Part 2

=Rule.=--_To find the large diameter of a conical drum, multiply the small diameter by the sum of the weight of the material to be hoisted, twice the weight of the cage and car, and twice the weight of the rope; divide this product by the sum of the weight of the material, and twice the weight of the cage and car._

Applying this rule to the problem given in Art. =14= and omitting friction,

7(4,000 + 12,000 + 6,000) _D_ = ------------------------- = 9.6 feet (4,000 + 12,000)

The drum would then be 7 feet in diameter at the small end and 9 feet 7¼ inches at the larger end.

=18=. Fig. 10 shows a special form of combined conical and cylindrical drum designed for hoisting a total balanced load of 25 tons through a vertical height of 550 feet.

Fig. 11 shows a combined conical and cylindrical drum; an unusual feature is the rope reel shown at each end of the drum, which permits of properly storing a few hundred feet of extra rope, allowing the rope to be lengthened, when needed, without splicing.

=19. Comparison of Cylindrical and Conical Drums.= The disadvantages of the cylindrical drum lie entirely in the fact that the load on the engines is variable, but it is possible to overcome this disadvantage by adding a tail-rope to the cages to balance the weight of the rope. This system gives its best results where hoisting is done from one level only, but in deep hoisting it is impracticable because of the extra weight added and because of possible excessive swaying of the rope.

The conical drum has two strong points in its favor: first, the load on the engine may be nearly equalized during the entire hoisting period; and, second, the starting of the engines with the load requires less power.

The disadvantages of the conical drum are as follows: To maintain a certain average speed of hoisting, the speed toward the end of the hoist is of necessity higher than the average and comes at a time when a slowing up should be taking place, so that more care must be exercised when making the landing. To prevent the rope from being drawn out of the grooves, the latter must be made deep and with a large pitch, thereby increasing the width of the face or length of the drum. In making a landing, when the rope is on the conical face, the rope must be kept taut, as any slackness will permit the rope to leave the groove, with the result that all the rope will pile up in the bottom grooves of the drum allowing the cage to drop into the mine, unless it is resting on the chairs. If there are several levels to be hoisted from, the equalizing of the load on the engines can only be realized for one level; for all other levels this advantage will be lost. For large depths, conical drums become very long and require correspondingly long leads from head-frame to drum. To hold the same amount of rope, conical drums are heavier than cylindrical ones, and as a result, the power required in starting the load is somewhat increased owing to the greater inertia of the rotating parts.

Some of these disadvantages have been overcome by making a combination of cone and cylindrical drums. The drums are so designed that the landing takes place only when the rope is on the cylindrical portion of the drum. For deep hoisting, the greater diameter of the drum and its length must be inconveniently large if the load is equalized. The length and diameter can be reduced by making one-half of the drum cylindrical and by having the rope from each end wind on the same cylindrical portion of the drum. In all cases, however, these modifications are made at the expense of the equalization of the load on the engines, and it is not possible to obtain the latter without including some serious disadvantage.

There are certain objections to both cylindrical and conical drums: their great size and weight, for large hoists, make them very expensive; their width necessitates placing the engines far apart, which adds to the cost of the engines, foundations, and buildings; the great weight of the drums is also objectionable, because it forms a large part of the mass to be put in motion and brought to rest at each hoist.

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.

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

200,000 This rope gives a factor of safety of -------- = 8.8. 22,600

Substituting the foregoing weights of material, skip, and rope in formula =4=, in Art. =17=, gives

(5,000 + 6,000 + 27,600) _D_ = _d_ ------------------------ . (5,000 + 6,000)

Hence, the equation of moments is _D_ = 3.5_d_. 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)π_d_², while the area included by the outer coil of rope is (¼)π_D_² hence, the area of annular space occupied by the rope is

(¼)π_D_² - (¼)π_d_² = (¼)π(_D_² - _d_²).

Such values for _D_ and _d_ must be chosen that the equation of moments in Art. =22= is satisfied, while the area (¼)π(_D_²-_d_²) must correspond to the space occupied by the given rope when rolled.

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[(3.5_d_)² - _d_²] = 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.

ROPE WHEELS

=24. Koepe System.=--In its lightest form, a drum requires a large amount of power to set it in motion, which power is absorbed by the brake and lost when it is brought to rest again. Furthermore, with deep shafts requiring long drums, the fleet, or angle that the rope makes with the head-sheave due to its traveling from one end of the drum to the other, is not only a disadvantage and possible cause of accident, but it is a source of wear. To overcome these objections and also the great cost of large cylindrical or conical drums, the =Koepe system= of hoisting, shown in Fig. 14, was devised by Mr. Frederick Koepe. A single grooved driving sheave _a_ is used in place of a drum. The winding rope _b_ passes from one cage _A_ up over a head-sheave, thence around the sheave _a_ and back over another head-sheave, and down to a second cage _B_; it encircles a little over half the periphery of the driving sheave and is driven by the friction between the sheave and rope. A balance rope _c_ beneath the cages and passing around the sheave _d_ gives an endless-rope arrangement with the cages fixed at the proper points. The driving sheave is stronger than an ordinary carrying sheave, as it has to do the driving and is usually lined with hardwood, which is grooved to receive the winding rope, the depth of the groove being generally equal to twice the diameter of the rope. Instead of being placed parallel, the head-sheaves are placed at an angle with each other, each pointing to the groove in the driving sheave, thus reducing the side friction of the rope on the sheaves.

