Machinery''''s Handbook 2th Episode 4 Part 8 docx

SILENT OF INVERTED TOOTH CHAIN 2955
Table 4b. Over-Pin Diameter Tolerances for ANSI
3
⁄
16
- in. Pitch and Larger
Silent Chain Sprocket Measurement (ANSI B29.2M-1982, R1987)
Pitch
Number of Teeth
Up to
15 16 - 24 25 - 35 36 - 48 49 - 63 64 - 80 81 - 99
100 -
120
121-
143 144 up
Tolerances,
a
Inches
a
All tolerances are negative.
0.1875 0.004 0.004 0.004 0.004 0.004 0.005 0.005 0.005 0.005 0.005
Tolerances,
a
Millimerers
4.76 0.10 0.10 0.10 0.10 0.10 0.13 0.13 0.13 0.13 0.13
Grooving tool may be either square or round end but groove must be full width down to diam-
eter of G. For values of G (max.) see footnote to Table 3a
Values of H (± 0.003 in.) = 0.051 in. are given only for chain numbers SC302 and SC402. M =
Max. overall width of chain. The maximum radius over a new chain engaged on a sprocket will
not exceed the sprocket pitch radius plus 75 per cent of the chain pitch. To obtain the chain

widths and sprocket face dimensions in millimeters, multiply each entry by 25.4.
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2956 SILENT OF INVERTED TOOTH CHAIN
Table 4c. ANSI
3
⁄
8
- in. Pitch and Larger Silent Chain Widths
and Sprocket Face Dimensions (ANSI B29.2M-1982, R1987)
Chain
No
Chain
Pitch Type
M
a

Max. A
C
±0.005
D
±0.010
F
+0.125
−0.000
R
±0.003
W
+0.010
−0.000

SC302 0.375
Side
Guide
b
0.594 0.133 ……0.200 0.410
SC303 Center
Guide
0.844 0.100 … 0.750 …
SC304 1.094 … 1.000 …
SC305 1.344 … 1.250 …
SC306 1.594 … 1.500 …
SC307 1.844 … 1.750 …
SC308 2.094 … 2.000 …
SC309 2.344 … 2.250 …
SC310 2.594 … 2.500 …
SC312 Double-
Guide
3.094 1.000 3.000 …
SC316 4.094 4.000 …
SC320 5.094 5.000 …
SC324 6.094 6.000 …
SC402 0.500
Side
Guide
b
0.750 0.133 …… 0.200 0.410
SC403 Center
Guide
0.875 0.100 … 0.750 …
SC404 1.125 … 1.000 …

SC405 1.375 … 1.250 …
SC406 1.625 … 1.500 …
SC407 1.875 … 1.750 …
SC408 2.125 … 2.000 …
SC409 2.375 … 2.250 …
SC410 2.625 … 2.500 …
SC411 2.875 … 2.750 …
SC412 3.125 … 3.000 …
SC414 3.625 … 3.500 …
SC416 Double-
Guide
4.125 1.000 4.000 …
SC420 5.125 5.000 …
SC424 6.125 6.000 …
SC432 8.125 8.000 …
SC504 0.625 Center-
Guide
1.156 0.177
0.125
… 1.000 0.250 …
SC505 1.406 … 1.250 …
SC506 1.656 1.500 …
SC507 1.906 1.750 …
SC508 2.156 2.000 …
SC510 2.656 2.500 …
SC512 3.156 3.000 …
SC516 4.156 4.000 …
SC520 Double-
Guide
5.156

2.000
5.000 …
SC524 6.156 6.000 …
SC528 7.156 7.000 …
SC532 8.156 8.000 …
SC540 10.156 10.000 …
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SILENT OF INVERTED TOOTH CHAIN 2957
SC604 0.750 Center-
Guide
1.187 0.274 0.180 … 1.000 0.360 …
SC605 1.437 … 1.250 …
SC606 1.687 … 1.500 …
SC608 2.187 … 2.000 …
SC610 2.687 … 2.500 …
SC612 3.187 … 3.000 …
SC614 3.687 … 3.500 …
SC616 4.187 … 4.000 …
SC620 5.187 … 5.000 …
SC624 6.187 4.000 6.000 …
SC628 Double
guide
7.187 7.000 …
SC632 8.187 8.000 …
SC636 9.187 9.000 …
SC640 10.187 10.000 …
SC648 12.187 12.000 …
SC808 1.000 Center
Guide

2.250 0.177 0.125 … 2.000 0.250 …
SC810 2.750 … 2.500 …
SC812 3.250 … 3.000 …
SC816 4.250 … 4.000 …
SC820 5.250 … 5.000 …
SC824 6.250 … 6.000 …
SC828 7.250 … 7.000 …
SC832 Double
guide
8.250 … 8.000 …
SC836 9.250 2.000 9.000 …
SC840 10.250 10.000 …
SC848 12.250 12.000 …
SC856 14.250 14.000 …
SC864 16.250 16.000 …
SC1010 1.25 Center
Guide
2.812 0.274 0.180 … 2.500
0.360 …
SC1012 3.312 … 3.000 …
SC1016 4.312 … 4.000 …
SC1020 5.312 … 5.000 …
SC1024 6.312 … 6.000 …
SC1028 7.312 … 7.000 …
SC1032 Double
guide
8.312 4.000 8.000 …
SC1036 9.312 9.000 …
SC1040 10.312 10.000 …
SC1048 12.312 12.000 …

SC1056 14.312 14.000 …
SC1064 16.312 16.000 …
SC1072 18.312 18.000 …
SC1080 20.312 20.000 …
Table 4c. (Continued) ANSI
3
⁄
8
- in. Pitch and Larger Silent Chain Widths
and Sprocket Face Dimensions (ANSI B29.2M-1982, R1987)
Chain
No
Chain
Pitch Type
M
a

Max. A
C
±0.005
D
±0.010
F
+0.125
−0.000
R
±0.003
W
+0.010
−0.000

Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2958 SILENT OF INVERTED TOOTH CHAIN
All dimensions in inches. M Max. overall width of chain.
SC1212 1.500 Center
Guide
3.375 0.274 0.180 … 3.000 0.360 …
SC1216 4.375 … 4.000 …
SC1220 5.375 … 5.000 …
SC1224 6.375 … 6.000 …
SC1228 7.375 … 7.000 …
SC1232 Double
guide
8.375 … 8.000 …
SC1236 9.375 4.000 9.000 …
SC1240 10.375 10.000 …
SC1248 12.375 12.000 …
SC1256 14.375 14.000 …
SC1264 16.375 16.000 …
SC1272 18.375 18.000 …
SC1280 20.375 20.000 …
SC1288 22.375 22.000 …
SC1296 24.375 24.000 …
SC1616 2.000 Center
Guide
4.500 0.274 0.218 … 4.000 0.360 …
SC1620 5.500 … 5.000 …
SC1624 6.500 … 6.000 …
SC1628 7.500 4.000 7.000 …
SC1632 Double

guide
8.500 8.000 …
SC1640 10.500 10.000 …
SC1648 12.500 12.000 …
SC1656 14.500 14.000 …
SC1664 16.500 16.000 …
SC1672 18.500 18.000 …
SC1680 20.500 20.000 …
SC1688 22.500 22.000 …
SC1696 24.500 24.000 …
SC16120 30.500 30.000 …
a
Specify side guide or center guide type.
b
Side Guide chains have single outside guides of same thickness as toothed links.
Table 4c. (Continued) ANSI
3
⁄
8
- in. Pitch and Larger Silent Chain Widths
and Sprocket Face Dimensions (ANSI B29.2M-1982, R1987)
Chain
No
Chain
Pitch Type
M
a

