V. F. GORBUNOV

ON THE CALCULATION OF MINIMUM PRESSING FORCES WHEN WORKING WITH HAND-HELD PNEUMATIC HAMMERS

(Presented by the Department of Mining Machines and Mine Transport)

The energy and vibration characteristics of pneumatic hammers vary depending on the pressure of the air supplied to the hammer and on the pressing force applied to its handle \([3—6]\). The influence of the pressing force on the energy characteristics of hammers is differentiated according to their design features. To determine the magnitudes of the pressing forces that must be created in order to ensure normal operation of hammers, let us consider the schematic diagrams of their impact assemblies.

The impact assembly of pneumatic hammers (Fig. 1) is a double-acting piston device. The piston-striker 1 performs reciprocating motion in the cylinder, the chambers of which, \(A\) and \(B\), alternately communicate with the compressed-air network (through channels 3 and 4) or with the atmosphere (through window 5). The stopping of the piston-striker in its extreme positions occurs under the action of the air cushion formed in chamber \(A\), and as a result of impact against the shank of tool 2. In the designs of drilling hammers (Fig. 1, б) the possibility of idle operation is provided. In this case, stopping of the piston-striker at the end of its working stroke (from left to right in Fig. 1, б) occurs because of a sharp increase in air pressure in chamber \(B\). The energy of the moving piston-striker is spent on compressing the air cushion, is partly converted into heat, and is partly returned to the piston during its reverse motion.

Fig. 1. Schematic diagrams of the impact assemblies of pneumatic hammers: \(a\) — chipping, riveting, and breaker hammers; \(б\) — drilling hammers.

In most designs of riveting, breaker, and chipping hammers (Fig. 1, \(a\)), idle operation is not provided. The shank of the tool enters directly into chamber \(B\) of the hammer cylinder. To ensure the transfer of energy to tool 2, the hammer must be pressed with a certain force \(Q\). If the force \(Q\) proves insuffici-

necessary to hold the hammer close to the tool, an impact of the striker piston against the barrel bridge 6 will occur. This is impermissible. Consequently, in order to ensure operation of the hammer (with the design arrangement of Fig. 1, a) without impacts of piston 1 against the barrel bridge 6, it is necessary to apply to the body a certain pressing force \(Q_{\min}\), preventing the hammer body from moving away from the tool.

According to data from sanitary-hygienic studies [1, 2], the pressing force when working with hand-held mechanized tools under production conditions may range from 10 to 25 kg. The normal condition for evaluating the vibration characteristics of hand-held hammers is considered to be a pressing force of 15 kg [10]. For evaluating hammer vibration it is recommended to use amplitude-frequency characteristics (the magnitude of the vibration amplitude of the hammer handle at a given frequency).

A number of researchers of pneumatic hammers have found that the vibration amplitude of the hammer body decreases as the pressing force increases. Thus, according to our measurements, increasing the pressing force, for example, on the KE-22 riveting hammer from 17 to 30 kg reduces the vibration amplitude by a factor of 3. Reducing the pressing force to 15 kg, however, leads to disruption of stable hammer operation and to the appearance of impacts of the striker against the barrel bridge.

To determine the causes of disruption of normal hammer operation and to determine the minimum necessary pressing force, let us consider the dynamics of operation of pneumatic hammers.

In Fig. 2, a, b, c are presented force diagrams for pneumatic hammers (KE-32—riveting, MR-4—chipping, and PR-20—drilling). The diagrams were constructed from oscillograms of air pressure in the cylinder at an air pressure in the mains of 5 ati. For hammers built according to the scheme of Fig. 1, a, the diagram of the resultant force from air pressure on the hammer body (1, Fig. 2, a) does not coincide with the diagram of force 2 acting on the striker. This is explained by the fact that the working area of the cross section of the striker on the side of the front cavity B of the hammer cylinder (Fig. 1, a) is greater than the annular area of the front inner wall of the cylinder by an amount equal to the section of the tool shank

Fig. 2. Force diagrams of one cycle of the piston stroke of pneumatic hammers.

\[ \frac{\pi}{4}D_b^2=\frac{\pi}{4}(D_c^2-d_i^2)+\frac{\pi}{4}d_i^2, \tag{1} \]

where \(D_b\) is the striker diameter \((D_b = D_c)\);
\(D_c\) is the internal diameter of the hammer cylinder;
\(d_i\) is the diameter of the tool shank.

