Methodology for Conducting Experiments in the Study of Impact Units of Pneumatic Drilling Hammers and Processing Experimental Data
Abstract Generated abstract
This paper describes an experimental methodology for studying the working process of pneumatic drilling hammers, with emphasis on piston kinematics and related energy quantities during drilling and idle operation. It presents a recording device for obtaining piston-stroke diagrams and recoil diagrams, procedures for conducting tests under controlled air and feed pressures, and methods for processing the diagrams to determine blow frequency, drilling time and rate, piston stroke timing, velocity, impact energy, hammer power, and specific work of rock destruction. The authors also analyze measurement errors for the principal calculated quantities, showing improved accuracy for some diagram-based measurements compared with stopwatch or vibrotachometer methods. The methodology is presented as a basis for identifying operating dependences relevant to the design and improvement of drilling hammers.
Full Text
Methodology for Conducting Experiments in the Study of Impact Units of Pneumatic Drilling Hammers and Processing Experimental Data
O. D. Alimov, I. G. Basov, V. F. Gorbunov, Ya. A. Serov
(Presented by Prof., Doctor of Technical Sciences P. M. Alabuzhev)
On the basis of a number of studies of drilling hammers [1, 2, 3, 5], it has been established that, for the design and calculation of the latter, it is necessary to study the working process of pneumatic drilling hammers during the drilling of rock under various operating conditions. For completeness of data on the working process, it is necessary to know the kinematic and dynamic characteristics of drilling hammers, the principal ones of which we considered to be the following: impact energy, number of impacts, duration of the working and idle stroke of the piston and their ratio, piston velocity, hammer power, specific work of destruction, and torque on the drill.
The present work gives a description of part of the study of drilling hammers, namely: a study of hammer kinematics with a partial calculation of certain energy quantities.
Instrument for Recording the Stroke of the Piston of a Drilling Hammer
To record the stroke of the piston of a drilling hammer, an instrument was designed, manufactured, and mastered in the course of the investigation. The instrument serves to record the diagram of the piston stroke of a drilling hammer on a moving paper tape, both during drilling and during idle operation of the hammer. The principle of operation of the instrument is as follows. One end of a steel rod 2, inserted into the hammer, is fastened in piston 1 of the drilling hammer (Fig. 1). At the other end of rod 2 a pencil 3 is fixed, which, together with piston 1 and rod 2, performs reciprocating motion and draws the curve of the piston stroke on the paper tape being pulled through. The tape-pulling mechanism is placed between two cheeks 4, rigidly fastened by three bolts 5, and consists of an idle drum with a roll of paper tape 6, two rollers 7, 8 for pulling the tape, and a supporting drum 9. To prevent rapid spontaneous unwinding of the tape from the idle drum 6, the latter is braked by a piece of felt 10 attached to screw 11. From the idle drum the paper tape is unwound and passes around supporting drum 9.
To increase the angle of wrap and improve the pressing of the paper tape against the supporting drum, the latter is deflected by frame 12, made of steel wire and fastened in the cheeks. After passing around supporting drum 9, the tape moves between rubber-covered rollers 7, 8, one of which is the drive roller and the other the pressure roller. Drive roller 7 receives rotation from electric motor 13 through belt drive 14 or a flexible shaft (the latter version is not shown in the drawing). Pressure roller 8, with the aid of steel springs 15, presses the paper tape against drive roller 7, thereby preventing slippage of the tape on the drive roller. The ca-
pencil 3, which records the piston-stroke curve, is pressed against the supporting drum 9 by rubber band 16.
During operation of the drilling hammer, piston 1 and rod 2 rotate. To eliminate the possibility of rotation of the pencil, bushing 17, together with pencil 3 fastened to it, rotates freely on rod 2. Tailpiece 18 of bushing 17 moves in two guides 19 and thereby prevents bushing 17 from turning together with rod 2. Guides 19 are fastened to the U-shaped frame 20.