Max. A
C

±0.005
D
±0.010
F
+0.125
−0.000
R
±0.003
W
+0.010
−0.000
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SILENT OF INVERTED TOOTH CHAIN 2959
All dimensions in inches. M = Max. overall width of chain.
To obtain chain width and sprocket face dimensions in millimeters, multiply each entry by 25.4.
Sprocket Hub Dimensions.—The important hub dimensions are the outside diameter,
the bore, and the length. The maximum hub diameter is limited by the need to clear the
chain guides and is of particular importance for sprockets with low numbers of teeth. The
American National Standard for inverted tooth chains and sprocket teeth ANSI B29.2M-
1982 (R1987) provides the following formulas for calculating maximum hub diameters,
MHD.
Table 4d. American National Standard
3
⁄
16
- in. Pitch and Larger Silent
Chain Widths and Sprocket Face Dimensions ANSI B29.2M-1982,1987
Values of H = 0.025 in. are given for chain numbers SC0305 through SC0315.
Chain

No
Chain
Pitch Type M Max. A
C
Max.
F
Min.
RW
±0.003
SC0305 0.1875 Side Guide 0.216 0.06 … 0.09 0.075
SC0307 0.278 … 0.138
SC0309 0.341 … 0.201
SC0311 Side Guide/
Center Guide
0.403 0.050 0.334 0.264
SC0313 0.466 0.396 0.327
SC0315 0.528 0.459 0.390
SC0317 Center Guide 0.591 0.521 …
SC0319 0.653 0.584 …
SC0321 0.716 0.646 …
SC0323 0.778 0.709 …
SC0325 0.850 0.771 …
SC0327 0.903 0.834
SC0329 0.966 0.896 …
SC0331 1.028 0.959 …
MHD(for hobbed teeth) P
180°
N

⎝⎠

⎛⎞
cot 1.33–=
MHD(for stradle cut teeth) P
180°
N

⎝⎠
⎛⎞
cot 1.25–=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2960 SILENT OF INVERTED TOOTH CHAIN
Maximum hub diameters for sprockets with from 17 to 31 teeth are given in Table 5.
Maximum hub diameters for other methods of cutting teeth may differ from thesevalues.
Recommended maximum bores are given in Table 6.
Table 5. American National Standard Minimum Hub Diameters for Silent chain
Sprockets (17 to 31 Teeth) ANSI B29.2M-1982,1987
All dimensions in inches.
Values shown are 1-inch pitch chain. For other pitches (
3
⁄
8
- inch and larger) multiply the values
given by the pitch.
Good practice indicates that teeth of sprockets up to and including 31 teeth should have a Rockwell
hardness of C50 min.
Table 6. Recommended maximum Sprocket Bores for Silent Chains
American Chain Association.
No. Teeth
Hob cut

Straddle
Cut
No.
Teeth
Hob cut
Straddle
Cut
No.
Teeth
Hob cut
Straddle
Cut
Min. Hub Diam. Min. Hub Diam. Min. Hub Diam.
17 4.019 4.099 22 5.626 5.706 27 7.226 7.306
18 4.341 4.421 23 5.946 6.026 28 7.546 7.626
19 4.662 4.742 24 6.265 6.345 29 7.865 7.945
20 4.983 5.063 25 6.586 6.666 30 8.185 8.265
21 5.304 5.384 26 6.905 6.985 31 8.503 8.583
Number
of Teeth
Chain Pitch, Inches
3
⁄
8
1
⁄
2
5
⁄
8

3
⁄
4
1
1
1
⁄
4
1
1
⁄
2
2
Maximum Sprocket Bore. Inches
17 1
1
3
⁄
8
1
3
⁄
4
2
2
3
⁄
4
3
3

⁄
8
4
1
⁄
8
5
1
⁄
4
19
1
1
⁄
4
1
5
⁄
8
2
2
3
⁄
8
3
1
⁄
4
4
4

7
⁄
8
6
3
⁄
4
21
1
3
⁄
8
1
7
⁄
8
2
1
⁄
4
2
3
⁄
4
3
3
⁄
4
4
1

⁄
2
5
1
⁄
2
7
3
⁄
4
23
1
5
⁄
8
2
1
⁄
8
2
5
⁄
8
3
1
⁄
4
4
3
⁄

8
5
1
⁄
2
6
1
⁄
2
9
25
1
3
⁄
4
2
3
⁄
8
3
3
5
⁄
8
4
3
⁄
4
6
7

1
⁄
4
10
27 2
2
5
⁄
8
3
3
⁄
8
3
7
⁄
8
5
3
⁄
8
6
3
⁄
4
8
1
⁄
8
11

1
⁄
4
29
2
1
⁄
8
2
13
⁄
16
3
5
⁄
8
4
3
⁄
8
5
3
⁄
4
7
3
⁄
8
9
1

⁄
8
12
1
⁄
4
31
2
5
⁄
16
3
1
⁄
16
3
7
⁄
8
4
5
⁄
8
6
3
⁄
8
8
9
7

⁄
8
13
1
⁄
4
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SILENT OF INVERTED TOOTH CHAIN 2961
Table 7a. Tooth Form for ANSI
3
⁄
8
- inch and larger Silent Tooth Sprocket
ANSI B29.2M-1982, R1987
Table 7b. Tooth Form for ANSI
3
⁄
16
- inch and larger Silent Tooth Sprocket ANSI
B29.2M-1982, R1987
P = Chain Pitch
N = Number of Teeth
E = Diameter to Center of Topping Curve
B = Diameter to Base of Working Face
EP
180°
N
cot 0.22–
⎝⎠

⎛⎞
=
BP1.515213
180°
N
cot 1.1–
⎝⎠
⎛⎞
2
+=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2962 SILENT OF INVERTED TOOTH CHAIN
Table 8. Straddle Cutters for American National Standard
3
⁄
8
- in. Pitch
and Larger Silent Chain Sprocket Teeth
All dimensions in inches. To obtain values in millimeters, multiply inch values by 25.4.
These data are given as supplementary information in ANSI B29.2M-1982, R1987 and are made
available by the American Chain Association.
Fig. 3. Identification of Inverted Tooth Chain Hobs.
Chain Pitch
P Mark Cutter
a
a
Range of teeth is indicated in the cutter marking.
Outside
Diam. 0.75P αθBore

b
b
Suggested standard. Bores other than standard must be specified.
0.375
SC3-15 thru 35
SC3-36 up
3.625 0.2813
22°-30′
27°-30′
12°
5°
1.250
0.500
SC4-15 thru 35
SC4-36 up
3.875 0.3750
22°-30′
27°-30′
12°
5°
1.250
0.625
SC5-15 thru 35
SC5-36 up
4.250 0.4688
22°-30′
27°-30′
2°
5°
1.250

0.750
SC6-15 thru 35
SC6-36 up
4.625 0.5625
22°-30′
27°-30′
12°
5°
1.250
1.000
SC8-15 thru 35
SC8-36 up
5.250 0.7500
22°-30′
27°-30′
12°
5°
1.500
1.250
SC10-15 thru 35
SC10-36 up
5.750 0.9375
22°-30′
27°-30′
12°
5°
1.500
1.500
SC12-15 thru 35
SC12-36 up

