STEAM ENGINE TESTING
The principal information sought in the usual test of a steam engine is:
1. The indicated horsepower developed under certain standard conditions.
2. The friction of the engine, from which is determined the mechanical
efficiency.
3. The steam consumption per indicated horsepower.
4. The general action of the valves.
5. The pressure conditions in the cylinder at different periods of the
stroke.
The ultimate object of an efficiency test is to determine the
foot-pounds of work delivered by the engine per pound of coal burned in
the boiler furnaces. The general method of finding the pounds of dry
steam evaporated per pound of coal has been treated in MACHINERY'S
Reference Series No. 67, "Boilers," under the head of "Boiler Testing."
In the present case it is, therefore, only necessary to carry the
process a step further and determine the foot-pounds of work developed
per pound of steam.
The apparatus used in engine testing, in addition to that used in boiler
testing, consists of a steam engine _indicator_ and reducing device for
taking diagrams, and a _planimeter_ for measuring them afterwards. If
the test is made independently of the boiler test, a calorimeter for
measuring the amount of moisture in the steam should be added to the
outfit.
It has already been shown how a diagram may be made to represent
graphically the work done in a steam engine cylinder during one stroke
of the piston. The diagrams shown thus far have been theoretical or
ideal cards constructed from assumed relations of the pressure acting
and the distance moved through by the piston. An indicator is a device
for making a diagram of what actually takes place in an engine cylinder
under working conditions. Such a diagram shows the points of admission,
cut-off, and release, and indicates accurately the pressures acting upon
both sides of the piston at all points of the stroke.
A common form of steam engine indicator is shown in Fig. 49. It consists
of a cylinder _C_ which is placed in communication at _E_ with one end
of the engine cylinder by a proper pipe connection, provided with a
quick opening and closing cock or valve. The cylinder _C_ contains a
piston, above which is placed a coil spring of such strength that a
given pressure per square inch acting upon the lower side of the piston
will compress the spring a definite and known amount. Extending through
the cap or head of cylinder _C_ is a stem attached to the piston below,
and connected by suitable levers with a pencil point _P_. The
arrangement of the levers is such that a certain rise of the piston
causes the point _P_ to move upward in a vertical line a proportional
amount.
The springs used above the piston vary in strength, and are designated
as 20-pound, 40-pound, 60-pound, etc. A 20-pound spring is of such
strength that a pressure of 20 pounds per square inch, acting beneath
the piston in cylinder _C_, will raise the pencil point 1 inch. With a
40-pound spring, a pressure of 40 pounds per square inch will be
required to raise the pencil 1 inch, and so on for the other strengths
of spring.
The hollow drum _D_ rotates back and forth upon a vertical stem at its
center, its motion being produced by the string _H_, which is attached
by means of a suitable reducing motion to the cross-head of the engine.
The return motion to the drum is obtained from a coil spring contained
within it and not shown. The paper upon which the diagram is to be drawn
is wound around the drum _D_, and held in place by the spring clip _F_.
In taking an indicator card, the length of stroke must be reduced to
come within the limits of the drum, that is, it must be somewhat less
than the circumference of drum _D_. In practice, the diagram is commonly
made from 3 to 4 inches in length. There are a number of devices in use
for reproducing the stroke of the engine on a smaller scale. The most
accurate consists of a series of pulleys over which the cord passes on
its way from the cross-head to the indicator drum.
The indicator is connected with the engine cylinder by means of special
openings tapped close to the heads and either plugged or closed by means
of stop-cocks when not in use. In some cases two indicators are used,
one being connected to each end of the cylinder, while in others a
single indicator is made to answer the purpose by being so piped that it
can be connected with either end by means of a three-way cock. After the
indicator is connected and the cord adjusted to give the proper motion
to the drum, a card is attached, after which the three-way cock is
opened and steam allowed to blow through the indicator to warm it up.
The cock is now closed and the pencil pressed against the drum to get
the so-called atmospheric line. The cock is again opened, and the pencil
pressed lightly against the drum during one complete revolution of the
engine. The cock is then thrown over to connect the indicator with the
other end of the cylinder and the operation is repeated.
[Illustration: Fig. 49. Steam Engine Indicator]
The indicator card obtained in this way is shown in Fig. 50. It is
sometimes preferred to take the diagrams of the two ends on separate
cards, but it is simpler to take them both on the same one, and also
easier to compare the working of the two ends of the cylinder.
The analysis of a card for practical purposes is shown in Fig. 51.
Suppose, for example, that the length of the diagram measures 3.6
inches; the distance to the point of cut-off is 1.2 inch; and the
distance to the point of release is 3.3 inches. Then, by dividing 1.2 by
3.6, the cut-off is found to occur at 1.2 / 3.6 = 1/3 of the stroke.
