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ELEMENTS OF METRIC GEAR TECHNOLOGY
Pressure angle
at outside circle
of gear
Half of top land
angle of outside
circle
Top land
thickness
Table 4-3
α a
θ
s a
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The Calculations of Top Land Thickness
No. Item Symbol Formula Example
1
2
3
4.6 Profile Shifted Spur Gear
d b
cos –1 (––)
d a
π 2x tan α
–– + –––––– + (inv α – inv α a)
2z z
(radian)
θd a
m = 2, α = 20°,
z = 16,
x = +0.3, d = 32,
d b = 30.07016
d a = 37.2
α a = 36.06616°
inv α a = 0.098835
inv α = 0.014904
θ = 1.59815°
(0.027893 radian)
s a = 1.03762
Figure 4-8 shows the meshing of a pair of profile shifted gears. The key items in profile
shifted gears are the operating (working) pitch diameters (d w )and the working (operating)
pressure angle (α w ). These values are obtainable from the operating (or i.e., actual) center
distance and the following formulas:
z 1
⎫
d w1 = 2a x –––––
z 1 + z 2
⎪ ⎪⎪
z 2
⎪
d w2
= 2a x ––––– ⎬ (4-5)
z 1 + z 2
⎪ ⎪⎪
d b1 + d b2
α w
= cos (–––––––)
–1
2a x
a x
⎪
⎭
Metric
0 10
I
R
T
1
2
3
4
5
6
7
8
9
10
d w1
11
d 1 d b1
α w
d f2
d b2
d 2
d w2
d a2
O 2
O 1
α w
12
13
Fig. 4-8 The Meshing of Profile Shifted Gears
(α = 20°, z 1 = 12, z 2 = 24, x 1
= +0.6, x 2 = +0.36)
14
15
T-39
A