Tool for cutting gear and method for cutting gear
AssigneeOgasawara Precision Engineering LTD
InventorHiroomi Ogasawara
Life of this patent
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Abstract
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 SatSC, 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 Sat, 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 βa, and a face width of the cutting edge portion is represented as bsc, b SC ≦ s at - s atSC tan β a is satisfied.
Claims13
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 SatSC, 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 Sat, 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 βa, and a face width of the cutting edge portion is represented as bsc, the following Expression 1 is satisfied
- b
- SC
- ≦
- s
- at
- -
- s
- atSC
- tan
-
-
- β
- a
- .
- Expression
-
-
- 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 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 (XS,YS,ZS) 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 (XS,YS,ZS) 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
- )
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.
Dependencies are inferred from the claim text.