O. D. Alimov, L. T. Dvornikov

Rotary Drilling of Blastholes

One of the principal parameters of the rotary method of drilling blastholes, affecting the productivity and economic expediency of drilling operations, is the drilling rate.

The drilling rate, in turn, may vary considerably depending on the magnitude of the axial thrust (feed) of the drilling tool against the bottom, the number of revolutions of the drilling tool per unit time, the physico-mechanical properties of the rock being drilled, the diameter and geometry of the drilling tool, the power of the drilling-machine motor, and the method of removing drill cuttings from the bottom of the blasthole. The influence of these factors on the drilling rate has been studied mainly experimentally [1—26]. Each of the indicated investigations, as a rule, covers a fairly narrow range of possible conditions, limited either by the capabilities of a particular drilling machine, or by a preset geometry of the cutting tool, or by particular physico-mechanical properties of the rocks, etc. Because of such specific features of the experiment, researchers obtained different results and gave recommendations that were often, at first glance, incomparable.

At the present time there has arisen a need to generalize all the accumulated material in order to develop recommendations for selecting rational regimes of rotary blasthole drilling in various rocks and for different parameters of drilling machines.

The authors of the present article have attempted to carry out such a generalization. The basis for this was provided by the numerous data on drilling regimes published in the literature, as well as by the results of experimental work by the authors carried out in recent years at the Tomsk Polytechnic Institute. This article presents only the principal results of the generalization.

The process of rotary drilling is significantly affected by physico-mechanical properties. To assess their influence, concepts such as brittleness, plasticity, hardness, contact strength, strength, abrasiveness, moisture content, and others have been introduced. In most cases researchers characterize the resistance of rocks to destruction during drilling either by hardness (compressive strength), or by hardness (indentation strength) and abrasiveness.

The mutual influence of these factors is very complex and can be taken into account only with a sufficiently complete study of elasticity, plasticity,

abrasiveness and other properties of various rocks, and their interrelations. In this connection, work on the study of the physicomechanical properties of rocks, carried out recently by the schools of Prof. M. M. Protodyakonov and L. A. Schreiner, is of considerable interest. For the time being, however, the available data do not make it possible to take into account and calculate with sufficient accuracy the influence of each of the factors. Therefore, the method proposed in its time by Prof. M. M. Protodyakonov [20] for accounting for the influence of the principal physicomechanical properties in aggregate by means of strength retains its value. Moreover, the absolute majority of data on blasthole drilling regimes are associated with rocks through the strength coefficient. A number of correlation dependences have been established between the strength coefficient and other characteristics of rocks (Schreiner hardness, Shore hardness, etc.). In setting ourselves the task of generalizing the results of experimental investigations and taking into account what has been stated above, we have taken the strength coefficient \(f\) as the principal mechanical characteristic of rocks.

Influence of the feed force

The magnitude of the axial pressing of the cutting tool against the bottom of the blasthole—the feed force—has a determining effect on the drilling speed.

The dependence of the speed in the rotary method of blasthole drilling on the feed force is accepted as the main indicator of drilling efficiency in most experimental investigations. At present, a considerable amount of data has accumulated on this dependence, covering a broad range of rocks with various physicomechanical properties. The qualitative dependence of drilling speed on feed force is presented most clearly by L. A. Schreiner [26] (Fig. 1).

Fig. 1.

This dependence is described by a curve that has three clearly expressed zones.

The 1st zone is characterized by destruction of the rock by abrasion. The cutting tool used is not absolutely sharp and therefore the resis-

comes into contact with the rock over some contact area \(F_{\text{w}}\). The feed force \(P_{\text{p}}\) in zone I is insufficient for penetration of the tool into the rock,

that is, the specific pressure of the tool on the bottomhole

\[ p=\frac{P_{\text{p}}}{F_{\text{w}}}\ \text{kg/mm}^{2} \]

is less than the hardness of the rock \(p_{\text{ind}}\), \(\text{kg/mm}^{2}\).

Zone II is characterized by the relation \(p_{\text{ind}} \geq p\) between the hardness \(p_{\text{ind}}\) and the specific pressure \(p\). This portion of the curve, according to G. N. Pokrovskii [19], is described by a power-law dependence between drilling rate and feed force,

\[ V=aP_{\text{p}}^{m}, \]

where \(V\) is the drilling rate;
\(a\) is a coefficient constant for a given rock;
\(m\) is an exponent depending on the physico-mechanical properties of the rocks.

In zones I and II the power of the drilling machine is expended mainly on overcoming the forces of friction of the tool against the bottomhole, which leads to considerable abrasive wear of the tool and low drilling productivity. The energy consumption of the destruction process in zones I and II is high. With an increase in feed force it decreases and in zone III reaches a minimum. In this case the power of the drilling machine is expended most expediently—on shearing off large particles of rock. On this basis, primary attention should be given to the study of the laws governing the processes of rock destruction in zone III.

Analyzing the data of various investigations, one may conclude that for all rocks of medium hardness with \(f \leq 10\text{—}12\), which can be effectively destroyed in rotary drilling by cutters of diameter \(40\text{—}45\ \text{mm}\), zone III (Fig. 1) occurs already at feed forces from 100 to 400 kg.

For rocks differing in hardness, the character of the dependence \(V=f(P_{\text{p}})\) in the zone of volumetric destruction remains the same; only \(\alpha\), the angle of inclination of the straight line (Fig. 1) to the abscissa axis, changes.

For most cases the portion of the curve in zone III may be described by the equation

\[ V=\kappa(P_{\text{p}}-P_{0}),\ \text{mm/min}, \tag{1} \]

where \(\kappa=b\cdot \tg \alpha\) is the feed force corresponding to the point of intersection of the straight line \(V=f(P_{\text{p}})\) (zone III) with the abscissa axis, kg;
\(b\) is a dimensional coefficient.

The value \(P_{0}\) is the minimum necessary feed force at which volumetric destruction of rocks begins, and it must satisfy the condition \(P_{0}\geq p_{\text{ind}}\cdot F_{\text{w}}\).

