Fig. 2650.
The effect of this inequality of centrifugal force will depend, in each case, upon the strength of the shaft in comparison with the amount of unbalanced centrifugal force. Suppose, for example, that the centrifugal force at a point a in [Fig. 2650] were 10 lbs. greater than at b at a given velocity, and that the strength of the shaft be such that it will bend 1⁄32 inch under a weight of 10 lbs., then the effort of the point a will be to swing in a circle 1⁄16 inch larger than that due to its diameter. Suppose, then, the stand be so firmly fixed at c as to be motionless in a vertical direction under this effort, then the point a will swing in an oval, as denoted by the dotted lines, the shaft vibrating as denoted by the arrows.
Fig. 2651.
Thus vibrations of the shaft, bearing, &c., occur whenever the excess of centrifugal motion on one side of a pulley is sufficient to spring the shaft, bearings, standard or foundation, as the case may be, and will occur most in the direction in which those parts will most easily succumb. From this it is evident that a pulley practically in balance, so far as being free from vibration at a certain speed, may be considerably out of balance at an increased speed. Thus, suppose a pulley p, in [Fig. 2651], has a rim of equal thickness, but the distance of a from the axis of rotation is 6 inches, while the distance of b is 8 inches; then the centrifugal force at b will, at any speed of rotation, be one-quarter more than that at a, because the distance is one-quarter greater. Suppose, then, that its shaft, bearings, and foundation be capable of resisting 100 lbs. without sensible flexure, but that sensible flexure of those parts will occur under any pressure over 100 lbs.
The centrifugal force of 1 lb. at a and at b, respectively, may be calculated by the following rule:—
Rule.—Multiply the square of the number of revolutions per minute by the diameter of the circle of rotation in feet, and divide the product by 5,870. The quotient is the centrifugal force in terms of the weight of the body.
In the case of a the pulley making, say, 200 revolutions per minute, we have by the rule:
| 2002 × 1 | = 6.81 = the centrifugal force. |
| 5,870 |