552. When energy has been stored in a fly-wheel, it can be withdrawn
either as a small force acting over a great distance, or as a large
force over a small distance. In the latter case the fly-wheel acts as
a mechanical power, and in this form it is used in the very important
machine to be next described. A model of the punching machine is shown
in Fig. 73.
The punching machine is usually worked by a steam-engine, a handle will
move our small model. The handle turns a shaft on which the fly-wheel
F is mounted. On the shaft is a small pinion D of 40 teeth: this works
into a large wheel E of 200 teeth, so that, when the fly and the pinion
have turned round 5 times, E will have turned round once, C is a
circular piece of wood called a cam, which has a hole bored through it,
between the centre and circumference; by means of this hole, the cam is
mounted on the same axle as E, to which it is rigidly fastened, so that
the two must revolve together. A is a lever of the first order, whose
fulcrum is at A: the remote end of this lever rests upon the cam C; the
other end B contains the punch. As the wheel E revolves it carries with
it the cam: this raises the lever and forces the punch down a hole in a
die, into which it fits exactly. The metal to be operated on is placed
under the punch before it is depressed by the cam, and the pressure
drives the punch through, cutting out a cylindrical piece of metal from
the plate: this model will, as you see, punch through ordinary tin.
[Illustration: FIG. 73.]
553. Let us examine the mode of action. The machine being made to
rotate rapidly, the punch is depressed once for every 5 revolutions of
the fly; the resistance which the metal opposes to being punched is no
doubt very great, but the lever acts at a twelve-fold advantage. When
the punch comes down on the surface of the metal, one of three things
must happen: either the motion must stop suddenly, or the machine must
be strained and injured, or the metal must be punched. But the motion
cannot be stopped suddenly, because, before this could happen, an
infinite force would be developed, which must make something yield.
If therefore we make the structure sufficiently massive to prevent
yielding, the metal must be punched. Such machines are necessarily
built strong enough to make the punching of the metal easier than
breaking the machine.
554. We shall be able to calculate, from what we have already seen in
Art. 248, the magnitude of the force required for punching. We there
learned that about 22·5 tons of pressure was necessary to shear a bar
of iron one square inch in section. Punching is so far analogous to
shearing that in each case a certain area of surface has to be cut; the
area in punching is measured by the cylinder of iron which is removed.
555. Suppose it be required to punch a hole 0"·5 in diameter through
a plate 0"·8 thick, the area of iron that has to be cut across is
²²/₇ × ½ × ⁴/₅ = 1·26 square inches: and as 22·5 tons per square inch
are required for shearing, this hole will require 22·5 × 1·26 = 28·4
tons. A force of this amount must therefore be exerted upon the punch:
which will require from the cam a force of more than 2 tons upon
its end of the lever. Though the iron must be pierced to a depth of
0"·8, yet it is obvious that almost immediately after the punch has
penetrated the surface of the iron, the cylinder must be entirely
cut and begin to emerge from the other side of the plate. We shall
certainly be correct in supposing that the punching is completed before
the punch has penetrated to a depth of 0"·2, and that for not more than
this distance has the great pressure of 28 tons been exerted; for a
small pressure is afterwards sufficient to overcome the friction which
opposes the motion of the cylinder of iron. Hence, though so great a
pressure has been required, yet the number of units of energy consumed
is not very large; it is ¹/₆₀ × 2240 × 28·4 = 1062.
The energy actually required to punch a hole of half an inch diameter
through a plate eight-tenths of an inch thick is therefore less than
that which would be expended in raising 1 cwt. to a height of ten feet.
556. The fly-wheel may be likened to the reservoir in Art. 545. The
time that is actually occupied in the punching is extremely small, and
the sudden expenditure of 1062 units is gradually reimbursed by the
engine. If the rotating fly-wheel contain 50,000 units of energy, the
abstraction of 1362 units will not perceptibly affect its velocity.
There is therefore an advantage in having a heavy fly sustained at a
high speed for the working of a punching machine.
LECTURE XVII.
_CIRCULAR MOTION._
The Nature of Circular Motion.—Circular motion in
Liquids.—The Applications of Circular Motion.—The
Permanent Axes.