=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.
[Illustration: 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
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: FIG. 13]