PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
NAMED AFTER S. M. KIROV, HOLDER OF THE ORDER OF THE RED BANNER OF LABOR

Volume 108  STUDY OF DRILLING MACHINES  1959

FACTORS DETERMINING THE PERFORMANCE OF CROSSCUT-DRILLING MACHINES

D. N. Malikov

The experience of mass drilling of raise holes in coal in our country already amounts to one and a half decades. Along with the widespread use of the crosscut-drilling machines SBM-3u, LBS-2, and LBS-4, in recent years a number of experimental models of new machines have been created—BRM-2, MBS-2, BSh—which carry out drilling with the use of rods, as well as the pneumatic drifter PPG-3 [1] and the BA-1 drilling automatic machine [2], which operate without the use of rods. Work is also under way on the creation of machines for drilling raise holes up to 1.0 m in diameter in ores with a hardness of 4–6 [3].

Despite the great accumulated experience in drilling raise holes and the broad scope of design and exploratory work, very little has been done on questions concerning the theory of operation of crosscut-drilling machines. In this connection we can note only two works by engineer B. F. Skafa [4, 5], whose investigations are directed toward improving the operating regime of the SBM-3u machine equipped with a pneumatic motor. On the basis of the investigations in these works, recommendations are given for improving the design of the drilling tool, lamps, and rods, as well as for using the pneumatic motor at increased air pressure. The aim of all the recommendations listed is to increase the mechanical drilling speed.

To determine the productivity of the SBM-3u machine during drilling, B. F. Skafa proposes the formula

\[ A_{\mathrm{cm}} = \frac{T - t_{\mathrm{p.z}}} {4.8 + \frac{H}{l}\left(\frac{1}{v_{\mathrm{p}}} + \frac{1}{v_{\mathrm{c}}}\right)} \ \text{m/shift}, \]

where \(T\) is the duration of the working shift, min;

\(t_{\mathrm{p.z}}\) is the time for preparatory and final operations, min.;

4.8 is the average duration of auxiliary operations performed manually, min/m;

\(H\) is the length of the full travel of the spindle screw, m;

\(l\) is the length of one rod, m;

\(v_p\) is the working feed rate of the spindle during drilling, m/min;

\(v_c\) is the feed rate during the idle stroke of the spindle, m/min.

An analogous formula is also given for determining the productivity of the machine when lowering the tool. The indicated formulas can be used for their direct purpose, and also for solving certain particular questions. But in them the content of the processes that they reflect is not sufficiently revealed. Thus, for example, in order to reduce the time spent on auxiliary operations, B. F. Skafa proposes increasing the length of the rod from 0.6 to 0.8–1.0 m. However, when the formula given above is considered, the advisability of such a recommendation is not confirmed. In fact, by increasing the rod length \(l\), we must increase the spindle stroke \(H\) to the same extent, as a result of which the ratio \(\frac{H}{l}\) for \(H - l = \mathrm{const}\) decreases only very slightly.

The absence of theoretical studies revealing the prospects for the development of crosscut-drilling machines leads to a one-sided approach to solving the problem of increasing their productivity.

The efforts of designers and inventors are directed above all toward achieving high drilling speeds, and so forth, for the drilling installation [6], while little attention is paid to other questions. At the same time they are deprived of the possibility of making even an approximate forecast of the increase in machine productivity.

The present work does not claim to resolve the broad range of questions that arise before the designer. It gives the derivation of productivity equations for crosscut-drilling machines for two technological schemes of drilling operations. Using the machines SBM-3u and LBS-4 as examples, these equations are analyzed in light of certain propositions of the theory of productivity of working machines developed by Prof. G. A. Shaumyan [7]. Consideration of specific machines in the perspective of their development, in our opinion, may to some extent help designers in their further creative searches.

The drilling of holes by crosscut-drilling machines is carried out according to one of the following technological schemes:

I — drilling the hole and subsequently extracting the tool;

II — drilling the hole and enlarging it on the return stroke.

When holes are made according to technological scheme II, extraction of the tool is combined with enlargement of the hole on the return stroke. Thus, there are two definite combinations of three different technological processes, the execution of which in each combination does not coincide in time. Pro-

we analyze each of the indicated technological processes—drilling, extracting the tool, and reaming.

