PROCEEDINGS
OF THE TOMSK ORDER OF THE RED BANNER OF LABOR
POLYTECHNIC INSTITUTE named after S. M. KIROV

Vol. 108  INVESTIGATION OF DRILLING MACHINES  1959

NOMOGRAMS FOR CALCULATING

CERTAIN PARAMETERS OF DRILLING HAMMERS

O. D. Alimov, A. A. Alimova

When designing new pneumatic drilling hammers, designers encounter many difficulties. The principal difficulties are due to the fact that in the technical literature of recent years there have not been sufficiently substantiated geometric dimensions and technical characteristics of pneumatic drilling hammers.

This shortcoming is gradually being eliminated. In recent years, both in the USSR and abroad, extensive experimental and theoretical investigations have been carried out and are being conducted; as a result, relationships are recommended for calculating the principal layouts and individual parts of drilling hammers. Such theoretical and experimental studies help designers choose and calculate the most appropriate parameters of new designs of drilling machines. Calculations can be accelerated and facilitated with the aid of nomograms.

Below are given nomograms for calculating the impact energy, impact frequency, feed force, and drilling speed of pneumatic drilling hammers. The nomograms are constructed with parallel logarithmic scales, since these are simple and convenient to use. In constructing them, we used a number of relationships obtained as a result of experimental and theoretical work carried out in recent years at the Department of Mining Machines and Mine Transport of the Tomsk Polytechnic Institute.

In order that calculations by the nomograms ensure high accuracy, the limits of variation of the individual quantities have been chosen as small as possible, but with due allowance for the fact that they must cover the ranges of variation of the corresponding quantities already tested in practice.

Nomogram 1 (Fig. 1) for determining impact energy is calculated by the formula

\[ A_y = k_a pQS \ \text{kgm}, \tag{1} \]

where
\(p\) is the air pressure in the line, \(\text{kg}/\text{cm}^2\);
\(Q\) is the working area of the piston-striker of the drilling hammer, \(\text{cm}^2\);
\(S\) is the piston stroke, \(m\);
\(k_a\) is a coefficient taking into account the change in air pressure in the working cavity of the cylinder during its expansion and the mechanical losses in the impact unit of the drilling hammer.

The indicated dependence, compiled [1] on the basis of the fundamental laws of mechanics, is sufficiently simple and, with a correct preliminary estimate of the numerical value of the coefficient, can give sufficiently accurate results. According to the investigations of V. F. Gorbunov, for modern designs of drilling hammers the value of \(k_a\) ranges from 0.5 to 0.55. The ranges of variation of the other quantities entering formula (1), in constructing nomogram 1, were chosen with allowance for modern trends in the creation of high-productivity drilling hammers [2].

Nomogram 2 (Fig. 2) for determining the blow frequency of a drilling hammer is calculated by the formula

\[ n = 0.6 \sqrt{\frac{Qp}{mS}} \cdot \frac{60}{1 + \frac{t_x}{t_p}} \ \text{blows/min}, \tag{2} \]

where \(m\) is the mass of the piston, \(\text{kgsec}^2/\text{m}\);
\(\dfrac{t_x}{t_p}\) is the ratio of the time of the return (idle) stroke of the piston-striker to the time of the working stroke.

Formula (2) was obtained by V. F. Gorbunov [1] on the basis of processing the test results of pneumatic drilling hammers of various designs and parameters. The ranges of variation of \(Q\), \(p\), and \(S\) are taken approximately the same as in nomogram 1.

The ranges of variation of the piston mass in modern hand-held drilling hammers are 0.16—0.27 \(\text{kgsec}^2/\text{m}\). In the nomogram these limits are somewhat expanded.

When calculating the blow frequency corresponding to the optimal operating modes of the drilling hammer, the value of the ratio \(\dfrac{t_x}{t_p}\) varies within the limits from 1.3 to 2.1, depending on the hammer design and the air-distribution scheme. A smaller value of \(\dfrac{t_x}{t_p}\), and consequently a higher blow frequency, other conditions being equal, is provided by drilling hammers with a drive

Fig. 1. Nomogram for calculating the energy of the blow of a drilling hammer.

Formula:

\[ A_y = k_a \cdot p \cdot Q \cdot S \]

Scheme of use:

Answer.