According to G. N. Pokrovskii [19], a sharp cutter of type RP, diameter \(42\ \text{mm}\), not previously used, already has a blunting area \(F_{\text{w}}\approx 5\ \text{mm}^{2}\). It follows from this that, for the most common tool in blasthole drilling,

\[ P_{0}\geq 5p_{\text{ind}}. \tag{2} \]

Theoretically, between \(p_{\text{ind}}\) and the compressive strength of rocks \(\sigma_{\text{comp}}\), \(\text{kg/mm}^{2}\), there exists the relation [26]

\[ \frac{p_{\text{ind}}}{\sigma_{\text{comp}}}=(1+2\pi)\approx 7. \tag{3} \]

We note only that this relation is not always confirmed experimentally and therefore may be accepted only as a rough approximation.

If one takes into account that the coefficient of strength of rocks, according to M. M. Protodyakonov [20], is \(f=\sigma_{\text{c}}\), then from (2) and (3) \(p_{\text{ind}}\simeq 7f\) and

\[ P_0 \geqslant 7 \cdot 5f = 35f . \tag{4} \]

For rocks with \(f\) from 3 to 12, the force \(P_0\) calculated by formula (4) will be \(P_0=(105 \div 420)\) kg, which agrees sufficiently well with the experimental data.

Between the value of the angle \(\alpha\) and the hardness of the rock, or the coefficient of strength according to the scale of Prof. M. M. Protodyakonov, one may note the existence of a dependence of the form

\[ \kappa = b \cdot \operatorname{tg}\alpha = \frac{a_1}{p_{\text{ind}}} \quad \text{or} \quad \kappa = b \cdot \operatorname{tg}\alpha = \frac{a_2}{f}, \]

where \(a_1\) and \(a_2\) are coefficients depending on the number of revolutions of the drill and the degree of wear of the cutter.

The maximum value of \(a_1\) and \(a_2\) corresponds to the optimum number of revolutions of the drill \(n_{\text{opt}}\), that is, to such a number at which the maximum drilling rate and the minimum energy consumption of the breakage process \(A_{\text{br}}\) are attained.

Table 1 summarizes data from many investigators showing the relationships between drilling rate and feed force at rotational speeds called optimum by the investigators for various rocks. In the same table, the mean values of \(P_0\) and \(\kappa\) have been calculated from formulas (1) and (4).

Table 1

Continuation of the table

*) The force $P_0$ was determined graphically from experimental data; $\kappa_{\mathrm{av}}$ was determined as $\kappa_{\mathrm{av}}=\dfrac{\sum \kappa}{n}$, where $\kappa=\dfrac{V}{P_{\mathrm{p}}-P_0}$.

For numbers of revolutions both smaller and larger than $n_{\mathrm{opt}}$, the value of $\kappa$ and the drilling rate decrease.

To illustrate what has been said, in Fig. 2, using the data of A. N. Volkov [9] (curve 1) and I. E. Rudavskii [22], we have plotted the dependence $\kappa=f(n)$ at a constant feed force. The maximum value of $\kappa$ corresponds to the number of revolutions of the drill per minute recommended by the authors as optimal.

Analyzing the results of various investigations, one can find that, at optimal rotational speeds of the drill, the value of $\kappa$ is constant for each rock.

On the basis of the data in Table 1, Fig. 3 plots the relationship between the value of $\kappa$ and the hardness coefficient $f$. This relationship, in our opinion, may be accepted as a first approximation as a characteristic of the efficiency of rotary drilling of blast holes of diamet—

with a diameter of 42 mm in rocks of different strength. The coefficient $k$ may be called the drilling-efficiency coefficient.

We consider it necessary to note that the drilling-efficiency coefficient $k$ is characteristic of a given tool and a given drilling method. Obviously, with other tool sizes and other drilling methods (diamond, shot drilling), it will be somewhat different.

If, in the near future, it were possible to determine similar efficiency characteristics for different drilling methods, this would considerably facilitate calculations of possible drilling rates and the selection and substantiation of suitable drilling equipment.

Fig. 2. Dependence of the proportionality coefficient $k$ on the rotational speed of the drilling tool at constant feed force.

Fig. 3. Dependence of the rotary-drilling efficiency coefficient on the strength of the rocks being drilled.

Indeed, using Fig. 3 and the formula $P_0 \approx 35 f$, it is easy, by formula (1), to find the possible maximum drilling rate for a given feed force $P_{\mathrm{n}}$ and the optimum number of revolutions. From Table 2

Table 2

it is evident that the calculated drilling speeds agree well with the experimental ones.

On the basis of the relationship (1) that was found, it proved possible to preliminarily calculate the drilling speeds of various rocks as a function of feed force (Fig. 4). The maximum possible values of rotary drilling speed will evidently be limited by the geometry and strength of the drilling tool. Therefore, the question of how significantly the zone of potential capabilities of rotary-action drilling machines can be increased is of interest. To answer this it is necessary to establish up to what values of feed force the linear relationship \(V=f(P_{\mathrm{п}})\) is preserved. The most obvious criteria for violation of the linearity of \(V=f(P_{\mathrm{п}})\) in the upper part of the curve are: the geometry of the cutters, their durability, and the intensity of removal of cuttings from under the cutter. Different investigators attach greater or lesser importance to each of these criteria.

In Fig. 4: vertical axis—“drilling speed, m/min”; horizontal axis—“feed force, kgf,” \(P_{\mathrm{п}}\). The curves are marked \(f=4\), \(f=6\), \(f=8\), \(f=10\), \(f=12\). The dashed boundary is labeled as the “zone of speeds limited by the maximum permissible feed forces according to data of various investigators.”

Fig. 4.

Of the geometric elements of the cutter, the clearance angle can above all affect the maximum drilling speed. This circumstance is taken into account by many investigators. The point is that, at large specific feeds per revolution, contact of the rear face of the cutter with the bottom of the blasthole may occur. The latter will cause the need for additional feed forces and machine power to overcome the forces of friction and crushing of the rock by the rear face of the cutter, that is, it will lead to a decrease in the rate at which drilling speed increases with feed force.