In the steady operation of a crosscut-drilling machine in performing one or another process, a periodic repetition is observed of a number of successively alternating manual and machine operations. The periodic character of the machine’s operation is due to the extension (during drilling) or shortening (during extraction of the tool and reaming) of the drill string. In the interval of time between changes of rods, a definite cycle of operations is performed, with the corresponding expenditures of time. Its content

Fig. 1. Diagram of spindle motions of a crosscut-drilling machine:
a, b, and c—positions of the spindle respectively at the moment of changing the rod, at the beginning and at the end of drilling.

and duration can be determined by analyzing the operation of the machine.

Let us consider the working cycle of the drilling process. The next rod is inserted into the chuck when the latter is in its extreme lower position (Fig. 1, a). After the machine is switched on, the rod is fed upward over a distance \(l_c + l_1\) (Fig. 1, b) at the maneuvering speed \(v_{\mathrm{в}}\) during the time

\[ t_1 = \frac{l_c + l_1}{v_{\mathrm{в}}}, \]

where \(l_c\) is the length of the connecting part of the rod;
\(l_1\) is the clearance between the drill string and the rod being added, inserted into the chuck when the latter is in its extreme lower position.

After this the rod is connected to the drill string and clamped in the chuck, and the machine is switched to the working feed speed, for which a time \(t_2\) is expended.

Then drilling is carried out at the operating feed rate \(v_b\) to a depth equal to the useful length of the rod \(L\), with some overdrilling \(l_2\) (Fig. 1, б, в), for which the time expended is

\[ t_b=\frac{L+l_2}{v_b}. \]

During drilling, one of the drillers, freed from operating the machine, loads the drill cuttings (sludge) for a time

\[ t''=t_b-t', \]

where \(t'\) is the time for the worker to move from operating the machine to loading the sludge and from loading the sludge back to operating the machine.

When drilling holes of large diameter and at a considerable speed, the time \(t''\) proves insufficient for complete removal of the drilled sludge. In this case, as drill cuttings accumulate, the machine is stopped several times during the shift and the sludge is loaded. For simplicity of presentation, we conventionally distribute these machine downtimes over each working cycle.

When drilling a hole of cross-sectional area \(F_1\) and length of one rod \(L\), coal is drilled out in the cycle in a volume \(Q_1=F_1L\ \text{m}^3\), part of which \(Q'=p't''\) is removed during operation of the machine, and the remaining part—\(Q''=Q_1-Q'=pt'_{\text{sh}}\)—is removed with the machine stopped, where \(t'_{\text{sh}}\) is the time for sludge removal not combined with operation of the machine, min; \(p'\) and \(p\) are the worker’s labor productivity in loading sludge, respectively during machine operation and during machine downtime, \(\text{m}^3/\text{min}\).

The quantities \(p'\) and \(p\) have approximately the following relation:

\[ p'=\frac{p}{2}, \]

therefore one may write

\[ Q_1=Q'+Q''=\frac{p}{2}t''+pt'_{\text{sh}} =\frac{p}{2}(t_b-t')+pt'_{\text{sh}}=F_1L, \]

whence

\[ t'_{\text{sh}}=\frac{F_1L}{p}-\frac{t_b-t'}{2} =\frac{F_1L}{p}-\frac{1}{2}\left(\frac{L+l_2}{v_b}-t'\right)\ \text{min}. \tag{1} \]

In the process of reaming the hole, the noncombined time for loading sludge is determined in an analogous manner, i.e.,

\[ t''_{\text{sh}}=\frac{F_2L}{p}-\frac{t_p-t'}{2} =\frac{F_2L}{p}-\frac{1}{2}\left(\frac{L+l_2}{v_p}-t'\right)\ \text{min}. \tag{2} \]

If, in calculating \(t'_{\text{sh}}\) (or \(t''_{\text{sh}}\)), the latter turns out to be a negative quantity, this will indicate an excess

time for the worker engaged in removing cuttings during operation of the machine. In this case, in equations (7), (8), (12), (13), the times \(t_{\text{ш}}'\) and \(t_{\text{ш}}''\) should not be taken into account.

