Tool for cutting gear and method for cutting gear
There is provided a tool for efficiently cutting a face gear to be meshed with a helical gear. When a circular tooth thickness of a tooth tip of a cutting edge portion is represented as S atSC , a circular tooth thickness on a virtual outside diameter of a tooth profile of the helical gear in a cross-sectional view perpendicular to an axis is represented as S at , a helix angle on the virtual outside diameter of the tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to the axis is represented as β a , and a face width of the cutting edge portion is represented as b sc , b SC ≦ s at - s atSC tan β a is satisfied.
1. A tool having a spur gear shape for cutting, as a gear to be cut, a skew gear to be meshed with a predetermined helical gear, the tool comprising a cutting edge portion having a cutting edge of a tooth-profile curvilinear shape that is the same as one of at least a pair of tooth-profile curvilinear shapes of a tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to an axis of the helical gear, wherein:
a circular tooth thickness of the cutting edge portion is smaller than a circular tooth thickness of the tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to the axis;
a tooth depth of the cutting edge portion is larger than a tooth depth of the helical gear; and
when a circular tooth thickness of a tooth tip of the cutting edge portion is represented as S atSC , a circular tooth thickness on a virtual outside diameter of the tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to the axis is represented as S at , a helix angle on the virtual outside diameter of the tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to the axis is represented as β a , and a face width of the cutting edge portion is represented as b sc , the following Expression 1 is satisfied
b
SC
≦
s
at
-
s
atSC
tan
β
a
.
Expression
1
2. The tool according to claim 1 , wherein
correspondingly to each pair of tooth-profile curvilinear shapes of the tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to the axis, the cutting edge portion has cutting edges of a tooth-profile curvilinear shape on a right side and a left side.
3. The tool according to claim 1 , wherein
the helical gear is an involute cylindrical gear.
4. The tool according to claim 3 , wherein
the gear to be cut is a face gear.
5. The tool according to claim 1 , further comprising two auxiliary plates provided to sandwich therebetween the cutting edge portion.
6. The tool according to claim 5 , wherein
each of the two auxiliary plates has a helical gear shape.
7. A tool having a spur gear shape for cutting, as a gear to be cut, a skew gear to be meshed with a predetermined helical gear, the tool comprising a cutting edge portion having at least one cutting edge having a tooth-profile curvilinear shape, wherein:
a circular tooth thickness of the cutting edge portion is smaller than a circular tooth thickness of a tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to an axis of the helical gear;
a tooth depth of the cutting edge portion is larger than a tooth depth of the helical gear; and
a face width of the cutting edge portion has an angle which causes a cutting edge to have a chevron shape in a cross-sectional view by a plane including the axis,
when a given point on an edge of a cutting edge having a tooth-profile curvilinear shape of a tool having a standard spur gear shape not having a chevron angle is represented as Expression 3,
Expression 3:
In XYZ coordinate system, when an origin is a center of a pinion, a Y axis is an axis of the pinion, and a Z axis is a center of tooth thickness of a tooth profile of the pinion in a cross-sectional view by a plane perpendicular to an axis of the pinion, coordinates (X S ,Y S ,Z S ) of a given point S of an edge of an acting cutting edge of a cutter having a standard spur gear shape not having a chevron angle are:
coordinates of the point S on a right tooth flank side
{
τ
s
=
-
φ
B
+
φ
0
2
+
inv
(
α
t
)
-
inv
(
α
S
)
X
S
=
R
S
sin
τ
S
Y
S
=
-
L
·
φ
B
Z
S
=
R
S
cos
τ
S
coordinates of the point S on a left tooth flank side
{
τ
s
=
φ
B
-
φ
0
2
-
inv
(
α
t
)
+
inv
(
α
S
)
X
S
=
R
S
sin
τ
S
Y
S
=
L
·
φ
B
Z
S
=
R
S
cos
τ
S
with the use of parameters of Expression 2,
the tooth-profile curvilinear shape of the cutting edge portion has a chevron angle that satisfies Expression 5,
Expression 5:
In XYZ coordinate system, when an origin is a center of a pinion, a Y axis is an axis of the pinion, and a Z axis is a center of tooth thickness of a tooth profile of the pinion in a cross-sectional view by a plane perpendicular to an axis of the pinion, coordinates (X S ,Y S ,Z S ) of a given point S of an edge of an acting cutting edge of a cutter having a spur gear shape having a chevron angle are:
coordinates of the point S on a right tooth flank side
{
τ
S
=
-
φ
B
+
φ
0
2
+
inv
(
α
t
)
-
inv
(
α
S
)
-
Δφ
X
S
=
R
S
sin
τ
S
Y
S
=
-
L
·
(
φ
B
+
Δφ
)
Z
S
=
R
S
cos
τ
s
coordinates of the point S on a left tooth flank side
{
τ
s
=
φ
B
-
φ
0
2
+
inv
(
α
t
)
-
inv
(
α
S
)
+
Δφ
X
S
=
R
S
sin
τ
S
Y
S
=
L
·
(
φ
B
+
Δφ
)
Z
S
=
R
S
cos
τ
s
with the use of parameters of Expression 4,
Expression
4
(
η
;
chevron
angle
Δφ
;
phase
angle
between
cutting
edge
end
surface
and
point
S
of
a
general
tool
having
a
spur
gear
shape
Δφ
satisfies
f
(
Δφ
)
=
(
R
aSC
-
R
s
cos
τ
S
)
tan
η
-
R
p
tan
β
·
Δφ
=
0
)
8. The tool according to claim 1 , wherein
a plurality of the cutting edge portions are axially provided.
9. The tool according to claim 8 , wherein
the plurality of cutting edge portions are provided at equal pitches therebetween with the same phase as each other.
10. The tool according to claim 8 , wherein
the plurality of cutting edge portions are provided with their phases being equally displaced from each other, in accordance with a tooth trace shape by the helix angle of the helical gear.
11. The tool according to claim 1 , wherein
a side surface of the tooth tip of the cutting edge portion is provided with a predetermined relief angle.
12. A method for cutting, as a gear to be cut, a skew gear to be meshed with a predetermined helical gear, with the use of the tool according to claim 1 .
13. A tool having a spur gear shape for cutting, as a gear to be cut, a skew gear to be meshed with a predetermined helical gear, the tool comprising:
a cutting edge portion having at least one cutting edge having a tooth-profile curvilinear shape, wherein:
a circular tooth thickness of the cutting edge portion is smaller than a circular tooth thickness of a tooth profile of the helical gear in a cross-sectional view by a plane perpendicular to an axis of the helical gear;
a tooth depth of the cutting edge portion is larger than a tooth depth of the helical gear; and
a face width of the cutting edge portion has an angle which causes a cutting edge to have a chevron shape in a cross-sectional view by a plane including the axis; and
the tool having a spur gear shape is configured to cut the skew gear which is configured to mesh with the helical gear.