During drilling, the cutter moves both along its own axis and around it. The angle of inclination of the helical path of motion of the cutter is not constant with respect to the radius; it decreases toward the periphery and increases toward the center of the cutter. The point angle (sharpening angle), however, is made identical along the entire length of the blade. It follows from this that, when the depth of penetration of the cutter per revolution is increased, the land of the rear face of the cutter may begin to touch the bottom with portions located closer to the center. A further increase in feed will cause the entire rear face to touch the bottom. To eliminate the possibility of contact between the rear face of the cutter and the bottom in the middle part of the cutters, near the center of their rotation, a slot is made. The size of the slot is evaluated by the slot diameter \(d_{\mathrm{p}}\).

The maximum value of the feed per revolution \(h_{\max}\), taking into account the diameter of the relief slot, at which the cutter operates without the rear face touching the bottom of the hole, can be determined by the formula

\[ h_{\max}=\pi d_p \tan \beta, \tag{5} \]

where \(\beta\) is the rear sharpening angle of the blade of the drilling tool. The rear angle \(\beta\) of cutters of type \(P_{\text{p}}\), currently manufactured, is \(18^\circ\), and the diameter of the relief slot is \(d_p=6\) mm. For this case \(h_{\max}=6.1\) mm. With such a feed per revolution, the proportional dependence \(V=f(P_{\text{p}})\) may be violated. Taking this into account, for rotation speeds of 200–400 rpm, which are most widely used in rotary drilling of blastholes, the maximum drilling speed at \(h_{\max}\) will be 610 and 2440 mm/min. Thus, the linear dependence \(V=f(P_{\text{p}})\) will be preserved only up to the indicated drilling speeds.

Increasing \(h\) beyond \(h_{\max}\) will lead to a sharp increase in \(A_{\text{ob}}\), since in this case a considerable part of the energy will be expended irrationally—on crushing and abrasion of the bottom by the rear face of the cutter. An increase in \(A_{\text{ob}}\) may also occur earlier owing to deterioration of the conditions for removing the destroyed fines. This has been recorded by some investigators [8, 25].

Figure 5 presents the dependence \(V=f(P_{\text{p}})\) in the most general form, taking into account the influence of contact of the cutter along the rear face at large specific feeds. Point \(A\) corresponds to the beginning of contact of the rear face of the cutter with the bottom (along the relief slot), and point \(B\) to contact of the rock with the entire rear face of the cutter.

Operation in zone IV is inadvisable, since it is associated with considerable feed forces.

It should be noted that contact of the bottom by the entire area of the rear face of RP cutters can occur only at very large specific feeds of the cutter, i.e., at very high drilling speeds. Thus, for a drill rotation speed \(n=200\) rpm, the corresponding drilling speed will be 8600 mm/min, and for \(n=400\) rpm, respectively, 17200 mm/min. In practice such drilling speeds cannot be obtained with modern drilling machines.

Fig. 5.

The maximum values of the feed forces, and consequently also the possible drilling speeds, will also be limited by the strength of the drilling tool. According to various investigators [2, 9, 25], for the existing drilling tool of 42 mm diameter, faced with hard alloy VK-8, VK-15, the axial force should not exceed 1200–1500 kg. These recommendations were made for the case of drilling the strongest rocks (\(f=8\) and higher), when destruction of the tool occurs mainly as a result of the axial force during contact of the tool with the rock. With lower rock strength

a great danger to the strength of the tool will be posed by the large torques required for shearing off a large chip.

Our investigations [2] have established that, for one and the same feed force, the magnitude of the torque is the greater, the lower the rock strength (Fig. 6). At the same time, the amplitude of torque oscillations increases and, consequently, the dynamic loads on the tool blades also increase; these loads have a decisive effect on the durability of the drilling tool. This, in part, explains why the recommended feed forces are the smaller, the lower the strength of the rock. Thus, if for rock with \(f > 10\) a feed force \(P_{\text{п}} = 1200\text{--}1500\) kg is recommended, then for \(f = 8\text{--}10\) it is reduced [9] to 800–1000 kg; for \(f = 6\text{--}7\) [19] to 750–800 kg, and for \(f = 4\text{--}5\) [15] to 400–500 kg.

Fig. 6. Zone of variation of the torque required for rotating the bit in rotary drilling: 1—sandstone and granite, 2—crown No. 4, \(d = 42\) mm.

On the basis of the data presented, the dependence of the maximum permissible feed forces on the coefficient of strength of rocks has been constructed for existing cutters of the RP type (Fig. 7).

This dependence can be used in designing special electric and pneumatic drills (intended for particular conditions), and also for substantiating the power of drill motors.

The creation of stronger materials for reinforcing cutters used in rotary drilling will, undoubtedly, make it possible to increase the limits of the maximum permissible feed forces indicated in Fig. 7 and, consequently, the drilling speeds. With stronger hard-alloy plates, it will also become possible to reduce the sharpening angle of the cutters and to increase the specific feed of the cutters per revolution.

Removal of drilling fines from under the cutter may also have a substantial influence on the upper limit of the linearity of the function \(V = f(P_{\text{п}})\). This circumstance is pointed out by many researchers [2, 8, 25].

The practice of drilling blastholes with flushing points to certain difficulties in its use at high drilling speeds, when large water expenditures are required to remove drill cuttings. It turns out that the amount of water supplied to the blasthole is substantially limited

Fig. 7.

by the capabilities of modern drilling tools and flushing devices (the through-flow cross sections of the internal channels of drill rods and bits, the supply couplings and hoses, etc.). Consequently, improving the quality of bit material and improving methods for removing drill cuttings from the blasthole will make it possible to expand the range of appropriate feed forces and possible drilling speeds.