When \(t_{\text{б}} \leq t'\) and \(t_{\text{р}} \leq t'\), all the cuttings are removed with the machine stopped, with the corresponding time expenditures \(t_{\text{ш}}' = \dfrac{F_1L}{p}\) and

\[ t_{\text{ш}}''=\frac{F_2L}{p}. \]

After drilling has been completed over the entire length of the rod, the machine is stopped, the gripper is brought up to the drill string, the motor is briefly switched on in reverse to loosen the wedges of the lock, and the latter are removed; the time spent on this is \(t_3\).

Fig. 2. Working cycles of a crosscut-drilling machine:
\(a\)—during drilling; \(б\)—during reaming; \(в\)—during lowering of the tool.

After switching from working speed to maneuvering speed, the lock is lowered to the extreme lower position at velocity \(v_{\text{н}}\) over a distance \(L+l_c+l_1+l_2\), with a time expenditure

\[ t_4=\frac{L+l_c+l_1+l_2}{v_{\text{н}}}. \]

Then the next rod is inserted into the lock, and the cycle of operations described above is repeated (Fig. 2, \(a\)).

Thus, in steady operation of the machine, for drilling a borehole of length one rod \(L\), the time expended is

\[ T_1=t_{\text{б}}+t_1+t_2+t_3+t_4+t_{\text{ш}}' = \]

\[ =\frac{L+l_2}{v_{\text{б}}}+\frac{l_c+l_1}{v_{\text{в}}}+\frac{L+l_c+l_1+l_2}{v_{\text{н}}}+t_2+t_3+t_{\text{ш}}'. \tag{3} \]

Assuming \(l_1=l_2=l_0\) and denoting the total time expenditures for the manual auxiliary operations of the cycle \(t_2+t_3\) by \(t_0\), equality (3) may be represented in the following form:

\[ T_1=\frac{L+l_0}{v_{\mathrm{б}}}+\frac{l_c+l_0}{v_{\mathrm{в}}}+\frac{L+l_c+2l_0}{v_{\mathrm{н}}}+t_0+t'_{\mathrm{ш}}\ \text{min}. \tag{4} \]

When reaming a borehole on the return stroke, the reverse sequence of operations is observed, with the opposite direction of their execution (Fig. 2, b) as compared with the drilling process (Fig. 2, a): from the lower extreme position, at maneuvering speed \(v_{\mathrm{в}}\), the chuck is fed to the upper extreme position \((t_1)\), and the drill string is wedged in the chuck \((t_2)\); then the borehole is reamed in the direction from top to bottom at feed speed \(v_{\mathrm{p}}\) during the time

\[ t_{\mathrm{p}}=\frac{L+l_2}{v_{\mathrm{p}}}, \]

after which the used rod is disconnected from the drill string and the machine is switched to maneuvering speed \((t_3)\); the chuck is lowered to the extreme lower position at speed \(v_{\mathrm{н}}\), and the rod is removed \((t_1)\). From what has been said it follows that the duration of the cycle during reaming will be

\[ T_2=\frac{L+l_0}{v_{\mathrm{p}}}+\frac{l_c+l_0}{v_{\mathrm{н}}}+\frac{L+l_c+2l_0}{v_{\mathrm{в}}}+t_0+t''_{\mathrm{ш}}\ \text{min}. \tag{5} \]

In the process of lowering the tool, exactly the same sequence of operations is observed as during reaming (Fig. 2, b, c), with the only difference that, instead of reaming, the lowering operation is performed at speed \(v_c\) and with a time expenditure

\[ t_c=\frac{L+l_2}{v_c} \]

and there is no removal of cuttings. Therefore it may be considered that, when the string is shortened by one rod in the process of idle lowering of the tool, the time expended is

\[ T_3=\frac{L+l_0}{v_c}+\frac{l_c+l_0}{v_{\mathrm{н}}}+\frac{L+l_c+2l_0}{v_{\mathrm{в}}}+t_0\ \text{min}. \tag{6} \]