6.250
1.1250
22°-30′
27°-30′
12°
5°
1.750
2.000
SC16-15 thru 35
SC16-36 up
6.500 1.5000
22°-30′
27°-30′
12°
5°
1.750
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SILENT OF INVERTED TOOTH CHAIN 2963
Table 9. Hobs for ANSI
3
⁄
8
- inch and larger Silent Tooth Sprocket
*

Sprocket Design and Tooth Form.—Except for tooth form, silent chain sprocket design
parallels the general design practice of roller chain sprockets as covered in the previous
section.
As shown in Tables 7a and 7b, sprockets for American National Standard silent chains

have teeth with straight-line working faces. The tops of teeth for
3
⁄
8
-in. and larger pitch
chains may be rounded or square. Bottom clearance below the working face is not speci-
fied but must be sufficient to clear the chain teeth. The standard tooth form for
3
⁄
8
-in. and
larger pitch chains is designed to mesh with link plate contours having an included angle of
60 degrees as shown in the diagram of Table 7a. The standard tooth form for
3
⁄
16
-in. pitch
chains has an included angle of 70 degrees as shown in Table 7b. It will be seen from these
tables that the angle between the faces of a given tooth [60°–720°/N for
3
⁄
8
-in. pitch and
larger; 70°–720°/N for
3
⁄
16
-in. pitch] becomes smaller as the number of teeth decreases.
Therefore, for a
3

⁄
8
-in. pitch or larger 12-tooth sprocket it will be zero. In other words the
tooth faces will be parallel.
For smaller tooth numbers the teeth would be undercut. For best results, 21 or more teeth
are recommended; less than 17 should not be used.
Cutting Silent Chain Sprocket Teeth.—Sprocket teeth may be cut by either a straddle
cutter or a hob. Essential dimensions for straddle cutters are given in Table 8 and for hobs
in Table 9 and 10. American National Standard silent chain hobs are stamped for identifi-
cation as shown on page 2375.
P = Chain Pitch
N = Number of Teeth
*
Source: American Chain Association.
HGD P
1
180°
N
sin
2
0.5625
1.5 30
180
N
–
⎝⎠
⎛⎞
°
sin
180°

N
sin
–+=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SILENT OF INVERTED TOOTH CHAIN 2965
Design of Silent Chain Drives.—The design of silent chain transmissions must be based
not only upon the power to be transmitted and the ratio between driving and driven shafts,
but also upon such factors as the speed of the faster running shaft, the available space,
assuming that it affects the sprocket diameters, the character of the load and certain other
factors. Determining the pitch of the chain and the number of teeth on the smallest sprocket
are the important initial steps. Usually any one of several combinations of pitches and
sprocket sizes may be employed for a given installation. In attempting to select the best
combination, it is advisable to consult with the manufacturer of the chain to be used. Some
of the more important fundamental points governing the design of silent chain transmis-
sions will be summarized.
The design of a silent chain drive consists, primarily, of the selection of the chain size,
sprockets, determination of chain length, center distance, lubrication method, and arrange-
ment of casings.
Pitch of Silent Chain.—The pitch is selected with reference to the speed of the faster run-
ning shaft which ordinarily is the driver and holds the smaller sprocket. The following
pitches are recommended: for a faster running shaft of 2000 to 5000 rpm,
3
⁄
8
-inch pitch; for
1500 to 2000 rpm,
1
⁄
2

-inch pitch; for 1200 to 1500 rpm,
5
⁄
8
-inch pitch, for 1000 to 1200 rpm,
3
⁄
4
-inch pitch; for 800 to 1000 rpm, 1-inch pitch; for 650 to 800 rpm, 1
1
⁄
4
-inch pitch; for 300
to 600 rpm, 1
1
⁄
2
-inch pitch; for 300 to 500 rpm, 2-inch pitch; and for below 300 rpm, 2
1
⁄
2
-
inch pitch. As the normal operating speeds increase, the allowable pitch decreases. Rec-
ommendations relating to the relationship between pitch and operating speed are intended
for normal or average conditions. Speeds for a given pitch may be exceeded under favor-
able conditions and may have to be reduced when conditions are unfavorable. In general,
smoother or quieter operation will result from using the smallest pitch suitable for a given
speed and load. However, a larger pitch which might be applicable under the same condi-
tions, will result in a narrower chain and a less expensive transmission. This relationship
usually is true when there is a small speed reduction and comparatively long center dis-

tance. If there is a large speed reduction and short center distance, drives having the smaller
pitches may be less expensive.
Maximum Ratios for Silent Chain Drives.—The maximum permissible ratios between
driving and driven sprockets vary somewhat for different conditions and usually range
from 6- or 7-to-1 up to 10-to-1. Some drives have even higher ratios, especially when the
operating conditions are exceptionally favorable. When a large speed reduction is neces-
sary, it is preferable as a general rule to use a double reduction or compound type of trans-
mission instead of obtaining the entire reduction with two sprockets. Drives should be so
proportioned that the angle between the two strands of a tight chain does not exceed 45
degrees. When the angle is larger, the chain does not have sufficient contact with the driv-
ing sprocket.
Sprocket Size and Chain Speed: A driving sprocket with not less than 17 teeth is gener-
ally recommended. For the driven sprocket, one manufacturer recommends 127 teeth as a
maximum limit and less than 100 as preferable. If practicable, the sprocket sizes should be
small enough to limit the chain speed to from 1200 to 1400 feet per minute. If the chain
speed exceeds these figures, this may indicate that the pitch is too large or that a smaller
pitch, and, consequently, a reduction in sprocket diameters (and chain speed) will result in
better operating conditions. Both sprockets should preferably have a “hunting tooth ratio”
relative to the number of chain links for uniform wear. See “Hunting Tooth Ratios,” page
1867.
If there is a small reduction in speed between the driving and driven shafts, both sprock-
ets may be made as small as is consistent with satisfactory operation, either to obtain a
compact drive or possibly to avoid excessive chain speed in cases where the rotative speed
is high for a given horsepower. Under such conditions, one manufacturer recommends
driving sprockets ranging from 17 to 30 teeth, and driven sprockets ranging from 19 to 33
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2966 SILENT OF INVERTED TOOTH CHAIN
teeth. If the number of revolutions per minute is low for a given horsepower and the center
distance comparatively long, then the recommended range for driving sprockets is from 23

to iii teeth, and driven sprockets from 27 to 129 teeth. The preferable range is from 17 to 75
teeth for the driving sprockets, and 19 to 102 teeth for the driven sprockets.
Center Distance for Silent Chain Drives.—If the ratio of the drive is small, it is possible
to locate the sprockets so close-that the teeth just clear; however, as a general rule, the min-
imum center-to-center distance should equal the sum of the diameters of both sprockets.
According to the Whitney Chain & Mfg. Co., if the speed ratio is not over 2
1
⁄
2
-to-1, the cen-
ter distance may be equal to one-half the sum of the sprocket diameters plus tooth clear-
ance, providing this distance is not less than the minimum given in Table 11. If the speed
ratio is greater than 2
1
⁄
2
-to-1, the center distance should not be less than the sum of the
sprocket diameters.
Table 11. Minimum Center Distancesfor Various Pitches
When the chain length in pitches is known, the equivalent center distance for a tight chain
may be determined by the formula for roller chain found on page 2348.
In selecting chain length, factors determining length should be adjusted so that the use of
offset links may be avoided wherever possible. Chain lengths of an uneven number of
pitches are also to be avoided.
Silent Tooth Chain Horsepower Capacity.—The horsepower ratings given in Tables
12a, 12b, and 12c have been established on a life expectancy of approximately 15,000
hours under optimum drive conditions, i.e. for a uniform rate of work where there is rela-
tively little shock or load variation throughout a single revolution of a driven sprocket.
Using these horsepower ratings as a basis, engineering judgment should be exercised as to
the severity of the operating conditions for the intended installation, taking into consider-