Pencil 21 draws the zero line on the paper tape and is pressed against supporting drum 9 by spring 22 (or by a rubber band); it is arranged so that the zero line determines the extreme possible forward position of pencil 3, which records the piston-stroke diagram, corresponding to the foremost extreme position of the piston in the cylinder.
The tape-pulling mechanism, by means of two brackets 23, is fastened to the U-shaped frame 20, made of angle steel. The U-shaped frame has two lugs at its ends, into which the tie bolts of the drilling hammer enter. The frame is fastened to the drilling hammer by the tie bolts. The instrument can rotate on brackets 23 about the axis 0—0. Rotation of the instrument about the axis 0—0 is provided to make it easy to replace pencil 3 and to adjust the tension of rubber band 16 when the length of pencil 3 changes.
To bring the instrument into its working position, the latter is turned to the right, supporting drum 9 is lowered, and pencil 3 is pressed against the supporting drum. Support 24 serves to secure the instrument in the working position. It is fastened to the U-shaped frame and has slots for securing the instrument at various distances from rod 2. A pencil, fastened by a holder to the guides of the drilling stand, records on the moving tape a diagram of the oscillation of the hammer body relative to the rock.
The drilling hammer is fastened on a stand for investigating the effect of feed force on drilling speed with pneumatic drilling hammers [7]. The force of the pneumatic feeder is transmitted to the hammer through the U-shaped frame 20.
For recording, it is preferable to use thick paper (photosensitive or graph paper) and hard pencils 2T—3T with strong wood.
Conducting the experiment begins with setting the required pressure in the feeder and the pressure supplied to the hammer; pencil 21 for recording the zero line is set opposite the extreme forward position of pencil 3 for recording the piston stroke. Three people take part in carrying out the experiment; their functions are as follows: the first switches on the hammer and the stopwatch, switches them off at the end of the experiment, and monitors the air pressure. The second switches on the motor of the piston-stroke recording instrument and monitors the recording of the recoil diagram; at the end of the experiment he records the final mark of the hammer position on the recoil diagram and switches off the motor of the piston-stroke recording instrument. The third measures the number of revolutions of the drill (with instrument [7] or with a cord) and monitors the condition of the shank and the drilling tool. The motor of the drum for recording the recoil diagram is switched on before the start of the experiment and switched off after the final mark has been recorded.
After the hammer and the stopwatch are switched off, the observation log is filled in with the experiment number, drilling time, working-line pressure and pressure in the feeder, and the number of revolutions of the drill during the experiment. On the piston-stroke diagram and the recoil diagram, the number is put down and, if necessary, notes are made on the stability of the hammer operation, the condition of the rock, etc. This completes the conduct of the experiment. The next experiment may be carried out immediately after the one described; beforehand it is only necessary to inspect the stand and the recording instrument, blow out the shank, and inspect its
Fig. 1. OM-506 drilling hammer with an instrument for recording its motions.
Inscriptions visible in the drawing: “View in the direction of arrow A”; dimensions: 930, 735.
condition; if necessary, new recording paper and pencils are installed.
Method for Processing Diagrams
Processing the Recoil Diagram
The recoil diagram serves to obtain the following data: the number of blows, drilling time, drilling rate, time of the piston-stroke cycle, displacement of the hammer from the line of penetration into the rock, and amplitude of oscillations of the hammer body.
- The number of blows of the hammer is determined by counting the number of oscillation cycles of the body per one revolution of the drum. The time of one revolution of the recoil drum is constant and equal to 1.75 sec. Consequently, the number of blows of the hammer is calculated by the formula:
\[ n=\frac{60}{1.75}\cdot n_1=34.3 n_1 \ \text{blows/min}, \]
where \(n_1\) is the number of cycles per one revolution of the drum. The relative error of the calculation in this case may be determined [4,6] by the formula:
\[ \frac{\Delta n}{n}=\frac{\Delta n_1}{n_1}+\frac{\Delta t_{ob}}{t_{ob}}, \]
where \(\Delta n_1\) is the absolute error in determining the number of hammer blows per 1 revolution of the drum. We take \(\Delta n_1=0.5\),
\(n_1\) is the number of hammer blows per 1 revolution of the drum. Taking the average number of hammer blows as 1700 blows/min, then
\[ n_1=\frac{1700\cdot 1.75}{60}=50, \]
\(\Delta t_{ob}\) is the absolute error in determining the time of 1 revolution of the drum; it is determined by the stopwatch error \(=0.2\) sec when determining the time of 10 drum revolutions. Thus, \(\Delta t_{ob}=0.02\) sec
\[ \frac{\Delta n}{n}=\frac{0.5}{50}+\frac{0.02}{1.75}=0.02 \ \text{or} \ 2\%. \]
Consequently, the accuracy of determining the number of hammer blows by means of the recoil diagram exceeds the accuracy of the vibrotachometer readings, which is 5%.