For riveting hammers of the KE type, the air pressure on the body acts only in the direction away from the tool, since in practice \(d_i = D_c\).

For drilling hammers, the diagrams of air pressure on the hammer body and on the piston-striker coincide \((1, 2,\) Fig. 2, \(c)\). The force diagram 3 for idle running of the PR-20 hammer is also shown here.

According to experimental data, during normal operation the maximum air pressure in the front cavity of the barrel of chipping-riveting, breaking, and also drilling hammers is approximately 0.7 of the line pressure, while in the rear cavity it reaches the line pressure. The magnitude of the displacement of the air-pressure diagram on the hammer body relative to the zero line can be calculated accurately by using the method of Doctor of Technical Sciences B. V. Sudnishnikov [9] for determining the displacement of the hammer body under the action of force impulses.

The magnitude of the displacement of the axis of the force diagram is precisely the force that must be applied to the body in order to prevent its continuous withdrawal from the limiting collar of the tool. If the actual pressing force on the hammer is less than this displacement, the hammer body will move away from the tool to such an extent that the striker will deliver blows on the bridge of the barrel.

The calculation of the minimum pressing force on a hammer required for it to operate without idle strokes and without blows of the striker on the bridge of the barrel, by the method of B. V. Sudnishnikov, is rather complicated. In addition, the calculation is applicable for analyzing already existing machines, for which it is necessary to obtain pressure diagrams in the hammer cavities. Recording diagrams is always associated with known difficulties. For practical design and engineering work, in our opinion, relations can be derived that are more convenient to use. The initial material for such derivations is provided by experimental and theoretical investigations by a number of authors [3—9].

As established by O. D. Alimov [4], to reveal the interrelation of the pressing force with the main parameters of hammers, the impulse theorem (the theorem on the change in the quantity of motion of a system) can be successfully applied. In [4], a theoretical justification is given for the applicability of this theorem, and equations are derived for determining the components of the feed force of pneumatic drilling hammers. In view of the distinguishing features of the designs of riveting, breaking, and chipping hammers in comparison with drilling hammers (the absence of a drill-rotation mechanism, the presence of access of the tool shank into the cylinder cavity, etc.), use of the final conclusions of [4] for calculating these hammers appears possible only after clarifying the significance of individual arguments entering into the equations, and of the numerical coefficients attached to them. To this end we have carried out an analysis of the dynamics of chipping-riveting and breaking hammers, taking into account the special features of their designs.

With the hammer in a horizontal position, the following external forces act on the “hammer body–striker” system for breaking, riveting, and chipping hammers (Fig. 1, \(a\)):

\(Q\) — the pressing force on the hammer handle;
\(F_1\) — the force arising when the striker impacts the tool shank;
\(F_2\) — the contact force of the body with the limiting collar of the tool;

$F_3$ — the resultant force of the air pressure on the striker due to the difference between the areas of the striker and the housing on the side of the front cavity $B$;

$F_{\mathrm{fr}}$ — the forces of resistance to the motion of the housing along the drill shank and the resistance of the hammer’s supporting devices (the worker’s hand, the resistance of the air hose).

