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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-90
PHONE: 516.328.3300 • FAX: 516.326.8827 • WWW.SDP-SI.COM
The ideal diameters of pins when calculated from the equations of Table 10-13 may not be
practical. So, in practice, we select a standard pin diameter close to the ideal value. After
the actual diameter of pin dp is determined, the over pin measurement dm can be calculated
from Table 10-14.
NOTE: The units of angles ψ/2 and f are radians.
Table 10-13 Equations for Calculating Ideal Pin Diameters
No. Item Symbol
Formula
Example
1
2
3
4
Half 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
dp
inv f
f
dm
ψ –2
ap
f
dp
See NOTE
p 2x tan a
(–– – inv a ) – ––––––
2z z
cos
zm cos a
–1 [–––––––––]
(z + 2x)m
ψ
tan ap +
2
ψ
zm cos a (inv f + ––)
2
dp p 2x tan a
––––––– – ––– + inv a + –––––––
mz cos a 2z z
Find from Involute Function Table
zm cos a
Even Teeth –––––––– + dp
cos f
zm cos a 90°
Odd Teeth –––––––– cos –– + dp
cos f z
m = 1
a = 20°
z = 20
x = 0
ψ
–– = 0.0636354
2
ap = 20°
f = 0.4276057
dp = 1.7245
No. Item Symbol
Formula
Example
1
2
3
4
Actual Diameter of Pin
Involute Function f
The Pressure Angle
at Pin Center
Over Pins
Measurement
Table 10-14 Equations for Over Pins Measurement for Spur Gears
NOTE: The value of the ideal pin diameter from Table 10-13, or its approximate value, is applied
as the actual diameter of pin dp here.
Table 10-15 is a dimensional table under the condition of module m = 1 and pressure
angle a = 20° with which the pin has the tangent point at d + 2xm circle.
Metric
0 10
Let dp = 1.7, then:
inv f = 0.0268197
f = 24.1350°
dm = 22.2941