Influence of the Rotational Speed of the Tool

At a constant feed force, the drilling speed of rock increases with an increase in the number of revolutions of the tool per minute, \(n\). Most researchers \([9, 12, 19, 22, 26]\) have established that a considerable increase in drilling speed is observed only up to a certain limiting value of the number of revolutions, after which the drilling speed begins to increase more slowly, reaches a maximum, and, with a further increase in the number of revolutions, even decreases.

This dependence is shown most clearly in the work of V. S. Fedorov \([24]\) (Fig. 8). Curves 1, 2, 3 correspond to feed forces \(P_1 > P_2 > P_3\). Such a change in drilling speed occurs as a result of the fact that the feed of the tool per revolution of the bit decreases as its rotational speed increases \([19]\), despite the fact that the dimensions of the tool and the magnitude of the feed force remain unchanged. There is no single opinion as to the physical essence of the phenomena which

Fig. 8. Dependence of drilling speed on the rotational speed of the drilling tool according to V. S. Fedorov.

lead to a decrease in the feed per revolution as the rotational speed of the cutter increases.

Increasing the rotational speed of the tool in order to attain maximum drilling rates is advisable only up to a certain limit (Fig. 8). These limits are characterized [9, 12, 19] by the so-called critical numbers of revolutions.

V. S. Fedorov and L. A. Shreiner indicate that the critical number of revolutions of the tool, \(n_{\text{cr}}\), depends on the feed force and the hardness of the rocks. With an increase in rock hardness, \(n_{\text{cr}}\) decreases; with an increase in feed force, \(n_{\text{cr}}\) increases somewhat. These conclusions are confirmed by the majority of experimental studies.

The rotational speed of the drill also has a substantial effect on the energy intensity of the breaking process. The minimum energy intensity corresponds to the maximum drilling rate for the given rock and the given feed force and to the critical number of revolutions of the drill. Both an increase and a decrease in the number of revolutions relative to the optimum value lead to an increase in energy consumption. With an increase in the mechanical strength of rocks, the minimum energy consumption corresponds to a smaller absolute number of revolutions.

Using the recommendations of researchers [7, 9, 11, 12, 18, 19, 22], it is possible to trace the dependence of the critical numbers of revolutions on the strength of the rocks being drilled. Table 3 gives the numbers of revolutions of the tool per minute recommended by various researchers for drilling different rocks as the most advantageous from the standpoint of drilling rates and minimum tool wear. These data served for a graphical representation of the dependence of interest to us, Fig. 9.

Fig. 9. Zone of optimum rotational speeds of the drilling tool as a function of rock strength.

Despite a certain scatter, the points plotted on the graph, Fig. 9, make it possible to trace the dependence \(n_{\text{cr}}=\varphi(f)\), which is represented by a certain zone. We have bounded this zone by curves which, in our opinion, show the range of maximum and minimum values of the optimum numbers of revolutions of the drilling tool in rotary drilling of blastholes.

Undoubtedly, this dependence requires refinement on the basis of additional experimental data. However, even now the zone of the most advantageous numbers of revolutions indicated in Fig. 9 may be recommended for practical use in the design of rotary drilling machines, and also in the selection of economically advantageous drilling regimes with mass-produced drills.

As a first approximation, the dependence of the mean value of the optimal

Table 3

of the number of revolutions as a function of the rock strength \(n_{\text{opt}}=\varphi(f)\) can be described by the formula

\[ n_{\text{opt}}=\frac{C}{f}, \tag{6} \]

where \(C\) is a constant coefficient.

If \(f\) is regarded as a dimensionless coefficient, then

\[ C=\frac{n}{f}\left[\frac{\text{rev}}{\text{min}}\right]. \]

For the conditions given in Table 3, the value of \(C\) varies from 3500 to 1200 rev/min. On average, for calculations, the value of this coefficient may be taken as equal to 2200 rev/min.

Thus, with a certain approximation one may assume that

\[ n_{\text{opt}}=\frac{2200}{f},\ \text{rev/min}. \tag{7} \]

The optimum numbers of revolutions calculated by formula (7) (dotted line in Fig. 9) agree sufficiently well with the average

values of the recommended quantities for rocks with \(f = 2 \div 10\). For rocks of greater strength, the calculated quantities prove to be somewhat overestimated.

Energy Intensity of Rotary Drilling

The physicomechanical properties also exert a substantial influence on the magnitude of the energy intensity of the destruction process. It has been established experimentally [26] that the volumetric work of destruction depends linearly on compressive strength \(\sigma_{\mathrm{comp}}\) and on indentation hardness (Fig. 10, a, b).

Fig. 10. Dependence of the volumetric work of destruction on the strength of rocks.

On this basis, one may write

\[ A_{\mathrm{vol}} = \delta_1 \cdot \sigma_{\mathrm{comp}} \]

or, knowing that \(\sigma_{\mathrm{comp}} = 100 f\), we obtain

\[ A_{\mathrm{vol}} = \delta \cdot f, \tag{8} \]

where \(\delta_1\) and \(\delta\) are proportionality coefficients, \(\delta = 100\delta_1\).

In the present case, the volumetric work of destruction is understood to mean its minimum possible value, obtained under drilling regimes that are most rational for the given rock.

On this basis, and having at our disposal numerous experimental data on the selection of expedient regimes for rotary blasthole drilling [1–26] in various rocks, we shall attempt to find the value of the coefficient \(\delta\) in (8).

Table 4 summarizes the recommendations of various investigators on rational drilling regimes for rocks differing both in mechani-

Table 4

Continuation of Table 4

...mechanical strength (from \(f = 1.8\) to \(f = 17\)), as well as in mineralogical composition.

The minimum specific volumetric work of destruction for all cases was calculated by us from the formula

\[ A_{\mathrm{vol}} = 6.12 \frac{N}{V S_{\mathrm{h}}}, \ \mathrm{kgm/cm^3} \tag{9} \]

where \(N\) is the power expended on drilling, W;
\(S_{\mathrm{h}}\) is the cross-sectional area of the blasthole, \(\mathrm{cm^2}\);
\(V\) is the drilling rate, \(\mathrm{cm/min}\).

