Demonstration to the Judges of Action of Reciprocating Parts.
Explanation of this Action. Mr. Williams’ Instrument for Exhibiting
this Action.
The subject of the equalizing action of the reciprocating parts of the
engine was not considered in the report of the judges. Indeed, the
speed of that engine, 125 revolutions per minute, was not sufficient
to develop this action to any important extent. But there was another
reason behind that. I invited the judges directly after the close of
the fair, but before making their report, to witness a demonstration of
this action in my little shop engine, which invitation was accepted by
them, and the following exhibition was made, but this was not alluded
to in their report, the reason of which will be given on a later page.
The engine had a 5-inch cylinder by 12 inches stroke, and its regular
speed was 300 revolutions per minute. I kept Saturday afternoon
holiday, one of the good things I had brought from England, and so on
Saturday afternoon I had a clear field for this exhibition.
I had previously prepared two governor pulleys to speed the engine up
to the increased speeds required, which speeds had been ascertained by
calculation. I was so certain of the correctness of this calculation
that I did not make any preliminary trial, did not think of such a
thing.
[Illustration: President F. A. P. BARNARD]
After running the engine for a short time at its usual speed, I changed
the governor pulley for the smaller one of the two I had prepared, by
which the speed would be increased to about 400 revolutions per minute,
and loosened the crank-pin brasses so that they were slack fully a
thirty-second of an inch. On starting the engine in this condition,
of course, it pounded violently on the crank-pin. As the speed was
gradually permitted to increase the knock softened, and just before the
governor rose it disappeared entirely, and at the calculated speed the
engine ran in entire silence.
After running in this manner for a while I prepared for the second
part of my show. I put the crank-pin brasses back to their usual
running adjustment, loosened the brasses of the cross-head pin fully a
thirty-second of an inch, and put on a larger governor pulley, which,
if I remember rightly, ran the engine at about 550 revolutions per
minute. Under these conditions we utilized only the inertia of piston,
rod and cross-head, without that of the connecting-rod.
On starting, the engine of course pounded heavily on the cross-head
pin. As the speed increased the same decrease in the noise was observed
as on the first trial, only later in the course of the acceleration,
and again just before the governor rose the pounding had completely
died away, and at the calculated speed the engine ran again in entire
silence.
Like everything else, this action seems mysterious until it comes to
be understood, when it is seen to be quite simple, as the following
explanation will show.
EXPLANATION OF THE ACTION OF THE RECIPROCATING PARTS OF A HORIZONTAL
STEAM ENGINE
Let us take a horizontal engine of 2 feet stroke, making 200
revolutions per minute, so having a piston travel or average velocity
of 800 feet per minute, which was my engine in the Paris Exposition of
1867.
We will suppose the piston to be driven through the crank, by which its
motion is controlled, the power being got from some other motor, and
that the cylinder heads have been removed so that the piston meets no
resistance. We will also disregard the effect of the angular vibration
of the connecting-rod, and assume the motion of the piston to be the
same at each end of the cylinder.
On each stroke the crank does two things: First, it increases the
motion of the piston from a state of rest to a velocity equal to the
uniform velocity of the crank-pin in its circular path: and, second,
it brings the piston to rest again, ready to have the same operation
repeated in the reverse direction during the return stroke.
At the mid-stroke the crank is at right angles with the line of
centers, and the velocity of the piston is 800 × ¹⁄₂π = 1256.64 feet
per minute, or 20.944 feet per second, and no pressure is being exerted
on the piston either to accelerate or retard its motion.
[Illustration]
The pressure of the crank during a stroke, first to impart motion to
the piston and second to arrest this motion, is represented by two
opposite and equal triangles. Let the line _AB_, in the above figure,
be the center line of a cylinder and its length represent the length
of the stroke. Let the line _AC_, normal to the line _AB_, represent
the force required to start the piston from a state of rest. Then the
triangle _AOC_ will represent the accelerating force that must be
exerted on the piston at every point in the half stroke to bring up its
velocity, until at _O_ this equals that of the crank-pin in its circle
of revolution, and the accelerating force, diminishing uniformly, has
ceased. The opposite equal triangle _BOD_ shows the resistance of the
crank required to bring the piston to rest again.
