Machinery's Handbook, 31st Edition
Spur Gearing 2221 The tooth thickness on the pitch circle can be determined very accurately by means of measurement over wires which are located in tooth spaces that are diametrically opposite or as nearly diametrically opposite as possible. Where measurement over wires is not fea sible, the circular or arc tooth thickness can be used in determining the chordal thickness which is the dimension measured with a gear tooth caliper. Circular Thickness of Tooth when Outside Diameter has been Enlarged.— When the out- side diameter of a small pinion is not standard but is enlarged to avoid undercut and to improve tooth action, the teeth are located farther out radially relative to the standard pitch diameter and consequently the circular tooth thickness at the standard pitch diam- eter is increased. To find this increased arc thickness the following formula is used, where t = tooth thickness; e = amount outside diameter is increased over standard; φ = pressure angle; and p = circular pitch at the standard pitch diameter. tan t p e 2 φ = + Example: The outside diameter of a pinion having 10 teeth of 5 diametral pitch and a pressure angle of 14 1 ∕ 2 degrees is to be increased by 0.2746 inch. The circular pitch equiva lent to 5 diametral pitch is 0.6283 inch. Find the arc tooth thickness at the standard pitch diameter. . . . . . . tan t t 2 0 6283 0 2746 14 2 1 0 3142 0 2746 0 25862 0 3852 inch # # ° = + = + = ^ a h k Circular Thickness of Tooth when Outside Diameter has been Reduced.— If the outside diameter of a gear is reduced, as is frequently done to maintain the standard center dis tance when the outside diameter of the mating pinion is increased, the circular thickness of the gear teeth at the standard pitch diameter will be reduced.This decreased circular thickness can be found by the following formula where t = circular thickness at the stan- dard pitch diameter; e = amount outside diameter is reduced under standard; φ = pressure angle; and p = circular pitch. tan t p e 2 φ = − Example: The outside diameter of a gear having a pressure angle of 14 1 ∕ 2 degrees is to be reduced by 0.2746 inch or an amount equal to the increase in diameter of its mating pinion. The circular pitch is 0.6283 inch. Determine the circular tooth thickness at the standard pitch diameter. . . . . . . tan t t 2 0 6283 0 2746 14 2 1 0 3142 0 2746 0 25862 0 2432 inch # # ° = − = − = ^ a h k Chordal Thickness of Tooth when Outside Diameter is Standard.— To find the chordal or straight line thickness of a gear tooth the following formula can be used where t c = chordal thickness; D = pitch diameter; and N = number of teeth. sin t D N 90 c ° = a k Example: A pinion has 15 teeth of 3 diametral pitch; the pitch diameter is equal to 15 ÷ 3 or 5 inches. Find the chordal thickness at the standard pitch diameter. . . sin sin t 5 15 90 5 6 5 0 10453 0 5226 inch c # ° ° = = = = a k
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