ation the source of power, the nature of the load, and the resulting effects of inertia, strain,
and shock. Thus, for other than optimum drive conditions, the specified horsepower must
be multiplied by the applicable service factor to obtain a “design” horsepower value. This
is the value used to enter Table 13 to obtain the required size of chain.
Service Factors: For a uniform type of load, a service factor of 1.0 for a 10-hour day and
1.3 for a 24-hour day are recommended. For a moderate shock load, service factors of 1.4 for
a 10-hour day and 1.7 for a 24-hour day are recommended. For heavy shock loads, service
factors of 1.7 for a 10-hour day and 2.0 for a 24-hour day are recommended. For extensive
table of service factor applications, see supplementary information in ANSI B29.2M-
1982.
Installation of Silent Chain Drives.—In installing chain transmissions of any kind, hori-
zontal drives are .those having driving and driven shafts in a horizontal plane. These are
always preferable to vertical drives, which have a vertical center line intersecting the driv-
ing and driven shafts. If one sprocket must be higher than the other, avoid a vertical drive if
possible by so locating the two sprockets that the common center line inclines from the ver-
tical as far as is permitted by other conditions which might govern the installation. If prac-
ticable, an adjustment should be provided for the center distance between the driving and
driven shafts.
Slack Side of Chain: As a general rule, the slack strand of a chain should be on the lower
side of a horizontal drive. If the drive is not horizontal but angular or at some angle less than
90 degrees from the vertical, the slack should preferably be on that side which causes the
strand to curve outward or away from the center line of the driving and driven shafts.
Whenever the slack strand is on the upper side of either a horizontal or inclined dnve,
Pitch, inches
3
⁄
8
1
⁄
2

5
⁄
8
3
⁄
4
1
1
1
⁄
4
1
1
⁄
2
Minimum Center Distances, inches 6 9 12 15 21 27 33
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SILENT OF INVERTED TOOTH CHAIN 2967
adjustment for the center distance is especially important to compensate for possible chain
elongation.
Lubrication: The life of a silent chain subjected to conditions such as are common to
automobile drives, depends largely upon the wear of the joints. On account of the high
speed and whipping action, it is important to have the chains well oiled. When splash lubri-
cation is employed, the supply pipe should be placed so that the oil will be directed against
the inside of the chain. It is preferable that silent chains be operated in an oil-retaining cas-
ing with provisions for lubrication. Avoid using greases of any kind. The viscosity of the
oil depends on temperature, as follows:
Double-Flexure Silent Chain.—In double-flexure chain, the teeth of the link plates
project on both sides of the chain and the chain flexes in both directions. This chain is used

where the drive arrangements require that sprockets contact both sides of the chain. Nei-
ther double-flexure chain nor sprockets are covered in American National Standard ANSI
29.2M-1982.
Horsepower Ratings Per Inch of Chain Width for Silent Chain Drives — 1982.—
The following industrial standard horsepower ratings for silent chain drives have been
supplied by the American Chain Association. These ratings are for American National
Standard silent chain as covered by ANSI B29.2M-1982. These values may require modi-
fication by using the appropriate service factors (see page 2379). These factors, which
apply to typical drives, are intended as a general guide only, and engineering judgment and
experience may indicate different modifications to suit the nature of the load.
Lubrication: The horsepower established from the sprocket and speed combinations of
the drive under consideration will indicate a method of lubrication. This method or a better
one must be used to obtain optimum chain life. The types of lubrication as indicated on the
tables are: Type I, manual, brush, or oil cup; Type II, bath or disk; Type III, circulating
pump.
Ambient Temp.
°F
Chain Pitch
Ambient Temp.
°F
Chain Pitch
3
⁄
16
&
3
⁄
8
inch
1

⁄
2
inch & larger
3
⁄
16
&
3
⁄
8
inch
1
⁄
2
inch & larger
Recommended Lubricant Recommended Lubricant
20-40 SAE 10 SAE 20 20-40 SAE 10 SAE 20
40-100 SAE 20 SAE 30 40-100 SAE 20 SAE 30
Horsepower capacity of chain per inch of width
Rating in Table 12A,12B
Service Factor
=
chainwidth for given total hp capacity
hp Service factor×
Rating per inch, Table 12A, 12B
=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
GEOMETRY FACTORS FOR GEAR TEETH 2971
GEARS AND GEARING

Geometry Factors For Gear Teeth
Contact and Bending Stresses.—To calculate the contact and bending stresses acting
between the teeth of a pair of gears meshing under load, it is necessary to include in the
stress formulas a number of factors that account for the geometry of the teeth, the physical
properties of the materials used, and the nature of the specific application.
AGMA 908-B89 Information Sheet
*
gives equations for calculating the pitting resis-
tance geometry factor, I, for external and internal spur and helical gears; and the bending
strength geometry factor, J, for external spur and helical gears that are generated by rack-
type tools (hobs, rack cutters, or generating grinding wheels) or pinion-type tools (shaper
cutters). The document includes 66 tables of geometry factors, I and J, for a range of typi-
cal gear sets and tooth forms of 14
1
⁄
2
-, 20-, and 25-deg pressure angles and 0-, 10-, 15-, 20-
, 25-, and 30-deg helix angles.
The Information sheet was prepared to assist designers making preliminary design stud-
ies and to present data useful to those without access to computer programs. Not all tooth
forms, pressure angles, and pinion and gear modifications are covered. Neither are these
data applicable to all gear designs; however, the data should be helpful to the majority of
gear designers. Data from this Information Sheet are used with the rating procedures
described in AGMA 2001-B88, Fundamental Rating Factors and Calculation Methods
for Involute Spur and Helical Gear Teeth, for evaluating various spur and helical gear
designs produced by using a generating process (see page 1834).
Geometry Factors for Pitting Resistance and Bending Strength.—The AGMA Infor-
mation Sheet includes a mathematical procedure to determine the pitting resistance geom-
etry factor, I, for internal and external gear sets of spur, conventional helical, and low-
axial-contact-ratio (LACR) helical design. A mathematical procedure is also included to

determine the bending strength geometry factor, J, for external gear sets of spur, conven-
tional helical, and low-axial-contact-ratio (LACR) helical designs. The calculation proce-
dure is valid for generated root fillets produced by both rack- and pinion-type tools.
Exceptions to the Information Sheet Data and Procedures.—The formulas in the
Information Sheet are not valid when any of the following conditions exist:
1) Spur gears with transverse contact ratio less than one, m
p
< 1.0; 2) spur or helical gears
with transverse contact ratio equal or greater than two, m
p
≥ 2.0; 3) interference exists
between the tips of teeth and root fillets; 4) the teeth are pointed; 5) backlash is zero; 6)
undercut exists in an area above the theoretical start of the active profile (the effect of this
undercut is to move the highest point of single tooth contact, negating the assumption of
this calculation method; however, the reduction in tooth thickness due to protuberance
below the active profile is handled correctly by this method); 7) the root profiles are
stepped or irregular (the J factor calculation uses the stress correction factors developed by
Dolan and Broghamer; the factors may not be valid for root forms that are not smooth
curves; for root profiles that are stepped or irregular, other stress correction factors may be
appropriate); 8) where root fillets of the gear teeth are produced by a process other than
generating; and 9) the helix angle at the standard (reference) diameter is greater than 50
deg.
In addition to these exceptions, it is assumed that 1) the friction effect on the direction of
force is neglected; and 2) the fillet radius is smooth (it is actually a series of scallops).
Basic Gear Geometry of Spur and Helical Gears.—The equations that follow apply to
spur and helical gears. Where double signs are used (e.g.,±), the upper sign applies to exter-
*
Extracted from AGMA 908-B89, Information Sheet, Geometry Factors for Determining the Pitting
Resistance and Bending Strength of Spur, Helical, and Herringbone Gear Teeth, with the permission of
the publisher, American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria,

