STEAM ENGINE TESTING
The princ.i.p.al 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 a.s.sumed 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 c.o.c.k 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 circ.u.mference 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 pa.s.ses 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-c.o.c.ks 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 c.o.c.k. 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 c.o.c.k is opened and steam allowed to blow through the indicator to warm it up.
The c.o.c.k is now closed and the pencil pressed against the drum to get the so-called atmospheric line. The c.o.c.k is again opened, and the pencil pressed lightly against the drum during one complete revolution of the engine. The c.o.c.k is then thrown over to connect the indicator with the other end of the cylinder and the operation is repeated.
[Ill.u.s.tration: 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 a.n.a.lysis 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 60 = 43.3 pounds per square inch.
[Ill.u.s.tration: 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. Subst.i.tuting 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.
[Ill.u.s.tration: Fig. 51. Diagram for Ill.u.s.trating 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 pa.s.sed over the diagram several times, and the reading divided by the number of times it is thus pa.s.sed 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.
[Ill.u.s.tration: 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 ill.u.s.tration.
_Example_--Let Fig. 53 represent a diagram taken from the head end of a 16 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.
[Ill.u.s.tration: 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 = ((2 201) - 7)/2 = 198 square inches, approximately. Then
198 48.2 2.5 300 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 ill.u.s.tration), 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 2.27 = 3.18 cubic feet. When the piston is at _Q_, the volume is 1.4 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 0.116 = 0.369 pounds. The weight of steam present when the piston is at _Q_ is 0.42 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.