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<strong>10</strong><br />
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A<br />
ELEMENTS OF METRIC GEAR TECHNOLOGY<br />
<strong>10</strong>.1.3 Helical Gears<br />
T-82<br />
PHONE: 516.328.3300 • FAX: 516.326.8827 • WWW.SDP-SI.COM<br />
The chordal thickness of helical gears should be measured on the normal surface basis<br />
as shown in Table <strong>10</strong>-3. Table <strong>10</strong>-4 presents the equations for chordal thickness of helical<br />
gears in the radial system.<br />
Table <strong>10</strong>-4 Equations for Chordal Thickness of Helical Gears in the Radial System<br />
No. Item Symbol<br />
Formula<br />
Example<br />
1<br />
2<br />
Normal Circular Tooth Thickness<br />
Number of Teeth in an Equivalent<br />
Spur Gear<br />
sn<br />
zv<br />
p<br />
(–– + 2xt tan at )mt cos b<br />
2<br />
z<br />
–––––<br />
cos<br />
m = 4<br />
at = 20°<br />
b = 22° 30' 00"<br />
z = 20<br />
xt = +0.3<br />
3<br />
4<br />
5<br />
Half of Tooth Angle at Pitch<br />
Circle<br />
Chordal Thickness<br />
Chordal Addendum<br />
qv<br />
sj<br />
hj<br />
ha = 4.7184<br />
sn = 6.6<strong>11</strong>9<br />
zv = 25.3620<br />
qv = 4.04196°<br />
sj = 6.6065<br />
hj = 4.8350<br />
NOTE: Table <strong>10</strong>-4 equations are also for the tooth profile of a Sunderland gear.<br />
3 b<br />
90 360xt tan at<br />
–– + –––––––––––<br />
zv pzv<br />
zv mt cos b sin qv<br />
zv mt cos b<br />
–––––––– (1– cos qv ) + ha<br />
2<br />
Table <strong>10</strong>-5 Equations for Chordal Thickness of Gleason Straight Bevel Gears<br />
No. Item Symbol<br />
Formula<br />
Example<br />
1<br />
2<br />
4<br />
5<br />
Table <strong>10</strong>-3 Equations for Chordal Thickness of Helical Gears in the Normal System<br />
No. Item Symbol<br />
Formula<br />
Example<br />
1<br />
2<br />
3<br />
4<br />
5<br />
Normal Circular Tooth Thickness<br />
Number of Teeth of an Equivalent<br />
Spur Gear<br />
Half of Tooth Angle at Pitch<br />
Circle<br />
Chordal Thickness<br />
Chordal Addendum<br />
Circular Tooth Thickness Factor<br />
(Coefficient of Horizontal Profile Shift)<br />
Circular Tooth Thickness<br />
Chordal Thickness<br />
Chordal Addendum<br />
K<br />
s1<br />
s2<br />
sj<br />
hj<br />
sn<br />
zv<br />
qv<br />
sj<br />
hj<br />
p<br />
(–– + 2xn tan an )mn<br />
2<br />
z<br />
––––––<br />
cos3 b<br />
Obtain from Figure <strong>10</strong>-2<br />
(on the following page)<br />
pm – s2<br />
90 360xn tan an<br />
–– + ––––––––––<br />
zv pzv<br />
pm<br />
––– – (ha1 – ha2) tan a – Km<br />
2<br />
s 3<br />
s – –––<br />
6d 2<br />
zv mn sin qv<br />
zv mn<br />
–––– (1– cos qv ) + ha<br />
2<br />
s 2 cos d<br />
ha + ––––––<br />
4d<br />
m = 4<br />
a = 20°<br />
S = 90°<br />
z1 = 16<br />
z2 = 40<br />
Metric<br />
0 <strong>10</strong><br />
mn = 5<br />
an = 20°<br />
b = 25° 00' 00"<br />
z = 16<br />
xn = +0.2<br />
ha = 6.0000<br />
sn = 8.5819<br />
zv = 21.4928<br />
qv = 4.57556°<br />
sj = 8.5728<br />
hj = 6.17<strong>12</strong><br />
z1<br />
–– = 0.4<br />
z2<br />
K = 0.0259<br />
ha1 = 5.5456<br />
ha2 = 2.4544<br />
d1 = 21.80<strong>14</strong>°<br />
d2 = 68.1986°<br />
s1 = 7.5<strong>11</strong>9<br />
s2 = 5.0545<br />
sj1 = 7.4946<br />
sj2 = 5.0536<br />
hj1 = 5.7502<br />
hj2 = 2.4692
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