FLAT ROPE REELS
20. To overcome the objections to conical and cylindrical drums, several other systems of hoisting have been tried, among them being one that uses a reel, [Fig. 12], and a flat rope. The hub a is increased in diameter, above what is necessary for strength, to such a size as is suitable to wind the rope on. It is then cored out from the inside, so as not to contain too great a mass of metal.
Fig. 12
The arms b of the reel extend radially from the hub to confine the rope laterally when it is all wound on the drum. These arms are connected at their outer ends by a continuous flange c, which flange is flared out, as shown at d, so as to take in the rope easily, if it is deflected at all sidewise.
In the larger-sized reels, the arms are bolted to the hub, and often the outer rim connecting the arms is omitted. Hardwood lining was formerly used on the arms under the impression that the wear on the rope would be less than with bare iron arms, but sand and grit become embedded in the wood and grind the rope. Polished iron arms with rounded corners and lubricated with oil or tar are best. The end of the rope is fastened in a pocket e provided for it in the hub.
The rope winds on itself, so that the diameter of the reel increases as the hoist is made and as the load due to the weight of the rope decreases. This serves to equalize the load due to the rope in the same manner as the conical drum. Two reels are generally put on the same shaft, and while one is hoisting from one compartment of the shaft the other is lowering into another compartment. The periphery of the hub where the rope winds should not be round but of gradually increasing radius, for if a flat rope be wrapped about a round hub the rope will have to abruptly mount itself at the end of the first revolution and so on for every revolution. The radius of the hub should increase at such a rate as to raise the rope an amount equal to its thickness in the first wrap, so that it will wind on itself without jar at the point of attachment, as well as on succeeding wraps.
21. In America, it is customary to wind on reels of small diameter, that is, starting at 3 or 5 feet and increasing to 8 or 12 feet; but several large plants have been built with reels starting at 8 feet and increasing to 19 feet. In England, reels have been made starting at 16 feet and increasing to 20 or 22 feet. Such large reels are easier on the rope but require large engines, as hoisting in balance is used to only a slight extent. The large reel is easy on the rope, both from the fact that it bends the rope but little and also gives less pressure on the bottom wraps, as each wrap adds to the pressure. These reels are driven by means of plain jaw or friction clutches.
The wear of a flat rope is excessive and the rope itself costs more than a round rope of the same strength, does not last as long, and requires more care and attention.
22. Calculating Size of Flat Rope and Reel.—The calculation of the size of a flat rope for given work is not so simple as that of a round rope, as there is a variable factor in the width and thickness of the rope that must be taken into account. To illustrate the method of calculation, suppose that it is required to hoist 5,000 pounds of material in a 3,000-pound skip from a vertical two-compartment shaft 2,000 feet deep under conditions requiring a factor of safety of about 9 for the rope.
The determination of the size of the rope and the small and large diameters of the reels must proceed together. The latter calculations are performed in much the same manner as for conical drums.
Referring to Table relating to flat wire ropes in Hoisting, Part 2, it is found that a flat steel rope 6 inches by ½ inch in size and with a breaking strength of 150,000 pounds weighs 5.1 pounds per foot; hence, 2,000 feet of it weighs 2,000 × 5.1 = 10,200 pounds. The total load on the rope will then be 19,000 pounds, made up as follows:
| Pounds | |
| Weight of material | 5,000 |
| Weight of skip | 3,000 |
| Friction, 10 per cent. | 800 |
| Weight of rope | 10,200 |
| Total | 19,000 |
This rope gives a factor of safety of 150,000/19,000 = 7.8, which is not quite enough when figured from the dead load without that due to acceleration.
An 8" × ½" rope with a breaking strength of 200,000 pounds weighs 6.9 pounds per foot; hence, 2,000 feet of it weighs 2,000 × 6.9 = 13,800 pounds. The load on the rope will then be 22,600 pounds, made up as follows:
| Pounds | |
| Weight of material | 5,000 |
| Weight of skip | 3,000 |
| Friction, 10 per cent. | 800 |
| Weight of rope | 13,800 |
| Total | 22,600 |
This rope gives a factor of safety of 200,000/22,600 = 8.8.
Substituting the foregoing weights of material, skip, and rope in formula 4, in [Art. 17], gives
| d(5,000 + 6,000 + 27,600) | |
| D = | ———————————— |
| (5,000 + 6,000) |
Hence, the equation of moments is D = 3.5d. In other words, the large diameter, or that of the last coil of rope, should be 3.5 times the small diameter, or that of the reel hub.
23. [Fig. 13] represents a coil of flat rope whose greater diameter D and smaller diameter d are to be determined. The area of the hub about which the rope is to coil is (¼)πd², while the area included by the outer coil of rope is (¼)πD² hence, the area of annular space occupied by the rope is
(¼)πD² - (¼)πd² = (¼)π(D² - d²).
Such values for D and d must be chosen that the equation of moments in [Art. 22] is satisfied, while the area (¼)π(D²-d²) must correspond to the space occupied by the given rope when rolled.
Fig. 13
Illustration.—2,000 feet of rope ½ inch thick requires
| 2,000 × 12 | |
| ————— | = 12,000 |
| 2 |
square inches in which to be coiled. To satisfy the equation of moments, D must equal 3.5 d; hence, to satisfy both these conditions
(¼)π[(3.5d)² - d²] = 12,000;
- d = 37 inches, or 3 feet 1 inch;
- D = 37 × 3.5 = 129.5 inches, or 10 feet 9½ inches.
The dimensions of the reel will then be: diameter of hub 3 feet 1 inch; width between flanges, 8½ inches, allowing ¼ inch on each side of the rope for clearance; diameter of the flanges where they flare, 10 feet 9½ inches.