CALCULATION AND STUDY OF THE AERODYNAMIC DRAG OF HAMMERS

V. I. Baburov, A. I. Proshev, A. I. Pashnin

(Presented by the scientific seminar of the Department of Mining Machines, Mine Transport, and Mining Mechanics)

A pneumatic hammer is a mechanical converter of the energy of compressed air into the kinetic energy of the striker, which, through impact, is converted into useful work. Consequently, the smaller the losses of air pressure in the converter, the more fully the energy of the compressed air will be utilized, and the more perfect the machine as a whole will be [4, 5].

Compressed air, as a body and as an energy carrier, is characterized by viscosity, density, flow rate, and velocity of motion.

Table 1

Characteristics of compressed air at a temperature of 20°C

Viscosity is inherent in all real gases and manifests itself during motion in the form of internal friction. The principal characteristics of compressed air under the experimental conditions are given in Table 1. The dynamic coefficient of viscosity at a temperature of 20°C is $180.9 \cdot 10^{-6}\ \text{g}/\text{cm}\cdot\text{s}$ [2].

The regime of gas motion (laminar or turbulent) depends on the ratio of the inertial forces and the viscous forces (internal friction) in the flow. This ratio is characterized by the dimensionless Reynolds number:

\[ R_e = \frac{V_0 D_0}{\nu}, \tag{1} \]

where $V_0$ is the flow velocity, m/s;
$D_0$ is the pipe diameter, m.

For each installation there exists a certain range of “critical” values of the number \(R_e\), at which transition from one regime to another occurs.

The lower limit of the Reynolds number in the case of a circular cross section is 2300, while the upper limit depends on the conditions at the pipe entrance, the condition of the wall surfaces, and other causes.

The conversion of part of the flow energy into heat is caused by the molecular and turbulent viscosity of the moving medium. These losses of compressed-air energy are called friction losses \((\Delta H_{\text{fr}})\), or losses along the length of the pipeline. In addition, there are also local losses \((\Delta H_{\text{loc}})\), which arise when the normal course of the flow is locally disturbed, when it separates from the wall, when vortices form at places where the pipeline configuration changes, when obstacles are encountered, etc. Local resistances (losses) also include the losses of velocity (dynamic) pressure when the flow leaves the network into a large volume (the atmosphere). In calculating aerodynamic resistances in hammers, the total losses were found by us by summation according to the superposition principle, i.e.,

\[ \Delta H_{\text{sum}}=\Delta H_{\text{fr}}+\Delta H_{\text{loc}}. \tag{2} \]

Over the entire path from the compressor to the hammer, the compressed air loses part of its energy in overcoming local resistances and friction along the length. Estimating these losses in hoses, the air-distribution device, and the hammer passages is of interest both in its formulation and in the possible conclusions.

1. Calculation of air pressure losses in hoses

In most cases, air is supplied to hammers through rigid and flexible pipelines of various dimensions, both in length and in diameter. Let us calculate the pressure losses of compressed air in hoses (flexible pipelines) as a function of their length and of the air consumption.

The hoses used in operation have an internal diameter of 16 mm. Their length from the rigid pipeline to the hammers is usually 10–20 m, and the air consumption, depending on the machine size, is 0.5–2.5 m\(^3\)/min. Measurement and calculation of air pressure losses in hoses were carried out using an experimental setup. The principal measuring elements of the setup were differential manometers. One of them was intended for accurate determination of air consumption, and the other for the pressure drop. A sharp-edged orifice of diameter 18 mm was selected as the throttling device of the differential manometer. From the readings of this differential manometer, filled with tinted water, the air consumption was calculated by the formula

\[ Q=\mu F_0 \sqrt{\frac{2g}{\gamma_1}(P_1-P_2)}, \ \text{m}^3/\text{min}, \tag{3} \]

where \(\mu\) is the coefficient of air flow through the orifice;
\(F_0\) is the area of the orifice opening, m\(^2\);
\(\gamma_1\) is the specific weight of the compressed air, kg/m\(^3\);
\(P_1, P_2\) are the readings of the differential manometer, kg/m\(^2\).
For practical calculations this formula is modified,

\[ Q=2.087\cdot 10^{-2} D_0^2 \varepsilon K_t \alpha \sqrt{\frac{P_1-P_2}{\gamma_1}}, \tag{4} \]

where \(D_0\) is the diameter of the diaphragm orifice, m;
\(\alpha\) is the discharge coefficient;
\(\varepsilon\) is a correction coefficient for gas expansion. It is customary to express the air flow rate by its volume reduced to the free state. Therefore, in equation (4) a correction for the specific weight \(\left(\dfrac{\gamma_1}{\gamma_0}\right)\) must be introduced. In addition, the influence of temperature must be taken into account. In our case the temperature taken as normal is \(20^\circ\text{C}\). Then the temperature correction coefficient is \(K_t=1\) [6].