- The drilling time (test time) is determined by counting
\[ t_{op}=t_{ob}\cdot n_b, \]
where \(t_{ob}=1.75\) sec is the time of 1 revolution of the drum for recording the recoil diagram,
\(n_b\) is the number of drum revolutions during the test.
The relative error of the calculation is
\[ \frac{\Delta t_{op}}{t_{op}}=\frac{\Delta t_{ob}}{t_{ob}}+\frac{\Delta n_b}{n_b}, \]
where \(\Delta t_{ob}=0.02\) sec is the absolute error in determining the time of one drum revolution,
\(\Delta n_b\) is the absolute error in measuring the number of drum revolutions. The circumference of the drum is 540 mm. We take the accuracy of marking the beginning and end of the recording to be 5 mm; then \(\Delta n_b\) will be equal to 10 mm.
The magnitude of the relative error in calculating the drilling time, \(\Delta t_{\text{op}}/t_{\text{op}}\), will depend on the duration of the experiment.
As is seen from the graph (Fig. 2), the relative error in determining the duration of the experiment from the recoil diagram does not exceed 5% even when the experiment lasts 1 sec., whereas the relative error in determining the duration of the experiment with a stopwatch decreases to 5% only when the experiment lasts 4–5 sec.
Fig. 2. Dependence of the relative error in determining drilling time on the measurement method and the duration of the experiment.
1—determination of the duration of the experiment from the recoil diagram; 2—determination of the duration of the experiment with a stopwatch.
It also follows from the graph that the method of determining the duration of the experiment from the recoil diagram is considerably more accurate than determining the drilling time with a stopwatch.
3. The drilling rate is determined by the formula:
\[ v=\frac{60\cdot l}{t_{\text{op}}}\ \text{mm/min}, \]
where \(l\) is the distance from the initial to the final mark of the hammer position, measured on the recoil diagram with a ruler, mm.
The accuracy of calculating the drilling rate was determined by us in [7] and falls within the permissible \(\pm 5\%\) for a definite duration of the experiment.
4. The cycle time (duration of one cycle) of the piston stroke is determined by the formula:
\[ t_A=\frac{60}{n}\cdot 1000\ \text{milliseconds}. \]
The relative error of the calculation is equal to the error in determining the number of blows, i.e., 2%.
5. The deviation of the hammer from the line of penetration into the rock is measured with a ruler from the recoil diagram [7].
6. A comparison is made of the character of the hammer oscillations with the character of the piston motion.
Processing the piston-stroke diagram
The piston-stroke diagram makes it possible to determine many quantities characterizing the working process: the piston stroke, the duration of the working and return strokes of the piston, their ratio, the velocity of piston motion, the impact energy, and the hammer power. Let us examine the procedure for processing a piston-stroke diagram using, as an example, an analysis of the diagram for the OM-506 hammer. To analyze the piston-stroke diagram, a model of the drilling hammer is made (Fig. 3), consisting of a drawing of the hammer in longitudinal section, made full size. The drawing has two slots: one along the line of the front wall of the valve box (the boundary between the distributing-valve device and the cylinder cavity), line \(O'\), and the second along the line of the upper boundary of the hexagonal opening in the lower part of the rotation sleeve (line \(O''\)). The length of the upper slot corresponds to the diameter of the hammer piston, and the length of the lower slot to the diameter of the piston rod.
