Machinery's Handbook, 31st Edition
2224 Spur Gearing Chordal Thickness of Tooth when Outside Diameter is Special.— When the outside diam- eter is larger or smaller than standard the chordal thickness at the standard pitch diam eter is found by the following formula where t c = chordal thickness at the standard pitch diameter D ; t = circular thickness at the standard pitch diameter of the enlarged pinion or reduced gear being measured. t t D t 6 c 2 3 # = − Example 1: The outside diameter of a pinion having 10 teeth of 5 diametral pitch has been enlarged by 0.2746 inch. This enlargement has increased the circular tooth thickness at the standard pitch diameter (as determined by the formula previously given) to 0.3852 inch. Find the equivalent chordal thickness. . . . . . t 03852 6 2 0 385 0 3852 0 0024 0 3828 inch c 2 3 # = − = − = (The error introduced by rounding the circular thickness to three significant figures be- fore cubing it only affects the fifth decimal place in the result.) Example 2: A gear having 30 teeth is to mesh with the pinion in Example 1 and is reduced so that the circular tooth thickness at the standard pitch diameter is 0.2432 inch. Find the equivalent chordal thickness. . . . . . t 02432 6 6 0 243 0 2432 0 00007 0 2431 inch c 2 3 # = − = − = Chordal Addendum.— In measuring the chordal thickness, the vertical scale of a gear tooth caliper is set to the chordal or “corrected” addendum to locate the caliper jaws at the pitch line (see Method of setting a gear tooth caliper on page 2227 ). The simplified formula which follows may be used in determining the chordal addendum either when the addendum is standard for full-depth or stub teeth or when the addendum is either longer or shorter than standard as in case of an enlarged pinion or a gear which is to mesh with an enlarged pinion and has a reduced addendum to maintain the standard center distance. If a c = chordal addendum; a = addendum; and t = circular thickness of tooth at pitch diameter D ; then, a a D t 4 c 2 = + Example 1: The outside diameter of an 8 diametral pitch 14-tooth pinion with 20-degree full-depth teeth is to be increased by using an enlarged addendum of 1.234 ÷ 8 = 0.1542 inch (see Table 7 on page 2225 ). The basic tooth thickness of the enlarged pinion is 1.741 ÷ 8 = 0.2176 inch. What is the chordal addendum? . . . 01542 4 14 8 02176 01610 Chordal addendum inch 2 # ' = + = ^ h Example 2: The outside diameter of a 14 1 ∕ 2 -degree pinion having 12 teeth of 2 diametral pitch is to be enlarged 0.624 inch to avoid undercut (see Table 8 on page 2225 ), thus increasing the addendum from 0.5000 to 0.8120 inch and the arc thickness at the pitch line from 0.7854 to 0.9467 inch. Then, . . . 08120 4 12 2 09467 08493 Chordal addendum of pinion inch 2 # ' = + = ^ h
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