How do we know this?
I will answer this question by the graphical method, the only one I
know, and which I think will be understood by readers generally.
First, we observe that the distance the piston must move from the
commencement to any point in the first half of its stroke, in order
that it shall keep up with the crank, is the versed sine of the angle
which the crank then forms with the line of centers. So the table of
versed sines tells us where the piston is when the crank is at any
point in its revolution, from 0 to 90°.
[Illustration]
For example, let the quadrant _AB_ in the following figure represent
the path of the crank, and the line _AO_ that of the piston. Let _OF_
be the position reached by the crank. _AOF_ is the angle formed by the
crank with line of centers, and supposed to be 60°. _FE_ normal to _AO_
is the sine of this angle, and _AE_ the versed sine. The latter is the
distance traveled by the piston from the point _A_, and is .5, the
length of the crank being 1.
Secondly, we ascertain how far the piston must advance for every degree
or minute or second of the revolution of the crank in its quadrant
by merely subtracting from its versed sine that of the preceding
one. Thus the versed sine of 60° being .5, and that of 59° being
.4849619251, the difference .0150380749 is the motion of the piston, or
its mean velocity while the crank is traversing the 60th degree of its
revolution.
Thirdly, we want to know the rate at which the motion of the piston is
accelerated during any interval.
This acceleration is found by subtracting from the motion during each
interval that during the preceding one. For example, the motion of the
piston during the 60th degree being, as already seen, .0150380749, and
that during the 59th degree being .0148811893, the difference between
them, .0001568856, is the acceleration or amount of motion added during
the 60th degree.
By this simple process we find the acceleration of the piston during
the first degree of the revolution of the crank to be .0003046096,
and that during the 90th degree to be .0000053161. But this latter is
the amount by which the acceleration was reduced during the preceding
degree. Therefore at the end of this degree the acceleration has ceased
entirely.
Now, by erecting on the center line _AC_, at the end of each degree,
ordinates which are extensions of the sine of the angle, and the
lengths of which represent the acceleration during that degree we find
that these all terminate on the diagonal line _CO_. Thus, when the
crank has reached the 60th degree, and the piston has advanced half
the distance to the mid-stroke or to _E_, Fig. 32, the acceleration
during the 60th degree has been .0001523049, or one half of that during
the first degree.
But how do we know the amount of the accelerating force exerted by the
crank at the beginning of the stroke? This question is answered as
follows:
We find that for the first three degrees the accelerating force is, for
the purpose of our computations, constant, the diminution not appearing
until we have passed the sixth place of decimals.
Let us now suppose the crank 1 foot in length to make 1 revolution per
minute, so moving through 6° of arc in 1 second. At this uniform rate
of acceleration the piston would be moved in 1 second the versed sine
of 1° .0001523048 × 6² = .0054829728 of a foot.
A falling body uniformly accelerated by a force equal to its own weight
moves in 1 second 16.083 feet. Therefore this uniform stress on the
crank is
.0054829728
----------- = .000341,
16.083
which is the well-established coefficient of centrifugal force--the
centrifugal force of one pound making one revolution per minute in a
circle of one foot radius.
So we find that the height _AC_ of this triangle represents the
centrifugal force of the reciprocating parts which, in any case, we can
ascertain by the formula
_WRr²C_,
_W_ being the weight of the body;
_R_ being the length of the crank;
_r_ being the number of revolutions per minute, and
_C_ being the coefficient .000341.
This accounts for the fact that the reciprocating parts are perfectly
balanced by an equal weight revolving opposite the crank.
In my treatise on the Richards Indicator and the Development and
Application of Force in the Steam-engine, I have given a full
exposition of this action here briefly outlined, and to that the reader
is referred.
I have only to add that this computation is for horizontal engines.