The piston model consists of one projection of the piston (full size), with grooves and channels on the piston body marked on it. The width of the piston model corresponds to the diameter of the piston and of the rod, while its length is made greater, for convenience in moving it in the slots of the hammer model. The dimensions of the piston along its length are marked on the model by the corresponding lines. The model of the hammer and piston is made of ordinary drawing paper or, to increase strength, of celluloid.
Fig. 3. Model of a drilling hammer for investigating the working process.
The model is fastened to a drawing board with drawing pins; the piston-stroke diagram is also fastened to it with pins, oriented with its zero line (indicating the extreme forward position of the piston) to the forward extreme position of the piston model on the hammer model. Thus, the piston-stroke diagram is “tied” to the model; by moving the piston over the model, we can mark each of its positions on the diagram and, for each characteristic point of the diagram, establish the position of the piston in the cylinder at that moment.
On the model of the impact unit, the following characteristic piston positions are indicated by lines: line \(O'\) is the extreme forward position, which corresponds to the case when the piston, with its front edge, fits tightly against the intermediate bushing. This position is recorded on the diagram as the zero line. Line I corresponds to the moment when the piston rod comes into contact with the drill shank in the case where the drill shank of length \(l_b = 107\) mm is fully inserted into the internal cavity of the hammer. At this moment the front edge of the piston completely closes channel “B,” which supplies air
into the front cavity of the hammer. The rear edge completely opens exhaust channel “A”; on the piston-stroke diagram this point is designated by the numeral 1.
Line II—the front edge of the piston is located at the rear edge of channel “B.” Half of exhaust port “A” is covered by the piston. On the diagram of the piston return stroke this corresponds to point 2; on the working stroke—to point 2′.
Line III—the rear edge of the piston is located at the rear edge of exhaust port “A.” During the working stroke (forward stroke) this corresponds to the beginning of exhaust from the rear chamber of compressed air (point 3′); during the return stroke—to the beginning of partial compression of air in the rear part of the hammer cylinder (point 3; part of the air is thereby displaced from the rear cavity through channel “B”).
Line IV—the front edge of the piston coincides with the front edge of the exhaust port. During the working stroke of the piston this corresponds to the beginning of compression of air in the front cavity of the hammer (point 4′). During the return stroke—to the beginning of air exhaust from the front cavity of the hammer and the beginning of closure of channel “B” (point 4).
Line V—the rear edge of the piston is located at the rear edge of channel “B,” which is covered by the piston. During the return stroke this corresponds to complete cut-off of air in the rear cavity of the hammer and the beginning of its compression (point 5). During the working stroke—to the beginning of opening of channel “B” and communication of the rear cavity of the hammer cylinder with the atmosphere (point 5′). The front cavity of the cylinder communicates with the atmosphere through channel “A,” opened by the piston by 0.5 of its width.
Line VI—the front edge of the piston coincides with the rear edge of port “A”; exhaust port “A” is open over its entire width. Line \(O'\)—the theoretically possible extreme rear position of the piston, when the rear edge of the piston comes into contact with the front wall of the cover of the valve chest. The extreme front position of the piston is designated on the diagram by the letter “H,” and the extreme rear position by the letter “B.” In the diagram presented, point “H” coincides with point “1.”
Processing of the piston-stroke diagrams is carried out in the following order:
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The diagram is placed on the layout so that it is possible to measure the parameters of 10 cycles corresponding to steady operation of the hammer under the given regime. For more accurate determination of the quantities characterizing the given operating regime of the hammer, two portions of the diagram are usually studied—one in the middle of the diagram, the other close to the end of the recording. At each portion, ten cycles are analyzed.
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Horizontal lines corresponding to the characteristic positions of the piston in the cylinder are drawn on the diagram.
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On the selected portion of the diagram, vertical lines perpendicular to the zero line are drawn from each peak of the curve, point “B.” These lines are the boundaries of the cycles and make it possible to determine the piston stroke, the time of the complete cycle, and the time of the working and return strokes.