On the basis of Table 4, in Fig. 10, c, the results of calculations of \(A_{\mathrm{vol}}\) as a function of \(f\) are plotted. Despite the considerable scatter of points, the dependence between \(A_{\mathrm{vol}}\) and \(f\) can, with some approximation, be represented as linear.

The scatter of the data is apparently due to a number of causes: the differing approaches of various investigators to determining the power expended on drilling; imperfections in the recording apparatus used; and, chiefly, the extreme variability of the mechanical properties of the rocks being drilled, even when drilling a single blasthole. Thus, according to G. N. Pokrovskii [19], errors in measuring the basic parameters of the drilling process amount to 20–30% of the result. Taking all this into account, we believe that for practical calculations one may use dependence (8), taking the average value of the coefficient \(\delta\) equal to \(2.8 \ \mathrm{kgm/cm^3}\).

Then

\[ A_{\mathrm{vol}} = 2.8 f \tag{10} \]

(\(2.8\) was taken as the arithmetic mean of 29 values of \(\delta\) corresponding to the rocks and drilling regimes indicated in Table 4). The mean error in determining \(\delta\) from the data of Table 1 is \(\pm 25\%\), that is, in magnitude it corresponds to the error of measurement of the basic drilling parameters.

The dependences of the volumetric work of destruction in drilling marble [2] on the feed force for cutters of different diameter are presented in Fig. 11, a.

It is seen from Fig. 11, a, that the character of the variation of \(A_{\mathrm{vol}} = f(P_{\mathrm{p}})\) is the same in both cases, but in quantitative terms the larger diameter corresponds to the greater volumetric work of destruction. Moreover, as the feed force increases, the difference in the values of the volumetric work decreases. This is apparently explained by the fact that at the periphery of a cutter of larger diameter, as the feed force increases, chipping of larger particles occurs.

On the basis of our data [2], which indicate that in order to maintain a constant drilling rate as the length of the cutter blade increases it is necessary to increase the feed force proportionally, and of G. N. Pokrovskii’s assertion [19] regarding the constancy of chip size with respect to the cutter diameter, it may be assumed that the energy intensity of the destruction process, other conditions being equal, is directly proportional to the cutter diameter.

The geometry of the drilling tool has a significant effect on the energy intensity of the destruction process. The dependence of the volumetric work of destruction [2] on the magnitude of the blasthole deepening per one revolution of the drill when drilling with various cutters (bits) is presented in Fig. 11, b. Bit No. 1 is an ordinary single-chisel bit intended for percussive-rotary drilling. Its main characteristic is the absence of kerfing and a negative front angle of \(55^\circ\). Bit No. 2 is of the type...

RP-2 with a front angle of \(0^\circ\) and with a kerf. Bit No. 4 differs from bit No. 2 by the presence of a front negative angle \(\beta = -25^\circ\).

The presence of a front negative angle leads to an increase in the volumetric work of destruction (Fig. 11, b). The use of bit No. 1 in compar-

Fig. 11. Dependence of the volumetric work of destruction on the feed force (a), hole deepening per revolution (b), and on the degree of thread wear (c) and (d).

ison with bit No. 2 increases the volumetric work of destruction by a factor of 3. From the standpoint of achieving the minimum volumetric work of destruction, a reduction in the cutter sharpening angle is extremely advantageous. But this can be accomplished only by using a strong material for reinforcing the cutters. Cutter blunting also has a great influence on the energy intensity of destruction, and the latter occurs the more intensively, the smaller the sharpening angle.

The geometry of the cutter must provide it with maximum durability at minimum energy expenditure for destruction. Therefore, the tendency that has recently become widespread of creating cutters for rota-

... of drilling with a negative rake angle within the limits \((-5^\circ)\div(-15^\circ)\) is indisputably correct.

The effect of cutter blunting on the energy consumption of breaking is shown in Fig. 11, v, g, according to our data [2] and those of G. N. Pokrovskii [19].

With an increase in feed force, as well as with a decrease in the rotational speed of the drill, the intensity of increase in the volumetric work of breaking due to blunting decreases. This, apparently, is explained by the influence of the scale factor. Hence it may be concluded that, up to a certain reasonable limit, it is advantageous to use a blunted cutter when applying considerable feed forces.

Power of drilling machines

The power of machines required for drilling rocks of different hardness may be determined from formula (9), if the values of the energy consumption of the breaking process are known.

For a rational drilling regime, when the optimum number of revolutions of the drill is used, in formula (9) \(A_{\mathrm{ob}}\) may be replaced by \(A_{\mathrm{ob}\min}\), but since \(A_{\mathrm{ob}\min}=2.8f\), then, substituting this expression into (1), we obtain

\[ 2.8f = 6.12\,\frac{N}{S_{\mathrm{sh}}\cdot V} \]

or

\[ N = 0.465\cdot S_{\mathrm{sh}}\cdot V\cdot f. \]

When determining the power of the drill motor \(N_{\mathrm{dv}}\), it is necessary to take into account its efficiency \(\eta\); then

\[ N_{\mathrm{dv}}=\frac{0.465\cdot S_{\mathrm{sh}}\cdot V\cdot f}{\eta}. \tag{11} \]

If \(S_{\mathrm{sh}}\) is taken as constant, then \((0.465\cdot S_{\mathrm{sh}})\) in (11) may be denoted by the coefficient \(A\); then

\[ N_{\mathrm{dv}}=\frac{A\cdot V\cdot f}{\eta}. \tag{12} \]

Substituting into expression (12) the velocity \(V\), according to formula (1), we obtain

\[ N=\frac{A\cdot \kappa\,(P_{\mathrm{p}}-P_0)\cdot f}{10\eta}. \tag{13} \]

The power of drill motors is determined mainly by the maximum permissible feed forces and by the hardness of the rocks. In this case, in formula (13) \(P_{\mathrm{p}}\) should be replaced by \(P_{\mathrm{p}\max}\); then

\[ N_{\mathrm{neobkh}}=\frac{A\cdot \kappa\,(P_{\mathrm{p}\max}-P_0)\cdot f}{10\cdot \eta}. \tag{14} \]

When designing universal drills intended for drilling the entire range of rocks in hardness from 2 to \(f=12\), it is apparently necessary to take as \(P_{\mathrm{p}\max}\) its value for the strongest rocks.