Virginia 22314.
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2972 GEOMETRY FACTORS FOR GEAR TEETH
nal gears and the lower sign to internal gears. The equations given are based on unity nor-
mal module (m
n
=1) or unity normal diametral pitch (P
nd
= 1) and are valid for any
consistent set of units. All angles are in radians unless otherwise specified. In using the
given equations, certain variables must be made dimensionless by dividing by the normal
module m
n
or multiplying by the normal diametral pitch P
nd
. For example, if a face width F
0.5 in. and the normal diametral pitch is 4, then the value of F to be used in the equations is
0.5 × 4 = 2. The variables to be so adjusted are F, R
01
, R
02
, R
oc
, R
c
, h
ao
, δ
ao

, ρ
ao
, and ∆
sn
.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Fig. 1 shows a view of the line of action in the transverse plane of two meshing gears. The
distances C
1
, through C
6
are derived from this figure taking into account the exceptions
noted previously with regard to undercut.
(11)
(12)
where R
02
= addendum radius of gear, for internal or external gears.
(13)
(14)
Gear ratio, m

G
n
2
n
1
= , Where n
1
and n
2
are pinion and gear tooth numbers
Standard (reference) pinion pitch radius, R
1
n
1
2 ψcos
=
Where ψ = standard helix angle.
Standard (reference) gear pitch radius, R
2
R
1
m
G
=
Standard transverse pressure angle, φ
φ
n
tan
ψcos

⎝⎠
⎛⎞
arctan=
Where φ
n
= standard normal pressure angle.
Pinion base radius, R
b1
R
1
φcos=
Gear base radius, R
b2
R
b1
m
G
=
Oparating transverse pressure angle, φ
r
R
b2
R
b1
±
C
r

⎝⎠
⎛⎞

arccos=
Where C
r
= Operating center distance.
Transverse base pitch, P
b
2πR
b1
n
1
=
Normal base pitch, P
N
πφ
n
cos=
Base helix angle, ψ
b
P
N
P
b

⎝⎠
⎛⎞
arccos=
C
6
C
r

φ
r
sin=
C
1
C
6
R
02
2
R
b2
2
–()
0.5
–[]±=
C
3
C
6
m
G
1±()
=
C
4
C
1
P
b

+=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2974 GEOMETRY FACTORS FOR GEAR TEETH
Minimum Lengths of Lines of Contact.—For spur gears with m
p
< 2.0 the minimum
length of contact lines, L
min
,
(21)
For helical gears, two cases must be considered:
(22)
(23)
where n
r
= fractional part of m
p
, and n
a
= fractional part of m
F
. For example, if m
p
= 1.4, then
n
r
= 0.4.
Load Sharing Ratio, m
N

.—The load sharing ratio m
n
, is calculated as follows:
(24)
(25)
For low axial contact ratio (LACR) helicals, m
F
≤ 1.0. Load sharing is accommodated by
the helical overlap factor C
ψ
[Equation (36)]; therefore,
(26)
(27)
(28)
Calculating the Pitting Resistance Geometry Factor, I.— The pitting resistance geom-
etry factor I is a dimensionless number that takes into account the effects of the radii of cur-
vature of the gear tooth surfaces, load sharing, and the normal component of the
transmitted load:
(29)
where
φ
r
=operating transverse pressure angle [Equation (7)];
C
ψ
=helical overlap factor [Equation (36)];
d=pinion operating pitch diameter [Equation (30)];
m
N
=load sharing ratio [Equation (24), (25), or (26)]; and

ρ
1
and ρ
2
= radii of curvature of pinion and gear profiles, respectively, at point of stress
calculation.
(30)
Radii of Curvature of Profiles at Contact Stress Calculation Point: For conventional
helical gears (m
F
> 1) the radii of curvature are calculated at the mean radius or middle of
the working profile of the pinion where
L
min
F=
CaseI: For n
a
1 n
r
–≤ ,L
min
m
p
Fn
a
n
r
p
x
–()

ψ
b
cos

=
CaseII: For n
a
1 n
r
–> ,L
min
m
p
F 1 n
a
–()1 n
r
–()p
x
–[]
ψ
b
cos
=
For helical gears, m
N
F
L
min
=

For spur gears with m
p
2.0≤ , Eq. (21) has L
min
F so that m
N
1.0==
m
N
1.0=
Operating helix angle, ψ
r
ψ
b
tan
φ
r
cos

⎝⎠
⎛⎞
arctan=
Operating normal pressure angle, φ
nr
ψ
b
cos φ
r
sin()arcsin=
I

φ
r
C
ψ
2
cos
1 ρ
1
⁄ 1 ρ
2
⁄+()dm
N
()[]
=
Operating pitch diameter of pinion, d
2c
r
m
G
1+()
=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2976 GEOMETRY FACTORS FOR GEAR TEETH
Virtual Spur Gear: Helical gears are considered to be virtual spur gears with the follow-
ing virtual geometry:
(40)
(41)
(42)
(43)

For spur gears, the virtual geometry is the same as the actual geometry:
(44)
(45)
(46)
(47)
Pressure Angle at Load Application Point.—The critical bending stress on a spur gear
tooth develops when all the applied load is carried at the highest point of single tooth con-
tact on the tooth. Spur gears having variations that prevent two pairs of teeth from sharing
the load may be stressed most heavily when the load is applied at the tips of the teeth. Table
1 has been used in previous standards to establish the variation in base pitch between the
Fig. 2. Load Angle and Load Radius
Fig. 3. Pressure Angle Where Tooth Comes to
Point
Virtual tooth number, n
n
1
ψcos
3

=
Standard (ref) pitch radius of virtual spur gear, r
n
n
2

=
Virtual base radius, r
nb
r
n

φ
n
cos=
Virtual outside radius, r
na
r
n
R
01
R
1
–+=
nn
1
=
r
n
R
1
=
r
nb
R
b1
=
r
na
R
01
=

Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2978 GEOMETRY FACTORS FOR GEAR TEETH
where ∆S
n
= amount gear tooth is thinned for backlash and x = addendum modification
coefficient at zero backlash,
(58)
where S
n
= normal circular tooth thickness measured on the standard (ref) pitch cylinder,
(59)
Load Angle and Load Radius: Fig. 2 defines the load angle φ
nl
and the load radius r
nl
. The
applied load is shown at an arbitrary point W such that:
(60)
where φ
np
= pressure angle where gear tooth is pointed, Fig. 3.
(61)
but,
(62)
and
(63)
so that
(64)
Then Equation (60) can be expressed as