Since the magnitude of the path traversed by the piston during the forward and return strokes is not constant (this is especially pronounced at small feed forces), we conventionally take as the piston stroke for a given cycle the path of the piston during the working stroke—\(t_p\).
The magnitude of the piston stroke is measured with a millimeter ruler along the vertical line from the peak of cycle “B” to the impact point (the lower point “H”).
The relative error in measuring the piston-stroke magnitude is determined by the ratio of the absolute error, consisting of the error of the recording instrument \(=2\) mm (pencil play) and the measurement error \(=1\) mm,
\[ \frac{\Delta S}{S_{cp}}=\frac{2+1}{60}=0.05 \text{ or } 5\%, \]
where \(S_{cp}\) is the average value of the piston stroke of the OM-506 hammer.
- The horizontal distance between adjacent cycle peaks is measured, and the duration of each cycle is determined by the formula
\[ t'_c=\frac{t_c}{l_c}\cdot l'_c,\ \mathrm{m/sec}, \]
where \(t_c\) is the cycle duration previously determined from the number of impacts, and has a relative error, like the number of impacts, equal to 2%;
\[ l_c=\frac{\sum l'_c}{10} \]
is the arithmetic mean value of the cycle length, mm;
\(l'_c\) is the length of the given cycle, mm.
The relative error in determining the duration of a single cycle is
\[ \frac{\Delta t'_c}{t'_c}=\frac{\Delta t_c}{t_c}+\frac{\Delta l_c}{10l_c}+\frac{\Delta l'_c}{l'_c}, \]
where \(\Delta l_c\) is the absolute error in measuring the width of 10 cycles with a millimeter ruler, 2 mm;
\(10l_c=300\ \mathrm{mm}\) is the width of 10 cycles;
\(\Delta l'_c=2\ \mathrm{mm}\) is the absolute error in measuring the width of one cycle, allowing for play in the recording pencil;
\(l'_c=30\ \mathrm{mm}\) is the width of 1 cycle.
\[ \frac{\Delta t'_c}{t'_c}=0.02+\frac{2}{300}+\frac{2}{30}=0.09\ \text{or }9\%. \]
- The distances \(l'_p\) and \(l'_x\), corresponding to the time of the working stroke and the time of the idle stroke of the piston, are measured, and on this basis the duration of the working stroke of the piston, \(t'_p\), and the duration of the idle stroke of the piston, \(t'_x\), are calculated for each cycle from the relations:
\[ t'_p=\frac{t_c}{l_c}\cdot l'_p,\quad \text{and}\quad t'_x=\frac{t_c}{l_c}\cdot l'_x. \]
The relative error in determining these quantities is
\[ \frac{\Delta t'_p}{t'_p}=\frac{\Delta t_c}{t_c}+\frac{\Delta l_c}{10l_c}+\frac{\Delta l'_p}{l'_p} \quad \text{and} \]
\[ \frac{\Delta t'_x}{t'_x}=\frac{\Delta t_c}{t_c}+\frac{\Delta l_c}{10l_c}+\frac{\Delta l'_x}{l'_x}, \]
where \(\Delta l'_p\) and \(\Delta l'_x\) are the absolute measurement errors, equal to 1 mm;
\(l'_p=12\ \mathrm{mm}\) is the average width of the piston working stroke on the diagram;
\(l'_x=18\ \mathrm{mm}\) is the average width of the piston idle stroke on the diagram.