The dimension of the constant coefficient \(A\), from \(A=0.465\,S_{\mathrm{sh}}\,\dfrac{\mathrm{W}\cdot\mathrm{min}}{\mathrm{cm}}\), is, that is, the dimension of the volumetric work of breaking per unit length of blasthole.

Therefore, the coefficient \(A\) may be called the volumetric work of breaking per unit length of blasthole when drilling rocks with a hardness coefficient equal to unity.

For standard cutters of the RP-2 and RP-7 types with a diameter of 42 mm,

\[ A = 0.465 \frac{\pi \cdot 4.2^2}{4} = 6.45 \frac{\mathrm{W}\cdot\mathrm{min}}{\mathrm{cm}}, \]

then

\[ N_{\mathrm{eng}} = 0.645 \frac{\kappa \cdot f\,(P_{\mathrm{p}\,\max} - P_0)}{\eta},\ \mathrm{kW} \tag{15} \]

This formula can be used in calculating the power of drill motors for various mining-engineering conditions.

Table 5 summarizes data from various investigators on the drilling speed of various rocks and the power required for this.

Table 5

On the basis of these data, relationships were plotted for drilling speed as a function of the strength coefficient of the rocks (Fig. 12). Each curve in Fig. 12 corresponds to a certain power consumed by the drill motor. As rock strength increases, the drilling speed decreases sharply. It also depends to a considerable degree on the power of the motor, especially for rocks with a strength coefficient below \(f = 10—12\). For rocks with \(f = 14\), an increase in motor power increases the drilling speed to a lesser extent. The conclusions of many researchers—that with the existing drilling tool the advisable range of application of rotary drilling is limited by a rock strength of \(f = 14\)—are well illustrated by Fig. 12. The drilling speeds for rocks with \(f = 14\) can be substantially increased if, in all cases, drilling is carried out with feed forces of about 1200 kg.

For the indicated limiting feed forces, using formula (1), it is possible to calculate the maximum possible drilling speeds for various rocks. The results of such calculations are given in Table 6.

On the basis of the data in Table 6, curve 1 was plotted in Fig. 13, showing the limit of possible drilling speeds with allowance for the durability of the drill bits used.

Fig. 12. Relationships of drilling speed to rock strength at various powers expended on drilling.

In the figure: vertical axis—drilling speed, mm/min; horizontal axis—rock strength coefficient, \(f\). Curve legend: 1.5 kW; 1.8 kW; 2.4 kW; 3.0 kW; 4.0 kW.

It was shown earlier that it is advisable to increase the feed force only until the cutter touches, with its rear face,

Table 6

the bottom of the blasthole. Knowing the maximum values of feed per one revolution of the bit, \(h_{\max}\), established from this condition, and the optimal bit rotation speeds \(n_{\text{opt}}\), it is possible to calculate, for various rocks, the maximum permissible drilling speeds from the standpoint of normal operation of the cutter, i.e., without contact between its rear face and the bottom. The results of such calculations are given in Table 7.

According to the data of Table 7, curve 2 in Fig. 13 has been constructed. Comparing curves 1 and 2, it can be established that for rocks with a strength coefficient up to \(f = 6\), the maximum possible drilling speeds are limited by the geometry of the tool; that is, any further increase in drilling speeds by increasing the feed force leads to contact of the rear face of the cutter with the bottom, with all the resulting consequences. Hence, for such rocks it is advisable to use cutters with a large clearance angle (with a smaller sharpening angle \(\gamma\)) than that of RP cutters.

For rocks with \(f > 6\), the limit of possible drilling speeds is determined by the strength of the drilling tool. In these cases (especially when drilling rocks with \(f > 10\)), it is evidently advisable to increase the strength of the blades and thereby also increase the drilling speed by reducing the clearance angle and creating a negative rake angle. This is also confirmed by the results of experimental work [18].

Fig. 13. Limitations of maximum drilling speeds.

Table 7

We have already noted that the feed force and the geometry of the tool create only the conditions for the destruction of rocks with one or another intensity. To carry out the actual destruction of the rock, however, a certain power is required, which is transmitted to the drilling tool from the motor of the drilling machine. The motor power of existing drilling machines in many cases substantially limits the drilling speed. Indeed, the power of the motors of drills currently being produced does not exceed 3 kW. To create the feed force, only a very small power is expended [8]. Together with losses in the motor and gearbox, in column-type drills it may be taken as 0.3–0.5 kW. Thus, up to 2.7 kW remains for creating torque. For hand drills this value is smaller and amounts to about 1 kW.

Table 8 presents data from various researchers on the magnitudes of torques required for drilling various rocks

Table 8

Continuation of Table 8

of rocks at various specific feeds per revolution. From these data, in Fig. 14 we plotted the dependences $M_{\mathrm{cr}} = \varphi$ for identical specific feeds per revolution.

Fig. 14.

Taking into account the power values of the motors of modern core and hand drills $N$ and the optimal rotational speeds recommended above, it is possible to calculate the torques that can be developed by these drills when drilling various rocks. The results of such calculations are presented in Table 9.

Table 9

According to the data in Table 9, in Fig. 14 lines I and II have been plotted, determining the possible feeds per revolution of the bit, respectively, for drills with rotational powers of 2.7 kW and 1.0 kW. These lines substantially limit the values of the specific feeds that can be used in drilling various rocks without overloading the drill motors. In Fig. 4 we plotted the values of the maximum drilling rates that can be achieved by existing drill designs having motors with a power of 2.5–3 kW.

Thus, the curve \(N—M\) characterizes the zone of “potential capabilities” of existing drilling machines. With a further increase in the power of the motors of drilling machines (and a corresponding increase in the feed forces), the zone of potential capabilities will expand.

