference of the punch holder 24 by means of bolts 33 so as to project
 radially outward. Incidentally, the guide rollers 32 may be guide pins
 that are not rotatable. The guide rollers 32 respectively fit into the
 lead grooves 31, at the time the first and second punches 25 and 26 move
 downward and strike against the top surfaces of the half-finished work 35
 and the finishing die 13, and roll along the lead grooves 31, and rotate
 the die holder 11 in the direction opposite the direction in which the
 half-finished work 35 is rotated with the finishing die 13 (in the arrow P
 direction in FIG. 3). By the way, the symbol 36 in FIG. 1 denotes a
 positioning ball for determining the initial position in the rotating
 direction of the die holder 11.
 Here, the half-finished work 35 is formed with a rough form-forging device
 B shown in FIG. 6. As seen in FIG. 6, a base ring 41 is secured on a
 support table 40. In the base ring 41 are stacked in succession a bottom
 ring 42, three flat bearings 43, and a receiving ring 44. The bottom ring
 42 is secured by press fitting into the inside circumference of the base
 ring 41. A holding ring 45 is brought into screw engagement with the
 inside circumference of the upper part of the base ring 41 to rotatably
 hold the flat bearing 43 and the receiving ring 44. An inner guide
 cylinder 46 guides the flat bearings 43 and the receiving ring 44, and its
 lower end part is fitted into and secured with the bottom ring 42.
 A die unit 50 is placed on the top surface of the receiving ring 44. The
 die unit 50 comprises a large diameter die holder 51 in the central part
 of which is press-fitted a tightening ring 52 into which are fitted a
 guide 53 and a rough forming die 54, both in cylindrical shape, in
 over-under disposition. The guide 53 is press-fitted into the upper part
 side of the tightening ring 52 by means of a taper surface diminishing
 upward, and the rough forming die 54 fitted to the lower part side of the
 tightening ring 52 by means of a cylindrical surface of an approximately
 constant diameter, and secured with a ring nut 57 screwed upward.
 The rough forming die 54 is for forming the half-finished work 35 and, as
 shown in FIGS. 7 and 8, its inside circumference has integral, twist
 forming teeth 55. In this example, the twist angle of the twist forming
 teeth 55 relative to a vertical direction line is set to about 18 degrees
 to the left. Each of the twist forming teeth 55 has a material introducing
 slope 55a, a forming part 55b, and a material discharging slope 55c, each
 being smoothly continuous from one to another, from the upper end part to
 be a material push-in port side to the lower part.
 The material introducing slope 55a is made so that its tooth height
 decreases gradually from the forming part 55b up (toward the material
 push-in port side) with a slope angle .alpha. of about 22.5 degrees (FIG.
 7). The hatched parts in FIGS. 7 and 8 are the upper side surfaces 55d-1
 and 55d-2 of the forming tooth 55, and sloped so that the tooth thickness
 decreases gradually from both sides of the upper end of a forming land
 55b-1 to the upper end of the forming tooth 55 with a slope angle of about
 1 to 2 degrees. As shown in FIG. 9, the right part ridge 55a-2 is rounded
 with a larger radius than the left part ridge 55a-1.
 The forming part 55b is formed with, in its vertical longitudinal direction
 central part, the forming land 55b-1 which is about 1.5 mm long and of the
 same tooth height and cross section as those of the work, with the tooth
 height on the upper side of the forming land 55b-1 gradually decreasing to
 the upper side with a gentle slope angle (about 3 degrees) to be
 continuous to the material introducing slope 55a, and with the tooth
 height on the lower side of the forming land 55b-1 gradually decreasing to
 the lower side with a gentle slope angle (about 1.5 degrees) to be
 continuous to the material discharging slope 55c. The material discharging
 slope 55c is made with its tooth height gradually decreased to the lower
 (material discharging) side with a slope angle .beta. of about 14 degrees.
