This section is from the book "Applied Science For Metal Workers", by William H. Dooley. Also available from Amazon: Applied Science For Metal Workers.

Repeated designs and tests of spur gears prove that the dedendum (or addendum) should always have a certain definite ratio or relation to the diametral pitch which is: dedendum times diametral pitch = 1, or, what is the same thing, dedendum = 1÷ diametral pitch. This relation, of course, holds true for the addendum, since the addendum and the dedendum are equal. It is well to remember this relation, since the diametral pitch is the most important thing to know about a spur gear and all gears are ordered and made according to their diametral pitch. The clearance is also referred to as the diametral pitch. Most gear-makers use the Brown and Sharpe rule which is to make the clearance times the diametral pitch equal .157; expressed as a formula this would read:

Fig. 156.

F = .157 ÷ P

Where F equals the clearance and P equals the diametral pitch.

Since we know that the outside diameter is equal to the pitch diameter plus the two addendums, and since the addendum equals

1 ÷ diametral pitch, we can make a formula for the outside diameter which will read:

O = D +1/P + 1/P or, adding up, we will have O = D + 2/P where 0 = outside diameter, P = diametral pitch, and D = pitch diameter.

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