The system has been in successful operation since 1877, and experiments made on it have determined that, with a rope passing only one-half turn around the drum sheave, the coefficient of adhesion with clean ropes is about .3. If the ropes are oiled, the adhesion becomes less, and sometimes slippage occurs, producing not only wear of the driving sheave lining but giving an incorrect reading of the hoist indicator and thus possibly producing overwinding, unless the position of the cage is indicated by marks on the rope, or unless the engineer can see the cage.

At the end of the hoist, if the upper cage is allowed to rest on the keep, its weight and the weight of the tail-rope are taken from the hoisting rope, and there is then not enough pull on the hoisting rope to produce sufficient friction with the drum sheave to start the next hoist. To prevent this trouble, the keeps are dispensed with, or the rope is made continuous and independent of the cage. To do this, crossheads are placed above and below each cage and connected by ropes or chains outside of the cages. The bridle chains are then hung from the top crosshead, and when the cage rests on the keeps, the weight of the winding and tail-ropes remains on the driving sheaves.

=25. Advantages and Disadvantages of the Koepe System.=--With this system, only one driving sheave is necessary for the operation of two compartments, and it is light, inexpensive to build, and very narrow, admitting of a short sheave shaft and small foundations. This system permits a perfect balance of rope and cage, so that the work to be done by the engine is uniform, except for the acceleration, and consists only in lifting the material and overcoming the friction. There is no fleeting of the rope between the driving sheaves and the head-sheaves.

The system has the following disadvantages, which prevent its being used to any considerable extent: Liability to slippage of the rope on the drum; if the rope breaks, both cages may fall to the bottom; hoisting from different levels cannot be well done, for, since the cages are at fixed distances from each other, the length of the rope is such that when one cage _A_ is at the top, the other cage _B_ is at the bottom. If hoisting is to be done from the bottom, this is satisfactory, but if hoisting is to be done from some upper level, cage _B_, which is at the bottom, must be hoisted to that level to be loaded before it can go to the top. Then, when cage _B_ goes to the top with its load, cage _A_ must go to the bottom, wait there while cage _B_ is being unloaded, and then be hoisted to the upper level to receive its load. For each trip, therefore, the time required for a cage to go from the bottom to the upper level and be loaded is lost; and two movements of the engines are necessary for a hoist instead of one.

=26. The Whiting System.=--This is a system of hoisting with round ropes, in which two rope wheels placed tandem are used in place of cylindrical or conical drums. As shown in Fig. 15, for a two-compartment shaft the rope passes from one cage _a_ up over a head-sheave _c_, down under a guide sheave _d_, and is then wound three times about the rope wheels _e_ and _f_, to secure a good hold, then around a fleet sheave _g_, and back under another guide sheave _h_, up over another head-sheave _i_, and down to the other cage _b_. When the system is to be used for a single-compartment shaft, one end of the rope carries the cage and the other end carries a balance weight, which is run up and down in a corner of the shaft. A balance rope below the cages, as shown, is generally used, though it is not essential to the working of the system, as it is in the Koepe system. When sinking a shaft, a balance rope cannot be used as it interferes with the work at the bottom of the shaft.

The drums or wheels _e_, _f_ are light, inexpensive, and narrow, thus permitting short sheave shafts and small foundations. They are lined with hardwood blocks, each lining having three rope grooves turned in it. The main wheel _e_ is driven by a hoisting engine, which may be either first or second motion. The following wheel _f_ is coupled to the main wheel by a pair of parallel rods, one on each side, like the drivers of a locomotive. As the rope wraps about the wheels _e_, _f_ three times, there are six semi-circumferences of driving contact with the rope, as compared with the one semi-circumference in the Koepe system, and there is no slipping of the rope on the wheels. The following wheel _f_ is best tilted or inclined from the vertical an amount equal, in the diameter of the wheels, to the pitch of the rope on the wheel, so that the rope may not run out of its groove and may run straight from one wheel to the other without any chafing between the ropes and the sides of the grooves.

The capacity of the wheels _e_, _f_ is unlimited, while grooved cylindrical drums, conical drums, and reels will hold only the fixed length of rope for which they are designed.

As shown by the dotted lines, the fleet sheave _g_ is arranged to travel backwards and forwards, in order to change the working length of the rope from time to time to provide for an increased depth of shaft, and for the changes in the length of rope due to stretching and when the ends are cut off to resocket the rope. The fleet sheave _g_ is moved a distance equal to half the change in the length of rope.