Example:

Given:

\[ Q = 30\ \text{cm}^2 \]

\[ S = 0.02\ \text{m} \]

\[ p = 5\ \text{atm} \]

\[ k_a = 0.5 \]

Labels on the nomogram:

• \(Q\) — cylinder cross-section, \(\text{cm}^2\)
• \(A_y\) — blow energy, kg·m
• \(S\) — working piston stroke, mm
• \(p\) — air pressure, atm
• \(k_a\) — coefficient

Visible scale values:

• Cylinder cross-section \(Q\), \(\text{cm}^2\): 25, 30, 40, 50, 60, 70
• Blow energy \(A_y\), kg·m: 0.8, 0.9, 1.0, 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
• Working piston stroke \(S\), mm: 18, 20, 25, 30, 40, 55
• Air pressure \(p\), atm: 4.0, 4.5, 5.0, 5.5, 6.0
• Coefficient \(k_a\): 0.30, 0.55, 0.50, 0.45

Fig. 2. Nomogram for determining the blow frequency of a drilling hammer.

Formula:

\[ n = 0.6\sqrt{\frac{Qp}{mS}} + \frac{60}{1 + t_x/t_p} \]

Scale labels and inscriptions visible in the nomogram:

• \(Q\) — cylinder cross-section, \(\text{cm}^2\)
• \(p\) — air pressure, atm
• \(n\) — blow frequency per minute
• \(m\) — piston mass, \(\text{kg}\cdot\text{s}^2/\text{m}\)
• \(S\) — piston stroke, mm
• \(\dfrac{t_x}{t_p}\)

Usage diagram:

• \(Q\)
• I
• II
• III
• \(m\)
• \(S\)
• \(\dfrac{t_x}{t_p}\)
• Answer

Example:

Given:

\[ Q = 40\ \text{cm}^2 \]

\[ p = 5\ \text{atm} \]

\[ m = 0.2\ \text{kg}\cdot\text{s}^2\text{m}^{-1} \]

\[ S = 40\ \text{mm} \]

\[ \frac{t_x}{t_p} = 1.8 \]

Answer:

\[ n = 2025\ \text{blows/min} \]

rotation of the drill bit during the forward stroke of the striker piston. For hammers with a drive of the rotation mechanism during the return stroke of the piston, the quantity \(\frac{t_x}{t_p}\) ranges from 1.5 to 2.1. Moreover, it is the greater, the smaller the filling of the front cavity of the hammer cylinder with compressed air. As an average value for hammers of the second group, one may take \(\frac{t_x}{t_p} = 1.7\).

Formula

\[ F_{\mathrm{op}}=\frac{pQ}{3.56}+4p \]

Diagram for use

\(p\) — given
\(F_{\mathrm{op}}\) — answer
\(Q\) — given

Example

Given:

\[ p=5\ \text{atm}, \qquad Q=30\ \text{cm}^3 \]

Answer:

\[ F_{\mathrm{op}}=62\ \text{kg} \]

Figure labels: \(p\); air pressure, atm; \(F_{\mathrm{op}}\); optimal feed force, kg; \(J\); cylinder cross section, cm².

Fig. 3. Nomogram for determining the optimal feed force.

Impact energy and impact frequency are the principal parameters determining the power of a pneumatic drilling hammer and, consequently, its potential capability to provide one or another drilling rate. But effective use of this power and attainment of the maximum drilling rate are possible only at definite feed forces [3—5]. Nomograms 3 and 4 (Figs. 3 and 4) make it possible to determine such optimal feed forces.

Nomogram 3 was constructed on the basis of the empirical formula proposed by I. G. Basov [5]

\[ F_{\mathrm{op}}=\frac{pQ}{3.56}+4p\ \mathrm{kg}, \tag{3} \]

where \(F_{\mathrm{op}}\) is the optimum feed force.

Fig. 4. Nomogram for determining the optimum feed force.

This relationship was derived on the basis of a generalization of extensive experimental material on the study of operating regimes of modern pneumatic drilling hammers. It is recommended that it be used to calculate the feed forces of existing drilling hammers in order to determine the most expedient areas of their application [6], as well as the parameters of feeding devices [7]. In analyzing variants of drilling hammers with specified or already known basic parameters of the impact units \((n, A, m)\), it is more expedient to use nomogram 4 (Fig. 4).

