The Influence of the Drive on Distortions of the Indicator Diagram
Abstract Generated abstract
This paper examines distortions in mechanical indicator diagrams of piston machines that arise not from the indicator mechanism itself, but from the drive transmitting piston motion to the indicator drum. Using a compressor test setup with a carefully calibrated Tkachenko stroke reducer, a double writing indicator, and simultaneous reference diagrams recorded by crank angle, the study compares several flexible connections, including cotton cord, braided hemp cord, metal cable, and cord combined with steel wire. The experiments show that cord deformation and reducer misalignment can shift diagram points along the abscissa by several percent of piston stroke, substantially altering diagram area and mean indicated pressure. The paper argues that accurate indication requires checking the reducer kinematics and installation, minimizing cord length and bends, avoiding stretchable twisted cord, and replacing straight cord sections with light steel wire where possible.
Full Text
Effect of the Drive on Distortions of the Indicator Diagram
Yu. N. Sokolov
Recording indicator diagrams by means of a mechanical indicator—with a spring, piston, and writing mechanism—has so far remained the most accessible method and, at moderate numbers of revolutions, also a sufficiently reliable method for investigating the operation of piston machines: internal-combustion engines, compressors, piston steam engines, and the like. In this process, as in other methods of indication, however, a number of distortions are inevitable and are not always taken into account when setting up the investigation.
While sufficient attention has been given in the literature to the question of distortions of the indicator diagram caused by the mechanism of the indicator itself, the role of the drive that provides the motion of the indicator drum has not been adequately studied from this point of view. In investigations carried out by the author, it was observed that in a number of cases one has to deal with distortions of the indicator diagram despite the flawless condition of the mechanism of the indicator itself and with its inertia being sufficiently small for the given case. The mean indicated pressure, determined from the area of the diagram, is then either implausibly small or, conversely, clearly exaggerated. It is obvious that in these cases distortions of the indicator diagram occur not along its ordinates but along its abscissae; and since these distortions during the forward and return strokes of the piston are usually in opposite directions, the area of the diagram changes sharply.
Sources of errors in the indicator drive may be explained both by improper transmission of the piston motion by the reducing mechanism and by deformations of the indicator cord, the quality of which is usually not given due attention.
In modern piston machines with closed crankcases, roller or parallelogram reducing mechanisms are not used; instead, various systems of articulated mechanisms placed inside the crankcase and serving to drive the indicator are, in most cases, sources of substantial distortions both because of their kinematic scheme itself and because of the rapidly appearing clearances in the hinged joints. A characteristic example of such distortions of the indicator diagram and of the mean indicated pressure determined from it may be provided by the results of mass tests carried out by the author as early as 1937 on a Diesel compressor engine at 235 revolutions per minute, when, at each operating condition, diagrams were taken successively with the same indicator by means of an articulated reducing mechanism and the Tkachenko reducing mechanism (see below), which is flawless from the kinematic point of view. The mean values, determined from the whole series of such diagrams, of the magnitude of the mean indicated pressure are given below.
| Test No. | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Approximate share of load, % | 35 | 55 | 80 | 100 | 106 |
| Mean indicated pressure — Kh/um. Tkachenko, \(p_i,\ \mathrm{kg}/\mathrm{cm}^2\) | 3.68 | 4.12 | 5.36 | 6.29 | 6.69 |
| Mean indicated pressure — hinged Kh/um., \(p'_i,\ \mathrm{kg}/\mathrm{cm}^2\) | 4.24 | 4.73 | 6.48 | 7.02 | 7.46 |
| Ratio \(p'_i/p_i\) | 1.15 | 1.15 | 1.21 | 1.11 | 1.12 |
The discrepancies, as we see, are very substantial and fluctuate within the range from 11 to 21%. This shows how great the distortion of the indicator diagram can be due to the reducing mechanism itself.
The reducing mechanism, however, can always be checked in advance in one way or another: its kinematic scheme can easily be investigated in the appropriate manner, and the mechanism put in order. Matters are considerably worse with distortions that are the result of deformations of the indicator cord: they cannot be taken into account in advance and cannot be eliminated with certainty. The question of the influence of the cord on distortions of the indicator diagram is therefore given primary attention in the present work.
