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?
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| S.W.P. for | S.W.P. for |S.W.P. for | S.W.P. | | in feet | cast-iron |spur mortise| cast-iron | for bevel | |per second. |spur gears. | gears. |bevel gears.|mortise gears.| +------------+------------+------------+------------+--------------+ | 2 | 368 | 178 | 258 | 178 | | 3 | 322 | 178 | 225 | 157 | | 6 | 255 | 178 | 178 | 125 | | 12 | 203 | 142 | 142 | 99 | | 18 | 177 | 124 | 124 | 87 | | 24 | 161 | 113 | 113 | 79 | | 30 | 150 | 105 | 105 | 74 | | 36 | 140 | 98 | 98 | 69 | | 42 | 133 | 93 | 93 | 65 | | 48 | 127 | 88 | 88 | 62 | +------------+------------+------------+------------+--------------+