 A counter punch 60 is coaxially disposed in the axial center part of the
 guide 53 and the rough forming die 54 and supported on the support table
 40 side. The counter punch 60 is formed, in its upper part 60a to be
 fitted into the guide 53, with a smaller diameter and, in its middle part
 60b to be fitted into the rough forming die 54 with a larger diameter. A
 connecting part between the parts 60a and 60b is made to be located at the
 material introducing slope 55a of the twist forming teeth 55. The lower
 part of the connecting part is formed with a taper part 60c thickening
 downward.
 A punch holder 61 moved up and down with a ram (not shown) is disposed
 above the die unit 50. A cylindrical punch 62 projecting downward is
 secured in the axially central part of the punch holder 61. A positioning
 member 63 is slidably fitted on the upper outside circumference of the
 punch 62, engage-stopped with the punch holder 61. A positioning member 63
 is slidably fitted on the upper outside circumference of the punch 62,
 engage-stopped with the punch holder 61, and urged with a compression coil
 spring 64 so as to project downward. The punch 62 is made to be able to,
 when moved downward, enter the gap between the guide 53 and the die unit
 50 and the upper part 60a of the counter punch 60. The positioning member
 63 serves to confirm the bottom dead point of the punch 62 when the punch
 62 moves downward by a specified amount and comes into contact with the
 top surface of the guide 53.
 The punch 62 pushes a short sized, cylindrical material 34 (34-1, 34-2,
 34-3) in intermittent succession into the gap between the guide 53 and the
 counter punch 60. In this case, the bottom dead point of the punch 62 is
 set as described below. That is, the punch 62 is deemed to be in the
 bottom dead point when the lower part (trailing part) material 34-1
 (half-finished work 35) passes over the material introducing slope 55a and
 at the same time the lower end (leading end) of the middle part (forward
 part) material 34-2 comes to the lower part (trailing part) of the
 material introducing slope 55a of the rough forming die 54. The middle
 part material 34-2 is temporarily stopped there.
 In this way, the half-finished work 35 (material 34-1) is preliminarily
 formed (into the state of the material 34-2 in FIG. 6) with the material
 introducing slope 55a of the twist forming teeth 55, and the side surface
 55d-1, 55d-2 of the material introducing slope 55a, and then passes the
 forming part 55b of the twist forming teeth 55 (in the state of the
 material 34-1 in FIG. 6) at a single stroke of the punch push-in motion of
 the next stage. As a result, no joint pattern due to interruption in the
 material flow is produced in the twist teeth part formed.
 As shown in FIGS. 8 and 9, while each twist forming tooth 55 formed on the
 rough forming die 54 has the right and left ridges 55a-2 and 55a-1 formed
 with the material introducing slope 55a and the side surfaces 55d (both
 side surfaces on the upper side), the right ridge 55a-2 is rounded with a
 larger radius of curvature than the left ridge 55a-1. Therefore, when a
 material 34 is forced in and a fiber flow 34a is produced, the fiber flow
 34a-1 arriving at the central part of the material introducing slope 55a
 goes from the right ridge 55a-2 side to the left side surface (behind
 surface) 55d side between the twist forming teeth 55. As a result, more
 amount of material 34 is supplied to the behind side surface, and a high
 surface pressure is produced on that side, so that the half-finished work
 35 has rough-formed twisted teeth containing less voids on the behind side
 surfaces.
 When the material 34a-2 passes over the material introducing slope 55a of
 the twist forming tooth 55, the material is compressed with the material
 introducing slope 55a area and the taper area 60c of the counter punch 60
 in the radially inward direction. As a result, the material is smoothly
 supplied to the recess between the twist forming tooth 55, so that the
 rough-formed tooth 35a of the half-finished work 35 is filled with the
 material to the tip of the tooth.
 The half-finished work 35 formed with the rough finish forging device B is
 finish-formed with the finish forging device A to obtain a helical gear
 having crown-shaped twist teeth. That is, with half-finished work 35 is
 brought into screw engagement with the upper part of the finishing die 13,
 the first and second punches 25 and 26 are lowered by means of the punch
 holder 24. In this way, first, the first punch 25 strikes against the top
 surface of the half-finished work 35 to force the half-finished work 35
 into the finishing die 13.
