RELATIONSHIP BETWEEN FEED FORCE AND THE MAIN PARAMETERS OF A DRILLING HAMMER

O. D. Alimov

As established by experimental investigations [1—5], the drilling speed of a borehole with a pneumatic drilling hammer depends on a number of factors. One such factor is the feed force, by which is meant the force applied to the hammer body in the direction of drilling the borehole. It is produced either manually by the worker, when working with “hand-held” drilling hammers, or by special devices—in telescopic and column-mounted drilling hammers. How significant the effect of the feed force is on the drilling speed that can be provided by one and the same pneumatic impact-rotary machine is clearly seen from Fig. 1.

Fig. 1. Drilling speed of the PR-25 hammer as a function of feed force and air pressure. Air pressure:
1—4 atm; 2—5 atm; 3—6 atm.

As a result of studies of the process of rock destruction during impact-rotary drilling [1] and of the operating regimes of modern pneumatic drilling hammers [2—5], it has been established that the feed force does not participate directly in the penetration of the tool into the rock. However, it has a substantial

…a substantial influence on the magnitude of other external forces acting on the parts of the drilling hammer, on the course of the processes inside the drilling hammer, and, thus, indirectly affects the use of the machine’s power for the destruction of rock with one or another intensity.

In this connection, solving such problems is of definite practical interest: establishing the interrelation of the feed force with other external forces and with the basic parameters of the drilling hammer (impact energy, number of blows per minute, etc.); determining the magnitudes of feed forces that ensure the most productive operating regimes of the machine; and also identifying possibilities for increasing the power of the drilling machine without a significant increase in the feed force.

Interrelation of the Feed Force with Other External Forces and with the Basic Parameters of the Drilling Hammer

In solving the problem of the interrelation of the feed force with other external forces and with the basic parameters of the hammer analytically, for example by means of differential equations, researchers encounter considerable difficulties, since the processes occurring inside the drilling hammer are in a complex dependence both on the principal design parameters of the hammer and on the magnitude and character of the application of external forces. Most of the external forces acting on the hammer are impact forces, and their magnitude depends on a number of factors that are sometimes completely random. Therefore, in most cases the choice of the optimum feed force is made only for particular cases of operation of the drilling hammer. In designing drilling machines, empirical relationships are still used mainly to determine their principal parameters, including the feed force.

In our opinion, the problem posed above can be solved in general form on the basis of the impulse theorem. Let us consider the basic prerequisites for this.

A pneumatic drilling hammer may be regarded as a piston machine with a freely moving piston. When air is admitted into the various cavities of the hammer cylinder, the piston performs a reciprocating motion along the axis of the cylinder. The change in the direction of air admission is effected either by the piston itself or by a special distributing mechanism. The translational motion of the piston is partially converted into rotation about the longitudinal axis of the cylinder by means of a helicoidal pair built into the hammer.

When the possible displacement of the piston in the hammer cylinder is limited by an external body (the drill shank), the kinetic energy of the piston is transmitted by impact to the drilling tool. The latter, acting on the rock, destroys it. Constant…

co-impact of the striker piston with the drill can be ensured only for a definite value of the feed force.

To determine the relationship between the feed force and the main parameters of the machine, let us consider the drilling hammer as a system consisting of two masses—the mass of the hammer body and the mass of the striker piston. In doing so, we shall, conventionally, assign the masses of all parts of the air-distribution mechanism and of the rotation device to the mass of the hammer body. The external forces acting on the system will include the following (Fig. 2):

\(N\)—the reaction of the support, acting on the hammer body from the guides of the feed mechanism; when drilling horizontal blastholes, the magnitude \(N\) is equal to the weight of the hammer \(G = G_{\text{p}} + G_{\text{k}}\), where \(G\) is the total weight of the drilling hammer; \(G_{\text{p}}\) is the weight of the striker piston, and \(G_{\text{k}}\) is the weight of the hammer body;

Fig. 2. Calculation diagram.

\(F\)—the sum of the friction forces arising between the hammer body and the guides of the feed mechanism;

\(p_1\)—the force arising when the striker piston strikes the shank of the drill;

\(p_2\)—the contact force of the hammer body with the limiting collar of the drill;

\(p_3\)—the reactive force due to the discharge of air from the exhaust opening of the hammer;

\(p_4\)—the force acting on the hammer body from the air-supply hose;

\(p_{\text{п}}\)—the feed force.

In addition to the indicated external forces, moments act on the system:

\(M_1\)—the moment of resistance to rotation of the drill in the blasthole, applied to the rotary bushing of the hammer;

\(M_2\)—the moment acting on the hammer body from the guiding mechanism of the feeder.

The magnitude of the external forces and moments depends on the operating regime of the hammer, which, for identical air pressures, is determined mainly by the feed force [1—6].