\[ \frac{\Delta t'_p}{t'_p}=0.02+\frac{2}{300}+\frac{1}{12}=0.11\ \text{or }11\%, \]
\[ \frac{\Delta t'_x}{t'_x}=0.02+\frac{2}{300}+\frac{1}{18}=0.09\ \text{or }9\%. \]
- The ratio \(t_x:t_p\) is calculated for each cycle. The relative error of the calculation is equal to the sum of the errors of the quantities entering into the ratio:
\[ \frac{\Delta(t_x:t_p)}{t_x:t_p}=11+9=20\%. \]
- The velocities of piston motion are determined. For this, with the aid of a drafting instrument, the angle is measured between the tangent drawn to the cri-
of the piston stroke at the given point and the horizontal. The accuracy of measuring the angle of inclination of the tangent is \(0.5^\circ\). Knowing the angle of inclination of the tangent, we determine the piston velocity at the given point by the formula:
\[ V = m_v \operatorname{tg}\alpha \ \text{m/sec}, \]
where \(\alpha\) is the angle of inclination of the tangent to the horizontal,
\(m_v\) is the velocity scale factor, determined from the ratio
\[ m_v = \frac{m_s}{m_t}. \]
In our case:
\[ m_s = 1 \ \text{m/m} \text{— the scale of the piston path,} \]
\[ m_t = \frac{t_u}{l_u}\cdot 1000 \ \frac{\text{sec}}{\text{m}} \text{— the time scale; hence} \]
\[ m_v = \frac{l_u}{1000\,t_u} = 0.001\,\frac{l_u}{t_u} \ \text{m/sec}. \]
It follows from this that
\[ V = \frac{l_u \cdot \operatorname{tg}\alpha}{1000\,t_u} \ \text{m/sec}. \]
The relative error in determining the piston velocity before impact will be:
\[ \frac{\Delta V_{ud}}{V_{ud}} = \frac{\Delta l_u}{l_u} + \frac{\Delta t_u}{t_u} + \frac{\Delta \operatorname{tg}\alpha}{\operatorname{tg}\alpha}. \]
The quantities \(\frac{\Delta l_u}{l_u}\) and \(\frac{\Delta t_u}{t_u}\), computed above, are in this case constant quantities and amount to \(2.1\%\). Consequently, the relative error in calculating the piston velocity will depend on the error in measuring the tangent of the angle of inclination of the piston-stroke curve.
From Fig. 4 it is clear that the speed of pulling the tape for recording the piston stroke must be chosen so that the angle of inclination of the curve at the point of impact does not exceed \(70^\circ\). In this case the relative error in determining the piston velocity will not exceed \(5\%\). The best results are obtained by measuring the angle of inclination of the curve when it is close to \(45^\circ\).
- Having determined the velocity of motion of the piston before collision with the drill steel, one can calculate the impact energy. By impact energy we mean the value of the kinetic energy of the piston before collision with the drill steel. Since the velocity of motion of the piston may be determined relative to the body of the drilling hammer, relative to the rock, and relative to the tool, the impact energy will likewise have the corresponding value, determined by the formula:
\[ A_{ud} = \frac{M V_{ud}^{2}}{2} \ \text{kgm}, \]
where
\[ M = \frac{Q_n}{g} \text{— mass of the piston, } \text{kg sec}^2/\text{m}; \]
\(G_n\) — weight of the piston of the OM-506 hammer with the rod for recording the stroke — \(2.07\ \text{kg}\);
\(g\) — acceleration of gravity;
\(V_{ud}\) — relative velocity of piston motion.
Relative error in determining the impact energy
\[ \frac{\Delta A_{yd}}{A_{yd}}= \frac{\Delta M}{M}+2\frac{\Delta V_{yd}}{V_{yd}} = \frac{\Delta G_{n}}{G_{n}}+2\frac{\Delta V_{yd}}{V_{yd}}, \]
where \(\Delta G_{n}=10\text{ g}\) is the error in determining the weight of the piston,
\[ \frac{\Delta A_{yd}}{A_{yd}} = \frac{10}{2070}+2\cdot 0.05=0.1 \quad\text{or}\quad 10\%. \]
The minimum error in determining the impact energy is \(8\%\) (for this method).
Fig. 4. Dependence of the relative error in calculating the piston velocity on the angle of inclination of the piston path curve. \(a\)—error in determining the width and cycle time; \(b\)—permissible error.