If the borehole length, equal to the useful length of one rod \(L\), is divided by the duration of one or another working cycle, we obtain the machine productivity for performing the corresponding process:

during drilling

\[ V_1=\frac{L}{T_1}= \frac{1}{ \frac{1}{v_b}\cdot\frac{L+l_0}{L} +\frac{1}{v_v}\cdot\frac{l_c+l_0}{L} +\frac{1}{v_n}\cdot\frac{L+l_c+2l_0}{L} +\frac{t_0+t'_{\mathrm{sh}}}{L} }\ \text{m/min}; \tag{7} \]

during reaming

\[ V_2=\frac{L}{T_2}= \frac{1}{ \frac{1}{v_p}\cdot\frac{L+l_0}{L} +\frac{1}{v_n}\cdot\frac{l_c+l_0}{L} +\frac{1}{v_v}\cdot\frac{L+l_c+2l_0}{L} +\frac{t_0+t''_{\mathrm{sh}}}{L} }\ \text{m/min}; \tag{8} \]

during lowering of the tool

\[ V_3=\frac{L}{T_3}= \frac{1}{ \frac{1}{v_c}\cdot\frac{L+l_0}{L} +\frac{1}{v_n}\cdot\frac{l_c+l_0}{L} +\frac{1}{v_v}\cdot\frac{L+l_c+2l_0}{L} +\frac{t_0}{L} }\ \text{m/min}. \tag{9} \]

For the SBM-3u, LBS-2, and LBS-4 machines, driven by electric motors, one may take \(v_c=v_n=v_v\). Denoting these speeds by \(v_m\) and assuming \(\frac{L+l_0}{L}\approx 1\), formulas (7–9) for the indicated machines may be written in a more compact form:

\[ V_1= \frac{1}{ \frac{1}{v_b} +\frac{1}{v_m}\left(\frac{2l_c+3l_0}{L}+1\right) +\frac{t_0+t'_{\mathrm{sh}}}{L} }\ \text{m/min}; \tag{7a} \]

\[ V_2= \frac{1}{ \frac{1}{v_p} +\frac{1}{v_m}\left(\frac{2l_c+3l_0}{L}+1\right) +\frac{t_0+t''_{\mathrm{sh}}}{L} }\ \text{m/min}; \tag{8a} \]

\[ V_3= \frac{1}{ \frac{1}{v_m}\left(\frac{2l_c+4l_0}{L}+2\right) +\frac{t_0}{L} }\ \text{m/min}. \tag{9a} \]

As already indicated, formulas (7–9) can be used to determine the productivity of the machine in performing the individual technological processes of driving a borehole. The result calculated from these formulas is expressed in units of unfinished output per unit time (m/hour of lowered tool, drilled borehole without lowering the tool, widened—

...borehole to a larger diameter). The formulas can be used for calculating production norms and for planning drilling work for one or two shifts. However, with their aid it is impossible to give a complete technical characterization of a given machine, since they do not take into account a number of labor-intensive operations associated with moving from one borehole location to another.

After completion of all work on drilling the borehole, the machine with the tool and starting equipment is moved to a new drilling site during the time \(t_{\mathrm{p}}\). Then the machine is set up in the direction of the line of the future borehole and collaring is performed, for which the time \(t_{\mathrm{y}}\) is expended. Then the drilling process is carried out over the entire length of the borehole \(H\) during the time

\[ t_{\mathrm{I}} = \frac{H}{V_1}. \]

After drilling is completed, one of the drillers goes up to the upper mouth of the borehole. Having verified that the borehole has broken through correctly, the driller descends back down to the machine. Sometimes the borehole does not come out into the overlying drift, and it has to be opened up, which is a very labor-intensive task requiring considerable time. Next, the tool is lowered during the time

\[ t_{\mathrm{III}} = \frac{H}{V_3}, \]

after which the above-described production drilling cycle according to technological scheme I is repeated.

If the drilled borehole is enlarged on the return stroke (technological scheme II), then, after checking the quality of the borehole, a return-stroke reamer is delivered to the upper mouth of the latter; it is installed on the drill string instead of the forward-stroke tool, for which the time \(t_{\mathrm{i}}\) is expended. This is followed by the process of enlarging the borehole during the time

\[ t_{\mathrm{II}} = \frac{H}{V_2}, \]

after which the cycle of drilling work according to this technology is repeated.