Release occurs at 3.3 / 3.6 = 0.92 of the stroke. Compression begins at
(3.6 - 0.5) / 3.6 = 0.86 of the stroke. The diagrams shown in Figs. 50
and 51 are from non-condensing engines, and the back-pressure line is
therefore above the atmospheric line, as indicated.
The indicator diagram gives a means of determining the mean effective
pressure, from which the power of the engine can be found from the
previously given equation
_APLN_
I. H. P. = ------.
33,000
The method of determining the mean effective pressure is as follows:
First measure the area of the card in square inches, by means of a
planimeter (an instrument described later), and divide this area by the
length in inches. This gives the mean ordinate; the mean ordinate, in
turn, multiplied by the strength of spring used, will give the mean
effective pressure in pounds per square inch. For example, suppose that
the card shown in Fig. 51 is taken with a 60-pound spring, and that the
area, as measured by a planimeter, is found to be 2.6 square inches.
Dividing the area by the length gives 2.6 / 3.6 = 0.722 inch as the mean
ordinate, and this multiplied by the strength of spring gives a mean
effective pressure of 0.722 x 60 = 43.3 pounds per square inch.
[Illustration: Fig. 50. A Typical Indicator Diagram]
In practice, diagrams taken from the two ends of the cylinder usually
vary more or less, due to inequalities in the valve action. Again, the
effective area of the piston on the crank end is less than that on the
head end, by an amount equal to the area of the piston rod. For these
reasons it is customary to compute the mean effective pressure of all
the cards separately, and take, for use in the formula, the average of
the various computations. The corrected value of the piston area is, as
already stated, equal to (2_A_ - _a_)/2, in which _A_ is the area of the
piston, and _a_ the area of the piston rod. Substituting these values
for _A_ and _P_ in the formula, together with the length of stroke and
average number of revolutions per minute, the indicated horsepower is
easily computed.
In making an ordinary test, diagrams are taken from both ends of the
cylinder at 10-minute intervals for several hours, depending upon the
accuracy required. The revolutions of the engine are counted for two or
three-minute periods each time a pair of cards are taken, or still
better, an automatic counter is used for the run, from which the average
number of revolutions per minute may be determined.
[Illustration: Fig. 51. Diagram for Illustrating Method of Computation]
The friction of the engine is determined by taking a pair of cards while
"running light," that is, with the belt thrown off, or the engine
uncoupled, from the dynamo, if part of a direct-connected outfit. The
friction load is then computed in horsepower from the indicator cards,
and subtracted from the indicated horsepower when loaded. Thus we obtain
the delivered or brake horsepower. The delivered horsepower divided by
the indicated horsepower gives the mechanical efficiency. This may be
expressed in the form of an equation as follows:
I. H. P. - friction loss
------------------------ = mechanical efficiency.
I. H. P.
Planimeter
The planimeter is an instrument for measuring areas in general, and
especially for measuring the areas of indicator cards. Some forms give
the mean effective pressure directly, without computations, by changing
the scale to correspond with the spring used in the indicator. A
planimeter of this type is shown in Fig. 52. The method of manipulating
this instrument is as follows. Set the arm _BD_ equal to the length of
the card _EF_, by means of the thumb screw _S_, and set the wheel at
zero on the scale, which must correspond to the spring used in the
indicator. Next, place the point _D_ at about the middle of the area to
be measured, and set point _C_ so that the arm _CB_ shall be
approximately at right angles with _BD_. Then move _D_ to the upper
left-hand corner of the diagram, and with the left hand move _C_ either
to the right or left until the wheel comes back exactly to the zero
point on the scale; then press the point firmly into the paper. Now, go
around the outline of the diagram with point _D_ from left to right,
finishing exactly at the starting point. The mean effective pressure may
now be read from the scale opposite the edge of the wheel.
When very accurate results are required, the tracer point _D_ may be
passed over the diagram several times, and the reading divided by the
number of times it is thus passed around. With short cards, 3 inches and
under in length, it is best to make the arm _BD_ twice the length of the
card, and go around the diagram twice, taking the reading directly from
the scale as in the first case.
Determining Steam Consumption
When it is desired to determine accurately the water rate of an engine,
a boiler test should be carried on simultaneously with the test upon the
engine, from which the pounds of dry steam supplied may be determined as
described in MACHINERY'S Reference Series No. 67, "Boilers." Knowing the
average weight of steam supplied per hour for the run, and the average
indicated horsepower developed during the same period, the water rate of
the engine is easily computed. Sometimes the average cylinder
condensation for a given type and make is known for certain standard
conditions. In this case an approximation may be made from an indicator
diagram which represents the average operation of the engine during the
test.