For the system of bodies “hammer body—piston,” on the basis of the impulse theorem one may write:

\[ m v_{xt} - m v_{x0} = \int_{0}^{t} p_n\,dt - \int_{0}^{t} p_1\,dt - \int_{0}^{t} p_2\,dt - \int_{0}^{t} p_{3x}\,dt - \int_{0}^{t} p_{4x}\,dt - \int_{0}^{t} F\,dt; \tag{1} \]

\[ m v_{yt} - m v_{y0} = \int_{0}^{t} N\,dt - \int_{0}^{t} p_{3y}\,dt - \int_{0}^{t} p_{4y}\,dt - \int_{0}^{t} G\,dt, \tag{2} \]

where
\[ m = m_{\mathrm{p}} + m_{\mathrm{k}} \]
is the reduced mass of the drilling hammer;

\[ m_{\mathrm{p}} = \frac{G_{\mathrm{p}}}{g} \]
is the mass of the piston-striker;

\[ m_{\mathrm{k}} = \frac{G_{\mathrm{k}}}{g} \]
is the reduced mass of the hammer body;

\(v_x\) and \(v_y\) are the projections of the velocities of the center of gravity of the system under consideration onto the corresponding axes.

Using the theorem on angular momentum, we obtain

\[ J(\omega_t - \omega_0) = \int_{0}^{t} M_1\,dt - \int_{0}^{t} M_2\,dt, \tag{3} \]

where \(J\) is the moment of inertia of the system;
\(\omega_0\) and \(\omega_t\) are the angular velocities of rotation of the system about the \(xx\) axis.

Equations (1), (2), and (3) can be used to solve a number of specific problems. Thus, to determine the relationship between the feed force and the parameters of the impact unit of the machine, one may use equation (1), and to determine the interrelation of the torques developed by the hammer, equations (1) and (3).

In the present work we solve mainly the first problem; in doing so, equation (1) can be simplified on the basis of the following assumptions.

With a constant value of the drilling rate and a sufficiently long time interval in comparison with the duration of one cycle of piston travel, it may be assumed that the entire system “hammer body—piston” moves translationally along the \(xx\) axis with constant velocity. Then it may be considered that the quantity of motion of the system along the \(xx\) axis will also be constant, i.e., \(m v_{xt} - m v_{x0} = 0\). For these same conditions it may be assumed that the mean values of the forces \(p_n\), \(F\), \(p_3\), and \(p_4\) are constant in magnitude and direction.

Then

\[ P_{\mathrm{п}} t = \int_{0}^{t} p_{1}\,dt + \int_{0}^{t} p_{2}\,dt + Ct, \tag{4} \]

where \(P_{\mathrm{п}}\) is the average value of the feed force;

\[ C = F + p_{3x} + p_{4x}. \]

Thus, the impulse of the averaged feed force may be represented as the sum of three impulses, and the average value of the feed force as the sum of three components. To determine these components, let us consider the impulses entering the right-hand side of equation (4).

The impulse from the contact of the piston with the drill steel during their impact

\[ \int_{0}^{t} p_{1}\,dt \]

is characterized by a very short duration of the action of the force (of the order of 0.001–0.002 sec.) and by its considerable magnitude. The ratio of the time and force magnitudes depends on the masses of the colliding parts, their geometrical shapes, their velocities before impact, and also on the interaction of these bodies with other bodies (contact of the drill bit with the rock, the action of compressed air on the piston, etc.). It is rather difficult to take into account the influence of all these factors and to determine the numerical values of the force \(p_{1}\) and the time of its action. To solve the problem posed before us, it is necessary to know only the total magnitude of the impulse. It can be determined from the change in the momentum of the hammer piston upon its impact with the shank of the drill steel:

\[ \int_{0}^{t} p_{1}\,dt = m_{\mathrm{п}}v'_{\mathrm{п}} - m_{\mathrm{п}}v_{\mathrm{п}}, \]

where \(v_{\mathrm{п}}\) is the velocity of the piston before impact with the drill steel;
\(v'_{\mathrm{п}}\) is the velocity of the piston after impact.

Denoting \(v'_{\mathrm{п}} = k_{1}v\), where \(k_{1}\) is the coefficient of rebound of the piston, we obtain

\[ \int_{0}^{t} p_{1}\,dt = m_{\mathrm{п}}v_{\mathrm{п}}(k - 1). \]

Experimental investigations [2, 6, 9] show that, when a pneumatic drilling hammer operates in the most characteristic modes, rebound of the piston from the shank of the drill steel is, as a rule, not observed. For these cases one may take \(k = 0\),

\[ \int_{0}^{t} p_{1}\,dt = -m_{\mathrm{п}}v_{\mathrm{п}}. \]

By the mean-value theorem one may write

\[ \int_0^t p_1\,dt = P_1't, \]

where \(P_1'\) is some mean value of the function in the interval from \(0\) to \(t\).

Then

\[ P_1't = -m_{\text{p}}v_{\text{p}}. \]

Hence the mean value of the force acting on the “hammer body—piston” system from the impact of the piston with the drill steel is

\[ P_1' = -\frac{m_{\text{p}}v_{\text{p}}}{t}. \]

Taking the time \(t\) equal to the cycle time \(\tau = \frac{1}{n}\), where \(n\) is the number of blows per second, we obtain

\[ P_1' = -m_{\text{p}}v_{\text{p}}n. \]

As can be seen, the force \(P_1'\) is directed opposite to the velocity that the piston has before impact with the drill steel.