Research Method and Apparatus
If the drive of the indicator is connected and, by manually rotating the machine intended for indication, marks are made of the position of the indicator writing pin on its drum every 10–15 degrees of crank rotation, we obtain a diagram similar to that shown in Fig. 1. As a rule, the marks corresponding to symmetrical positions of the connecting-rod-and-crank mechanism during the forward and return strokes of the piston will not coincide and, after returning the machine to its initial (zero degrees of the crank circle) position, we shall not obtain coincidence of the new mark with the initial one; this is evidence of distortions in the indicator drive. If, in this case, the reducing mechanism has been properly adjusted and practically produced no distortions, then such distortions are possible only due to deformations of the indicator cord. In such a check, the inertial forces in the moving parts of the drive mechanism and in the indicator drum are practically not manifested, while the deformations of the cord are caused only by the tensions exerted by its spring inside the indicator drum; for this reason we shall call it “static.”
Fig. 1
A static check can serve only for preliminary studies of distortions in the drive, for which purpose we used it; the actual operating conditions of the indicator drive on a sufficiently high-speed machine will be different because of dynamic phenomena. Therefore, in addition to the static check, the operation of the drive must also be studied during the normal recording of the indicator diagram. For this purpose we used a special indicator with a double writing mecha-
... mechanism (Fig. 2), assembled and made from parts of “Rosenkranz” model II indicators by the mechanic A. Ya. Tkachenko. It made it possible simultaneously to record an indicator diagram on two independent drums and, having been previously checked on an oil press, gave practically identical “spring scales” on each of these drums. One of the drums of this indicator was connected to the normal drive under investigation; the other was replaced by a special one, driven through two pairs of helical gears from the main shaft of the machine, and thereby provided the taking of a diagram developed according to the angle of rotation of the crank (Fig. 3). By friction on the axis of this drum the clearances in its drive were taken up, and the diagram obtained on it could thus serve as a reference diagram, free from distortions due to the drive. For comparison with it, the diagram obtained with the drive under investigation was then graphically developed according to the angle of rotation of the crank, while the diagram taken according to the angle of rotation of the crank was, in turn, rearranged according to the piston travel and superposed on the diagram under investigation (see below Figs. 6, 7, 8, and 9). Comparison of such diagrams made it possible to investigate the distortions produced by the drive, determining their sign and absolute magnitude in individual sections.
Fig. 2
Fig. 3
Without setting ourselves the task of investigating distortions of indicator diagrams for their various forms, as determined by the working process in the machine being indicated, we chose as the basis for carrying out the tests a single-stage compressor “KM-2.” The easily established and, at constant back pressure, practically unchanging working process in this compressor afforded considerable convenience. The moderate number of revolutions of the compressor (270–275 per minute) corresponded to the medium speed range of the indicator used and ensured the absence of noticeable distortions of the indicator diagram along its ordinates.
Since the principal task was to investigate the influence of the cord, measures were taken to eliminate distortions due to the stroke reducer. For this purpose the stroke reducer of the A. Ya. Tkachenko system (author’s certificate No. 31662), already mentioned above, was used; it is a very refined mechanism, kinematically similar to the connecting-rod-and-crank mechanism of the machine being indicated. A separate work by the author is devoted to the study of this device; here we shall confine ourselves only to noting that the Tkachenko stroke reducer (Fig. 4) makes it possible to set it to any ratio of the connecting-rod length to the crank radius (the same as was brought into correspondence with the indicated machine) and to take diagrams with any displacement of them in the angle of rotation of the crank circle, without disconnecting the drive.
Before the experiments were carried out, the stroke reducer was adjusted very carefully, special attention being paid to the coincidence of the angle of wedging of its crank with the mechanism of the indicated machine. A special check established that the deviations from proportionality of the motion of the stroke-reducer slide to the actual stroke of the machine piston do not exceed 0.2% of the latter; i.e., the distortions created by the stroke reducer itself are practically imperceptible.
In all cases the cord under investigation had an operating length of about 115 cm and two bends over rollers 28 mm in diameter at an angle of about 90°—in the stroke reducer itself and at the exit from it. The bend of the cord in its approach to the indicator drum was reduced to a minimum. In special cases (see below), the cord on individual portions of its length was replaced by steel wire or by a special very flexible small cable.
