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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-92
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Table 10-16A Equations for Over Pins Measurement of Helical Racks
No. Item Symbol
Formula
Example
1
2
Ideal Pin Diameter
Over Pins
Measurement
dp'
dm
pmn – sj
––––––––
cos an
pmn – sj dp 1
H – –––––––– + ––– (1 + –––––)
2 tan an 2 sin an
mn = 1
sj = 1.5708
Ideal Pin Diameter
Actual Pin Diameter
H = 14.0000
an = 20°
b = 15°
dp' = 1.6716
dp = 1.7
dm = 15.1774
10.3.3 Internal Gears
As shown in Figure 10-10, measuring an
internal gear needs a proper pin which has its
tangent point at d + 2xm cir cle. The equations
are in Table 10-17 for obtaining the ideal pin
diameter. The equations for calculating the
between pin measurement, dm, are given in
Table 10-18.
f
tan ap
ap
inv ap
ψ
––
2
inv f
Fig. 10-10 Between Pin Dimension of Internal Gears
Table 10-17 Equations for Calculating Pin Size for Internal Gears
NOTE: The units of angles ψ/2 and f are radians.
db
d
d + 2xm
No. Item Symbol
Formula
Example
1
2
3
4
Half of Tooth Space Angle
at Base Circle
The Pressure Angle at the Point Pin is
Tangent to Tooth Surface
The Pressure Angle at
Pin Center
Ideal Pin Diameter
ψ –2
ap
f
dp
p 2x tan a
(––– + inv a) + ––––––
2z z
zm cos a
cos –1 [–––––––––]
(z + 2x)m
ψ
tan ap – ––
2
ψ
zm cos a (–– – inv f) 2
m = 1
a = 20°
z = 40
x = 0
ψ
–– = 0.054174
2
ap = 20°
f = 0.309796
dp = 1.6489
dm