19-2. Calculation formula for dislocation spur gear

19-2.Calculation formula for dislocation spur gear Symbol description and unit
　　
1. Center distance increase coefficient y=ax/m-(z1+z2)/2
y=		 ax：Center distance [mm]
m： module
z1： Number of teeth of gear 1
z2： Number of teeth of gear 2
2. Engagement pressure angle αb=Cos-1(Cosα0/(2*y/(z1+z2)+1)) [ Every time]
αb=		 α0： Pressure angle[]
y： Center distance increase coefficient
z1：Number of teeth of gear 1
z2： Number of teeth of gear 2
3. Sum of dislocation coefficients x=x1+x2
=(z1+z2)*(invαb-invα0)/(2*tanα0)
=(z1+z2)*((tanαb-αb)-(tanα0-α0))/(2*tanα0)
x=		 αb：Engagement pressure angle[ Every time]
α0： Pressure angle[ Every time]
z1： Number of teeth of gear 1
z2： Number of teeth of gear 2
4. Dislocation amount x1*m=

x2*m=(x-x1)*m
=		 x： Sum of dislocation coefficients
x1： Dislocation coefficient 1
m： module
5. Pitch circle diameter d01=z1*m [mm]
d01=

d02=z2*m [mm]
d02= 		z1： Number of teeth of gear 1
z2： Number of teeth of gear 2
m： module
6. Base circle diameter dg1=d01*Cosα0[mm]
dg1=

dg2=d02*Cosα0 [mm]
dg2= 		d01： Pitch circle diameter1 [mm]
d02： Pitch circle diameter 2 [mm]
α0: Pressure angle [ Every time]
7.Engagement pitch circle diameter db1=dg1/Cosαb[mm]
db1=

db2=dg2/Cosαb[mm]
db2= 		dg1：Base circle diameter 1 [mm]
dg2：Base circle diameter 2 [mm]
αb：Engagement pressure angle [ Every time]
8.Take of the end of the tooth ｈｋ1=(1+y-x2)*m
ｈｋ1=

hk2=(1+y-x1)*m
hk2= 		y：Center distance increase coefficient


x1：Dislocation coefficient 1


x2： Dislocation coefficient 2


m： module





9. All teeth h=(2.25+y-(x1+x2))*m
h=
10. Tooth tip circle diameter dk1=d01+2*ｈｋ1[mm]
dk1=

dk2=d02+2*ｈｋ2 [mm]
dk2= 		d01： Pitch circle diameter 1 [mm]
d02：Pitch circle diameter 2 [mm]
ｈｋ1：Take of the end of the tooth 1
hk2：Take of the end of the tooth 2
11.Tooth bottom circle diameter dr1=dk1-2*ｈ [mm]
dr1=

dr2=dk2-2*ｈ [mm]
dr2= 		dk1： Tooth tip circle diameter 1 [mm]
dk2：Tooth tip circle diameter 2 [mm]
h： All teeth
Glossary
1. Dislocation gear A shift gear is an impotence gear when it is engaged with a reference rack without a pack rush. The reference pitch circle and the reference pitch line do not touch each other.
2. Pressure angle The angle between the radius line and the tangent to the tooth profile at one point on the tooth surface is called the pressure angle, but it is usually called the pressure angle. It means the pressure angle at the pitch point.
3. Kamiai pressure angle 一 The pressure angle on the kami eye pitch circle of the pair of meshing gears.
4. module The value obtained by dividing the reference pitch by the circumference ratio. It defines the size of the tooth and is expressed in millimeters.
5. Dislocation coefficient The value obtained by dividing the amount of dislocation by the module. For Hasba gears, the values ??obtained by dividing the amount of dislocation by the front module or the right-angled tooth module are called the frontal dislocation coefficient and the right-angled dislocation coefficient, respectively.
6. Kamiai rate The value obtained by dividing the length of the contact arc by the circular pitch. In the case of involute gear, it is equal to the value obtained by dividing the length of the kamiai by the normal pitch.
7. Kamiai pitch circle 一When a pair of gears mesh，Circles belonging to each gear that are in contact with each other and make a rolling motion. These radii are the values ??obtained by dividing the center distance proportionally to the number of teeth.
8. Base circle diameter The diameter of the circle in which the involute tooth profile is created as the involute。
9. Bamboo at the end of the tooth Radius difference between gear pitch circle and tooth tip circle。
10. All teeth タケ The length of the entire tooth in the direction of the tooth bamboo. It is equal to the sum of the bamboo at the end of the tooth and the bamboo at the base of the tooth.
Reference: "Design of Cylindrical Gears" (Kinki Gear Social gathering)　 Japanese Industrial Standards JIS B 0102-1966 Gear terminology, page 223, quoted from the type of gear.