Proceeding from the condition we have adopted, namely that the change in the momentum of the system is zero, the sum of the impulses of the external forces acting on the system must likewise be equal to zero. Therefore, to compensate the action on the system of the force \(P_1'\), an equal force must be applied to this same system, but directed in the opposite direction. Such a force \(P_1\) is the part of the feed force that is applied to the hammer body,

\[ P_1 = -P_1' = m_{\text{p}}v_{\text{p}}n. \tag{5} \]

In what follows we shall regard the quantity \(P_1\) as the mean value of the first component of the feed force and shall call it the first component. Substituting into equation (5)

\[ v = \sqrt{\frac{2A}{m_{\text{p}}}}, \]

where \(A\) is the energy of the piston before impact with the drill steel, we obtain

\[ P_1 = m_{\text{p}}n\sqrt{\frac{2A}{m_{\text{p}}}} = n\sqrt{2Am_{\text{p}}}. \tag{6} \]

If the energy of the piston before impact is expressed through the principal parameters of the hammer,

\[ A = slp_{\text{av}}\eta, \]

where \(S\) is the piston area;
\(h\) is the piston stroke;
\(p_{\mathrm{av}}\) is the average value of the air pressure during the forward stroke;
\(\eta\) is the mechanical efficiency of the impact unit,

\[ P_1 = n \sqrt{2 s h m_{\mathrm{p}} p_{\mathrm{av}}\eta}. \tag{7} \]

From the formulas given above it is clear that, for the normal operation of a percussion machine, there must be a definite balance between the quantity of motion of the piston-striker before its collision with the external body and the impulse of one of the components of the feed force. When one of these quantities changes, the other must inevitably change as well.

Fig. 3. Kinetic energy of the piston, blow frequency, and rebound as functions of feed force. PR-25 hammer. Air pressure:
\(1\)—4 atm; \(2\)—5 atm; \(3\)—6 atm.

This conclusion is well confirmed by the results of investigations of the working process of drilling hammers [6–9].

Figure 3 presents experimental data on the change in blow energy, blow frequency, and the so-called “rebound”—the rebound of the body of the drilling hammer from the limiting shoulder of the drill shank—as a function of the feed force. The character of the dependences shown in Fig. 3 is inherent in all modern pneumatic drilling hammers. On the basis of these dependences, the influence of the feed force on the working process of the hammer may be represented as follows.

In the absence of feed force, after the very first blows on the shank of the drill the drilling hammer, owing to the impulse it has received, ...

the impulse of the external forces moves away from the limiting collar of the drill bit backward by such an amount that, in subsequent cycles of the piston, collision of the striker piston with the drill-bit shank does not occur and the hammer operates idly. Under this operating regime of the hammer, stopping of the striker piston in the extreme forward and rear positions occurs as a result of the action of internal forces in the “hammer body—piston” system, due to compression of the front and rear air buffers.

As the feed force is applied and further increased, the hammer body moves in the direction of the hole; the drill-bit shank enters the hammer cavity and limits the extreme forward position of the striker piston. The distance between the limiting collar of the drill bit and the hammer body—the “recoil”—decreases as the feed force increases. The values of the “recoils” shown in Fig. 3 were determined by the TPI method [10].

With a comparatively small feed force and a large “recoil,” part of the kinetic energy acquired by the piston in the first half of the working stroke is expended on compression of the front air buffer, while part is transmitted to the drill bit by impact. As the “recoil” decreases, an ever larger part of the kinetic energy of the piston is transmitted to the drill bit, and an ever smaller part is expended on compression of the front buffer. In most drilling hammers the length of the drill-bit shank is calculated from the condition that, when the “recoil” is reduced to zero, collision of the piston with the drill-bit shank is ensured at the maximum possible piston velocity.

When the drill-bit shank is introduced into the hammer body, the length of the piston stroke is shortened and the duration of the working and idle strokes of the piston is reduced; consequently, the blow frequency of the hammer increases. Thus, increasing the feed force up to a certain value (Fig. 3) leads to an increase in the kinetic energy transmitted to the drill bit and in the blow frequency. At the same time, the quantity of motion of the striker piston transmitted to the drill bit also changes.

The equilibrium noted above between the quantity of motion transmitted by the piston to the drill bit and the first component of the feed force exists at different “recoils” of the hammer body from the limiting collar of the drill bit.

The second component of the feed force, \(P_2\), is in turn related to the magnitude of the “recoil”; it must compensate for the effect on the system of impulses from contact between the hammer body and the limiting collar of the drill bit. At small values of feed force and large “recoils,” contact between the hammer body and the limiting collar of the drill bit may not occur, \(P_2 = 0\). When operating in such regimes, the total value of the feed force can be calculated by formula (5) or (6) with the addition of the constant force value \(C\). As the “recoil” decreases, collisions of the hammer body with the limiting collar of the drill bit begin; as a rule, they occur at the moment of the return stroke of the pis-

...the piston. Moreover, at small feed forces such impacts are repeated over several cycles of piston travel; as the feed force increases, the frequency of impacts increases, approaching the frequency of piston blows on the drill shank. With a further increase in the feed force, along with impacts, longer contacts of the drill collar with the hammer body are observed.