Using the data of Fig. 14, it is possible, with a certain approximation, to find the maximum possible values of the specific feeds for rocks of different hardness; then, knowing the optimum numbers of revolutions for these rocks, it is easy to calculate the maximum possible drilling rates limited by motor power. The values of the maximum permissible specific feeds calculated in this way and the corresponding drilling rates are given in Table 10.

Table 10

On the basis of these data, curves 3 and 4 have been constructed in Fig. 13. Analyzing the relationships obtained, one may conclude that the drills currently used, with motor powers of 2.7 kW for drilling rocks with \(f\) up to 8, do not use all the capabilities of modern tools for increasing drilling rates. This applies to an even greater extent to hand drills with a drive power of 1 kW.

For more complete utilization of the capabilities of the tool, on the basis of the data of Fig. 13, it would be advisable to increase substantially the drive power of drilling machines for drilling blastholes in rocks with hardness up to \(f = 8\).

In drawing this conclusion, we take into account the recommendations of various authors on reserves for increasing the specific feed, based on the strength of the tool (cutters).

The use of the reserve indicated above will lead to substantial specific feeds and, consequently, to substantial torques on the drilling tool. The values of these torques in a number of cases may exceed those permissible with respect to the strength of the tool. Therefore Fig. 13 should be supplemented with data limiting the drilling rates by the permissible torques. Unfortunately, we do not have such data. Limitations on maximum

drilling speeds, from the condition of satisfactory removal of drill cuttings from the blasthole, are represented by curves 5—when using helical drill rods, and 6—when using flushing.

If the recommendations on permissible feed forces are taken into account, then, using formula 15, it is possible to determine the powers of drilling machines (Table 11) which, as a first approximation, may be recommended as limiting values for the existing drilling tool.

Table 11

On the basis of the data in Table 11, Fig. 13 gives the dependence of the required drilling power (curve 7) on the strength of the rocks being drilled.

Taking into account the permissible powers of drill bits (Fig. 13), the optimum numbers of revolutions (Fig. 8), and the permissible specific feeds per revolution, it is possible to determine the possible maximum drilling speeds for various rocks.

A few words should be said about the power of drilling machines intended for drilling rocks with $f = 2$. In Table 11 it is 1.2 kW. Such power provides a drilling speed, at optimum numbers of revolutions, of about 600 mm/min.

Such a low maximum permissible drilling speed gives grounds for concern as to the correctness of determining the required power for drilling rocks of low strength (18). In deriving formula (18), a number of approximations were adopted, one of which is the determination of $P_0$ as $35 f$. For rocks with $f = 4$ and higher, the value of $P_0$, calculated by formula (4), is considerably less than $P_{\mathrm{p\,max}}$, whereas for $f = 2$ they are comparable. The error thereby introduced evidently has a very substantial effect both on the determination of the permissible power of the drill bit and on the maximum drilling speed.

For rocks with $f = 2$, according to the data of investigations [7], volumetric crushing begins already at feed forces of 20–25 kg. Then, substituting $P_0 = 20$ kg instead of $P_0 = 35 f$, we obtain $N_{\mathrm{dv}} = 2.5$ kW; this motor power of the drill bit will correspond to a drilling speed of up to 2000 mm/min.

Such drilling speeds in rocks with $f = 2$ were achieved by investigators when using hand drills with the aid of a 1 kW motor. In this case, however, repeated overloads of the motor were observed. Thus, M. G. Krashivin [16] indicates that when drilling gypsum with $f = 1.8$–2.2 at a speed of 1.5–2.0 m/min (number of revolutions 1000 rpm), the drill motor is loaded up to 3.6–4.0 kW. Increasing the power of the motors of hand drills, however, is hardly advisable, since it will considerably increase the weight of the drills, in fact nullify their main advantage—high maneuverability—and turn work with such drills into one of the heaviest kinds of manual labor. Therefore we believe that, for hand drills, the rotational speeds of the bit should be limited to 500–600 rpm, the motor powers to 1.2–1.4 kW, and these machines should be used only for a small volume of drilling work. For a large

volume of drilling operations in breaking rocks even of low strength, \(f \simeq 2\), more powerful drills should be developed, with special devices for setting them at the face and for feeding them during drilling. In this case it will be expedient to use high drill rotation speeds (on the order of 1100 and more rpm) and motor powers on the order of 2.0–2.5 kW. Undoubtedly, the drive power of drills that is more precisely expedient must be established with allowance for the convenience of operating machines of one design or another, under particular conditions. This problem can be solved by studying the designs of drilling machines and the conditions of their application.

The analysis carried out of the basic parameters of the rotary method of drilling blastholes, taking into account the experimental data of many investigators, enables us to recommend, as a first approximation, rational drilling regimes for rocks of different strength (Table 12).

Table 12

*) In the numerator is the average value of the drill speed; in the denominator, the optimal zone.

The regimes given in Table 12 can be achieved with reliable cleaning of the blasthole bottom from drill cuttings (by flushing, blowing) and with the use of sharp cutters. In the present work the question of cutter wear was not considered, but the data available in the literature on this question have been studied by us. They make it possible to conclude that, for all rocks with a strength coefficient in the range \(f = 2 \div 12\), the serviceability of cutters (the number of hole-meters drilled before the appearance on the blades of a blunting land 3 mm wide), under rational drilling regimes, is 2 or more running meters. It follows from this that, under such conditions, each blasthole can be drilled with a sufficiently sharp cutter and, in the course of drilling the blasthole, no time will be required for changing the tool.

