Device for Processing Expanded Indicator Diagrams
Abstract Generated abstract
The article addresses the difficulty of deriving mean indicated pressure and related working-process parameters from developed indicator diagrams of high-speed internal-combustion engines. It describes a mechanical device, termed a diagramometer, that uses a guide, tracing pin, crank mechanism, and planimeter attachment to convert pressure diagrams recorded against crank angle or time into diagrams referred to piston stroke, while also enabling calculation of polytropic exponents and pressure-rise rates. The proposed instrument is presented as a means of mechanizing otherwise laborious graphical processing during engine tests, with prototype laboratory studies reporting processing errors within about ±2.5 percent.
Full Text
DEVICE FOR PROCESSING DEVELOPED INDICATOR DIAGRAMS
S. I. Shubovich
The investigation of the working process of internal-combustion engines is, as a rule, associated with indication, i.e., with recording the change in pressure in the engine cylinder over the piston stroke, over the angle of rotation of the crankshaft, or over time.
Indication of slow-speed engines is usually carried out with mechanical spring indicators, which produce indicator diagrams over the piston stroke. The indication of high-speed engines, however, is usually performed with more complex indicators of stroboscopic type (pneumo-electric indicators) or of electrical types (piezoquartz, capacitive, inductive, etc., indicators with an oscillograph). Stroboscopic and electrical indicators produce diagrams over the angle of rotation of the crankshaft or over time, i.e., so-called developed diagrams.
From diagrams taken over the piston stroke, a whole series of parameters and indices of the working process can be determined directly by measuring them, including the mean indicated pressure of the cycle, $p_i$, which is one of the principal characteristics of the working cycle as a whole.
Developed diagrams, representing the dependence of the pressure in the cylinder on the angle of rotation of the crankshaft or on time, are especially convenient for analyzing the combustion process in the cylinder (determining the rate of combustion, etc.). However, calculation from these diagrams of the mean indicated pressure is difficult. To determine the mean indicated pressure, as well as the indices of the compression and expansion polytropes, the developed diagram must be converted into a diagram over the piston stroke.
The known methods of converting developed diagrams [1; 2] into diagrams over the piston stroke are cumbersome and are not free from errors that arise when carrying out the necessary calculations and graphical constructions; therefore, the results obtained cannot claim high accuracy. The processing of such diagrams is associated with a considerable expenditure of time. This usually precludes the possibility of processing them during engine testing, which creates certain inconveniences in conducting tests.
The author of the present article has proposed and designed, and the internal-combustion-engine laboratory of the Tomsk Polytechnic Institute named after S. M. Kirov has manufactured, a special device that has received the provisional name “diagramometer.” This device makes it possible to mechanize and thereby considerably accelerate the process of converting a developed indicator diagram into an ordinary diagram over the piston stroke.
The arrangement of the diagramometer can be seen from the diagram (Fig. 1) and from the...
…of the photographs taken (Figs. 2 and 3). A ruler 1 with a longitudinal slot is fastened to the drawing board by two needles; it serves as a guide in moving the instrument along the vertical axis of the diagram 2 being processed, which is oriented before being fastened to the board relative to the axis of ruler 1. The frame of the instrument rests on three rollers, two of which (3 and 4), with their flanges, enter the slot of ruler 1 and thereby ensure a rectilinear translational motion of the entire instrument along the ordinate axis of the diagram. The third roller 5, provided with knurling and graduations on its rim, is a supporting roller, but it can also be used for measuring the ordinates of the diagram, i.e., for determining the magnitude of the pressures in the cylinder.
On the front side of the instrument there is a guide rail 6 with a carriage 7, provided with a tracing pin 8. A steel cord 9 is attached to carriage 7,
Fig. 1
a steel cord 9, which passes around the rim of disk 10 (to prevent slipping of the cord, the latter passes around the rim of disk 10 in two turns and is fastened at one point on the rim). The diameter of the rim of disk 10 must be equal to the diameter of the indicator drum by which the developed diagram was taken; then the displacement of tracing pin 8 along the abscissa axis by a certain amount \(x\) will cause disk 10 to rotate through an angle equal to the angle of rotation of the crankshaft expressed by the abscissa \(x\) on the developed diagram.
The connecting-rod-and-crank mechanism of the instrument, consisting of crank 11 fastened to disk 10, connecting rod 12, slide 13, and guide slide bar 14, converts the rotary motion of the disk into a reciprocating motion of slide 13, which, provided that the kinematic—
…of kinematic similarity¹) of the crank mechanisms of the instrument and of the indicated engine, will express, on a certain scale, the motion of the engine piston.
Fig. 2
¹) In order to observe this kinematic similarity, it is necessary, by means of the telescopic device of the connecting-rod bar 12, to set such a length \(l\) for it that equality of the ratios of the crank radius to the connecting-rod length is ensured in the diagrammeter and in the indicated engine.
\[ \frac{r}{l}=\mu \text{ of the instrument}=\frac{R}{L}=\mu \text{ of the engine}. \]
holder. Slide 13 has a pencil in a metal holder 15 for tracing the diagram according to the piston stroke and a special socket serving for attachment of the tracer arm of an ordinary polar planimeter 16.
Fig. 3.
