19-1. Calculation formula for standard spur gear
19-1.Calculation formula for standard spur gear
Symbol description and unit
1. Tooth tip circle diameter
d
k
=(z+2)*m 〔mm〕
d
k
=
z： Number of teeth
m： module
2.Reference pitch circle diameter
d
o
=z*m 〔mm〕
d
o
=
3. All teeth
( Notch depth）
h=2*m+c
k
〔mm〕
h=
c
k
：Get it=0.25*m
4. Devaluation limit number of teeth
Z
c
=2/Sin
2
α
0
Z
c
=
α
0
:Pressure angle [ Every time]
5. Engagement rate ε
ε
1
=(((z
1
+2)
2
-(z
1
*Cosα
0
)
2
)
0.5
-z
1
*Sinα
0
)/(2*π*Cosα
0
)
ε
1
=
ε
2
=(((z
2
+2)
2
-(z
2
*Cosα
0
)
2
)
0.5
-z
2
*Sinα
0
)/(2*π*Cosα
0
)
ε
2
=
ε=ε
1
+ε
2
z
1
: Number of teeth of gear 1
z
2
:Number of teeth of gear 2
α
0
: Pressure angle [ Every time]
Glossary
1. Spur gear
A cylindrical gear that is a straight line parallel to the tooth streak axis.
Transmits rotational motion between two normally parallel axes.
2.Standard gear
A gear whose arc tooth thickness on the reference pitch circle is 1/2 of the reference pitch.
3.Reference pitch circle
A circle that serves as a reference when determining the dimensions of gears. The length of the circumference is multiple the number of teeth of the reference pitch for cylindrical gears. ， For worms, the diameter coefficient of the axial pitch is doubled, and for worm wheels, the number of teeth is multiplied.
4. Top Gear
The distance from the tip circle of the gear to the bottom circle of the gear that meshes with it.
5. All tooth bamboo
The length of the entire tooth in the direction of the tooth take. It is equal to the sum of the take at the end of the tooth and the take at the base of the tooth.
6. Take at the end of the tooth
Radius difference between the pitch circle of the gear and the tip circle.
7. Take at the base of the teeth
Radius difference between the pitch circle of the gear and the tooth bottom circle.
8. Pressure angle
At one point on the tooth surface, the angle between the radius line and the tangent to the tooth profile is called pressure.Usually it means the pressure angle of the pitch point.
9.module
The value obtained by dividing the reference pitch by the circumference ratio. It defines the size of the tooth. ， Expressed in millimeters.
10.contact rate
The value obtained by dividing the length of the contact arc by the circular pitch.In the case of involute gearsカミアイ長サをEqual to the value divided by the normal pitch。
11.切下ゲ
Phenomenon that a part of the tooth profile curve at the tooth root is cut off at the tooth tip of the tool。
Reference: "Design of Cylindrical Gears" (Kinki Gear Association) Tooth profile design of cylindrical gears Tooth profile design of spur gears Page 68 Refer to standard gears.
Reference: "Design of Cylindrical Gears" （Kinki Gear Social gathering） Japanese Industrial Standards JIS B 0102-1966 Gear terminology, page 221 Quoted from the type of gear.