=27=. Hoisting from intermediate levels can be readily done with the Whiting system; for instance, if the cage _a_ is at the top and cage _b_ at the bottom, and hoisting is to be done from some upper level, it is only necessary to run the fleet sheave _g_ out, and thus shorten the working length of the rope until cage _b_ comes up to the upper level. It can then be loaded and go to the top. While cage _b_ goes to the top, cage _a_ descends to the same level, where it can be loaded while cage _b_ is being unloaded, and can then go directly to the top without any of the lost time, as is the case in the Koepe system.

The system permits a perfect balance of rope and cage, so that the work to be done by the engines is uniform, except for the acceleration, and consists only in lifting the material and overcoming the friction.

There is no fleeting of the rope, so the rope wheels can be placed as close to the shaft as may be desired.

=28.= This system was tried as early as 1862 in Eastern Pennsylvania, but it was not used extensively because hoisting from great depths was not necessary, since, for depths of less than 1,000 feet, cylindrical and conical drums are quite satisfactory. In the Lake Superior copper region, there are now three Whiting hoists, two of which are probably the largest hoisting plants in the world. Each plant consists of a pair of triple-expansion, vertical, inverted-beam engines, driving direct a pair of 19-foot drums. The high-pressure cylinders are 20 inches in diameter, the intermediate cylinders 32 inches, and the low-pressure cylinders 50 inches, and all six of them have a 72-inch stroke. The rope used is a 2¼-inch plow-steel rope and hoists 10 tons of material at a trip, in one case from a depth of 4,980 feet, the deepest shaft in the world. Several plants on the Whiting system have been built in England, and two or more are working in South Africa.

=29. Modified Whiting System.=--A modification of the Whiting system is sometimes used in which a large drum keyed to the crank-shaft replaces the small tandem drums, and even the slight probability of the rope slipping in the Whiting system is thus obviated. One rope is fastened to one end of the drum, and the other rope to the other end in such a way that while one is winding on the other will be winding off the drum. One rope passes directly to the head-sheave while the other passes first around a fleet sheave, similar to that used for the Whiting system, but preferably placed horizontal, and thence to the head-sheave. This system possesses the same advantages as the Whiting system except that the depth of hoist is limited by the size of the drum, and that there is a fleet of the rope. Up to the limiting depth, as determined by the size of the drum, this system can be used with equal economy for any depth. This hoist, as well as the Whiting, is therefore especially suitable for a place where one mining company operates several mines, for it enables the company to select one size for all their permanent work, with all the advantages that come from duplicate machinery.

ROPE FASTENINGS

=30.= A common method of fastening a rope to a drum, Fig. 16 (_a_), is to pass the rope through a hole in the drum rim and then around the shaft, clamping the end to the rope between the shaft and shell, as shown. Care should be taken to make the radius of curvature of the hole at _a_ as large as possible so that the rope will not be bent any sharper than is necessary. When an iron drum is used, the thickness of the rim does not afford enough depth in which to bend the rope and it is necessary to build in a pocket for the purpose, as shown at Fig. 16 (_b_). It is well to make both sides of this pocket with a long radius to avoid damaging the rope in case all the rope is accidentally unwound and the drum backed so as to bring the rope against the other side of the pocket.

CLUTCHES

=31.= It is often desired to have the drum of a hoisting engine run loosely on the engine shaft, so that it may run independently of the engine. With such loose-running drums, the engine generally runs only in the direction required to hoist the load, while the cage is lowered entirely by means of the brake. In this way, one engine provided with several drums may be used for hoisting from several shafts or from several levels in the same shaft at the same time. Such a loose-running drum is connected to the engine shaft when a load is to be hoisted by means of a clutch, of which there are two forms commonly used for hoisting machinery: _jaw_ or _piston clutches_ and _friction clutches_.

=32. Jaw Clutch.=--Fig. 17 shows a =jaw clutch=, one-half _a_ of which is shown ready to be bolted to a drum or flat rope reel, which is loose on the shaft _b_. The other half _c_ of the clutch is moved back so that the jaws _d_ are not in contact with the jaws _e_ on the part _a_. The half _c_ slides freely on a feather key _f_, which is driven tightly into a deep key seat in the shaft _b_; a collar _g_, fitting loosely in a groove in the hub of _c_, is provided with trunnions _h_ on each side; levers _i_ connect these trunnions with the lever _j_ attached to a suitable handle, by means of which the clutch is made to slide endwise on the shaft so that the jaws _d_ engage or disengage the jaws _e_ and thus connect or disconnect the drum or reel from the clutch. There are generally four or six jaws _d_ that engage the same number of jaws _e_ on the drum, and it is necessary to have little or no play between _d_ and _e_ when the clutch is connected or there will be too much shock. The clutch is about 2 feet in diameter, and the jaws are 3 or 4 inches deep for the average 20" × 48" first-motion hoisting engine. Instead of the clutch being fastened to the shaft by feather keys, the shaft may be hexagonal where the clutch slides on it and the clutch is machined to match. Jaw clutches are made of either cast-iron or cast-steel, and should be in halves, for convenience of repair, and securely bolted together.