Thus, the duration of the production cycle of drilling work, depending on the technology used to make the borehole, consists of the following time elements: when drilling with tool lowering,

\[ T_{\mathrm{I}} = t_{\mathrm{I}} + t_{\mathrm{III}} + t_{\mathrm{p}} + t_{\mathrm{y}} + t_{\mathrm{pr}} \ \text{min.}; \]

when drilling with enlargement on the return stroke,

\[ T_{\mathrm{II}} = t_{\mathrm{I}} + t_{\mathrm{II}} + t_{\mathrm{p}} + t_{\mathrm{y}} + t_{\mathrm{pr}} + t_{\mathrm{i}} \ \text{min.}, \]

where \(t_{\text{pr}}\) is other time expenditures, not combined with machine operation, referred to one borehole (checking the quality of the borehole, installing and removing the dust collector, supplying mine cars for loading sludge, connecting the machine to the electric power network and grounding it, lubricating the machine, etc.), min.

Dividing the borehole length \(H\) by the duration of drilling it, we obtain the operating performance of the machine for the corresponding drilling technology: when drilling with lowering of the tool,

\[ V_{\mathrm{I}}=\frac{H}{T_{\mathrm{I}}}\,60 =\frac{H}{\dfrac{H}{V_1}+\dfrac{H}{V_3}+t_{\text{p}}+t_{\text{y}}+t_{\text{pr}}}\,60\ \text{m/hour}; \tag{10} \]

when drilling with reaming on the return stroke,

\[ V_{\mathrm{II}}=\frac{H}{T_{\mathrm{II}}}\,60 =\frac{H}{\dfrac{H}{V_1}+\dfrac{H}{V_2}+t_{\text{p}}+t_{\text{y}}+t_{\text{i}}+t_{\text{pr}}}\,60\ \text{m/hour}. \tag{11} \]

Substituting into equations (10–11) the values of \(v_1\), \(v_2\), and \(v_3\) according to formulas (7, a—9, a), after transformation we obtain:

\[ V_{\mathrm{I}}= \frac{1}{ \dfrac{1}{v_{\text{b}}} +\dfrac{1}{v_{\text{m}}} \left( \dfrac{4l_{\text{c}}+7l_{\text{o}}}{L}+3 \right) +\dfrac{2t_0+t'''_{\text{sh}}+t'_{\text{sh}}}{L} +\dfrac{t_{\text{p}}+t_{\text{y}}+t_{\text{pr}}}{H} } \,60\ \text{m/hour}; \tag{12} \]

\[ V_{\mathrm{II}}= \frac{1}{ \dfrac{1}{v_{\text{b}}} +\dfrac{1}{v_{\text{p}}} +\dfrac{1}{v_{\text{m}}} \left( \dfrac{4l_{\text{c}}+6l_{\text{o}}}{L}+2 \right) +\dfrac{2t_0+t''_{\text{sh}}}{L} +\dfrac{t_{\text{p}}+t_{\text{y}}+t_{\text{i}}+t_{\text{pr}}}{H} } \,60\text{ m/hour}. \tag{13} \]

The performance of rodless chipping-and-drilling machines (PPG-3, BA-1) may be expressed by the following equation:

\[ V_{\mathrm{III}}= \frac{1}{ \dfrac{1}{v_{\text{b}}} +\dfrac{1}{v_{\text{x}}} +\dfrac{t_{\text{sh}}+t_{\text{p}}+t_{\text{y}}+t_{\text{pr}}}{H} } \,60\ \text{m/hour}, \tag{14} \]

where \(v_{\text{x}}\) is the speed of idle lowering of the machine along the drilled borehole, m/min;

\(t_{\text{sh}}\) is the noncombined time for loading sludge during the drilling of the entire borehole, min.

Equations (10–14) express the linear performance of the machine, where the unit of output is taken to be 1 m of borehole. If the linear performance is multiplied by the cross-sectional area

the cross-sectional area of the borehole \(F\), we obtain the volumetric productivity of the machine

\[ Q_{\mathrm{I}} = V_{\mathrm{I}} F \ \text{m}^3/\text{hour}; \tag{15} \]

\[ Q_{\mathrm{II}} = V_{\mathrm{II}} F \ \text{m}^3/\text{hour}; \tag{16} \]

\[ Q_{\mathrm{III}} = V_{\mathrm{III}} F \ \text{m}^3/\text{hour}. \tag{17} \]

All terms of equations (12–17) that denote velocity, length, area, and time will, for convenience of exposition, be called factors in what follows.