Nomogram 4 was constructed on the basis of the formula

\[ F_{\mathrm{op}} = 1.55\,\frac{n}{60}\sqrt{2A_y m}\ \mathrm{kg}, \tag{4} \]

which is the result of simplifying formulas obtained by us on the basis of a study of the operating dynamics of a drilling hammer [8].

Using formulas (3) and (4), one can calculate, with accuracy sufficient for practice, the feed force of a drilling hammer when drilling horizontal blast holes. For cases of drilling inclined blast holes and for calculating feed mechanisms of various types, it is necessary additionally to take into account the components due to the weight of the hammer and the friction forces during motion of the hammer body along the feed guides.

From nomogram 4 one can also determine one of the main components of the feed force, \(F_1\), whose magnitude depends chiefly on the parameters of the impact assembly [8].

Nomogram 5 (Fig. 5) is intended for determining the rate of drilling of blast holes. The basis for its construction is the formula [9]:

\[ V = \frac{60 \cdot 102N\eta}{\dfrac{\pi d^2}{4} A_{\mathrm{ob}}}\ \mathrm{cm/min}, \tag{5} \]

where \(N\) is the power of the drilling machine, kW;
\(d\) is the diameter of the blast hole, cm;
\(A_{\mathrm{ob}}\) is the volumetric work of destruction, kgm/cm\(^3\);
\(\eta\) is the efficiency of power transmission from the machine drive to the tool.

The volumetric work of destruction determines the resistance of the rock to destruction by the given method. Its magnitude may be determined either on the basis of the results of special investigations, for example, of the mechanism of rock destruction, or on the basis of test data for existing designs of drilling machines. In the first case, this quantity does not include energy losses during its transmission by the machine transmission; therefore, when the drilling rate is determined by formula (5), these losses are taken into account by the corresponding efficiency coefficient.

In the second case, the magnitude of the energy losses in the machine in most cases is included in the value of the volumetric work of destruction. In this case, calculations by formula (5) should be carried out without taking \(\eta\) into account, and the final result when calculating by nomogram 5 should be determined from the \(V_1\) scale. Nomogram 5 may also be used to calculate the drilling rate of rotary machines.

Fig. 5. Nomogram for determining the drilling speed of a blasthole

Formula

\[ v=\frac{N\cdot 10^{2}\cdot 60\cdot \eta}{\dfrac{\pi d^{2}}{4}\cdot A_{\mathrm{ob}}} \]

Scheme of use

Given → Answer → Answer → Answer

Example

Given:

\(d=4\ \mathrm{cm}\)

\(A=8\ \mathrm{kg/cm^{3}}\)

\(N=2.5\ \mathrm{kW}\)

\(\eta=0.1\)

Answer: \(v=107\ \mathrm{cm/min}\)

Scale labels:

• \(d\) — blasthole diameter, cm
• \(A_{\mathrm{ob}}\) — volumetric work of failure, kg/cm³
• \(v\) — drilling speed, cm/min
• \(N\) — machine power, kW
• \(\eta\) — efficiency coefficient

References

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

2. O. D. Alimov, V. F. Gorbunov. On contemporary trends in the design of high-productivity pneumatic drilling hammers. Proceedings of TPI, vol. 106, Metallurgizdat, 1958.

3. O. D. Alimov. The influence of feed force on the drilling speed of pneumatic drilling hammers. Proceedings of TPI, vol. 88, Tomsk, 1956.

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

5. I. G. Basov. Study of the influence of feed force on the drilling speed and operating mode of pneumatic drilling hammers. Candidate dissertation, TPI, Tomsk, 1958.

6. O. D. Alimov, I. G. Basov, V. F. Gorbunov. On the question of developing a rational series of pneumatic drilling hammers. Article in the present collection.

7. I. G. Basov. Analysis of the operation of drilling hammers on pneumatic supports. Article in the present collection.

8. O. D. Alimov. The interrelation of feed force with the principal parameters of a drilling hammer. Article in the present collection.

9. O. D. Alimov. On evaluating the quality of machines for drilling blast holes. Article in the present collection.