Using the impulse theorem according to the method set forth in [4], the principal components of the pressing force can be determined from the expressions:

\[ Q_1 = n\sqrt{2 A m_b}(\kappa + 1), \tag{2} \]

\[ Q_2 = n m_k V_k(\kappa_1 + 1), \tag{3} \]

\[ Q_3 = p_{\mathrm{av}} f_i \frac{t_1}{t_c}, \tag{4} \]

\[ Q_{\mathrm{fr}} = \frac{\displaystyle \int_0^t F_{\mathrm{fr}}\,dt}{t_c}, \tag{5} \]

where
$A$ — impact energy of the striker;
$n$ — impact frequency;
$m_b$ — mass of the striker;
$\kappa$ — coefficient of rebound of the striker after impact on the tool;
$f_i$ — cross-sectional area of the tool shank;
$P_{\mathrm{av}}$ — time-averaged air pressure in cavity $B$;
$t_1$ — duration of action of the pressure $p_{\mathrm{av}}$;
$t_c$ — cycle time;
$m_k$ — mass of the hammer housing;
$V_k$ — velocity of collision of the housing with the tool;
$\kappa_1$ — coefficient of rebound upon collision of the housing with the tool.

As is evident from equation (2), the force $Q_1$ is that part of the pressing force called by O. D. Alimov [4] the first component of the feed force, which must be applied to the housing in order to compensate for the action on the system of the force $F_1$ (Fig. 1) of contact between the striker and the shank of the tool.

The force $Q_2$ must be applied to the housing only in the case when collisions of the hammer housing with the tool occur; the conditions for this will be shown below.

The third component of the pressing force must compensate for the air pressure on the cross-sectional area of the striker equal to the cross-sectional area of the tool shank (the forces $F_3$, Fig. 1, a). Consequently, $Q_3$ can be determined when processing real pressure oscillograms of hammers.

The component of the pressing force $Q_{\mathrm{fr}}$ may be taken as:

a) in practical calculations, equal to 1–2 kg,

b) in the mathematical description and modeling of the system,

\[ Q_{\mathrm{fr}} = \kappa_{\mathrm{fr}} \frac{d x_k}{dt} \quad \text{or} \quad Q_{\mathrm{fr}} = R_{\mathrm{fr}} \operatorname{sgn}\frac{d x_k}{dt} \]

(corresponding to viscous or dry friction).

The ratio of the components of the pressing force can be shown more clearly graphically. Figure 3 shows a simplified diagram of the distribution of the pressing force into components as a function of its magnitude. The graph of the interrelation between the pressing force and its components was constructed as follows.

Along the coordinate axes are laid off scales of the pressing force and of its components \(Q_i\). At an angle to the axes a straight line \(OAB\) (\(Q_i=Q\)) is drawn, corresponding to the pressing forces actually applied to the hammer. On the graph, the dependences of the components of the pressing force on its magnitude are constructed, calculated from formulas (2), (3), (4), (5), or determined experimentally. In order to clarify the principle of constructing the graph, let us make the entirely possible assumptions that:

Fig. 3. Distribution of the pressing force into individual components.

a) the friction forces \(Q_{\text{fr}}\) do not depend on the pressing force;

b) the air pressure in the front cavity decreases somewhat with increasing pressing force [6]; therefore \(Q_3=F(Q)\) has the character of an inclined straight line;

c) the dependence \(Q_1=F(Q)\) also has the form of an inclined straight line, owing to the decrease in the impact energy of the striker [6] with increasing pressing force. We shall also assume that the rebound coefficient of the striker upon impact against the tool does not depend on the pressing force on the hammer.

Plotting the dependences \(Q_1\), \(Q_3\), and \(Q_{\text{fr}}\) on the pressing force on the graph and summing them graphically, we obtain the line \(BB\) (Fig. 3), which characterizes the pressing force required to compensate these components. Let us divide the graph into characteristic zones of pressing forces, the boundaries of which are marked by points \(A\) and \(B\).

In zone I, operation of the hammer is impossible, since the pressing force \(Q\) produced is less than the force required to compensate \(F_3\) and \(F_{\text{fr}}\). Immediately after the hammer is started, the body will move away from the tool by an amount exceeding the length of the tool shank (Fig. 1), and the hammer will cease to operate.