For cases in which the contact of the hammer body with the stop collar of the drill has the character of mutual impacts, the second component of the feed force \(P_2\) can be determined proceeding from the same assumptions that were advanced in determining the first component. Namely: the magnitude of the impulse \(\int_0^t p_2\,dt\) may be equated to the change in the momentum of the hammer body upon impact against the stop collar of the drill.

\[ \int_0^t p_2\,dt = -\left(m_k v'_k - m_k v_k\right) = m_k v_k (K_2 - 1), \]

where
\[ \begin{aligned} v_k &\text{ is the velocity of the body before impact with the drill;}\\ v'_k &\text{ is the velocity of the body after impact with the drill;}\\ K_2 &\text{ is the coefficient of restitution in the impact of the hammer body}\\ &\text{ against the stop collar of the drill.} \end{aligned} \]

Taking \(K_2 = 0\) and replacing

\[ \int_0^t p_2\,dt = P'_2 t, \]

where \(P'_2\) is a certain mean value of the function over the interval from \(0\) to \(t\), we have:

\[ P'_2 t = -m_k v_k; \]

\[ P'_2 = -\frac{m_k v_k}{t}. \]

For \(t=\tau=\dfrac{1}{n}\), the second component of the feed force is

\[ P_2 = -P'_2 = m_k v_k n. \tag{8} \]

For the indicated particular case, the velocity of the hammer body before impact with the drill collar can be determined from the formula

\[ v_k = v_p - \frac{m_p s' p'_{\mathrm{av}}}{m_k s p_{\mathrm{av}}}, \]

where \(s'\) and \(s\) are, respectively, the cross-sectional areas of the front and rear cavities of the hammer cylinder;
\(p'_{\mathrm{av}}\) and \(p_{\mathrm{av}}\) are, respectively, the mean air pressures in the front and rear cavities of the cylinder.

Substituting these values into formula (8), we obtain

\[ P_2 = m_{\mathrm{p}} v_{\mathrm{p}} n \left(\frac{s' p'_{\mathrm{av}}}{s p_{\mathrm{av}}}\right). \tag{9} \]

The third component of the feed force \(C\) must compensate for the action on the system of the sum of the forces \(F_1 p_{3x}\) and \(p_{4x}\). The friction force depends on the design of the feeding mechanism and the operating conditions. With permissible accuracy it can be determined as \(F = fN\), where \(f\) is the coefficient of friction when the machine body moves along the feeder guides.

The reaction from the outflow of air from the exhaust openings of the hammer can be determined by the formula

\[ p_3 = \frac{\gamma_{\mathrm{v}} Q_{\mathrm{v}}^2}{g \delta}, \tag{10} \]

where
\(\gamma_{\mathrm{v}}\) is the specific weight of air \((\gamma_{\mathrm{v}} = 1.25\ \mathrm{kg}/\mathrm{m}^3)\);
\(Q_{\mathrm{v}}\) is the air flow rate per second, \(\mathrm{m}^3/\mathrm{sec}\);
\(g\) is the acceleration of gravity;
\(\delta\) is the area of the exhaust openings, \(\mathrm{m}^2\).

Calculations show that, for all modern hammers, the value of \(C\) is \(5\)–\(10\ \mathrm{kg}\). Indeed, with a hammer weight of \(30\)–\(40\ \mathrm{kg}\) and a coefficient of friction of the hammer body against the guides \(f = 0.1 \div 0.2\), the friction forces amount to \(3\)–\(8\ \mathrm{kg}\). The exhaust reaction has still smaller values. Thus, at an air flow rate per second \(Q_{\mathrm{v}} = 0.0666\ \mathrm{m}^3/\mathrm{sec}\) \((4\ \mathrm{m}^3/\mathrm{min})\), which is characteristic of the most powerful hammers, and with the area of the exhaust ports \(\delta = 4\ \mathrm{cm}^2\), the reaction \(p_3\), calculated by formula (10), is \(1.4\ \mathrm{kg}\).

The force from the air hose \(p_4\) depends on the weight and stiffness of the hose and on the method of its attachment. In practice, when drilling horizontal blastholes, the magnitude of this force does not exceed the exhaust reaction.

Figure 4 gives the values of the individual components of the feed force for different actual values of the latter. The calculations were made for the operating conditions of the PR-25 hammer at an air pressure of \(4\ \mathrm{atm}\). The values of \(P_1\) were determined by formula (6) on the basis of the energy and blow frequency of the PR-25 hammer, determined experimentally (Fig. 3) [9]. The second component was determined by the formula \(P_2 = P_{\mathrm{p}} - (P_1 + C)\). The third component for the PR-25 hammer was taken as \(C = 6\ \mathrm{kg}\). Figure 4 also plots the relationships showing the change in the relative drilling speed with feed force.

As can be seen from Fig. 4, depending on the magnitude of the individual components of the feed force, and on the magnitude and nature of the change in drilling speed, the entire range of possible feed forces of a drilling hammer can be divided into a number of characteristic zones.

At comparatively small feed forces—the zone \(A\)—the magnitude of the feed force, determined experimentally, is equal to the sum \(P_1 + C\). In this zone, as a rule, there are no impacts of the hammer body against the limiting collar of the drill. Owing to the considerable displacement of the hammer body away from the limiting collar of the drill,

Fig. 4. Magnitudes of the components \(P_1\), \(P_2\), and \(C\), and relative drilling speeds for the PR-25 hammer at an air pressure of 4 atm.

the power transmitted to the drill is small. As a result, the drilling speed is insignificant. Zone \(A\) may be characterized as a nonworking zone.