The general view of the experimental setup is shown in Fig. 5, where a is the Tkachenko stroke reducer, b the double writing mechanism of the indicator, c its drum driven by the stroke reducer and cord, d the drum rotated according to the crank angle, e the shaft of its drive, and f an eccentric stroke reducer not used in the experiments described.
The procedure for carrying out each experiment was as follows. After the drives had been installed and connected from the stroke reducer and according to the crank angle, the entire system (compressor—drive—indicator) was turned for several minutes and then stopped again. Having thus eliminated random clearances and deformations in the drives, marks corresponding to the dead points of the machine were made on the paper placed on drum d by the writing pin of the indicator. Upon the subsequent starting of the compressor (without any disconnections or changes in the drives) and after the desired operating regime had been reached, atmospheric lines were drawn and diagrams were taken quickly and simultaneously on both indicator drums. In doing this, we tried, as far as possible, to record on the diagrams only one working cycle. After this the machine was stopped, and the correspondence of the marks made on the drum to the dead points of the compressor mechanism was checked again. The subsequent processing of the diagrams obtained was carried out as indicated above; moreover, specially prepared tables were used to transfer the diagrams by angle of rotation into normal coordinates (by piston stroke) and back. To determine the changes in the mean indicated pressure, the diagram distorted by the drive and transferred from the diagram recorded by angle of crank rotation was planimetered.
Fig. 4
Fig. 5
Results of the Experiments
Of the total number of experiments carried out with various types of connection between the indicator and the travel reducer, and under various operating conditions of the compressor that served as the experimental base, we shall dwell only on the results of the most characteristic ones. These include the investigation of the indicator drive with the following types of flexible connections: a twisted cotton cord, commonly used recently in taking indicator diagrams, with a single loop connection and a normal indicator hook; a special (“indicator”) braided hemp cord, stretched and preloaded under load, with the same type of connection; a very flexible cable made of 104 strands of white metal, each \(0.07\ \text{mm}\) in diameter, continuous along its entire length from the travel-reducer slide to the indicator drum; a special indicator cord with a copper strand and hemp braiding, replaced by a thin steel wire on the rectilinear sections of the connection. The total length of the connections, as already indicated, was in all cases about \(115\ \text{cm}\).
Even the static test (see above) of the motion of the indicator drum showed the presence of considerable distortions. Its results, with a cord tension produced by the spring of the indicator drum of \(2\text{–}3\ \text{kg}\), are presented in Table 1, where, for each type of connection investigated, the travel of the indicator drum \(x\) (as a percentage of the full length of the diagram) corresponding to the given angle of rotation of the crank is given, and the error \(\Delta\), obtained by comparing it with the actual travel of the piston of the machine being indicated, is calculated. This error is considered positive if the travel of the indicator drum (from the top dead center) is greater than the actual travel of the piston, and negative in the opposite case. Its magnitude reaches \(3.4 \div 3.6\) percent of the full piston stroke when a twisted cotton cord is used, \(1.7\text{–}2.0\) percent with a braided hemp cord, \(0.9\text{–}1.0\) percent with a cord having a copper strand and wire, and a minimum (\(0.4\text{–}0.5\) percent) when the cable is used. In the first half of the forward stroke of the piston the error, as a rule, is negative, which corresponds to a lag in the motion of the drum when the cord is being released by the travel reducer. During the return stroke of the piston the error changes sign, which again is readily explained by the tensioning of the cord in this case and by the lag in the motion of the drum during its return. Some uncertainty in the sign and magnitude of the error in the second half of the forward stroke is evidently explained by accidental circumstances, and, when the cable is used, by its elasticity, which manifests itself at bends.
The results of simultaneous recording of diagrams according to piston travel and according to the angle of rotation of the crank circle are presented in Figs. 6, 7, 8, and 9. The diagram obtained directly with the given drive according to piston travel is in all cases drawn with a solid line, and the one transferred into these coordinates from that recorded according to the angle of rotation is shown by a dashed line. The solid lines of the lower diagrams, developed according to the angle of rotation of the crank, likewise correspond to those recorded directly, and the dashed lines to the transferred ones.