At pressing forces less than \(Q_{\min}\) (zone II, Fig. 3), operation of the hammer is possible, but inadvisable. The pressing force produced compensates the friction forces \((F_{\text{fr}})\), the resultant \(F_3\) (as in zone I), and partially compensates the reaction from the collision of the striker with the tool shank \((F_1)\). However, in this zone \(Q<Q_1+Q_3+Q_{\text{fr}}\); consequently, the entire impulse of the force \(\int_0^t F_1 dt\) cannot be transmitted to the drill, but only part of it. The quantity of motion of the striker not transmitted to the drill must be closed in the “hammer body–striker” system. It may be denoted by \(Q_4 t_c\), where

\[ Q_4=(Q_1+Q_3+Q_{\text{fr}})-Q. \tag{6} \]

Consequently, at pressing forces less than \(Q_{\min}\) (point \(B\)), part of the striker energy stored by it during the working stroke is spent on destruc-

tion of the barrel bridge 6 (Fig. 1, a), or in compression of the front air buffer B (Fig. 1, b) in the front chamber of the hammer. Obviously, such an operating mode of a pneumatic hammer should not be considered normal. The operating pressing force must be greater than \(Q_{\min}\).

In zone III (Fig. 3), the pressing force being produced exceeds that required to compensate the impulses of the forces \(F_1\), \(F_3\), and \(F_{\mathrm{tr}}\). It becomes possible to compensate the contact force between the hammer body and the tool. The component of the pressing force \(Q_2\) increases in zone III in proportion to \(Q\), owing to an increase in the contact time of the hammer body with the limiting collar of the tool.

It should be noted that impacts of the hammer body against the tool are also possible in zone III of pressing forces, but they are of a highly random nature and are repeated very rarely. Therefore their influence on the change in the described relation of force impulses is insignificant.

Using the dependences given above and, additionally, certain experimental materials, it is possible to determine rational pressing forces for pneumatic hammers of various purposes. Table 1 gives the components of the pressing force for KE-type hammers, determined from formulas (2), (3), and (4). The energy data of the hammers and the rebound coefficients of the striker and body upon impact against the tool were obtained experimentally.

Table 1

Values of the components of the pressing force

However, such a calculation cannot always be acceptable for production engineers, owing to the absence of reliable data on the magnitudes of the rebound coefficient in the collision of hammer elements, as well as

in the absence of the possibility of obtaining experimental data on the hammer being designed. Therefore, using the accumulated knowledge and experimental data, let us derive simpler relationships.

With comparatively small error it may be assumed that the force diagram of a pneumatic hammer is a sinusoidal function (Fig. 2). In this case it is evidently possible to draw the mean line of the force diagram, taking as a guide the amplitude values of the acting forces. Let us provisionally call this mean line the “axis of the sinusoid.” Then the displacement of the axis relative to the real zero straight line (the time axis of the diagram) will represent that minimum value of the pressing force which must be applied to the hammer in order to eliminate idle strokes and blows of the striker against the barrel bridge.

As can be seen from the graphs (Fig. 2), the determination of \(Q_{\min}\) is easily performed by the formula

\[ Q_{\min}=\frac{P_{\max}-P_{\min}}{2}, \tag{7} \]

in which, under the assumptions adopted above, the arguments may be found from the expressions:

\[ P_{\max}=\frac{\pi}{4}p_cD_{\mathrm{ц}}^{2}, \]

\[ P_{\min}=\frac{\pi}{4}\alpha p_c\left(D_{\mathrm{ц}}^{2}-d_{\mathrm{н}}^{2}\right), \]

where \(\alpha=\dfrac{p_2}{p_{c1}}\) is the ratio of the air pressure in the front cavity to the air pressure in the line.

Fig. 4. Nomogram for calculating the minimum pressing force and selecting the cylinder diameter of pneumatic hammers.

