Machinery's Handbook, 31st Edition
2250
Internal Gearing Rules for Internal Gears – 20-degree Full-Depth Teeth
To Find
Rule
Rule: To find the pitch diameter of an internal gear, divide the number of internal gear teeth by the diametral pitch. The pitch diameter of the mating pinion also equals the number of pinion teeth divided by the diametral pitch, the same as for external spur gears. Rule 1: For internal gears to mesh with pinions having 16 teeth or more, subtract 1.2 from the number of teeth and divide the remainder by the diametral pitch. Example: An internal gear has 72 teeth of 6 diametral pitch and the mating pinion has 18 teeth; then . . 6 72 12 118 Internal diameter inches = − = Rule 2: If circular pitch is used, subtract 1.2 from the number of internal gear teeth, multiply the remainder by the circular pitch, and divide the product by 3.1416. Rule: If the internal gear is to be designed to conform to a spur gear turned outside in, subtract 2 from the number of teeth and divide the remainder by the diametral pitch to find the internal diameter. Example: (Same as Example above.) . 6 72 2 11666 Internal diameter inches = − = Note: If the internal gearing is to be proportioned like standard spur gearing, use the rule or formula previously given for spur gears in determining the outside diameter. The rule and formula following apply to a pinion that is enlarged and intended to mesh with an internal gear enlarged as determined by the preceding Rules 1 and 2 above. Rule: For pinions having 16 teeth or more, add 2.5 to the number of pinion teeth and divide by the diametral pitch. Example 1: A pinion for driving an internal gear is to have 18 teeth (full depth) of 6 diametral pitch; then . . 6 18 25 3416 Outside diameter inches = + = By using the rule for external spur gears, the outside diameter = 3.333 inches. Rule: Subtract the number of pinion teeth from the number of internal gear teeth and divide the remainder by two times the diametral pitch. See paragraphs, Arc Thickness of Internal Gear Tooth and Effect of Diameter of Cutting on Profile and Pressure Angle of Worms , on previous page.
Pitch Diameter
Internal
Diameter (Enlarged to Avoid Interference)
Internal
Diameter (Based upon Spur Gear Reversed)
Outside
Diameter of Pinion for Internal Gear
Center
Distance
Tooth
Thickness
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