(65)
Equation (65) gives the load angle φ
nL
for any load position specified by tan φ
nW
found
from Equation (48) and (49).
As may be seen from Fig. 3, the virtual radius is
(66)
Tables of Geometry Factors, I and J.—Included here are some of the tables of precalcu-
lated values of I and J extracted from the Information Sheet. For additional data, tables, and
related information for other combinations of gear sets, tooth forms, pressure angles, helix
angles, cutting tool dimensions, and addendum coefficients, refer to the Information
Sheet. It should be noted that the formulas and data in the Information Sheet are not appli-
cable to bending stresses in internal gears, since no simplified model for calculating bend-
ing stresses in internal gears is available.
Using the Tables.—Each of the tables in the Information Sheet and those presented here
were generated for a specific tool form (basic rack) defined by whole depth factor, normal
pressure (profile) angle, and tool tip radius. Only those tables applicable to spur gears are
presented here; those for helical gear sets are available in the Information Sheet.
Whole Depth: Whole depth is expressed in the tables as a “whole depth factor” and is the
whole depth of a basic rack for I normal module or I normal diametral pitch. The actual
generated depths will be slightly greater due to tooth thinning for backlash
x
S
n
S
n
∆
π

2
–+
⎝⎠
⎛⎞
2 φ
n
tan()
=
S
n
π
2
2x
g
φ
n
tan+=
φ
nl
φ
nw
tan INVφ
np
–=
INVφ
np
INVφ
n
s
n

2r
n

+=
INVφ
n
φ
n
tan φ–=
2r
n
n=
INVφ
np
φ
n
tan φ
n
–
s
n
n
+=
φ
nl
φ
nW
tan φ
n
tan– φ

n
s
n
n

–+=
r
nl
r
nb
φ
nL
cos
=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
GEOMETRY FACTORS FOR GEAR TEETH 2979
Outside Diameter: The tabulated values are for gears having an outside diameter (for
normal module or normal diametral pitch = 1), equal to
(67)
(68)
where n
1
and n
2
are the pinion and gear tooth numbers, respectively; ψ = standard helix
angle, deg.; and D
a1
and D
a2

are the pinion and gear addendum, respectively.
Center Distance: The tables apply to gearsets that operate at standard center distance.
This center distance is the tight-mesh center distance for gears not yet thinned for backlash:
(69)
where C = standard center distance. For this center distance the sum of the addendum mod-
ification coefficients for pinion and gear is zero:
(70)
Tooth Thickness Backlash Allowance: Values in the tables were calculated based on a
backlash allowance. The circular tooth thickness for the pinion and gear are each thinned
by an amount ∆sn:
(71)
If the gears being evaluated have different minimum tooth thicknesses than from Equa-
tion (71), the bending strength geometry factor, J, can be approximated by using Equation
(72). The pitting resistance geometry factor, I, is unaffected by variations in tooth thick-
ness:
(72)
where J
1
= adjusted geometry factor; J
s
= geometry factor from table; s
n1
= adjusted circu-
lar tooth thickness; and s
ns
= standard tooth thickness thinned per Equation (71).
As an example, from Table 4, for 20-deg pressure angle spur gears loaded at the highest
point of single tooth contact, the J factor for a 21-tooth pinion operating with a 35-tooth
gear is found to be 0.31. The table values are based on a circular tooth thickness of π/2 −
0.024 = 3.1416/2− 0.024 = 1.547 for diametral pitch.

For a 10 normal diametral pitch pinion or gear, the equivalent circular tooth thickness
would be 1.547/10 = 0.155.
If a J value for a 0.010 in. thinner pinion, having a circular thickness of 0.155 −0.010=
0.145 in. is required, the approximate value is 0.34(0.145/0.155)
2
= 0.30 =J
1
so that a 6.5
per cent reduction in tooth thickness reduces the J factor by 12 percent.
Undercutting: The tables do not include geometry factors that may be needed if an
undercutting condition exists in either of the two gears. Undercutting can be evaluated
using Equation (73) and Fig. 4 where the generating-rack shift coefficient, x
g
, must be
equal to or greater than the expression in Equation (73):
(73)
D
a1
n
1
ψcos
21x
1
+()+=
D
a2
n
2
ψcos
21x

2
+()+=
C
n
1
n
2
+()
2 ψcos
=
x
1
x
2
+0=
s
n
∆
0.024
P
nd

0.024 for P
nd
1===
J
1
J
S
s

n1
s
ns

⎝⎠
⎛⎞
2
=
x
gmin
h
ao
ρ
ao
1 φ
n
sin–()–
n
2

⎝⎠
⎛⎞
φ
n
sin
2
–=
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
GEOMETRY FACTORS FOR GEAR TEETH 2981

Table 2. Geometry Factors I and J for Various Number Combinations for
Module = 1 or Normal Diametral Pitch = 1
The addendum modification coefficients x
1
and x
2
are for zero backlash gears meshing at standard
center distance.
Num-
ber of
Gear
Teeth
14.5 -deg Pressure Angle 2.157 Whole Depth Factor
0.0-deg Helix Angle 0.024 Tooth Thinning for Backlash
0.0157 Tool Edge Radius Loaded at Tip of Gears
Number of Pinion Teeth
21 26 35 55 135
Pinion Gear Pinion Gear Pinion Gear Pinion Gear Pinion Gear
Equal Addendum Coefficients (x
1
= x
2
= 0)
35
I 0.061
J 0.29 0.29
55
I 0.074 0.061
J 0.30 0.31 0.33 0.33
135

I 0.096 0.088 0.061
J 0.31 0.34 0.35 0.35 0.38 0.38
25 percent Long Addendum Pinion (x
1
= 0.25)
25 percent Short Addendum Gear (x
2
= −0.25)
26
I 0.060
J 0.32 0.22
35
I 0.071 0.059
J 0.32 0.24 0.34 0.24
55
I 0.087 0.077 0.060
J 0.33 0.27 0.35 0.27 0.37 0.29
135
I 0.111 0.106 0.092 0.060
J 0.35 0.29 0.36 0.30 0.39 0.32 0.41 0.35
50 percent Long Addendum Pinion (x
1
= 0.50)
50 percent Short Addendum Gear (x
2
= −0.50)
21
I 0.056
J 0.35 0.15
26

I 0.067 0.056
J 0.36 0.17 0.37 0.17
35
I 0.081 0.071 0.056
J 0.36 0.19 0.37 0.20 0.38 0.20
55
I 0.100 0.091 0.078 0.057
J 0.37 0.22 0.38 0.23 0.39 0.24 0.41 0.25
135
I 0.127 0.123 0.114 0.096 0.060
J 0.38 0.26 0.39 0.26 0.40 0.27 0.42 0.29 0.43 0.32
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2982 GEOMETRY FACTORS FOR GEAR TEETH
Table 3. Geometry Factors I and J for Various Number Combinations for
Module = 1 or Normal Diametral Pitch = 1
The addendum modification coefficients x
1
and x
2
are for zero backlash gears meshing at standard
center distance.
Num-
ber of
Gear
Teeth
14.5 -deg Pressure Angle 2.157 Whole Depth Factor
0.0-deg Helix Angle 0.024 Tooth Thinning for Backlash
0.0157 Tool Edge Radius Loaded at HPSTC of Gears
Number of Pinion Teeth