Considering equations (12) and (13), it is not difficult to see that the productivity of the machine increases if we simultaneously:

1) increase the rod length \(L\), the drilling speed \(v_b\), the reaming speed \(v_p\), and the spindle traverse speed \(v_m\), the borehole length \(H\); and

2) decrease the values \(l_c\) and \(l_0\) and the time expenditures \(t_0\), \(t'_{\sh}\), \(t''_{\sh}\), \(t_p\), \(t_y\), \(t_i\), \(t_{pr}\).

If the parameters of the first group are decreased and those of the second increased, the productivity of the machine will decline. Accordingly, in what follows we shall distinguish a positive change in a factor, when the productivity of the machine increases, and a negative one, when productivity decreases.

Obviously, the greatest increase in machine productivity can be expected in the case of a positive change in all factors simultaneously. In practice, however, when creating new machines and improving existing working machines, this does not always appear possible. Often a positive change in one factor entails a negative change in another or in a number of other factors. Finally, a positive change in one factor or another may be limited by the state of development of science and technology in the corresponding field at a given stage. Therefore, when creating new machines and improving existing ones, it is important to know in advance what the implementation of particular technical solutions or the pursuit of a particular objective of scientific research will lead to.

An approximate answer to the question posed can, in our opinion, be given by an analysis of the machine productivity equation.

Crosscut-drilling machines perform useful work only during drilling (reaming). Therefore, in the productivity equations we have derived, the drilling (reaming) speed is the initial factor, while the remaining factors are its companions. The presence of the latter is determined by the production technology and by those technical means with the help of which the useful work—drilling—is carried out. Hence the productivity of a machine may be regarded as the result of the interaction of the initial factor with organizational and technical factors.

However, the drilling speed is not an independent factor. It, in turn, depends on the power \(N\) transmitted to the tool, the energy intensity of the breaking process \(q\), and the cross-sectional area of the borehole \(F\), and is determined, as is known, by the relation

\[ v_b = \frac{N}{q}\,F . \]

It follows from the relation given that, for a specified borehole diameter (\(F=\mathrm{const}\)), an increase in drilling speed can be achieved in two ways:

1) by reducing the energy intensity of the drilling process through the use of a more advanced drilling tool and the establishment of optimal operating conditions for it;

2) by increasing the power of the machine.

In the first case, an increase in drilling speed can cause only an increase in machine downtime due to loading of the cuttings (1), (2), while the other factors will remain unchanged.

In the second case, an increase in drilling speed may lead not only to longer machine downtime due to loading of the cuttings. An increase in the power transmitted to the drilling tool, other conditions being equal, is accompanied by an increase in the dimensions and weight of the machine and rods, and consequently in the time spent on auxiliary and preparatory operations. According to what law will these time expenditures increase? Equations (12), (13) do not answer this question. Hence there arises the need for further refinement of the productivity equation in order to determine the relationships among the factors.

In the present work we shall confine ourselves only to a general analysis of equations (12) and (13), which reflect essentially the relationship between the machine’s productivity and the factors determining it. In doing so we shall make the assumption that a change in one factor does not affect the magnitude of another. As an exception, only the duration of loading of the cuttings, not combined with machine operation, will vary when \(v_b\), \(v_p\), \(L\), and \(F\) are changed in accordance with conditions (1) and (2).

Below, in the table, are given the parameters of existing machines and the time expenditures for individual operations, established on the basis of time-study observations carried out when drilling boreholes under specified conditions (distance between boreholes \(6\ \text{m}\); borehole length \(50\ \text{m}\); the machine is installed in a previously prepared niche of the main drift; the upper mouth of the borehole coincides with the drift; cars for loading cuttings are supplied as needed; there is no worker downtime). The productivity of the machine, calculated by formulas (12) and (13) using the data given in the table, may be regarded as actual (under the above-indicated operating conditions).

* According to KuzNIUI data

Let some machine, for example the LBS-4, which performs drilling with feed rate \(v_b\) and has an actual output \(V_1\), as a result of using a tool of improved design begin to develop a higher drilling speed \(v'_b\) and, according to equation (12), attain an output \(V'_1\). In other words, as a result of increasing the drilling speed by

\[ x=\frac{v'_b}{v_b} \]

times, the output of the machine increased by

\[ y=\frac{V'_1}{V_1} \]

times. By assigning different values to \(x\), we shall also obtain the corresponding values of \(y\). In exactly the same way one can calculate the relative increase in the machine output when other factors are changed. For example, to a given value

\[ x=\frac{t'_p}{t_p} \]

there will correspond, according to formula (12), a definite value

\[ y=\frac{V'_1}{V_1} \]

and so on.