The pressure drop in the manometer tubes is related to the difference in the levels of the liquid in the differential manometer by the equation [6]

\[ P_1-P_2=h\cdot \gamma_{\mathrm{liq}}\cdot 10^{-4}, \tag{5} \]

where \(h\) is the difference in liquid levels in the manometer tubes, m;
\(\gamma_{\mathrm{liq}}\) is the specific weight of the manometer liquid \((0.998\ \text{g}/\text{cm}^3)\), kg/m\(^3\).

For a known value of the air flow rate, the pressure losses in the hose are found in the following order:

1. The velocity of air motion is

\[ V=\frac{Q}{F_{\mathrm{h}}}, \tag{6} \]

where \(F_{\mathrm{h}}\) is the internal cross section of the hose, m\(^2\).

1. The Reynolds number at this velocity is

\[ R_e=\frac{V D_{\mathrm{g}}}{\nu}, \qquad D_{\mathrm{g}}=\frac{4F_{\mathrm{h}}}{P}, \]

where \(D_{\mathrm{g}}\) is the hydraulic diameter of the adopted section, m;
\(P\) is the perimeter of the section, m.

1. Then the coefficient of friction along the length will be equal to

\[ \zeta_{\mathrm{fr}}=\lambda \frac{l}{D_{\mathrm{g}}}, \]

where \(l\) is the length of the section (hose), m;
\(\lambda\) is the coefficient of frictional resistance of a unit relative length of the section being calculated (determined from the tables and diagrams of I. E. Idelchik) [4].

1. Since the coefficient of local resistance \(\xi_{\mathrm{m}}=0\),

\[ \zeta_{\mathrm{sum}}=\zeta_{\mathrm{fr}}+\zeta_{\mathrm{m}}=\zeta_{\mathrm{fr}}. \]

1. Then

\[ \zeta_{\mathrm{red}}=\zeta_{\mathrm{sum}}\frac{\gamma_0}{\gamma_i}, \tag{7} \]

where \(\gamma_i\) is the specific weight of air at its corresponding pressure.

1. The pressure losses are determined from the data already found, namely:

\[ \Delta H=\zeta_{\mathrm{red}}\frac{V^2\gamma_0}{2g}. \tag{8} \]

Table 2 gives the values of compressed-air pressure losses at 5 ati in a supply hose 15 m long and 16 mm in diameter (GOST 8318-57), calculated in the manner described above. The calculations show that the resistance of hoses is proportional to their length and to the air flow rate. For practical engineering calculations we have proposed the empirical formula:

\[ \Delta H = 0.009 Q^{1.7} L,\quad \text{kg/cm}^2, \tag{9} \]

where \(L\) is the hose length, m.

Table 2

Compressed-air pressure losses in a hose 15 m long

In the case of operation of several hammers of the same type, but with different lengths of supply hoses, the total losses, taking into account hose bending, can be calculated by the formula

\[ \Delta H_{\text{sum}} = \sum_{i=1}^{n} \left(0.009 Q^{1.7} L_i + \alpha L\right), \tag{10} \]

where \(\alpha\) is a coefficient that accounts for additional air pressure losses as a result of hose bending \((\alpha = 0.004\text{–}0.009)\).

2. Determination of the aerodynamic resistances of hammer starting devices

The resistances of starting devices were determined theoretically and experimentally. If in hoses the principal resistances are lengthwise resistances, then in the structural elements of hammers the corresponding resistances are local resistances. Therefore, in this case it is more convenient to calculate losses by summing the reduced resistance coefficients of the individual sections of the network.

The starting devices of the chipping and riveting hammers of the Tomsk Electromechanical Plant, MP and KE, are completely identical. Dividing the air-duct path of the starting device into 9 sections and determining the losses at an air pressure in the network of 5 ati, we established that the modern designs of hammer starting devices are far from perfect.

The pressure losses calculated for the individual sections, for the entire starting device, were also checked by us experimentally. The difference amounts to thousandths, i.e., it is insignificant. The main point in the analytical calculation is the precise determination of the magnitude of the overall resistance coefficient. It can also be found from the same formula (8), if the total air pressure losses are measured experimentally, as was done using the setup shown in Fig. 1.

In this way the values of the resistance coefficients of the starting devices of hammers of various designs were found. For the PM-D8 hammers of the Gorky Automobile Plant it is equal to 1.62; for the Izhevsk Mechanical Plant ...