When the feed force of the PR-25 hammer is increased from 30 to 90 kg (zones \(B\) and \(V\)), the number of movements and the power transmitted to the drill increase. The magnitude of the first component of the feed force and the drilling speed increase. In zones \(B\) and \(V\), impacts of the hammer body against the limiting collar of the drill are observed.

which at the beginning of the zone occur after several cycles of piston travel and then become more frequent as the feed force increases. As a result, the value \(P_2\) appears and increases. At the same time it should be noted that the intensity of the increase of \(P_2\), as the feed force increases in zones Б and В, is greater than the intensity of the increase of \(P_1\).

Increasing the feed force above \(80\text{—}100\) kg (zone Г) leads to a decrease in the component \(P_1\) and to a significant increase in \(P_2\). The latter occurs no longer because of an increase in the frequency of impacts of the hammer body against the limiting collar of the drill steel, but as a consequence of an increase in the duration of contact during impact.

In zone Г the clearances are completely taken up both between the hammer body and the limiting collar of the drill steel, and between the bit blade and the bottom of the borehole. Contact of the drill bit blade with the rock is then present not only at the moment of impact, but also in the intervals between impacts. This leads to a considerable increase in the torque required to rotate the drill. Since the impact and rotary units in modern pneumatic hammers are kinematically connected, a considerable part of the forces driving the piston in the hammer cylinder is expended in overcoming the resistance to drill rotation under these conditions. The velocity of motion of the piston-striker in the hammer cylinder decreases. The hammer reduces the energy and frequency of impacts, and with a further increase in feed force it ceases to operate altogether—it stalls. Zone Г may be characterized as a zone of unstable hammer operation.

To ensure the maximum drilling rate, the hammer must operate at feed forces lying within the limits of zone В. In this case the deviation of the drilling rate from the maximum value does not exceed 40%. At feed forces that ensure the maximum drilling rate, the value \(P_1\) is maximal, and the value \(P_2 = (0.45\text{—}0.68)P_1\).

It is necessary to note that the definite ratio of the quantities \(P_1\) and \(P_2\) in the zone of optimal feed forces is preserved only during stable operation of the hammer. When the stability of operation is disturbed, this ratio is disrupted. Thus, for example, if a hammer, operating at optimal feed forces, as a consequence of accidentally arising considerable resistances to rotation of the drill, cannot turn the drill or even only reduces the energy and frequency of impacts, then the component \(P_1\) will immediately decrease. With a constant value of the feed force \(P\), created by one feeder or another, this will lead to an increase in \(P_2\), which, in turn, will further increase the resistance to rotation of the drill and will cause the drilling hammer to stop—“the hammer will stall.”

To resume operation of the hammer, the driller is forced to reduce the feed force to such a value at which the resistance to rotation of the drill will be equal to or less than the torque

…moment that the hammer can develop. Only then will the hammer begin to operate again and the component \(P_1\) arise again. After this, the feed force can be increased to the optimum value and the ratio of the quantities \(P_1\) and \(P_2\) corresponding to the given regime can be restored. The component \(B\), with accuracy sufficient for calculations, may be taken as constant, independent of the feed force.

Fig. 5. Quantities of the components \(P_1\), \(P_2\), and \(C\), and relative drilling speeds for the RH-754 hammer as functions of feed force \(P_n\). Air pressure:
\(1\)—4 atm; \(2\)—5 atm; \(3\)—6 atm.

The relationships indicated above are characteristic of the operation of any drilling hammer at various air pressures (Fig. 5).

Determination of the feed forces ensuring operation of the drilling hammer under the most rational regimes

In view of the above-noted features of the operation of pneumatic drilling hammers, the feed force to which the feeding mechanism must be adjusted should be equal to or somewhat less than the force that ensures the maximum drilling speed.

To determine the feed force limiting the working zone \(B\), the following relationships may be recommended.

The minimum feed force must ensure stable operation of the hammer and constant impact of the piston against the shank…

of the drill bit. This force may be determined from formula (6) by adding the constant forces \(C\) and the force needed to overcome the weight of the hammer when the drilling machine is set at an angle to the horizon.

\[ P_{\mathrm{p}\,\min}=n\sqrt{2Am_{\mathrm{p}}}+C+G\sin\alpha, \tag{11} \]

where \(A\) and \(n\) are the calculated values of the energy and frequency of the hammer blows when it operates under optimum conditions;

\(\alpha\) is the angle of inclination of the blast-holes to the horizon, in degrees.