 When the half-finished work 35 is forced into the central part, in the
 vertical direction, of the finishing die 13, the second punch strikes the
 top surface of the finishing die 13, so that the finishing die 13 is
 lowered along the taper surface 12a of the tightening ring 12, and that
 the diameter of the finishing die 13 is elastically reduced to compress
 the half-finished work 35 in the radial direction. Along with that
 process, each of the guide rollers 32 provided on the punch holder 24 fits
 in each of the lead grooves 31 of the die holder 11 to rotate the die
 holder 11 in the direction opposite the direction in which the
 half-finished work 35 is rotated with the finishing die 13 (in the arrow P
 direction in FIG. 3).
 Through a series of actions described above, the half-finished work 35
 undergoes plastic deformation in both axial and radial directions while
 producing frictional forces on the contact surfaces of the crown twist
 forming teeth 14 of the finishing die 13 and the core 20. Also, the both
 of the side surfaces of the twist teeth 35a of the half-finished work 35
 undergoes plastic deformation while being almost uniformly pressed with
 both of the side surfaces 14a and 14b (FIG. 5) of the crown twist forming
 teeth 14. That is, since the half-finished work 35 is subjected to plastic
 deformation in the axial and radial directions while producing frictional
 forces on both of the contact surfaces, pressure is made uniform. As a
 result, the twist tooth 35a of the half-finished work 35 is made into a
 high precision crown-shaped twist tooth, with the tooth thickness
 gradually increasing from both of the axial and to the middle in the axial
 direction.
 The pressure acting on the half-finished work 35 during the above-described
 forming process tends to be higher on the upper side (the first punch 25
 side) and lower toward the lower side and the outside diameter of the
 formed work tends to be smaller on the lower side than the upper side. In
 this case, however, since compensation is made so that the elastic
 deformation in the axial direction of the finishing die 13 becomes smaller
 toward the lower part by making the taper angle of the taper surface 12a
 of the tightening ring 12 is slightly smaller than that of the taper
 surface 13a of the finishing die 13, the diameter of the finishing die 13
 is kept almost uniform from its upper to lower parts without being
 affected with the difference between pressures acting on the upper and
 lower parts of the half-finished work 35. Therefore, the tooth height of
 the crown-shaped twist tooth formed on the outside circumference of the
 half-finished work 35 (diameter of the helical gear) is approximately
 uniform over the entire length or from top to bottom of the tooth.
 When the first and second punch 25 and 26 retracts upward after forming as
 described above, the diameter of the finishing die 13 is restored to the
 original as the finishing die 13 moves up within the tightening ring 12
 due to reactional forces of itself and the return spring 17. In this way,
 the formed work or the helical gear having crown-shaped twist teeth may be
 easily removed upward from the finishing die 13.
 FIG. 11 shows another finish-forming forging device as a second embodiment
 of the invention. That is, a finish-forming forging device A' is for
 forming the outside circumferential surface part of a solid material into
 a half-finished work 35' having roughly formed twist teeth 35a. The first
 punch 25' of this device for depressing the half-finished work 35' is
 formed in a cylindrical form. The counter punch 70 is erected upright to
 be capable of vertical movement on the bottom disk 2. The upper end part
 of the counter punch 70 is fitted into the lower end part of the finishing
 die 13 to restrict the downward movement of the half-finished work 35' at
 a specified position. An ejector pin 71 is disposed in the lower axial
 center part of the counter punch 70 so as to move the counter punch 70
 upward and remove the formed work (helical gear) upward from the finishing
 die 13. Since other constitution of this embodiment is the same as that of
 the finish forming forging device A of the first embodiment, the same
 parts are provided with the same symbols as those in the first embodiment
 and the explanation thereof is omitted.
 In the case the half-finished work 35' is formed with the finish-forming
 forging device A', the half-finished work 35' is brought into screw
 engagement with the upper part of the finishing die 13, and the first and
 second punches 25' and 26 are lowered. In that way, first, the first punch
 25' forces the half-finished work 35' into the finishing die 13. At the
 point where the half-finished work 35' is forced into the middle part in
 the vertical direction of the finishing die 13, the second punch 26 lowers
 the finishing die 13 along the taper surface 12a of the tightening ring 12
 to elastically deform and reduce the diameter of the finishing die 13.