21 26 35 55 135
Pinion Gear Pinion Gear Pinion Gear Pinion Gear Pinion Gear
Equal Addendum Coefficients (x
1
= x
2
= 0)
35
I 0.061
J 0.29 0.29
55
I 0.074 0.061
J 0.30 0.31 0.33 0.33
135
I 0.096 0.088 0.061
J 0.31 0.34 0.35 0.35 0.38 0.38
25 percent Long Addendum Pinion (x
1
= 0.25)
25 percent Short Addendum Gear (x
2
= −0.25)
26
I 0.060
J 0.32 0.22
35
I 0.071 0.059
J 0.32 0.24 0.34 0.24
55
I 0.087 0.077 0.060

J 0.33 0.27 0.35 0.27 0.37 0.29
135
I 0.111 0.106 0.092 0.060
J 0.35 0.29 0.36 0.30 0.39 0.32 0.41 0.35
50 percent Long Addendum Pinion (x
1
= 0.50)
50 percent Short Addendum Gear (x
2
= −0.50)
21
I 0.056
J 0.35 0.15
26
I 0.067 0.056
J 0.36 0.17 0.37 0.17
35
I 0.081 0.071 0.056
J 0.36 0.19 0.37 0.20 0.38 0.20
55
I 0.100 0.091 0.078 0.057
J 0.37 0.22 0.38 0.23 0.39 0.24 0.41 0.25
135
I 0.127 0.123 0.114 0.096 0.060
J 0.38 0.26 0.39 0.26 0.40 0.27 0.42 0.29 0.43 0.32
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2984 GEOMETRY FACTORS FOR GEAR TEETH
Table 5. Geometry Factors I and J for Various Number Combinations for
Module = 1 or Normal Diametral Pitch = 1

The addendum modification coefficients x
1
and x
2
are for zero backlash gears meshing at standard
center distance.
Number
of Gear
Teeth
14.5 -deg Pressure Angle 2.25 Whole Depth Factor
0.0-deg Helix Angle 0.024 Tooth Thinning for Backlash
0.250 Tool Edge Radius Loaded at HPSTC of Gears
Number of Pinion Teeth
14 17 21 26 35 55 135
PGPGPGPG P G PGPG
Equal Addendum Coefficients (x
1
= x
2
= 0)
21
I 0.078
J 0.33 0.33
26
I 0.084 0.079
J 0.33 0.35 0.35 0.35
35
I 0.091 0.088 0.080
J 0.34 0.37 0.36 0.38 0.39 0.39
55

I 0.102 0.101 0.095 0.080
J 0.34 0.40 0.37 0.41 0.40 0.42 0.43 0.43
135
I 0.118 0.121 0.120 0.112 0.080
J 0.35 0.43 0.38 0.44 0.41 0.45 0.45 0.47 0.49 0.49
25 percent Long Addendum Pinion (x
1
= 0.25)
25 percent Short Addendum Gear (x
2
= −0.25)
17
I 0.080
J 0.36 0.24
21
I 0.087 0.080
J 0.37 0.26 0.39 0.27
26
I 0.094 0.088 0.080
J 0.37 0.29 0.39 0.29 0.41 0.30
35
I 0.103 0.106 0.092 0.080
J 0.37 0.32 0.40 0.32 0.41 0.33 0.43 0.34
55
I 0.115 0.113 0.108 0.099 0.080
J 0.38 0.35 0.40 0.36 0.42 0.36 0.44 0.37 0.47 0.39
135
I 0.131 0.134 0.133 0.129 0.116 0.080
J 0.39 0.39 0.41 0.40 0.43 0.41 0.45 0.42 0.48 0.44 0.51 0.46
50 percent Long Addendum Pinion (x

1
= 0.50)
50 percent Short Addendum Gear (x
2
= −0.50)
14
I 0.080
J 0.40 0.14
17
I 0.088 0.080
J 0.41 0.17 0.42 0.18
21
I 0.097 0.090 0.080
J 0.41 0.20 0.43 0.21 0.44 0.21
26
I 0.105 0.099 0.090 0.080
J 0.41 0.23 0.43 0.23 0.45 0.24 0.46 0.24
35
I 0.116 0.111 0.103 0.094 0.080
J 0.42 0.26 0.43 0.27 0.45 0.27 0.46 0.28 0.48 0.29
55
I 0.130 0.127 0.122 0.114 0.101 0.080
J 0.42 0.30 0.44 0.31 0.45 0.31 0.47 0.32 0.48 0.33 0.50 0.34
135
I 0.148 0.149 0.148 0.145 0.136 0.120 0.080
J 0.43 0.34 0.44 0.35 0.46 0.36 0.47 0.37 0.49 0.38 0.50 0.40 0.52 0.43
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
GEOMETRY FACTORS FOR GEAR TEETH 2985
Table 6. Geometry Factors I and J for Various Number Combinations for

Module = 1 or Normal Diametral Pitch = 1
The addendum modification coefficients x
1
and x
2
are for zero backlash gears meshing at standard
center distance.
Number
of Gear
Teeth
25 -deg Pressure Angle 2.350 Whole Depth Factor
0.0-deg Helix Angle 0.024 Tooth Thinning for Backlash
0.027 Tool Edge Radius Loaded at Tip ofGears
Number of Pinion Teeth
12 14 17 21 26 35 55 135
PGPGPGPGP GPGPGPG
Equal Addendum Coefficients (x
1
= x
2
= 0)
14
I 0.086
J 0.28 0.28
17
I 0.091 0.090
J 0.28 0.30 0.30 0.30
21
I 0.095 0.096 0.092
J 0.28 0.31 0.30 0.31 0.31 0.31

26
I 0.100 0.101 0.099 0.094
J 0.28 0.33 0.30 0.33 0.31 0.33 0.33 0.33
35
I 0.106 0.109 0.108 0.104 0.095
J 0.28 0.34 0.30 0.34 0.31 0.34 0.33 0.34 0.34 0.34
55
I 0.113 0.119 0.121 0.119 0.112 0.095
J 0.28 0.36 0.30 0.36 0.31 0.36 0.33 0.36 0.34 0.36 0.36 0.36
135
I 0.123 0.132 0.139 0.142 0.141 0.131 0.096
J 0.28 0.38 0.30 0.38 0.31 0.38 0.33 0.38 0.34 0.38 0.36 0.38 0.49 0.49
25 percent Long Addendum Pinion (x
1
= 0.25)
25 percent Short Addendum Gear (x
2
= −0.25)
14
I 0.095 0.093
J 0.32 0.22 0.33 0.22
17
I 0.100 0.099 0.094
J 0.32 0.25 0.33 0.25 0.34 0.25
21
I 0.106 0.106 0.102 0.095
J 0.32 0.27 0.33 0.27 0.34 0.27 0.36 0.27
26
I 0.111 0.112 0.109 0.103 0.095 0.095
J 0.32 0.29 0.33 0.29 0.34 0.29 0.36 0.29 0.36 0.29 0.36 0.29

35
I 0.118 0.120 0.119 0.115 0.108 0.096
J 0.32 0.31 0.33 0.31 0.34 0.31 0.36 0.31 0.36 0.31 0.37 0.31
55
I 0.127 0.131 0.133 0.131 0.126 0.116 0.096
J 0.32 0.34 0.33 0.34 0.34 0.34 0.36 0.34 0.36 0.34 0.37 0.34 0.38 0.34
135
I 0.138 0.145 0.151 0.153 0.153 0.148 0.135 0.096
J 0.32 0.37 0.33 0.37 0.34 0.27 0.36 0.37 0.36 0.37 0.37 0.37 0.38 0.37 0.39 0.37
50 percent Long Addendum Pinion (x
1
= 0.50)
50 percent Short Addendum Gear (x
2
= −0.50)
21
I 0.096
J 0.40 0.23
26
I 0.106 0.096
J 0.40 0.25 0.40 0.25
35
I 0.120 0.110 0.096
J 0.40 0.28 0.40 0.28 0.40 0.28
55
I 0.139 0.131 0.118 0.096
J 0.40 0.32 0.40 0.32 0.40 0.32 0.40 0.32
135
I 0.167 0.163 0.155 0.138 0.096
J 0.40 0.36 0.40 0.36 0.40 0.36 0.40 0.36 0.40 0.36

Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2986 GEOMETRY FACTORS FOR GEAR TEETH
Table 7. Geometry Factors I and J for Various Number Combinations for
Module = 1 or Normal Diametral Pitch = 1
The addendum modification coefficients x
1
and x
2
are for zero backlash gears meshing at standard
center distance.
Number
of Gear
Teeth
25 -deg Pressure Angle 2.350 Whole Depth Factor
0.0-deg Helix Angle 0.024 Tooth Thinning for Backlash
0.270 Tool Edge Radius Loaded at HPSTC of Gears
Number of Pinion Teeth
12 14 17 21 26 35 55 135
PGPGPGPGP GPGPGPG
Equal Addendum Coefficients (x
1
= x
2
= 0)
14
I 0.086
J 0.33 0.33
17
I 0.091 0.090

J 0.33 0.36 0.36 0.36
21
I 0.095 0.096 0.092
J 0.33 0.39 0.36 0.39 0.39 0.39
26
I 0.100 0.101 0.099 0.094
J 0.33 0.41 0.37 0.42 0.40 0.42 0.43 0.43
35
I 0.106 0.109 0.108 0.104 0.095
J 0.34 0.44 0.37 0.45 0.40 0.45 0.43 0.46 0.46 0.46
55
I 0.113 0.119 0.121 0.119 0.112 0.095
J 0.34 0.47 0.38 0.48 0.41 0.49 0.43 0.49 0.47 0.50 0.51 0.51
135
I 0.123 0.132 0.139 0.142 0.141 0.131 0.096
J 0.35 0.51 0.38 0.52 0.42 0.53 0.45 0.53 0.48 0.54 0.53 0.56 0.57 0.57
25 percent Long Addendum Pinion (x
1
= 0.25)
25 percent Short Addendum Gear (x
2
= −0.25)
14
I 0.095 0.093
J 0.38 0.25 0.40 0.25
17
I 0.100 0.099 0.094
J 0.38 0.29 0.40 0.29 0.43 0.29
21
I 0.106 0.106 0.102 0.095

J 0.38 0.32 0.41 0.32 0.43 0.33 0.46 0.33
26
I 0.111 0.112 0.109 0.103 0.095
J 0.39 0.35 0.41 0.35 0.44 0.36 0.46 0.36 0.48 0.37
35
I 0.118 0.120 0.119 0.115 0.108 0.096
J 0.39 0.38 0.41 0.39 0.44 0.39 0.47 0.40 0.49 0.41 0.51 0.41
55
I 0.127 0.131 0.133 0.131 0.126 0.116 0.096
J 0.39 0.42 0.42 0.43 0.44 0.44 0.47 0.44 0.49 0.45 0.52 0.46 0.55 0.47
135
I 0.138 0.145 0.151 0.153 0.153 0.148 0.135 0.096
J 0.40 0.47 0.42 0.48 0.45 0.49 0.48 0.49 0.50 0.50 0.53 0.51 0.56 0.53 0.59 0.55
50 percent Long Addendum Pinion (x
1
= 0.50)
50 percent Short Addendum Gear (x
2
= −0.50)
21
I 0.096
J 0.52 0.27
26
I 0.106 0.096
J 0.52 0.30 0.53 0.31
35
I 0.120 0.110 0.096
J 0.52 0.35 0.53 0.35 0.55 0.36
55
I 0.139 0.131 0.118 0.096

J 0.52 0.40 0.54 0.41 0.56 0.42 0.58 0.43
135
I 0.167 0.163 0.155 0.138 0.096
J 0.53 0.46 0.54 0.47 0.56 0.48 0.58 0.50 0.60 0.53
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
POWER TRANSMITTING CAPACITY OF SPUR GEARS 2987
Power–Transmitting Capacity of Spur Gears
Modes of Failure.—When sets of spur gears are made, installed, and lubricated properly,
they normally may be subject to three primary modes of failure, as discussed below.
Tooth Scoring: Tooth scoring is a scuffing or welding type of tooth failure, caused by
high sliding speed combined with high contact stress. Scoring is not a fatigue failure but
rather a failure of the lubricant caused by increases in lubricant viscosity with pressure.
The lubricant must provide cooling to the gears as well as reducing friction. Well propor-
tioned commercial gears with a pitchline velocity of less than 7000 ft/min will normally
not score if they have a reasonably good surface finish and are properly lubricated. If scor-
ing does occur or if it is suspected to be critical in a new high speed design, the scoring tem-
perature index should be determined by the method shown in American Gear
Manufacturers Standard AGMA 217.01 or by some similar method.
Pitting: In surface pitting, small cracks first develop on and under the surfaces of gear
teeth as a result of metal fatigue. Pieces of the surface then break away, and those that do
not fall clear cause further damage or broken teeth. Vacuummelted steels have gone far
toward reducing pitting. Failure usually occurs at a point just below the pitch surface on the
driving pinion and may be anticipated in the gear design by a determination of the gear set
contact compressive stress.
Tooth Breakage: Tooth breakage is usually a tensile fatigue failure at the weakest section
of the gear tooth when considered as a cantilever beam. The weakest point is normally the
tensile side of the gear tooth fillet, and it may be anticipated in the gear design by determin-
ing the stress at this weakest section of the gear tooth.
Strength Calculations for Spur and Helical Gears.—Many standards and procedures

for the design, manufacture, inspection, and application of gears have been published for
the guidance of both the users and the manufacturers of gears and gear products. Among
such publications, those of the American Gear Manufacturers Association (AGMA) repre-
sent an authoritative resource for information and standards on all phases of design,
inspection, manufacture, application, and other aspects of gear technology.
American Gear Manufacturers Association Standard, AGMA 2001–B88, Fundamental
Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth, is a
revision of, and supersedes, AGMA 218.01. The Standard presents general formulas for
rating the pitting resistance and the bending strength of spur and helical involute gear teeth
and is intended to establish a common base for rating various types of gears for differing
applications and to encourage the maximum practical degree of uniformity and consis-
tency between rating practices in the gear industry. Standard 2001–B88 provides the basis
from which more detailed AGMA Application Standards are developed and is a means for
calculation of approximate ratings in the absence of such standards. Where applicable
AGMA standards exist, they should be used in preference to this Standard. Where no
applicable standards exist, numerical values may be estimated for the factors used in the
general equations presented in the standard. The values of these factors may vary signifi-
cantly, depending on the application, system effects, gear accuracy, manufacturing prac-
tice, and definition of what constitutes gear failure. Proper evaluation of these factors is
essential for realistic ratings.
Information on the geometry factors, I and J, used in pitting resistance and bending
strength calculations has been amplified, and moved from the old AGMA 218.01 standard
to AGMA 908–B89, Geometry Factors for Determining the Pitting Resistance and Bend-
ing Strength of Spur, Helical, and Herringbone Gear Teeth. AGMA Standard 908–B89 is
covered on Handbook pages 1853–1866.
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY