I R 1 2 3 4 5 6 7 8 9 10 11 12 13 T 14 15 A
I R 1 2 3 4 5 6 7 8 9 10 11 12 13 T 14 15 A
I R 1 2 3 4 5 6 7 8 9 10 11 12 13 T 14 15 A
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I<br />
R<br />
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9<br />
<strong>10</strong><br />
<strong>11</strong><br />
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<strong>13</strong><br />
<strong>14</strong><br />
<strong>15</strong><br />
A<br />
ELEMENTS OF METRIC GEAR TECHNOLOGY<br />
T-84<br />
PHONE: 516.328.3300 • FAX: 516.326.8827 • WWW.SDP-SI.COM<br />
If a standard straight bevel gear is cut by a Gleason straight bevel cutter, the tooth angle<br />
should be adjusted according to:<br />
180° s<br />
tooth angle (°) = –––– (–– + hf tan a) (<strong>10</strong>-1)<br />
pRe 2<br />
This angle is used as a reference in determining the circular tooth thickness, s, in setting<br />
up the gear cutting machine.<br />
Table <strong>10</strong>-7 presents equations for chordal thickness of a Gleason spiral bevel gear.<br />
No. Item Symbol<br />
Formula<br />
Example<br />
1<br />
2<br />
Circular Tooth<br />
Thickness Factor<br />
Circular Tooth<br />
Thickness<br />
Figure <strong>10</strong>-3 is shown on the following page.<br />
The calculations of circular thickness of a Gleason spiral bevel gear are so complicated<br />
that we do not intend to go further in this presentation.<br />
<strong>10</strong>.1.5 Worms And Worm Gears<br />
K<br />
s1<br />
s2<br />
Obtain from Figure <strong>10</strong>-3<br />
p – s2<br />
p tan an<br />
–– – (ha1 – ha2) –––––– – Km<br />
2 cos bm<br />
S = 90° m = 3 an = 20°<br />
z 1 = 20 z2 = 40 bm = 35°<br />
ha1 = 3.4275 ha2 = 1.6725<br />
K = 0.060<br />
p = 9.4248<br />
s1 = 5.6722 s2 = 3.7526<br />
Table <strong>10</strong>-8 presents equations for chordal thickness of axial module worms and worm<br />
gears.<br />
Table <strong>10</strong>-8 Equations for Chordal Thickness of Axial Module Worms and Worm Gears<br />
No. Item Symbol Formula<br />
Example<br />
1<br />
2<br />
3<br />
4<br />
5<br />
Axial Circular Tooth<br />
Thickness of Worm<br />
Radial Circular Tooth<br />
Thickness of Worm Gear<br />
No. of Teeth in an<br />
Equivalent Spur Gear<br />
(Worm Gear)<br />
Half of Tooth Angle at Pitch<br />
Circle (Worm Gear)<br />
Chordal Thickness<br />
Chordal Addendum<br />
sx1<br />
sx2<br />
zv2<br />
qv2<br />
sj1<br />
sj2<br />
hj1<br />
hj2<br />
pmx<br />
––––<br />
2<br />
(––<br />
p<br />
+ 2x x2 tan ax)mx<br />
2<br />
z2<br />
–––––<br />
cos 3 g<br />
90 360 xx2 tan ax<br />
––– + ––––––––––<br />
zv2 pzv2<br />
sx1 cos g<br />
zv mx cos g sin qv2<br />
(sx1 sin g cos g) 2<br />
ha1 + –––––––––––<br />
4d1<br />
zv mx cos g<br />
ha2 + –––––––– (1 – cos qv2)<br />
2<br />
Metric<br />
0 <strong>10</strong><br />
mx = 3<br />
an = 20°<br />
zw = 2 z2 = 30<br />
d1 = 38 d2 = 90<br />
ax = 65<br />
xx2 = +0.33333<br />
ha1 = 3.0000 ha2 = 4.0000<br />
g = 8.97263°<br />
ax = 20.22780°<br />
sx1 = 4.7<strong>12</strong>39 sx2 = 5.44934<br />
zv2 = 31.<strong>12</strong>885<br />
qv2 = 3.34335°<br />
sj1 = 4.6547 sj2 = 5.3796<br />
hj1 = 3.0035 hj2 = 4.0785
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