[Illustration: Fig. 52. General Construction of Planimeter]
A diagram shows by direct measurement the pressure and volume at any
point of the stroke, and the weight of steam per cubic foot for any
given pressure may be taken directly from a steam table. The method,
then, of finding the weight of steam at any point in the stroke is to
find the volume in cubic feet, including the clearance and piston
displacement to the given point, which must be taken at cut-off or
later, and to multiply this by the weight per cubic foot corresponding
to the pressure at the given point measured on the diagram. As this
includes the steam used for compression, it must be corrected, as
follows, to obtain the actual weight used per stroke. Take some
convenient point on the compression curve, as _Q_, in Fig. 53; measure
its absolute pressure from the vacuum line _OX_ and compute the weight
of steam to this point. Subtract this weight from that computed above
for the given point on the expansion line, and the result will be the
weight of steam used per stroke. The best point on the expansion line to
use for this purpose is just before release, both because the maximum
amount of leakage has taken place, and also because of the
re-evaporation of a portion of the steam condensed during admission. The
actual computation of the steam consumption from an indicator diagram is
best shown by a practical illustration.
_Example_--Let Fig. 53 represent a diagram taken from the head end of a
16 x 30-inch non-condensing engine, running at a speed of 150
revolutions per minute; the card is taken with a 60-pound spring; the
clearance of the engine is 6 per cent; the average cylinder condensation
is 20 per cent of the total steam consumption; the diameter of the
piston rod is 3 inches.
[Illustration: Fig. 53. Diagram for Calculating Steam Consumption]
Measuring the card with a planimeter shows the mean effective pressure
to be 48.2 pounds. The area of the piston is 201 square inches; the area
of the piston rod is 7 square inches; hence, the average piston area =
((2 x 201) - 7)/2 = 198 square inches, approximately. Then
198 x 48.2 x 2.5 x 300
I. H. P. = ---------------------- = 217.
33,000
In Fig. 53, _GH_ is the atmospheric line; _OX_ is the line of vacuum or
zero pressure, drawn so that _GO_ = 14.7 pounds on the scale; and _OY_
is the clearance line, so drawn that _ON_ = 0.06 _NX_. The line _PQ_ is
drawn from _OX_ to some point on the compression line, as at _Q_. From
_C_, a point on the expansion line, just before release, the line _CF_
is drawn perpendicular to _OX_. The following dimensions are now
carefully measured from the actual diagram (not the one shown in the
illustration), with the results given:
_OX_ = 3.71 _OP_ = 0.42
_NX_ = 3.50 _CF_ = 0.81
_OF_ = 3.20 _QP_ = 0.81
On the indicator diagram, being taken with a 60-pound spring, all
vertical distances represent pounds per square inch, in the ratio of 60
pounds per inch of height. The stroke of the engine is 30 inches or 2.5
feet. The length of the diagram _NX_ is 3.5 inches; hence, each inch in
length represents 2.5/3.5 = 0.71 feet. From the above it is evident that
vertical distances in Fig. 53 must be multiplied by 60 to reduce them to
pounds pressure per square inch, and that horizontal distances must be
multiplied by 0.71 to reduce them to feet. Making these reductions
gives:
_OX_ = 2.63 feet. _OP_ = 0.30 foot.
_NX_ = 2.49 feet. _CF_ = 48.6 pounds.
_OF_ = 2.27 feet. _QP_ = 48.6 pounds.
As a card from the head end of the cylinder is taken to avoid
corrections for the piston rod, the area is 201 square inches or 1.4
square foot. With the above data the volume and weight of the steam in
the cylinder can be computed at any point in the stroke. When the piston
is at _C_, the volume is 1.4 x 2.27 = 3.18 cubic feet. When the piston
is at _Q_, the volume is 1.4 x 0.30 = 0.42 cubic foot. From a steam
table the weight of a cubic foot of steam at 48.6 pounds absolute
pressure is found to be 0.116 pounds. Therefore, the weight of steam
present when the piston is at _C_ is 3.18 x 0.116 = 0.369 pounds. The
weight of steam present when the piston is at _Q_ is 0.42 x 0.116 =
0.049 pound. That is the weight of steam in the cylinder at release is
0.369 pound, and the weight kept at exhaust closure for compression is
0.049 pound.
The weight exhausted per stroke is therefore 0.369 - 0.049 = 0.32 pound.
The number of strokes per hour is 150 x 2 x 60 = 18,000, from which the
steam accounted for by the diagram is found to be 18,000 x 0.32 = 5760
pounds, or 5760 / 217 = 26.5 pounds per indicated horsepower per hour.
If the cylinder condensation for this type of engine is 20 per cent of
the total steam consumption, the water rate will be 26.5 / 0.8 = 33.1
pounds per indicated horsepower per hour.
In the present case it has been assumed, for simplicity, that the
head- and crank-end diagrams were exactly alike, except for the piston
rod. Ordinarily, the above process should be carried out for both head
and crank ends, and the results averaged.