The maximum feed force must ensure the highest drilling rate and stable operation of the drilling hammer. It may be determined from the formula

\[ P_{\mathrm{p}\,\max}=n\sqrt{2Am_{\mathrm{p}}}\left(1+\frac{s'p'_{\mathrm{cp}}}{sp_{\mathrm{cp}}}\right)+C+G\sin\alpha, \tag{12} \]

or

\[ P_{\mathrm{p}\,\max}=\xi n\sqrt{2Am_{\mathrm{p}}}+C+G\sin\alpha, \tag{13} \]

where

\[ \xi=\left(1+\frac{s'p'_{\mathrm{cp}}}{sp_{\mathrm{cp}}}\right). \]

Taking into account that the value of the coefficient \(\xi\) for modern drilling hammers varies within fairly narrow limits, \(\xi=(1.45\text{--}1.68)\), for calculations of feeding devices it is possible to recommend the simplified formula

\[ P_{\mathrm{p}\,\max}=1.55n\sqrt{2Am_{\mathrm{p}}}+C+G\sin\alpha. \tag{14} \]

As can be seen from the data in the table given, the feed forces calculated by formulas (11) and (14) determine operating conditions of drilling hammers at which the drilling rates amount to 50--100% of the maximum. The value of the feed force calculated by formula (14) is sufficiently close to the optimum feed forces determined experimentally [5].

The indicated relations have been derived from the condition that constant contact of the hammer body with the limiting collar of the drill bit is not obligatory and necessary either from the standpoint of effective destruction of rock by the percussive-rotary method or from the standpoint of ensuring stable operation of the drilling machine.

Some researchers believe that the creation of feed mechanisms ensuring constant contact of the hammer with the limiting collar of the drill bit will make it possible to increase the efficiency of impact-energy transmission and thereby improve the effectiveness of pneumatic drilling hammers. To ensure constant contact between the hammer body and the limiting collar of the drill bit, the magnitude of the feed force must be greater

force moving the piston during the working stroke. This force can be determined from the formula

\[ P' = S p_{\mathrm{net}}, \tag{15} \]

where \(p_{\mathrm{net}}\) is the maximum air pressure in the hammer cylinder, equal to the maximum pressure in the air-supply network;

\(S\) is the piston area, equal to the area of the rear cavity of the cylinder.

From the data given in the table it is clear that the forces calculated by this formula exceed by a factor of 2--3 both the optimal and the maximum feed forces at which the hammer can operate while rotating the drill.

But if operation under such regimes were ensured by appropriate designs of drilling hammers, then this, in our opinion, would lead to an increase in...

...the main advantage of rotary-percussive drilling, causing great wear of the drilling tool.

The relationship established above between the feed force and the principal parameters of a drilling hammer, as an impact machine, makes it possible to use these dependencies to calculate the required feed forces for other impact machines as well—breakers, riveting hammers, chipping hammers—irrespective of the type of their drive.

On ways of reducing the feed forces of impact drilling machines

The regularities revealed above make it possible to outline ways to reduce the required feed forces of impact drilling machines. The need for this is determined by the following circumstances.

First, most drilling hammers currently in existence are hand-held machines. When operating such a machine, the worker is forced to hold it in the required position and to feed it to the face manually. The feed force and the weight of such machines should be chosen as small as possible, since the smaller the required feed force and the weight of the machine, the easier the worker’s labor will be. The need to reduce the feed force of drilling machines also remains in cases where these machines are intended for installation on special supporting-and-feeding devices. For the smaller the required feed force, the more compact, lighter, and more convenient in operation the entire drilling rig will be.

Second, one of the basic characteristics of a drilling machine is the drilling rate, which, for a given method of drilling, tool geometry, and rock hardness, depends on the power of the machine. The greater the power of the machine, the higher the drilling rate that can be achieved. In striving to increase the drilling rate, designers create ever more powerful drilling machines.

As the power of the machine increases, as a rule, its weight and the required feed force increase as well. In recent years designers have created several very powerful drilling machines and, in doing so, have neglected the solution of questions concerning the required feed forces. Therefore the potential capabilities of such machines are not utilized, and under manual operation they give the same drilling rate as less powerful drilling hammers [4].

To outline a solution to these contradictory problems—creating powerful machines with small feed forces—we shall compare the dependencies obtained above for determining the required feed forces with the dependencies determining the power of the machine.

The power of a percussive machine is directly proportional to the energy and frequency of blows and may be determined from the formula

\[ N=\frac{A n}{75}\ \text{h.p.} \tag{16} \]

Let us consider what influence the energy and frequency of blows have on the individual components of the feed force.

As we have already noted above, without the presence of the first component of the feed force \(P_1\), it is impossible, over a certain interval of time, to transmit momentum—and consequently power—from the percussive machine to the drilling tool. From a comparison of formulas (6) and (16) it is evident that both the power and the magnitude of the first component of the feed force \(P_1\) vary proportionally to the frequency of blows. As for the blow energy, the power varies in proportion to the blow energy to the first power, whereas \(P_1\) varies in inverse proportion to the square of the energy. On this basis it may be concluded that, in order to reduce \(P_1\) at a given machine power, one should

Fig. 6. Component \(P_1\) as a function of the kinetic energy of the piston and the power of the machine, with piston mass \(m_p = 0.2\ \mathrm{kg\,sec^2/m}\).

Vertical axis: component of feed force \(P_1\), kg.
Horizontal axis: kinetic energy of the piston, kgm.
Curves: \(N = 3.0\) h.p.; \(2.5\) h.p.; \(2.0\) h.p.; \(1.5\) h.p.; \(1.0\) h.p.; \(0.5\) h.p.

one should strive to create impact units with the greatest possible energy of each blow. The same should be observed when increasing the power of the machine. According to Fig. 6, at one and the same machine power, increasing the blow energy from 2 to 15 kgm makes it possible to reduce \(P_1\) by more than a factor of two.