In vertical engines the effect of gravity must be considered, adding
on the upward stroke and deducting on the downward stroke. Also the
counterbalance in the crank-disk of vertical engines must be limited to
the horizontal fling of the crank end of the connecting-rod, and all
balancing must be as nearly as possible in the same plane.
In this respect double-crank engines have this advantage, that one half
of the counterweight can be put on each side of the center line.
It is evident that the heavier the reciprocating parts and the more
rapid the speed the greater the security for smooth and silent running.
However loose the brasses and however sudden the impact of the steam on
the piston, and however early or late the admission, there can be no
sound or jar, if the inertia of the reciprocating parts is sufficient
to equal the force of the entering steam, and if this is in excess it
can do no harm. It is also evident that under these conditions at any
point in the stroke the change of pressure to the opposite side of the
crank-pin is made insensibly.
Some two or three weeks after this exhibition I received a note from
President Barnard asking me to call upon him. On my responding to
this invitation, he said to me that he had listened to my exposition
of this action before the Polytechnic Club of the Institute, but he
did not understand it; he had witnessed the experiments with my shop
engine, but while he could not question the action in silencing all
knock on the centers, still he did not understand it, and not until he
investigated the problem in his own way by the method of the calculus
did it become plain to him, and he could not see how I had ever been
able to arrive at the exposition of the action without employing that
method. This explains why the subject had not been considered in the
report of the judges. President Barnard afterward kindly gave me a copy
of his demonstration, to insert in my book on the Richards Indicator.
It seems appropriate to insert here the following letter received long
after from a very prominent engineer of that day.
“LONG BRANCH, N. J., Aug. 7th, 1872.
“Mr. CHAS. T. PORTER:
“_My dear Sir:_ Since I had the pleasure of reading the paper which
you read before the Polytechnic Club last winter, I have regarded
your demonstration as not less original than subversive. It is,
for the first time I believe, apprehended and asserted, not merely
that the _vis inertia_ of the reciprocating masses is not primarily
an adverse element in the economy of the crank-engine, but that a
certain amount of weight in the piston and its connections, and
in high-speed engines a very considerable amount, is an absolute
theoretical necessity.
“As this will be deemed rank heresy by folks who have been making
skeleton pistons of wrought iron, it is well perhaps that you are
entrenched at the outset behind the _experimentum crucis_ of loose
brasses.
“Very truly yours,
“JOSEPH NASON.”
The following figures represent an elegant invention of Mr. Edwin F.
Williams, which exhibits graphically the acceleration and retardation
of the reciprocating parts of an engine.
In these views, _A_ is the cross-head in its mid-position; _B_ is the
lath by which the paper drum of an indicator is actuated through the
cord _n_. The lower end of this lath is fixed in its position on the
cross-head by the stud _j_, on which it turns freely. _y_ is the end
of a vibrating arm, which permits the point of suspension of the lath
_B_ to fall below the position shown, as required in the motion of the
cross-head on account of the lower end of the lath being so fixed. _d_
is a cylindrical box, partly open, which is secured on the side of the
cross-head, in a position parallel with motion, by the arm _P_. The end
of this arm is on the stud _j_, inside the lath _B_. It is prevented
from turning on this stud by the set-screw _K_, and its fixed position
is further assured by the stud _r_.
In the box _d_ is the cylindrical weight _h_, running freely on
rollers, not shown, and bored to receive a spring _e_, of known
strength. This spring is secured in two heads, one of which is screwed
into the box and the other into the weight. The force required to move
the weight _h_ is thus applied to it through the spring.
The operation of this instrument is as follows: The cross-head being
at its mid-stroke, as represented, has acquired its full velocity. At
this point no force is being exerted, either to impart or to arrest its
motion. The same is the case with the free weight _h_. No pressure is
here being exerted, either to compress or to elongate the spring _e_.
[Illustration: JOSEPH NASON]
[Illustration:
Fig. 1
Fig. 2
Fig. 5
SCALE 40
265 REVS. PER MIN.
11¹⁄₄″ × 16″ PORTER-ALLEN.