The nature of the distortions of the diagram caused by deformations of the cord is the same in all cases: the lag in the motion of the drum during the forward stroke of the piston, corresponding to release of the cord, entails a steeper fall of the expansion line than it should have in reality; and during the return stroke, corresponding to tensioning of the cord, the compression line shifts to the left. As a result, the area of the diagram becomes greater than the true one owing to distortions both during the forward and during the return stroke of the piston, and this causes a very considerable error in determining the mean indicated pressure. The nature of the distortions chan—
Table 1
Static verification of the motion of the indicator drum
| $\alpha$, degrees of crank circumference | $X_T$, actual piston stroke % | Cotton twisted cord, forward stroke $x\%$ | Cotton twisted cord, forward stroke $\Delta\%$ | Cotton twisted cord, return stroke $x\%$ | Cotton twisted cord, return stroke $\Delta\%$ | Hemp braided cord, forward stroke $x\%$ | Hemp braided cord, forward stroke $\Delta\%$ | Hemp braided cord, return stroke $x\%$ | Hemp braided cord, return stroke $\Delta\%$ | Cord with copper spacer—wire—cord with copper spacer, forward stroke $x\%$ | Cord with copper spacer—wire—cord with copper spacer, forward stroke $\Delta\%$ | Cord with copper spacer—wire—cord with copper spacer, return stroke $x\%$ | Cord with copper spacer—wire—cord with copper spacer, return stroke $\Delta\%$ | Cable, forward stroke $x\%$ | Cable, forward stroke $\Delta\%$ | Cable, return stroke $x\%$ | Cable, return stroke $\Delta\%$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.0 | 0.0 | — | 3.6 | +3.6 | 0.0 | — | 0.5 | +0.5 | 0.0 | — | 0.0 | — | 0.0 | — | 0.2 | +0.2 |
| 10 | 0.9 | — | — | 4.3 | +3.4 | — | — | 1.3 | +0.4 | — | — | 0.9 | 0.0 | 0.6 | −0.3 | 1.0 | +0.1 |
| 20 | 3.7 | 0.6 | −3.1 | 6.6 | +2.9 | 1.7 | −2.0 | 3.2 | −0.5 | 2.7 | −1.0 | 3.8 | +0.1 | 3.5 | −0.2 | 3.8 | +0.1 |
| 30 | 8.1 | 4.7 | −3.4 | 10.2 | +2.1 | 6.4 | −1.7 | 8.5 | +0.4 | 7.2 | −0.9 | 8.2 | +0.1 | 8.1 | 0.0 | 8.3 | +0.2 |
| 40 | 14.1 | 10.8 | −3.3 | 16.7 | +2.6 | 12.6 | −1.5 | 14.9 | +0.8 | 13.2 | −0.9 | 14.4 | +0.3 | 14.5 | +0.4 | 14.2 | +0.1 |
| 50 | 21.2 | 19.2 | −2.0 | 23.7 | +2.5 | 19.7 | −1.5 | 21.7 | +0.5 | 20.5 | −0.7 | 21.7 | +0.5 | 21.1 | −0.1 | 21.6 | +0.4 |
| 60 | 29.3 | 27.1 | −2.2 | 32.1 | +2.8 | 28.3 | −1.0 | 29.8 | +0.5 | 28.9 | −0.4 | 29.8 | +0.5 | 29.3 | 0.0 | 29.8 | +0.5 |
| 70 | 38.0 | 37.1 | −0.9 | 41.2 | +3.2 | 37.2 | −0.8 | 39.1 | +1.1 | 37.6 | −0.4 | 38.5 | +0.5 | 37.8 | −0.2 | 38.2 | +0.2 |
| 80 | 46.9 | 46.4 | −0.5 | 50.1 | +3.2 | 46.7 | −0.2 | 47.7 | +0.8 | 46.8 | −0.1 | 47.7 | +0.8 | 46.8 | −0.1 | 47.4 | +0.5 |
| 90 | 55.7 | 55.6 | −0.1 | 58.7 | +3.0 | 55.8 | +0.1 | 57.1 | +1.4 | 55.8 | +0.1 | 56.3 | +0.6 | 55.9 | +0.2 | 56.1 | +0.4 |
| 100 | 64.3 | 64.3 | −0.0 | 66.7 | +2.4 | 64.5 | +0.2 | 65.5 | +1.2 | 64.3 | 0.0 | 65.0 | +0.7 | 64.2 | −0.1 | 64.6 | +0.3 |
| 110 | 72.2 | 72.9 | +0.7 | 75.3 | +3.1 | 71.9 | −0.3 | 73.7 | +1.5 | 72.2 | 0.0 | 73.0 | +0.8 | 72.1 | −0.1 | 72.7 | +0.5 |
| 120 | 79.3 | 80.2 | +0.9 | 82.3 | +3.0 | 79.5 | +0.2 | 81.0 | +1.7 | 79.5 | +0.2 | 80.2 | +0.9 | 79.6 | +0.3 | 79.8 | +0.5 |