The maximum permissible blow energy of drilling hammers is limited by the strength of the drilling tool and, for drilling blastholes 40–45 mm in diameter, with the present design and materials of the drilling tool, amounts to 7–8 kgm. Lacking the possibility of accepting a greater blow energy, designers, when creating new machines, increase their power by increasing the blow frequency. According to formula (6), this leads to an increase in the first component \(P_1\) and in the total feed force of the machine. Consequently, solving the problem of reducing the feed force of drilling hammers is connected with the task of finding stronger materials for manufacturing the drilling tool.

One and the same kinetic energy of the piston can be attained with different values of its mass by a corresponding change in the piston velocity before impact; in this case the quantity of motion will also change (Fig. 7). In order to determine what effect a different ratio of piston mass and velocity, at a given machine power, has on the magnitude \(P_1\), it is sufficient to compare the expression for determining the kinetic energy of the piston \(A = \dfrac{m v_{\text{p}}^2}{2}\) with formula (5), where the magnitude \(P_1\) is expressed through the quantity of motion.

From this comparison it may be concluded that, at one and the same frequency and energy of blows, in order to reduce the magnitude \(P_1\), one should strive to reduce the piston mass. To obtain specified values of the energy of each blow, the piston velocity before impact should be increased.

According to Fig. 8, changing the piston weight within the range of 1–5 kg makes it possible to change \(P_1\) by a factor of 2–3.

Thus, at one and the same machine power, the first and principal component of the feed force \(P_1\) can vary substantially depending both on the magnitude of the blow energy and on the ratio of piston velocity and mass. At a given machine power, in order to reduce the magnitude \(P_1\), one should increase the energy of each blow by increasing the piston velocity before collision with the drilling tool and by reducing the piston mass. It should be noted that this path has already been partially used in drilling practice by abandoning, as hand drilling machines, the so-called “piston” drilling hammers [11], in which the drilling tool (drill) was connected with the piston of the machine and performed all motions together with it. The required feed forces of such machines were considerably greater than for machines of the same power but made

according to the “hammer” principle, where the piston transmits energy to the drill bit as a result of collision with it.

It is impossible to decrease the piston weight without limit and to increase its velocity before collision with the drill bit. It should be borne in mind that, with a constant drill-bit mass, the efficiency of transmission of impact energy decreases substantially as the piston mass is reduced [12]. Therefore the final choice of the mass and velocity of the piston for a particular machine must be made on the basis of ensuring the maximum power transmitted by the machine to the destruction of rock, taking into account the efficiency of transmission of impact energy.

Fig. 7. Dependence of the velocity and quantity of motion of the piston before collision with the drill bit on mass, at specified kinetic energies of the piston:
— — — piston velocity; ——— quantity of motion.

The magnitude of the piston mass is also limited in a number of cases by design factors. With a small piston mass and a considerable cylinder diameter of the machine, at present it is difficult to make, from existing grades of steel, a piston that would be ...

sufficiently strong and have the necessary guides for a stable position in the machine cylinder. In this connection, it is urgent to seek new materials for making striker pistons which would have a specific weight less than that of steel, while not being inferior to it in strength.

The maximum possible velocity of the piston before its collision with the drill is limited by the strength of the parts being struck.

Fig. 8. Dependence of the feed-force component \(P_1\) on piston weight, at piston kinetic energy \(4\ \mathrm{kgm}\):
solid line—feed force \(P_1\); dashed line—piston velocity.

Some investigators [13] recommend, for determining the maximum possible collision velocity, using the formula derived from the condition of transmission of the impact energy without residual deformation of the colliding surfaces [14]:

\[ v \leq \sigma_y \sqrt{\frac{g}{E\gamma}}, \tag{17} \]

where
\(\sigma_y\) is the elastic limit of the material;
\(E\) is the modulus of elasticity of the material of the colliding parts;
\(\gamma\) is the specific weight of the material.

If this formula is used, then for steels U7; U8; 45; 45KhN; 12KhN3A and others, from which the pistons and drilling tools of drilling hammers are presently manufactured, the limiting possible piston velocities may reach 20 m/sec. In practice, however, the velocity of piston motion in modern drilling hammers does not exceed 7.0–8.0 m/sec.

The large discrepancy between the velocity values determined by formula (17) and those existing in drilling hammers can be explained by the following circumstances. Formula (17) was derived from the condition of absence of residual deformation of the impacting parts under a single blow. The impacting parts in drilling hammers, however, are subjected to a repeatedly recurring impact load and, as practice shows, these parts most often fail as a result of impact fatigue. Consequently, the determination of the limiting permissible velocities by formula (17) should be carried out by substituting into it, instead of the elastic limit, the limit of impact fatigue of the steel. In this characteristic, many factors influencing the resistance of the parts to cyclic impact loading must be taken into account—the composition of the steel, the presence of internal defects, heat treatment and the structure obtained as a result of it, the surface finish of the parts, etc. Unfortunately, such data for the above-mentioned grades of steel are still not available in the literature known to us. Therefore, the resolution of these questions, as well as the search for lighter materials for pistons, requires special investigations.