In Fig. 3, a, the dependences \(y=f(x)\) are presented, constructed for a number of factors when drilling holes with lowering of the tool by the LBS-4 machine.

Curve 1, expressing the dependence

\[ \frac{V'_1}{V_1}=f\left(\frac{v'_b}{v_b}\right), \]

shows that the output of the machine increases not in proportion to the increase in drilling speed: at first it grows comparatively rapidly, then the growth of output gradually

slows down and, finally, practically ceases. Thus, increasing the drilling speed twofold \((x = 2)\) raises the machine productivity by 9% \((y = 1.09)\); at \(x = 4\) we have, respectively, \(y = 1.15\), and at \(x = \infty\), \(y = 1.25\). Consequently, however great our achievements may be in creating an efficient drilling tool, with the given machine design and drilling-work technology we shall not be able to increase machine productivity by more than 25%. An even smaller result is obtained by increasing the drilling speed of the SBM-3u machine (curve 1, Fig. 4, a).

A more substantial influence on the productivity of the same machine is exerted by the drilling speed (and reaming speed) when driving a borehole with subsequent enlargement on the return stroke.

Fig. 3. Influence of various factors on the productivity of the LBS-4 crosscut-drilling machine:
\(a\)—when drilling with tool lowering; \(b\)—when drilling with reaming on the return stroke; 1—drilling (reaming) speed; 2—spindle idle-stroke speed; 3—rod length; 4—manual auxiliary time of the working cycle; 5—machine travel time; 6—time for setting up the machine and collaring.

Curve 1 (Figs. 3, b; 4, b) represents the dependence

\[ \frac{V'_{\mathrm{II}}}{V_{\mathrm{II}}} = f\left(\frac{v'_{\mathrm{br}}}{v_{\mathrm{br}}}\right), \]

where

\[ v_{\mathrm{br}}=\frac{v_b v_r}{v_b+v_r} \]

is the equivalent rate of advance of the borehole face in machine time.

The breaks in curve 1 (Fig. 3, b) are explained by the following circumstance. When \(v_b\) and \(v_r\) are increased by a factor of 1.3 (point \(m\)), the time for loading cuttings is completely combined with machine operation. A further increase in the drilling and reaming speeds leads to increasing machine downtimes due to loading of cuttings; at point \(n\) these reach their maximum value and then remain constant.

If the time spent on loading cuttings is eliminated, for example by mechanizing this process, then an increase in \(v_b\) and \(v_r\)

will lead to a higher relative increase in the machine’s productivity (curve 1, Figs. 3, 4).

In the case of drilling a hole with lowering of the tool, an increase in the idle-travel speed of the spindle of the LBS-4 machine will lead to the same increase in its productivity as an increase in \(v_b\) (curve 2, Fig. 3, a), while it will have an even greater effect on the increase in productivity of the SBM-3u machine than the drilling speed (curve 2, Fig. 4, a).

Curve 3 (Figs. 3, 4) indicates the possibility of increasing machine productivity by increasing the length of the rod. However, such an increase in productivity will be ensured only if the time losses associated with replacing the rod, moving the machine, setting it in position, and collaring remain unchanged.

Fig. 4. Influence of various factors on the productivity of the SBM-3u crosscut-drilling machine:

\(a\)—when drilling with lowering of the tool; \(b\)—when drilling with a drilling reverse stroke; 1—drilling speed (reaming speed); 2—idle-travel speed of the spindle; 3—rod length; 4—manual auxiliary time of the working cycle; 5—time for moving the machine; 6—time for setting up the machine and collaring.

In reality, however, increasing the rod by some amount \(\Delta L\) will make it necessary to increase the machine dimension along the spindle axis by \(2\Delta L\), which, in turn, may cause difficulties in moving the machine through the working, in setting it up at the workplace, and will also complicate machine control. The indicated circumstances will be reflected to some extent in an increase in the times \(t_0\), \(t_{\mathrm{p}}\), and \(t_y\), which may partially or completely offset the productivity increase shown by curve 3. The actual influence of the rod length on machine productivity can be determined only after establishing the dependences \(t_0=f(L)\), \(t_{\mathrm{p}}=f(L)\), \(t_y=f(L)\). From consideration of equations (1), (2), (12), and (13) it also follows that the shorter the time \(t_0\), the smaller the influence exerted by the rod length on machine productivity.

