The quotient is the number required.
Example.—What is the number of teeth in a wheel whose pitch diameter is 42 inches, and pitch is 21⁄2 inches?
First, the pitch diameter, 1 tooth, 21⁄2-inch pitch, is 0.7958 inches.
| Second. | 42 | = 52.8. Answer. |
| 0.7958 |
This gives a fractional number of teeth, which is impossible; so the pitch diameter will have to be increased to correspond to 53 teeth, or the pitch changed so as to have the number of teeth come an even number.
Whenever two parallel shafts are connected together by gearing, the distance between centres being a fixed quantity, and the speeds of the shafts being of a fixed ratio, then the pitch is generally the best proportion to be changed, and necessarily may not be of standard size. Suppose there are two shafts situated in this manner, so that the distance between their centres is 84 inches, and the speed of one is 21⁄2 times that of the other, what size wheels shall be used? In this case the pitch diameter and number of teeth of the wheel on the slow-running shaft have to be 21⁄2 times those of the wheel on the fast-running shaft; so that 84 inches must be divided into two parts, one of which is 21⁄2 times the other, and these quantities will be the pitch radii of the wheels; that is, 84 inches are to be divided into 31⁄2 equal parts, 1 of which is the radius of one wheel, and 21⁄2 of which the radius of the other, thus 84′′/31⁄2 = 24 inches. So that 24 inches is the pitch radius of pinion, pitch diameter = 48 inches; and 21⁄2 × 24 inches = 60 inches is the pitch radius of the wheel, pitch diameter = 120 inches. The pitch used depends upon the power to be transmitted; suppose that 25⁄8 inches had been decided as about the pitch to be used, it is found by Rule 3 that the number of teeth are respectively 143.6, and 57.4 for wheel and pinion. As this is impossible, some whole number of teeth, nearest these in value, have to be taken, one of which is 21⁄2 times the other; thus 145 and 58 are the nearest, and the pitch for these values is found by Rule 2 to be 2.6 inches, being the best that can be done under the circumstances.
Fig. 183.