This brake is self-acting when the drum revolves so as to pull on the shorter arm, as indicated by the arrows; that is, the motion of the drum helps to set the brake when the latter is once applied. When, however, the drum revolves in the opposite direction, the action of the brake is opposed, instead of being assisted, by the motion of the drum. As a consequence, this particular form of brake is not adapted to hoisting drums that revolve in opposite directions at each alternate hoist. Differential brakes are not generally used.
Fig. 27
45. Power for Brakes.—For small drums and light loads, the brakes are usually applied by hand power through suitable lever connections. The force that a man can exert can be multiplied indefinitely by levers and combinations of levers; but while the force is multiplied, the distance through which it can act is divided in the same ratio. A certain amount of motion is required to free the brake band from the drum, when the brake is off; this, then, limits the leverage that a man can use. Suppose, for instance, that with a strap brake the band moves from the drum ½ inch, thus increasing the diameter 1 inch, or the circumference about 3 inches. Then, supposing that a man can exert his force to advantage through 3 feet, or 36 inches, the available leverage is ³⁶/₃ = 12. That is, if a man can pull 50 pounds on his hand lever, he can exert 50 × 12 = 600 pounds circumferentially on the brake band, with simple levers. If any form of differential levers is used, the ratio by which the force applied at the hand lever can be increased will be considerably larger. A diagram will explain this more clearly.
46. In [Fig. 27], a is the hand lever, with a fulcrum at b and a pin at c by which it takes hold of a reach rod or connection d. This rod is connected to the end h of the brake lever e, which is connected by pins at f, g to the brake bands. If the leverage of the hand lever a is made 6 to 1, that is, if
| ab | 6 | |
| —— | = | —— |
| cb | 1 |
and a force of 50 pounds is applied at a, a pull of 300 pounds will be exerted at the pin c and, consequently, along the rod d to the end of the brake lever e. Then, if the brake lever is made with a ratio of 4 to 1, that is, if
| eh | 4 | eh | ||
| —— | = | —— | = | —— |
| eg | 1 | ef |
a pull of 300 pounds × 4 = 1,200 pounds will be exerted at the pin f or g. This total pull must be divided equally between the arms eg and ef, giving 600 pounds pull on each. According to the principle of the lever, the distances through which these forces act are inversely proportional to the forces acting. It is assumed that the brakeman can exert the force of 50 pounds through 36 inches; if this is the motion of the end of the hand lever a, one-sixth of this, or 6 inches, will be the motion at c and, therefore, at h; one-fourth of 6 inches or 1½ inches will be the motion at f and g; that is, f will increase its half of the brake band 1½ inches in circumference, and g will do likewise with its half, making the total circumference 3 inches more, or the diameter 1 inch more, and thereby moving the band away from the drum ½ inch radially. The levers are all shown in mid-position to make the figure more simple, but the relative leverages remain the same at all points in the motion.
This is an example of simple levers, but the force applied at the hand lever may be increased in a much greater ratio by the use of a device known as a differential lever.