According to experimental data [3, 5, 7], one may take \(\alpha=0.7\); then formula (7) takes the form

\[ Q_{\min}=\frac{\pi}{8}p_c\left(0.3D_{\mathrm{ц}}^{2}+0.7d_{\mathrm{н}}^{2}\right). \tag{8} \]

As we see, to calculate the minimum pressing forces that ensure normal operation of the hammer, by formula (8) it is sufficient to know the diameters of the cylinder and of the tool shank and to specify the possible working air pressure. The best combination of hammer dimensions for assigned pressing forces is conveniently selected from the nomogram (Fig. 4).

For an inclined position of the hammer, corrections should be introduced for the component of the hammer weight

\[ Q'_{\min}=Q_{\min}\pm G_{\mathrm{m}}\sin\beta, \]

where \(\beta\) is the angle of inclination of the hammer to the horizontal,
\(G_{\mathrm{m}}\) is the weight of the hammer.

For certain types of pneumatic hammers, the minimum forces calculated by formula (8) are given in Table 2. The minimum pressing forces obtained by formula (8) and from the components \(Q_1\) and \(Q_3\) (Table 1) differ very little, which demonstrates the applicability of the proposed simplification for calculating \(Q_{\min}\).

Table 2

Some technical characteristics of pneumatic hammers
\((p_c = 5\ \text{atm})\)

*) In the presence of impact on the tool shank.

The analysis carried out of the dynamics of operation of hand-held pneumatic hammers provides the basis for the following conclusions.

1. The pressing force in pneumatic chipping-riveting, breaker, and drilling hammers is a factor that ensures the transfer of energy to the working tool.

2. The magnitude of the minimally necessary pressing force on the hammer is determined mainly by the momentum transmitted from the machine to the working tool, the frequency of blows, and the diameter of the tool shank. The value of \(Q_{\min}\) can be determined with accuracy sufficient for practice by the formula (8) given in the article and by the nomogram (Fig. 4).

3. To ensure normal operation with hand-held riveting hammers (of the KE type) and breaker hammers in the horizontal position, it is necessary to create a pressing force of not less than 16–18 kg. Thus, it is inadvisable to evaluate their vibration at standardized pressing forces of 15 kg [10].

4. In order to reduce the minimum required pressing force when working with hand-held pneumatic hammers, one should strive to reduce the cross-section of the tool shank to the minimum allowed by the conditions of its strength. For example, the diameter of the tool shank of KE-type hammers is unjustifiably overestimated. As a result, the pressing force required for normal operation of these hammers is greater than for breaker hammers, although the latter have a larger cylinder diameter and possess greater power.

REFERENCES

1. E. Ts. Andreeva-Galanina. Vibration and Its Significance in Occupational Hygiene. Medgiz, 1956.

2. E. Ts. Andreeva-Galanina, V. G. Artamonova, E. A. Drogichina. Vibration Disease. Medgiz, 1961.

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

4. O. D. Alimov. Relationship between the feed force and the basic parameters of a drilling hammer. Izvestiya TPI, vol. 108, Metallurgizdat, 1959.

5. V. F. Gorbunov. The working process of drilling hammers with a ring spool valve. Izvestiya TPI, vol. 108, Metallurgizdat, 1959.

6. V. F. Gorbunov, V. I. Baburov. Investigation of the internal processes and parameters of chipping and riveting hammers. Izvestiya TPI, vol. 123, Tomsk University Press, 1963.

7. V. F. Zinin. The influence of axial force on the drilling speed of percussion drills. Izvestiya vuzov, Mining Journal, No. 6, 1961.

8. A. M. Petreev. On the theory of the working cycle of pneumatic impact machines. In: Mathematical Methods in Mining, Part 1, Mining Machines and Automation. Publishing House of the Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1963.

9. B. V. Sudnishnikov. Influence of the parameters of the direct stroke on the power and recoil of a pneumatic hammer. Percussive-Rotary Drilling. Impact Machines. Novosibirsk Book Publishing House, 1956.

10. Collection of the Most Important Official Materials on Questions of Occupational Hygiene and Industrial Sanitation, issue 11. Medgiz, 1962.