To determine the mean indicated pressure from the developed diagram and to reconstruct it according to the piston stroke, it is necessary to fasten the diagram to the board so that its vertical axis with the mark “top dead center” coincides with the axis of symmetry of the device, to fasten a clean sheet of paper in the field of action of pencil 15, and to trace the outline of the diagram
with tracing pin 8. In this case pencil 15 will draw the diagram according to the piston travel, and the difference between the final and initial readings of the planimeter will give, on a certain scale, the mean indicated pressure \(p_i\). As usual, it is advisable to set the length of the tracing lever of the planimeter equal to the length of the diagram being drawn according to the piston travel; then the sought mean indicated pressure is determined by the formula:
\[ p_i=\frac{\Delta \cdot C}{f}\ \text{kg}/\text{cm}^2, \tag{1} \]
where \(\Delta\) is the difference between the final and initial readings of the planimeter,
\(C\) is the planimeter constant,
\(f\) is the pressure scale (the scale of the indicator spring).
To determine the mean exponent of the compression polytrope \(n_1\) on any section of the compression line, it is sufficient to trace with tracing pin 8 the contour bounded by this section and the coordinate axes (Fig. 4), and to compute the desired exponent by the formula:
Fig. 4
\[ n_1=\frac{\Delta_1}{\Delta_2}+\frac{\overline{P}}{C(\varepsilon-1)\Delta_2}, \tag{2} \]
where \(\Delta_1\) is the difference between the final and initial readings of the planimeter when tracing the contour
\[ a-b-1-2-a, \]
\(\Delta_2\) is the difference between the final and initial readings of the planimeter when tracing the contour
\[ a-b-3-4-a, \]
\(\overline{P}\) is the pressure difference at points \(b\) and \(a\), expressed in mm (measured, for example, by means of roller 5),
\(\varepsilon\) is the compression ratio of the engine being indicated,
\(C\) is the planimeter constant.
In an analogous manner, the exponent of the expansion polytrope may also be determined, with the only difference that here one must trace with the pin the contour bounded by the section of the expansion line of interest and by the same coordinate axes.
Formula (2) is derived on the basis of the known method for determining the polytropic exponent
\[ n = \frac{\displaystyle \int_{p_1}^{p_2} -v\,dp} {\displaystyle \int_{v_1}^{v_2} p\,dv} = \frac{\text{area } a—c—d—b—a} {\text{area } a—b—3—4—a} = \frac{Q_1}{Q_2}, \]
where the indicated areas (Fig. 5) are found by planimetry [3].
Fig. 5
The area \(Q_1(a—c—d—b—a)\) can be represented as the sum of areas:
\[ Q_1 = F_1 + F_2, \]
where \(F_1\) is the area \(a—2—1—b—a\),
\[ F_2 \]
is the area \(1—2—c—d—1\).
The areas \(F_1\) and \(F_2\) can be represented in the following form:
\[ F_1 = \Delta_1 \cdot C \cdot R \]
\[ F_2 = \bar{P}\cdot \bar{V}_c = \bar{P}\cdot \frac{\bar{V}_h}{\varepsilon - 1}, \]
where \(R\) is the length of the tracing arm of the planimeter,
\(\bar{V}_h\) is the length of the diagram being traced.
Then
\[ Q_1=\Delta_1 \cdot C \cdot R+\frac{\overline{P}\cdot \overline{V}_h}{\varepsilon-1} \tag{a} \]
The area \(Q_2\) \((a—b—3—4—a,\) Fig. 5), by analogy with the area \(F_1\), can be represented in the following form:
\[ Q_2=\Delta_2 \cdot C \cdot R \tag{b} \]
Dividing expression \((a)\) by \((b)\) and taking into account that the length of the tracing arm of the planimeter \(R\) is set equal to the length of the developed indicator diagram \((R=\overline{V}_h)\), we obtain:
\[ n_1=\frac{\Delta_1}{\Delta_2}+\frac{\overline{P}}{C(\varepsilon-1)\Delta_2}. \]
The diagramometer can also be used to determine the rate of pressure rise on the combustion line, \(\dfrac{\Delta p}{\Delta \alpha}\), which characterizes the rigidity of engine operation. For this it is sufficient to trace, with the instrument’s tracing pin, the section of the combustion line of interest; to note the displacement of the entire instrument along the pressure axis by roller 5 and the displacement of carriage 7 along the abscissa axis by the divisions on guide rail 6. Dividing the magnitude of the instrument displacement by the magnitude of the carriage displacement, we obtain, on a certain scale, the rate of pressure rise \(\dfrac{\Delta p}{\Delta \alpha}\).
Thus, the diagramometer will make it possible, without unnecessary expenditure of time on the laborious reconstruction of a developed diagram into a diagram according to piston travel, to obtain all the data on the working process that are usually found from indicator diagrams. The time required to obtain all the above-listed quantities with the aid of the diagramometer is only a few minutes; therefore, the processing of developed diagrams by means of the described instrument can successfully be carried out during engine tests, which is sometimes necessary for judging the nature of the working process of the engine under test.
As studies of a prototype of the instrument, carried out in the laboratory of the Tomsk Polytechnic Institute, have shown, the error in the results of processing developed diagrams by means of the diagramometer lies within \(\pm 2.5\%\), which fully satisfies the requirements of most laboratory investigations. There is reason to believe that the diagramometer can find wide application in the practice of factory and laboratory tests and, above all, should become an indispensable accessory of pneumoelectric indicators.
LITERATURE
- Engines of Combat Vehicles, part 1, edited by Prof. A. S. Orlin. Mashgiz, 1946.
- G. M. Simanovich. Testing of Diesel Engines. ONTI, 1937.
- Machine Building, encyclopedic handbook, vol. 1, book one. Mashgiz, 1947.