 Along with the above-described action, the die holder 11 is rotated in the
 direction opposite the direction in which the half-finished work 35' is
 rotated with the finishing die 13. In the final process, the lower end of
 the half-finished work 35' comes into contact with the top surface of the
 top surface of the counter punch 70. With these series of actions, the
 half-finished work 35' produces frictional forces on its surface in
 contact with the crown twist forming teeth 14 of the finished die 13, and
 is subjected to plastic deformation in axial and radial directions while
 the pressing forces on it is being equalized. As a result, high precision
 crown-shaped twist teeth like those in the first embodiment are formed.
 After the forming, the counter punch 70 is raised with the ejector pin 71
 to remove the formed work (helical gear) upward from the finishing die 13.
 Incidentally, this invention may also be embodied so that the work (the
 helical gear having the crown-formed twist teeth) formed with the finish
 forming forging device A (FIG. 1) of the first embodiment and the finish
 forming forging device A' (FIG. 11) is turned upside down and re-formed
 with the finish forming forging devices A and A'. In that case, the taper
 angle of the taper surface 12a of the die holder 11 is preferably about
 the same as that of the taper surface 13a of the finishing die 13. In such
 a way, a higher quality work is obtained. This invention also makes it
 possible to form a half-finished work having a flange on its one axial
 direction end and roughly formed twist teeth on its outside
 circumferential surface. In that case, the flange side should be on the
 upside when it is brought into screw engagement with the finishing die 13.
 As is clear from the above explanation, with the present invention since
 the half-finished work is compression-formed in axial and radial direction
 while frictional forces are produced on its surface in contact with the
 finishing die, the pressing forces produced with the crown twist forming
 teeth of the finishing die are equalized. As a result, the helical gear
 having the crown twist teeth with their tooth width thicker in the middle
 part in the axial direction of the tooth than on its both ends is formed
 easily.
 With the invention, since compensation is made so that the taper angle of
 the taper surface of the tightening ring is slightly smaller than the
 taper angle of the taper surface of the finishing die and that the amount
 of elastic deformation of the finishing die in the axial direction becomes
 smaller toward its lower end, the outside diameter of the finishing die is
 kept almost uniform from its upper to lower parts without being affected
 with the difference between pressures acting on the upper and lower parts
 of the half-finished work. Therefore, the helical gear is formed with the
 tooth height of the crown-shaped twist tooth being approximately uniform
 over its the entire length. Therefore, the helical gear having an about
 uniform diameter over its entire length is formed.
 With the invention, the amount of the elastic deformation of the middle
 part, in the axial direction, of the finishing die is adjusted by making
 the taper angle of the taper surface on the smaller diameter side of the
 tightening ring slightly smaller than the taper angle of the taper surface
 of the finishing die. As a result, a long-sized helical gear having the
 crown twist teeth are formed with a high precision.
 With the invention, since the finishing die is elastically deformed in the
 shrinking direction when the half-finished work is located in the middle
 part in the axial direction of the die, the rough formed twist teeth of
 the half-finished work is smoothly formed into the crown-shaped twist
 teeth.
 With the invention, since it is possible to adapt both of the side surfaces
 of the twist tooth of the half-finished work to the shape of both of the
 side surfaces of the crown twist forming tooth, the crown twist teeth are
 formed with a high precision.
 With the invention, it is possible to form a cylindrical helical gear with
 its outside circumferential surface having crown-shaped twist teeth with a
 high precision.
 With the invention, it is possible to form a round column-shaped helical
 gear with its outside circumferential surface having crown-shaped twist
 teeth with a high precision.
 This invention may be embodied in other specific forms without departing
 from the spirit or essential characteristics thereof. The present
 embodiments are therefore to be considered in all respects as illustrative
 and not restrictive, the scope of the invention being indicated by the
 appended claims rather than by the foregoing description, and all the
 changes which come within the meaning and range of equivalency of the
 claims are therefore intended to be embraced therein.