| 130 | 85.5 | 86.4 | +0.9 | 88.3 | +2.8 | 85.7 | +0.2 | 86.8 | +1.3 | 85.6 | +0.1 | 86.3 | +0.8 | 85.6 | +0.1 | 86.0 | +0.5 |
| 140 | 90.7 | 91.1 | +0.4 | 93.7 | +3.0 | 90.6 | −0.1 | 92.1 | +1.4 | 90.7 | 0.0 | 91.3 | +0.6 | 90.8 | +0.1 | 91.2 | +0.5 |
| 150 | 94.7 | 95.4 | +0.7 | 97.7 | +3.0 | 94.8 | +0.1 | 94.9 | +0.2 | 94.8 | +0.1 | 95.6 | +0.9 | 94.8 | +0.1 | 95.1 | +0.4 |
| 160 | 97.7 | 97.9 | +0.2 | — | — | 98.0 | +0.3 | 99.0 | +1.3 | 97.6 | −0.1 | 98.4 | +0.7 | 97.7 | 0.0 | 97.9 | +0.2 |
| 170 | 99.4 | 99.4 | 0.0 | 98.2(?) | −1.2(?) | 99.4 | 0.0 | — | — | 99.5 | +0.1 | 99.8 | +0.4 | 99.5 | +0.1 | 99.7 | +0.3 |
| 180 | 100.0 | 100.0 | — | 100.0 | — | 100.0 | — | 100.0 | — | 100.0 | — | 100.0 | — | 100.1 | — | 100.1 | — |
the line at \(-90^\circ\) of the diagram (such a displacement is often practiced in investigating the combustion process in internal-combustion engines) is presented in Fig. 8—c. Here, both during compression and during expansion, there is
Cotton-paper twisted cord.
Hemp braided cord.
Fig. 6 Fig. 7
slack in the cord, as a result of which the corresponding curves were displaced all the time from their normal (dotted) position to the right.
Cord with copper wire — cord with copper wire
Fig. 8
a) Normal ignition.
c) Displacement by \(-90^\circ\).
slack of the cord
cord tension
b)
d)
The magnitude of the distortion of the diagram depends entirely on the type of connection used between the stroke reducer and the indicator drum. When a twisted cotton cord is used, these distortions are so considerable that the shape of the diagram is completely altered, and the error in determining the mean indicated pressure (the area of the diagram) reaches 25%. A braided hemp cord gives somewhat smaller distortions, but even in this case they are still very noticeable, and the error in determining the mean indicated pressure reaches 10%. Somewhat better results are obtained by using a cord with a copper insert in connection with a wire on the straight-line section of the drive. The error in the area of the diagram here is about 8%.
Fig. 9
Fig. 10
It was not possible to use a continuous cable (from the slide of the stroke reducer to the indicator drum) for taking diagrams, since, in the presence of two bends in different planes in the Tkachenko stroke reducer itself, the cable very quickly unwound and broke. Attempts to use a continuous thin (0.2–0.3 mm) wire or a violin string were not successful for the same reasons. In order nevertheless to obtain a diagram with the least distortions, it was necessary to use a cord with a copper core (within the limits of the stroke reducer itself) in connection with a cable on the straight-line section of the drive and on the indicator drum. In this case (Fig. 9) the distortions of the diagram are indeed barely noticeable. The cable, however, even in this case fairly quickly went out of service, and it is not advisable to recommend its use when taking indicator diagrams under ordinary conditions.
In order to establish the absolute magnitude of the possible distortions along the abscissas of the indicator diagram, the displacements of the expansion and compression curves at various angles of rotation of the crank, in the characteristic diagrams given, ...