Fig. 4
SCALE 40
265 REVS. PER MIN.
4.416 „ „ SEC.
Fig. 3
Apparatus for Graphically Showing the Acceleration and Retardation of
the Reciprocating Parts of an Engine.]
Let the motion be in the direction from the crank. The crank now begins
insensibly, by pulling through the spring _e_, to arrest the motion of
the weight _h_. This pull will increase in intensity to the end of the
stroke, when the weight is brought to rest, and the spring will become
correspondingly elongated. Then, by a continuance of the same pull, the
crank puts the cross-head and this free weight in motion in the reverse
direction. This pull gradually relaxes, until at the mid-stroke it has
ceased. The weight _h_ has acquired its full velocity again; all stress
is off the spring, and the spring and weight are back in the positions
in the box _d_ from which they started. This action is repeated during
the opposite half of the revolution, but in the reverse direction, the
pull being changed to a push, and the spring being compressed instead
of elongated. Thus at every point the position of this free weight
shows the amount of the accelerating or retarding force that is being
exerted upon it at that point, elongating or compressing the spring.
This varying accelerating or retarding force is recorded as follows:
A paper _b_, Fig. 2, is stretched on the surface _ff_. This surface
is the arc of a circle described about the center _j_, and is secured
on the lath _B_, so that as this lath vibrates by the motion of the
cross-head the different points in the length of the paper pass
successively under the pencil. This is set in the end of the long
arm _a_ of the right-angled lever-arms 4 to 1 seen in Fig. 2, which
is actuated by the rod _e_ passing centrally through the spring
and secured in the head _c_. This pencil has thus imparted to it a
transverse motion four times as great as the longitudinal motion of the
weight _h_ in the box _d_. The pencil is kept lifted from the paper (as
permitted by the elasticity of the arm _a_) by the cord _m_. By letting
the pencil down and turning the engine by hand, the neutral line _x_,
Fig. 2, is drawn. Then when the engine is running, on letting the
pencil come in contact with the paper, the diagonal lines are drawn as
shown on Fig. 2.
[Illustration: EDWIN F. WILLIAMS]
If the rotation of the shaft were uniform and there were no lost
motion in the shaft or connecting-rod, this diagonal line would
repeat itself precisely, and would be a straight line modified by the
angular vibration of the connecting-rod. On the other hand, these
lost motions and the variations in the rotative speed must be exactly
recorded, the latter being exhibited with a degree of accuracy not
attainable by computation and plotting, and their correctness would
be self-demonstrated. For this purpose this instrument must be found
highly valuable, if it is really desired to have these variations
revealed rather than concealed. Fig. 5 represents the inertia diagram
drawn by this instrument applied to a Porter-Allen engine running in
the Boston Post Office at the speed of 265 revolutions per minute.
Fig. 4 shows the same diagram with the transverse motion of the pencil
enlarged to correspond with the scale of the indicator, so exhibiting
the force actually exerted on the crank-pin at every point, which is
represented by the shaded area, and from which the rotative effect
on the crank can be computed. The steam pressure absorbed at the
commencement of the stroke by the inertia of these parts is represented
by the blank area above the atmospheric line _xx_. This is not all
imparted to the crank at the end on account of the compression.
I have myself had no experience in the use of this instrument, but I
do not see why it might not be so made that the diagonal line or lines
in Fig. 4 would be drawn at once. The variations of motion would thus
be shown much more accurately than they can be by the enlargement of
these small indications. This would require the spring _e_ to bear the
same relation to the inertia of the weight _h_ that the spring of the
indicator bears to the steam pressure on its piston area. The steam
diagram and the inertia diagram would then be drawn to the same scale.
A separate instrument would be required for each scale. It would seem
desirable that this instrument, which is not expensive, should be
brought before the public in this practical shape.
The 16″×30″ engine exhibited at this fair of the American Institute was
sold from the exhibition to the Arlington Mills, at Lawrence, Mass. For
a reason that will appear later, I have always regarded this sale as
the most important one that I ever made.