- On the basis of determining the impact energy and the number of blows of the hammer, the hammer power is calculated by the formula:
\[ N_{yd}=\frac{A_{yd}\cdot n}{60\cdot 75}\ \text{hp}. \]
Relative error of calculation
\[ \frac{\Delta N_{yd}}{N_{yd}} = \frac{\Delta A_{yd}}{A_{yd}} + \frac{\Delta n}{n} = 0.1+0.02=0.12 \quad\text{or}\quad 12\%. \]
- Knowing the hammer power and the drilling rate, one can determine the specific work of rock destruction under the given operating regime of the hammer
\[ A_{v}=k\cdot\frac{N_{yd}}{V}\ \text{kgf}\cdot\text{m}/\text{cm}^{3}, \]
where \(k\) is the borehole-diameter coefficient and may be determined as follows: \(1\ \text{cm}\) of borehole depth contains \(\frac{\pi}{4}\cdot d^{2}\), i.e., \(0.785d^{2}\ \text{cm}^{3}\) of vol-
... substituting the diameter of the blasthole (approximately equal to the diameter of the drill bit crown), one can determine the volumetric equivalent of 1 cm of blasthole depth. Expressing the dimension of the ratio
\[ \frac{N_{ud}}{V}=\left[\frac{\text{hp}}{\text{mm/min}}\right] \quad \text{through} \quad k\left[\frac{\text{kgm}}{\text{cm}^3}\right], \]
we obtain the value of the blasthole-diameter coefficient
\[ k=\frac{60.75}{0.785\cdot d^2}=\frac{5732}{d^2}. \]
The formula for the specific work of destruction will take the form:
\[ A_v=\frac{5732\,N_{ud}}{d^2V}\ \text{kgm/cm}^3. \]
Relative error of determination:
\[ \frac{\Delta A_v}{A_v} = \frac{\Delta N_{ud}}{N_{ud}} + \frac{\Delta V}{V} + 2\,\frac{\Delta d}{d}, \]
where \(\Delta d=1\) mm is the error in determining the blasthole diameter;
\(d\) is the blasthole diameter \(=43\) mm
\[ \frac{\Delta A_v}{A_v} = 0.12+0.05+\frac{2}{43} = 0.22 \text{ or } 22\%. \]
In the case of the smallest error in determining the impact energy, equal to 8%, the error in determining the specific work of destruction will be 20%, which lies well within the error limits for determining the specific work of destruction of rock as a result of nonuniformity of structure, amounting to 30%.
- The average compression of the upper and lower buffers is also determined with the aid of the template. For this purpose the front cavity of the cylinder below inlet port “B” is divided into 10 parts; each division corresponds to compression of the lower air cushion by 10, 20, 30%, etc. The percentage compression of the buffer is read to an accuracy of 5% on the scale marked on the template, and along the lower edge of the piston at the moment when the lower plane of the rod coincides horizontally with the point of impact on the piston-stroke diagram. The upper cavity of the cylinder, from the edge of the exhaust port to the valve chest, is also divided into ten parts, corresponding to 10% compression of the upper buffer. The degree of compression of the upper buffer is determined along the upper edge of the piston with an accuracy of 5%.
In the same way, the degree of opening of the exhaust port during the return stroke of the piston is determined; the divisions are marked along the opening of channel “A.” Each division corresponds to 20% of the port cross-section; the reading accuracy is 10%.
Subsequent analysis of the piston-stroke diagram proceeds according to the characteristic features of the diagram.
The data obtained in the course of processing the diagrams and the experimental data are entered in the table of experimental data, which has the following form:
| Experiment no. | \(P\), atm | \(F\), kg | \(n\), impacts/min | \(t_i\), msec | \(t_x\), [[unclear: unit]] | \(V_{ud}\), m/sec | \(A_{ud}\), kgm | \(N_{ud}\), hp | \(A_v\), kgm/cm\(^3\) | \(V\), mm/min | \(\alpha_b\), deg | \(H\), mm | \(B_n\), % | \(B_v\), % |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
On the basis of the table of experimental data, graphs of the dependences under study are plotted.
Investigations carried out by this methodology \[8, 9\] made it possible to reveal a number of dependences that must be taken into account when designing new drilling hammers and improving the design of existing ones.
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