Table 2
Displacements along the abscissas of indicator diagrams
| \(a\), degrees of crank circle | \(X_T\), actual piston stroke, % | Cotton twisted cord, forward stroke, mm | Cotton twisted cord, forward stroke, % | Cotton twisted cord, return stroke, mm | Cotton twisted cord, return stroke, % | Hemp braided cord, forward stroke, mm | Hemp braided cord, forward stroke, % | Hemp braided cord, return stroke, mm | Hemp braided cord, return stroke, % | Cord with copper gasket—wire rope—cord with copper gasket, forward stroke, mm | Cord with copper gasket—wire rope—cord with copper gasket, forward stroke, % | Cord with copper gasket—wire rope—cord with copper gasket, return stroke, mm | Cord with copper gasket—wire rope—cord with copper gasket, return stroke, % | Cord with copper gasket—cable, forward stroke, mm | Cord with copper gasket—cable, forward stroke, % | Cord with copper gasket—cable, return stroke, mm | Cord with copper gasket—cable, return stroke, % |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 10 | 0.9 | −0.6 | −0.9 | +0.5 | +0.7 | −0.3 | −0.4 | +0.5 | +0.7 | −0.4 | −0.6 | +0.7 | +1.0 | −0.2 | −0.3 | +0.3 | +0.4 |
| 20 | 3.7 | −1.8 | −2.6 | +0.6 | +0.9 | −0.8 | −1.1 | +0.4 | +0.6 | −0.7 | −1.0 | +0.7 | +1.0 | −0.3 | −0.4 | +0.4 | +0.5 |
| 30 | 8.1 | −3.2 | −4.6 | +1.6 | +2.3 | −1.7 | −2.4 | 0.0 | 0.0 | −0.7 | −1.0 | +0.8 | +1.1 | −0.2 | −0.3 | +0.3 | +0.4 |
| 40 | 14.1 | −4.3 | −6.2 | +1.7 | +2.5 | −1.9 | −2.7 | −0.3 | −0.4 | −0.6 | −0.8 | +1.0 | +1.4 | — | — | 0.0 | 0.0 |
| 50 | 21.2 | −5.7 | −8.2 | +2.3 | +3.3 | −1.2 | −1.7 | 0.0 | 0.0 | — | — | +1.4 | +2.0 | — | — | +0.7 | +0.9 |
| 60 | 29.3 | −5.7 | −8.2 | +2.4 | +3.4 | — | — | +1.2 | +1.7 | — | — | +1.4 | +2.0 | — | — | +0.9 | +1.2 |
| 70 | 38.0 | — | — | +2.4 | +3.4 | — | — | +1.3 | +1.9 | — | — | +1.4 | +2.0 | — | — | +1.1 | +1.5 |
| 80 | 46.9 | — | — | +2.7 | +3.9 | — | — | +1.3 | +1.9 | — | — | +2.1 | +2.9 | — | — | +1.3 | +1.8 |
| 90 | 55.7 | — | — | +2.8 | +4.0 | — | — | +1.3 | +1.9 | — | — | +2.2 | +3.1 | — | — | — | — |
| 100 | 64.3 | — | — | +3.1 | +4.5 | — | — | +2.4 | +3.4 | — | — | +2.4 | +3.4 | — | — | — | — |
| 110 | 72.2 | — | — | — | — | — | — | +2.8 | +4.0 | — | — | +2.4 | +3.4 | — | — | — | — |
| 120 | 79.3 | — | — | — | — | — | — | +4.0 | +5.7 | — | — | +2.4 | +3.4 | — | — | — | — |
| 130 | 85.5 | — | — | — | — | — | — | — | — | — | — | +2.6 | +3.6 | — | — | — | — |
were measured on the diagrams. The results of these measurements are presented in Table 2; however, since they could be made only on portions of the diagrams corresponding to a sharp change in pressure, the data could not be given for all positions of the crank. The magnitude of the linear displacements along the piston stroke, in its first half, as a rule increases with distance from the top dead center and decreases on returning to it. This is evidently explained by the corresponding changes in the speed of displacement of the drive. The displacements are negative (that is, in the direction opposite to the forward stroke of the piston) when the cord is being released (forward stroke), and positive when it is being tensioned (return stroke), while their greatest absolute values reach 4.5–8.2% of the piston stroke (up to 15° of crank angle) when a cotton twisted cord is used; 2.7–5.7% with a braided hemp cord; 1.0–3.6% with a cord with a copper lining and wire; and only with a cord with a copper lining and a cable do they amount to 0.4–1.8%.