Comparing the formula for determining the power of the machine (16) with formula (9), one may conclude that carrying out the measures outlined above for reducing the first component \(P_1\) will at the same time also make it possible to reduce the value of \(P_2\). In contrast to \(P_1\), the second component \(P_2\) is not absolutely necessary for the normal operation of percussion-action drilling machines. At first glance, it may be assumed that, in the presence of \(P_2\), as a result of systematic impacts of the hammer body against the limiting collar of the drill, additional energy is imparted to the drill, which makes it possible to use the presence of \(P_2\) to increase the drilling speed.

However, the calculations we carried out showed that the values of the energy and power transmitted to the drill in these cases are insignificant. Therefore, in designing new drilling hammers it is advisable to strive to reduce the component \(P_2\) to a minimum by reducing the frequency and velocity of impact of the hammer body against the limiting collar of the drill. This can be achieved by a suitable selection of the length of the drill shank and of the parameters of the hammer air distribution (the location of the air-supply channels) in the design of two-piston high-frequency hammers with oppositely moving pistons, and also by creating special dynamic absorbers of vibrations of the hammer body.

The quantities entering into the third component of the feed force, \(C\), may also change when the power and design of the machine change. The quantity \(F\) depends on the weight of the machine, on the design, and on the operating conditions of the feeder guides. If an increase in power is accompanied by an increase in the weight of the machine, then the quantity \(F\) will also increase. As the power of the pneumatic machine increases, the air consumption will rise. An increase in air consumption will lead to an increase in \(P_3\) only if the direction of the exhaust ports of the drilling hammer coincides with the direction of drilling. In this case the reaction from the exhaust is directed opposite to the feed force. With a suitable direction of the exhaust ports, the feed force can be reduced somewhat. At the existing power of drilling hammers this gain is very small. Thus, for the most powerful hammers it may amount to 2–3 kg. Therefore, primary attention should be paid to reducing the feed force by means of the first and second components.

Conclusions

1. The feed force in pneumatic impact machines is a factor that ensures the transfer of the machine power to the drilling tool with one or another intensity.

2. The magnitude of the feed force of modern drilling hammers is determined mainly by the quantity of motion transmitted from the machine to the drilling tool, and by the frequency of impacts.

3. For one and the same machine power, the magnitude of the feed force required for the full utilization of this power may differ depending on the ratio of the kinetic energy of the piston and the impact frequency, and on the mass and velocity of the piston before collision with the drill.

4. When creating new machines of one or another power, in order to reduce the required feed force it is necessary to increase the energy of each impact and decrease the impact frequency, to increase the velocity of motion and decrease the mass of the piston. The limiting values of these quantities must be established in each specific case, taking into account the efficiency of impact transmission, the material, and the strength of the colliding parts.

5. To create powerful pneumatic drilling hammers of low weight and with small feed forces, it is necessary to carry out special studies aimed at improving and creating new materials for manufacturing impact assemblies and drilling tools. The necessary qualities of such materials should be low specific weight and high limiting stress under impact fatigue.

In conclusion it should be noted that the method and the basic relationships set forth by us in the present work may be used

... are suitable for investigating other impact-action machines—breaker, riveting, and chipping hammers, tampers, etc., both with pneumatic and with other types of drive.

REFERENCES

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2. P. M. Alabuzhev, O. D. Alimov. The influence of feed force and the angle of rotation of the drill between blows on the speed of percussive-rotary drilling of blast holes. Proceedings of TPI, vol. 75, Tomsk, 1954.

3. O. D. Alimov. The influence of feed force on the drilling speed of pneumatic drilling hammers. Proceedings of TPI, vol. 75, 1954.

4. O. D. Alimov, I. G. Basov, P. A. Samoilov. Some results of investigating the operating modes of pneumatic drilling hammers. Proceedings of TPI, vol. 106, Metallurgizdat, 1958.

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7. O. D. Alimov, V. F. Gorbunov, V. Kh. Koshevoi. Investigation of the working process of the OM-506 and RP-17 pneumatic drilling hammers. TsITI, Mining Machines, Collection No. 1, Ugletekhizdat, 1958.

8. O. D. Alimov, V. F. Gorbunov. Investigation of the working process of a high-frequency drilling hammer with valveless air distribution. Proceedings of TPI, vol. 106, Metallurgizdat, 1958.

9. V. F. Gorbunov. Experimental investigation of the working process of pneumatic drilling hammers. Candidate dissertation, TPI, Tomsk, 1958.

10. O. D. Alimov, I. G. Basov, V. F. Gorbunov. Methodology of laboratory investigation of the influence of feed force on the drilling speed by pneumatic drilling hammers. Proceedings of TPI, vol. 88, Tomsk, 1956.

11. V. K. Buchnev. Drilling-and-blasting operations. Ugletekhizdat, 1955.

12. P. M. Alabuzhev, O. D. Alimov, A. G. Tsukanov. On the coefficient of useful action of the blow in drilling hammers. Proceedings of TPI, vol. 75, 1954.

13. V. M. Mostkov. Fundamentals of the theory of pneumatic drilling. Ugletekhizdat, 1952.

14. N. M. Gersevanov. Theory of longitudinal elastic impact as applied to determining pile resistances. Collected Works, vol. 1, Stroyvoenmorizdat, 1948.