Multiply the breadth of the tooth by the square of its thickness, and the product by the strength of the material, per square inch of section, of which the teeth are composed, and divide this last product by the distance of the pitch line from the root, and the quotient will give a tooth thickness having a strength equal to the weight of the load, but having no margin for safety, and no allowance for wear; hence, the result thus obtained must be multiplied by the factor of safety (which for this class of tooth may be taken as 6), and must have an additional thickness added to allow for wear, so that the factor of safety will be constant notwithstanding the wear.

Another, and in some respects more convenient method, for obtaining the strength of a tooth, is to take the strength of a tooth having 1-inch pitch, and 1 inch of breadth, and multiply this quantity of strength by the pitch and the face of the tooth it is required to find the strength of, both teeth being of the same material.

Example.—The safe working pressure for a cast-iron tooth of an inch pitch, and an inch broad will transmit, being taken as 400 lbs., what pressure will a tooth of 3⁄4-inch pitch and 3 inches broad transmit with safety?

Here 400 lbs. × 3⁄4 pitch × 3 breadth = 900 = safe working pressure of tooth 3⁄4-inch pitch and 3 inches broad.

Again, the safe working pressure of a cast-iron tooth, 1 inch in breadth and of 1-inch pitch, being considered as 400 lbs., what is the safe working pressure of a tooth of 1-inch pitch and 4-inch breadth?

Here 400 × 1 × 4 = 1600.

The philosophy of this is apparent when we consider that four wheels of 1-inch pitch and an inch face, placed together side by side, would constitute, if welded together, one wheel of an inch pitch and 4 inches face. (The term face is applied to the wheel, and the term breadth to the tooth, because such is the custom of the workshop, both terms, however, mean, in the case of spur-wheels, the dimension of the tooth in a direction parallel to the axis of the wheel shaft or wheel bore.)

The following table gives the safe working pressures for wheels having an inch pitch and an inch face when working at the given velocities, S.W.P. standing for “safe working pressure:”—

Velocity of
pitch circle
in feet
per second.		S.W.P.
for cast-iron
spur gears.		S.W.P.
for spur mor-
tise gears.		S.W.P.
for cast-iron
bevel gears.		S.W.P.
for bevel
mortise gears.
2368178258178
3322178225157
6255178178125
1220314214299
1817712412487
2416111311379
3015010510574
36140989869
42133939365
48127888862

For velocities less than 2 feet per second, use the same value as for 2 feet per second.