Fig. 1. 1 — pneumatic hammer; 2, 4 — differential manometers; 3 — throttling device; 5 — connecting tubes; 6 — valve

of type R-1, 2, 3—2.0; from the Nikolaev Plant named after Nosenko PM-35, 55, 75—1.7, respectively, and the air pressure losses in them are: 0.31 kg/cm², 0.38 kg/cm², and 0.32 kg/cm², i.e., considerably higher in comparison with hammers of the MP and KE types (Table 3).

Table 3

Air pressure losses in the starting devices of hammers at 5 ati

The magnitude of the aerodynamic drag of the starting devices of hammers can also be evaluated as a percentage, according to the index

\[ \eta = \frac{P_0 - \Delta H}{P_0}, \tag{11} \]

where \(P_0\) is the air pressure at the inlet to the starting device, ati;
\(\eta\) is the index of perfection of the design of the starting device (handle); the values of \(\eta\) are given in Table 3.

Analysis of the drag values of individual sections of the air-supply path shows that the largest of them are the local resistances of the ball shutoff device. Thus, for the case considered, the drag coefficient of the handle path without the spring-

... of the rod, the ball, and the pusher is 0.44, while the losses in this case are equal to 0.16 kg/cm², which constitutes 57% of the sum of all losses.

An important aspect of these studies is also that they made it possible to compare and evaluate the magnitudes of local resistances and resistances along the length.

In hammers of the MP and KE types, about 5–10% of the total pressure losses are losses caused by resistance along the length, while the remaining 80–95% of the losses are due to the presence of local resistances. In other hammer designs this ratio differs still more. The data presented show how important it is, in the design and manufacture of hammers, to provide for the maximum reduction of resistances to air motion.

The magnitude of the resistance coefficient depends not only on the design of the hammer elements, but also on the air flow rate and its pressure in the network. For this reason, under the same conditions, the losses for KE-type hammers are greater than for MP-type hammers, which have a lower compressed-air consumption.

3. Calculation and study of the aerodynamic resistances of the air-distribution devices of hammers

Significant resistances to air motion occur in air-distribution systems. These resistances are found both in the distribution mechanism and in the channels through which air enters the rear and front cavities of the hammer. Depending on the design features of the air distributor and on the standard sizes of the machines, the hydraulic resistances will, naturally, be different.

Using the calculation procedure described above, we calculated the resistances of the air-distribution device of the MP-5 chipping hammer.

On the whole, when air moves into the front cavity of the hammer, the total coefficient of aerodynamic resistance is 3.6, i.e., almost twice as high as the resistance coefficient of the starting device.

Air is supplied to the rear cavity of the hammer along a shorter path; therefore the aerodynamic resistances of this tract are much smaller. Calculations show that they are equal to 1.96. The maximum values of compressed-air pressures in the hammer cavities are in approximately the same ratio to one another. The losses in the distribution device of the BS3-135V hammer are somewhat smaller. They are respectively equal to 0.47 kg/cm² and 0.30 kg/cm².

Table 4

Coefficients of hydraulic resistances

Table 4 gives the values of the coefficients of aerodynamic drag of the hammers as a whole. From these data it follows that hammers with valve air distribution are characterized by greater aerodynamic drag than hammers with spool distribution.

Conclusions

1. The studies we carried out and the analysis of hammer designs from the standpoint of the magnitude of aerodynamic drag showed that, in creating these machines, absolutely no measures are provided for reducing the resistance of the air-conducting path. Smooth transitions are absent, and the walls of the elements have considerable roughness. Nevertheless, fairly simple design changes make it possible to noticeably reduce the resistance of hammers and thereby increase their energy parameters. Thus, in this respect, hand riveting hammers have hidden reserves.

2. According to the research data, the greatest aerodynamic drag is characteristic of the BS3-135B hammer. If air is supplied directly to the valve chamber, bypassing the starting device and the flexible hose, then the drag coefficient of the hammer will decrease by 3.5, i.e., almost by a factor of 2. Experiments have established that the volumetric chipping rate in this case increases by 11%. This indicates that, as a result of reducing aerodynamic drag, it is possible to increase the impact power of the machine with only a slight increase in air consumption.

References

1. V. I. Baburov. Study of pneumatic chipping-riveting hammers. Candidate dissertation. Tomsk, 1964.

2. N. B. Vargafik. Handbook on the thermophysical properties of gases and liquids. Gosfizmatizdat, 1963.

3. V. F. Gorbunov, V. I. Baburov et al. Hand pneumatic hammers. Mashgiz, 1967.

4. I. V. Idelchik. Hydraulic Resistances. Gosenergoizdat, 1961.

5. A. S. Ilyichev. Mine Pneumatic Installations. Gosgortekhizdat, 1954.

6. P. P. Kremlevskii. Flowmeters. Mashgiz, 1960.