On the Elastic Displacement of an Elongated Rod Under Longitudinal Impact

A. G. Tsukanov, V. I. Chiryev

(Presented by the scientific seminar of the Department of Theoretical Mechanics)

In percussive drilling, the energy required to destroy a certain volume of rock is transmitted to the face through a joint of drill rods in the form of an impact impulse. When passing through the joint, part of the energy and impulse is lost \[1, 2, 3, 6\], and only part of the impact energy is transmitted to the volume of rock being destroyed. In the process of transmitting impact energy, an essential role is played by the behavior of the rod joint as an intermediate elastic link of the impact system. Theoretical studies on this question have not yet provided an acceptable solution to the problem and indicate the need for experimental investigations. In laboratory studies, the results of which are presented below, the influence on the behavior of the rod joint was considered when varying such parameters as the length of the joint, the dimensions and geometry of the striker, and the type of breaking tool.

The experiments were carried out on an installation consisting of a rod joint made of round drill steel, a pendulum with an interchangeable striker, adopted as the source of the impact energy, a breaking tool (a chisel bit, a tip with an embedded steel ball), and reference bars made of steel 30, which were adopted as the medium absorbing the impact energy transmitted along the rod joint. The rods were arranged horizontally; the rods were connected by end couplings.

The experimental installation included recording and measuring apparatus specially developed and manufactured at the department. The displacement of the rods and the tool was measured by a photoelectronic displacement sensor, the output signal of which was fed to the input of an S1-8A oscilloscope.

The contact time of the striker with the joint and of the joint with the energy-absorbing medium was recorded by a contact-time sensor.

The investigated parameters were as follows:

Diameter of the steel ball . . . . . . mm 12.7
Number of couplings . . . . . . . . pcs. 1–6
Threaded connection . . . . . . . . M30

Below, some results of the study of the displacement of the rod under the action of a single impact are presented.

In Fig. 1 oscillograms are given for the displacement of the tool at varying rod length; in this case the impact was delivered by a striker 220 mm long, with a velocity at the initial instant of impact contact of 3.05 m/sec and an impact energy of 6.31 kg·m.

Fig. 1. Rod length: 1—5.5 m, 2—10.5 m; 3—15.5 m; 4—20.5 m; 5—25.5 m. Tool: a) bit; b) tip with a ball; c) tip with a ball

From the oscillograms shown in Fig. 1 it follows that, for example, for a rod 15.5 m long, penetration of the tool into the medium absorbing the energy (a steel specimen) occurs over a time of 2.5–3 msec, while the maximum time of motion of the rod in the direction of impact reaches a value of 9 msec. However, no clearly expressed regularity in the change of the depth of tool penetration with change in rod length was found. It should be noted that, for all rod lengths, repeated displacement of the tool in the direction of impact is characteristic. And only after this repeated displacement does rebound of the rod from the material being destroyed occur.

In Fig. 1,c oscillograms of displacement and of the time of impact contact are compared. The upper oscillogram shows the contact time

the striker with the drill string; in this case the upper level corresponds to contact of the striker with the shank, the middle level corresponds to simultaneous contact of the striker, the rod, and the medium being broken, and the lower level corresponds to contact of the rod only with the medium being broken. It follows from Fig. 1, c, that the repeated motion of the drill string in the direction of impact coincides in time with the repeated collision of the striker with the shank of the drill string; the rebound of the drill string has a periodic (stepped on the oscillogram) character, which is caused by the repeated passage and reflection of the impact stress pulse from the tool and the shank of the drill string.

Figure 2 presents oscillograms of the elastic displacements of the rod material, recorded in different cross sections along the length of the drill string.

Here two types of boundary conditions were considered:

a) during impact the drill string is in contact with the medium by means of the bit;

b) the end of the drill-string tip is rigidly clamped.

From the oscillograms considered it follows that a cross section recorded at different points along the length of the rod begins to move after the start of impact after the lapse of time \(t = \frac{l}{a}\), where \(l\) is the distance of the given section from the shank; \(a\) is the speed of sound in steel.

Fig. 2. Displacement of transverse sections recorded along the length of the rod at a distance from the striker: 1 — 0.5 m; 2 — 10.5 m; 3 — 20.5 m; 4 — 25 m; total length of the rod — 25.5 m

Comparing the oscillograms of the displacement of the transverse sections of the drill string obtained for the case of rigid clamping of the end with the oscillograms when penetration of the bit into a medium absorbing the impact energy took place, one can determine the magnitude of the displacement of the recorded section of the drill string caused by the advance of the impact stress pulse, as well as the magnitude of the indicated penetration. Since the magnitude of penetration can be obtained by direct measurement, for example with a clock-type indicator, a control comparison was made between the penetration values obtained by the indicator and those obtained from the oscillograms. The difference in the numerical values did not exceed 10%. Of definite interest is a comparison of the displacement values obtained at different points along the length of the rod. Thus, for example, the displacement in the direction of impact of the end section of the shank and of sections located sufficiently close to it is approximately 50% greater than the displacement

end section at the bit. This is explained by the elastic deformation of the shank material, the dynamic compliance of the elastic joint, and possible longitudinal bending [4]. The greatest displacement of the shank tail corresponds to a shank length of 15.5 m. The results of the experiments carried out are of definite interest in designing percussion drilling machines. As an example, let us consider the question of the duration of displacement of drilling shanks. In the literature [5] it is asserted that displacement of the shank ceases by the time the second or third reflected stress impact pulses arrive and that, consequently, the shank, as an intermediate link of the impact system, has no influence on the operating regime of the drilling machine.

Fig. 3. Displacement of the tail of a shank 25.5 m long, impact energy—6.31 kgm:
a) the shank is fitted with a bit;
b) the shank is rigidly clamped

To analyze this question, which is important for practice, let us consider Fig. 3, which gives oscillograms of the displacement of a shank 25.5 m long when it collides with a cylindrical striker 220 m long.

Suppose that the shank length is 25 m; then, in accordance with the statement made above, the motion of the shank after the next collision with the striker should cease after 20–25 m/sec; further, if the frequency of blows is taken to be 3000 per minute, then every 20 m/sec the striker will deliver a blow to the tail of the shank, which by the beginning of the collision will have ceased its motion. Analysis of the oscillograms in Fig. 3a shows that by the beginning of the next collision with the striker the shank is not at rest; the duration of its displacement is 220 m/sec, and, consequently, by the beginning of the next collision the shank will be moving counter to the working stroke of the striker and, of course, will affect the overall regime of the impact system.

Further analysis of the experimental data shows that, in order to ensure effective percussion drilling, the blow frequency of the drilling machine must be selected in accordance with the length of the shank.

REFERENCES

1. Roberts, Hooks, Farby. Energy transfer in percussion drilling. Express Information. “Mining Industry,” No. 2, 1963.

2. A. G. Tsukanov. On losses of impact energy in elongated shanks. Izvestiya vuzov, “Mining Journal,” No. 10, 1965.

3. K. I. Ivanov, V. D. Andreev. On the calculation of stresses in percussion drilling. Collection “Blasting,” No. 56/13, Nedra, 1964.

4. K. I. Ivanov, V. D. Andreev. Face processes and the energy intensity of rock destruction in drilling. Collection “Blasting,” No. 56/13, Nedra, 1964.

5. K. I. Ivanov, M. I. Ermolenko, V. I. Dusev, V. D. Andreev. Drilling Technology, Nedra, 1966.

6. S. Takaoka. Reflection of elastic waves in jointed connections of a drill rod. Translated from Japanese, VINITI, 1963.