The material presented characterizes distortions of indicator diagrams caused by deformations in the flexible connection of the motion reducer with the indicator drum. The motion reducer itself here, being correctly installed and calibrated, was not a source of noticeable errors. We have pointed out, however, that incorrect installation of the motion reducer may also be the cause of very substantial distortions of the indicator diagram. In order to confirm this circumstance, we give the results of one of the experiments involving a change in the wedging angle of the motion reducer relative to the crank of the machine being indicated. The three diagrams shown in Fig. 10 were taken under one and the same operating condition of the compressor and with identical flexible connections (cord with copper lining—wire—cord with copper lining). The upper of them, a, was taken with the motion reducer displaced by 1 degree of the crank circle in the direction of rotation of the machine; the middle one, b, with normal wedging; and the lower one, c, with a displacement of 1 degree against the direction of rotation. The dashed curves in all cases correspond to the correct form of the diagram, obtained by transferring the simultaneously taken diagram according to the crank angle. The distortions are caused mainly by deformations in the flexible connection; however, in case a they are further increased by the displacement in the installation of the motion reducer, while in case c they are compensated to a considerable extent by this displacement. Comparison of these diagrams shows that even such a slight change in the wedging angle of the motion reducer sharply changes the form and area of the diagram.
Conclusion
The investigations presented cannot lay claim to absolute significance; nor can they serve as a basis for establishing general corrections to distortions of indicator diagrams due to the influence of the drive. Such corrections generally cannot be established in the general case, since in each instance they are determined by the specific features of the motion reducer and by the form, length, and quality of the flexible connections. If, however, one speaks of the area of the indicator diagram, then even for given linear distortions the error in its value will depend on the very form of the diagram, that is, on the characteristics of the particular machine being indicated in the given specific case.
The experiments presented and described above, however, quite clearly show how large the distortions of the indicator diagram due to the drive may be, and they give grounds for indicating the principal ways of reducing them. From this point of view it is necessary to note the following.
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Obtaining a correct indicator diagram is determined not only by the sound condition and sufficient speed of response of the indicator itself, but also depends to a considerable extent on its drive. Distortions of the diagram due to the drive may reach a very substantial magnitude; moreover, they have an especially strong effect on the area of the diagram and, consequently, on the value of the mean indicated pressure.
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To obtain a correct indicator diagram it is necessary to have a fully serviceable stroke-reducing mechanism that kinematically transmits correctly the motion of the piston of the machine being indicated to the indicator drum. This circumstance must be specially checked every time; attention must be paid not only to the fundamental correctness of the kinematic scheme of the stroke reducer, but also to the serviceable condition of its mechanism (clearances in hinged joints, etc.) and to its proper installation (angle of jamming).
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The presence of a flexible connection (cord) between the stroke reducer and the indicator drum may serve as a source of entirely inadmissible distortions of the indicator diagram; moreover, the displacements of its individual points along the abscissae, even with a relatively short but poor-quality cord, can easily amount to several percent of the total length of the diagram. Changes in the area of the diagram due to the displacement of the compression and expansion lines in opposite directions are then measured in tens of percent. In order to reduce distortions of the indicator diagram resulting from this circumstance, one should, where possible, use a short indicator cord with the smallest number of the smoothest possible bends. The use of a twisted cord that stretches easily is entirely inadmissible. The best result is given by a hemp braided cord with an internal copper strand; however, even it may cause noticeable distortions. For this reason, on the straight-line sections of the drive the cord should be replaced by a thin (and light) steel wire, leaving the flexible connection only in those places where it is absolutely necessary (at the pulleys, at the indicator drum, etc.).
Taking into account the possibility of distortions of the indicator diagram owing to imperfection of the drive, and adopting the measures indicated above to reduce these distortions, are absolutely necessary in any investigation of the operation of a piston machine by means of a mechanical indicator.