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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-86
PHONE: 516.328.3300 • FAX: 516.326.8827 • WWW.SDP-SI.COM
Table 10-9 contains the equations for chordal thickness of normal module worms and
worm gears.
Table 10-9 Equations for Chordal Thickness of Normal Module Worms and Worm Gears
No. Item Symbol Formula
Example
1
2
3
4
5
Axial Circular Tooth
Thickness of Worm
Radial Circular Tooth
Thickness of Worm Gear
No. of Teeth in an
Equivalent Spur Gear
(Worm Gear)
Half of Tooth Angle at Pitch
Circle (Worm Gear)
Chordal Thickness
Chordal Addendum
10.2 Span Measurement Of Teeth
sn1
sn2
zv2
qv2
sj1
sj2
hj1
hj2
pmn
––––
2
p
(––– + 2xn2 tan an)mn
2
z2
–––––
cos 3 g
90 360 xn2 tan an
–– + –––––––––––
zv2 pzv2
sn1 cos g
zv mn cos g sin qv2
(sn1 sin g) 2
ha1 + ––––––––
4d1
zv mn cos g
ha2 + –––––––– (1 – cos qv2)
2
mn = 3
an = 20°
zw = 2 z2 = 30
d1 = 38 d2 = 91.1433
ax = 65
xn2 = 0.14278
ha1 = 3.0000 ha2 = 3.42835
g = 9.08472°
sn1 = 4.71239 sn2 = 5.02419
zv2 = 31.15789
qv2 = 3.07964°
sj1 = 4.7124 sj2 = 5.0218
hj1 = 3.0036 hj2 = 3.4958
Span measurement of teeth, sm, is a measure over a number of teeth, zm, made by means
of a special tooth thickness micrometer. The value measured is the sum of normal circular
tooth thickness on the base circle, sbn , and normal pitch, pen (zm – 1).
10.2.1 Spur And Internal Gears
The applicable equations are presented in Table 10-10.
Table 10-10 Span Measurement of Spur and Internal Gear Teeth
No. Item Symbol Formula
Example
1
2
Span Number of Teeth
Span Measurement
zm
sm
z mth = zK(f) + 0.5 See NOTE
Select the nearest natural number of
z mth as zm.
m cos a [p (zm – 0.5) +z inv a ] + 2xm sin a
Metric
0 10
m = 3
a = 20°
z = 24
x = +0.4
z mth = 3.78787
zm = 4
sm = 32.8266
NOTE:
1
K(f) = –– [sec a √(1 + 2f ) 2 – cos2 a – inv a – 2f tan a]
p
x
where f =
z
(10-2)