Curves 4, 5, and 6, characterizing the influence of the corresponding time expenditures \(t_0\), \(t_{\mathrm{p}}\), and \(t_y\) on machine productivity, indicate the advisability of reducing them as much as possible.

Let us now consider the question of which technological scheme is more expedient for drilling holes of one and the same diameter and using one and the same machine, if cases of defective holes are excluded. Comparing equations (12) and (13) with each other, we find that the productivity of the machine in both cases will be the same, \(V_I = V_{II}\), under the condition

\[ \frac{1}{v_{б1}}+\frac{1}{v_м}=\frac{1}{v_б}+\frac{1}{v_р}+\frac{t_и}{H}, \tag{18} \]

where \(v_{б1}\) is the tool feed rate in one-pass drilling of a hole of final diameter.

Both parts of equality (18) represent the time expenditures for performing the corresponding operations, referred to 1 m of hole. If, for example, as a result of tests it is established that

\[ \frac{1}{v_{б1}}>\frac{1}{v_б}+\frac{1}{v_р}+\frac{t_и}{H}-\frac{1}{v_м} \]

by an amount \(\Delta t\) min, then this will indicate that, under scheme I, an additional \(\Delta t\) min is expended per meter of hole in comparison with scheme II, and that the latter is preferable to the former.

From consideration of equations (12), (15) and (14), (17) it follows that, provided the values of the factors of the same name are equal, drilling 1 m of hole with rodless machines requires

\[ \Delta t=\frac{1}{v_м}\left(\frac{4l_c+7l_0}{L}+2\right)+\frac{2t_0}{L}\ \text{min.} \]

less time than with rod machines.

From all that has been considered above it follows that, by positively changing any single factor, even to its limiting value, it is impossible to achieve a substantial increase in machine productivity. A sharp increase in it is possible only with a simultaneous positive change in all or several of the most significant factors. For the machines considered above (as an example), LBS-4 and SBM-3u, the following may be regarded as the most significant factors:

1) the drilling and reaming speeds, which must be increased by reducing the energy intensity of the drilling process and by increasing the power referred to the unit weight of the machine;

2) the non-overlapped time for loading cuttings, which must be reduced to a minimum by mechanizing this process;

3) the spindle idle-travel speed, the increase of which presents no particular difficulties;

4) the manual auxiliary time of the working cycle \(t_0\), which must be reduced by improving the design of the drill lock and the machine control system;

5) the time for moving the machine from one working place to another, the reduction of which can be achieved by increasing its transportability and maneuverability.

Along with improving rod-type crosscut-drilling machines, it is necessary to continue work on the creation and introduction into production of more advanced, in our view, rodless machines, which at present have not yet passed beyond the experimental stage.

REFERENCES

1. M. S. Safoхin, A. I. Kuprin. Crosscut-drilling machines. Ugletekhizdat, 1958.

2. I. E. Lomov. A new mechanism for drilling deep boreholes in coal. Mechanization of labor-intensive and heavy work, No. 7, 1958.

3. E. A. Sorokin. Giprorudmash Institute. Mining Journal, No. 8, 1957.

4. B. F. Skafa. Determination of the power at the spindle of the SBM-3u crosscut-drilling machine when drilling raise boreholes in coal in steeply dipping seams. Operating regimes of mining machines. Collection of articles No. 16, Ugletekhizdat, 1958.

5. B. F. Skafa. Determination of the productivity of the SBM-3u crosscut-drilling machine with a pneumatic motor. Operating regimes of mining machines. Collection of articles No. 16, Ugletekhizdat, 1958.

6. O. D. Alimov, I. V. Rodionov, D. N. Malikov, V. N. Karminsky. Machines for drilling raise boreholes. Proceedings of TPI, vol. 106, Metallurgizdat, 1958.

7. G. A. Shaumyan. Fundamentals of the theory of designing automatic machine tools and automatic lines. Mashgiz, 1949.

Noted Misprints

Order 29