1.A deep-mine hoist utilizes a single line of 2-inch extra improved plow steel (EIPS) wire rope wrapped on a cast carbon-steel drum that has a diameter of 6 feet. The rope is used to vertically lift loads of ore weighing about 4 tons from a shaft that is 500 feet deep. The maximum hoisting speed is 1200 ft/min and the maximum acceleration is 2 ft/sec2 .
a. Estimate the maximum direct stress in the “straight” portion of the 2-inch single-line wire rope.
b. Estimate the maximum bending stress in the “outer” wires of the 2-inch wire rope as it wraps onto the 6-footdiameter drum.
c. Estimate the maximum unit radial pressure (compressive stress) between the rope and the sheave. Hint: Model the 2-inch single-line rope wrapped around the 6-foot sheave as a “band brake,” utilizing equation (16-76) with and , to find .
d. Estimate the fatigue life of the 2-inch wire rope as used in this application.