The intensity of removal of drill cuttings from a blasthole has a significant effect on the drilling rate and energy consumption. If the bottom is not cleaned in time of the products of destruction, they are additionally crushed by the tool and the drill rod, which leads to additional power consumption and a reduction in drilling rate. The most effective methods for cleaning blastholes are air blowing and flushing. According to M. K. Tsekhin [25] and A. N. Volkov [9], the use of water flushing of a blasthole to remove drill cuttings makes it possible substantially to increase the rate and reduce the energy consumption of drilling, as compared with removal of drill cuttings by auger rods. M. K. Tsekhin and A. N. Volkov recorded cases in which the use of intensive flushing made it possible to reduce the energy consumption of drilling by a factor of 2. An even greater effect can be obtained when drill cuttings are removed from the blasthole by compressed air [23]. In practice, preference is still given to flushing, because air blowing without additional devices for capturing drill cuttings is harmful from the standpoint of hygiene.

A further increase in drilling rates, with a simultaneous reduction in the energy consumption of the breaking process, can be achieved only on condition that the problem of intensive removal of drill cuttings from the blasthole is solved radically. For this purpose, along with further improvement of methods for removing drill cuttings by flushing the blasthole with water, it is necessary to improve and develop such methods as blowing the blasthole with compressed air and with an air–water mixture, as well as methods for extracting air together with drill cuttings from the blasthole.

Conclusions

1. A considerable amount of experimental data on the study of the rotary method of drilling blastholes makes it possible to carry out certain generalizations in order to identify relationships among the principal parameters of the drilling process through empirical coefficients.

The relationships thus established between the drilling rate \(V\), the feed force \(P_{\text{p}}\), the number of revolutions of the bit \(n\), the rock-strength coefficient \(f\), the volumetric work of breaking \(A_{\text{ob}}\), and the power of the drill motor \(N_{\text{dv}}\) make it possible, with a sufficient degree of accuracy, to perform calculations of drilling conditions.

1. Refinement of the empirical coefficients identified in the present work is a very important task and can be accomplished by carrying out special studies.

2. An increase in the productivity of rotary drilling machines can be achieved by applying rational operating conditions, improving the drilling tool, and improving the designs of the machines themselves.

References

1. V. L. Azarkh, A. D. Imas, O. P. Shumovskii. Determination of Drilling Conditions for Handheld Electric Drills. Ugletekhizdat, 1952.

2. O. D. Alimov. Investigation of Rock-Breaking Processes in Blasthole Drilling. Publishing House of Tomsk University, 1960.

3. O. D. Alimov, I. G. Basov, V. F. Gorbunov, D. N. Malikov. Drilling Machines. Gosgortekhizdat, 1960.

4. O. D. Alimov, L. T. Dvornikov. Long-stroke electric drill with hydraulic feed. In: Improvement of Coal Production, Kemerovo, 1963.

5. O. D. Alimov, N. S. Kolodyazhnyi, V. N. Karminskii. On the design of long-stroke electric drills with mechanical feed. Proceedings of Higher Educational Institutions, Mining Journal, no. 2, 1963.

1. V. K. Buchnev. Drilling-and-blasting operations. Ugletekhizdat, 1951.

2. G. P. Vereskunov. Investigation of rotary blasthole drilling regimes in hard rocks. Author’s abstract of dissertation, Dnepropetrovsk, 1955.

3. A. A. Volkov. Investigation of the electric drive of column-mounted electric drills. Candidate dissertation. Kharkov, 1955.

4. A. N. Volkov. Substantiation and selection of the principal parameters of drilling machines by rock for mines of the Prokop’evsk–Kiselevsk district of Kuzbass. Candidate dissertation, Prokop’evsk, KuzNIUI, 1958.

5. F. M. Gelfand, L. D. Markman. Investigation of the net drilling rate in the electro-rotary method of drilling blastholes. Scientific Transactions of KNIUI, collection 3, Ugletekhizdat, 1958.

6. V. F. Zimin, V. F. Borovkov, E. I. Soldatov. Rotary drilling of rocks at bauxite mines. Mining Journal, No. 8, 1962.

7. A. D. Imas. Work on introducing rational technological regimes for the destruction of coals and side rocks by mining machines. In: Destruction of Coals and Rocks, Ugletekhizdat, 1958.

8. A. D. Imas, V. L. Azarkh. Determination of drilling regimes for rocks. TsITI, Ugletekhizdat, 1952.

9. P. N. Iudin. Application of electric drills for drilling blastholes in rocks. TsITI-uglestroy, Ugletekhizdat, 1957.

10. N. S. Kolodazhnyi. Investigation and creation of long-stroke electric drills. Candidate dissertation, Tomsk, 1963.

11. M. G. Krapivin. On the parameters of self-propelled drilling units for blasthole drilling in underground extraction of rock salt and gypsum. Information letter on a conference on problems of rock destruction, May 20–22, 1958, IGD, Moscow, 1959.

12. I. F. Medvedev, M. N. Smolyaninov, V. I. Tyurin. Electric drill with hydraulic feed ESGP-4. In: New equipment for drilling blastholes and boreholes, TsITI uglya, 1960.

13. V. G. Mikhailov. Investigation of blasthole drilling. Doctoral dissertation, Tomsk, 1940.

14. G. N. Pokrovskii. Investigation of the process of rock destruction in rotary blasthole drilling with constant feed force. Candidate dissertation, Novosibirsk, 1954.

15. M. M. Protodyakonov. Materials for a schedule standard for mining operations. Moscow, Publishing House of the Central Committee of Miners, 1926.

16. G. V. Rodionov. Column-mounted electric drill EK-2. Mining Journal, No. 3, 1938.

17. I. E. Rudavskii. Establishing rational limits for the application of the electro-rotary method of blasthole drilling in driving exploratory mine workings. Candidate dissertation, Moscow, 1960.

18. V. T. Sai. Experimental introduction of rotary blasthole drilling with flushing in Kuzbass. Novokuznetsk, 1958.

19. V. S. Fedorov. Scientific foundations of drilling regimes. State Scientific and Technical Publishing House of Petroleum and Mining Literature, 1951.

20. M. K. Tsekhin. Investigation of drilling-and-blasting operations and increasing their efficiency in driving horizontal workings through rock at the mines of the Prokop’evsk ore field. Candidate dissertation, Tomsk, 1955.

21. L. A. Schreiner. Physical foundations of rock mechanics. Gostoptekhizdat, 1950.