On the Transmission of Impact Energy Through an Elongated Rod
Abstract Generated abstract
This paper reports an experimental study of how impact energy is transmitted through an elongated drill rod to an elastoplastic medium, a problem relevant to percussive drilling tools and to evaluating theoretical models of impact energetics. Using a pendulum hammer, assembled steel rods up to 30 m long, and a steel ball bit producing calibrated spherical indentations in polished steel specimens, the transmitted energy was estimated from the indentation diameter and compared with the initial striker energy. The experiments found that the energy transfer coefficient in the tested collision system was relatively high, averaging about 75 to 80 percent, and changed only slightly as the composite rod length increased to 30 m. The results suggest that efficient transfer under these conditions is associated with the wave component of the impact energy.
Full Text
On the Transmission of Impact Energy Through an Elongated Rod
A. G. Tsukanov
(Presented by the Department of Theoretical Mechanics)
The article presents the results of an experimental study of the transmission of impact energy through an elongated rod. This question is of considerable importance in the design of machines and tools of impact action intended for drilling geological-prospecting and drilling-and-blasting boreholes; it is also important for experimental verification of theoretical assumptions used in analytical studies of problems in impact energetics.
The losses of the impact energy of a striker upon collision in the system “striker — tool — material” are usually reflected by introducing the corresponding coefficients, and the overall coefficient of energy transmission is represented by the formula
\[ \eta = \eta_1 \eta_2, \]
where \(\eta_1\) is the coefficient accounting for unproductive expenditures of energy in the collision of the striker and the drill rod;
\(\eta_2\) is the coefficient accounting for energy losses in the collision of the rod and the material being fractured.
In determining the coefficient \(\eta_1\), the formula proposed by B. I. Bokii [1] and Yu. M. Malakhov [2] is most often used,
\[ \eta_1 = (1 + c_1)^2 \frac{m_1 m_2}{(m_1 + m_2)^2} \]
and the formula of P. S. Kucherov [3]
\[ \eta_1 = 1 - (1 - c_1^2)\frac{m_2}{m_1 + m_2}, \]
where \(C_1\) is the coefficient of restitution upon impact; \(m_1, m_2\) are, respectively, the masses of the striker and of the rod.
Our investigations of the coefficient \(\eta_1\) are set forth in work [4]. The coefficient \(\eta_2\) has been less studied, although its significance in the question of transmitting impact energy to the volume being fractured is very great. It does not have sufficiently clear mathematical dependencies that would reflect the actual picture of the energy losses occurring during impact contact of the crown blade with the rock. This coefficient synthesizes the mechanical properties of both the tool and the material or rock being worked. It depends on the geometry of the tool.
The coefficient \(\eta_2\) must reflect the discontinuous character of the destruction of rock or other specific features of destruction characteristic, for example, of frozen soil or metal. To determine the coefficient \(\eta_2\), the formula most commonly used is
\[ \eta_2 = 1 - c_2^2, \]
where \(c_2\) is the coefficient of restitution in the collision of the tool and the material being destroyed.
There are other formulas for the indicated coefficients, based on theoretical premises of the wave theory of impact [5, 6]. In deriving these formulas, the law of linear penetration of the tool into the medium being worked is used. However, the discrepancy between the theoretical premises adopted in deriving the indicated formulas and the characteristic laws governing the process of destruction of materials, especially rocks, makes it impossible to assess the actual losses of impact energy.
This article presents the results of investigations in which an attempt is made, by experimental means, to give a quantitative estimate of that part of the hammer energy which is transmitted through the drill rod to an elastoplastic medium, without taking into account the discontinuous process of material destruction. These experimental conditions correspond to a greater extent to the theoretical premises adopted in deriving formulas for the coefficients of energy transmission.
The experiment was based on the idea of a calibration curve reflecting the change in the diameter of a spherical indentation as a function of different values of impact energy. The source of impact energy was a pendulum hammer, into the striking part of which a drill bit was screwed; instead of a hard-alloy plate, the bit was equipped with a steel ball. The weight of the pendulum hammer was \(94.5\ \mathrm{N}\).
To obtain the calibration curve, spherical impact indentations corresponding to different values of the pendulum-hammer energy were made on polished specimens of steel 30. After the calibration curve had been obtained, the bit with the sphere was screwed onto the rod, and a hammer identical in geometry and weight, but without a sphere on its end face, was screwed into the pendulum. With this end-hardened part of the hammer, the pendulum struck the shank of the rod.
The set of rods consisted of an assemblage of round bars made of steel 45, \(32\ \mathrm{mm}\) in diameter, each \(5\ \mathrm{m}\) long. Threads were provided at both ends of the rods. The end planes of the rods were well machined, which is extremely necessary for obtaining the best impact contact.
In carrying out the experiment, the length of the rod participating in the collision was gradually increased by adding subsequent rods. They were screwed together by means of couplings, ensuring, as far as possible, the best end contact during collision. The total length of the assembled rod reached \(30\ \mathrm{m}\). The rods were arranged horizontally on flexible wire suspensions; at the same time, the end of the rod equipped with the bit with the ball rested against the specimen intended for obtaining the indentation. The second end of the rod was struck by the pendulum hammer. The impact energy of the hammer, \(A_1\), was kept constant for a given series of experiments. For example, curves (a) and (b) in Fig. 1 were obtained with initial hammer energies respectively equal to \(82.2\ \mathrm{J}\) and \(41.1\ \mathrm{J}\).
During the impact, a certain part of this energy was transmitted through the rod to the bit with the ball, ensuring impact contact with the specimen. A spherical indentation remained on the surface of the specimen, reflecting the work of plastic deformation corresponding to that part of the energy of the pendulum hammer which was transmitted by means of the rod. The work
of plastic deformation in the given collision will be the “useful” work of the impact. To determine the numerical value of the energy \(A_2\) corresponding to this work, it is sufficient to measure the diameter of the resulting impression and use the calibration curve. The ratio of the obtained value of the energy \(A_2\) to the energy of the striker pendulum before impact, \(A_1\), will determine the energy-transfer coefficient in the collision system under consideration.
Thus, we obtained the possibility of giving a quantitative estimate of the impact energy transmitted from the striker through the rod to the specimen. Depending on the mechanical and other properties of the medium being treated or destroyed, this useful part of the energy will pass into other forms of energy, while performing a certain amount of work of varying efficiency.
Fig. 1. Experimental values of the impact-energy transfer coefficient.
\(a\)—curve corresponding to an impact energy of \(82.2\) J; \(b\)—curve corresponding to an impact energy of \(41.1\) J.
In our experiment, the indicated part of the useful energy of the striker is represented in the form of the work of plastic deformation.
Conclusions
The results of the experiment show that the coefficient of transfer of impact energy in the collision system of bodies under consideration is fairly large and averages \(75\text{–}80\%\) of the initial energy of the striker. With an increase in the length of the composite rod up to \(30\) m, the energy-transfer coefficient changes only slightly, remaining practically constant. This high efficiency of energy transfer can be achieved only by virtue of the wave component of the impact energy.
Literature
- B. I. Bokii. A Practical Course in Mining Art, 1931.
- Yu. M. Malakhov. Mining Journal, No. 2, 1934.
- P. S. Kucherov. Coal, No. 93, 1933.
- A. G. Tsukanov. On the transfer of energy upon impact in drilling percussive hammers. Proceedings of Higher Educational Institutions, Mining Journal, No. 6, 1962.
- V. M. Mostkov. Fundamentals of the Theory of Pneumatic Drilling. Ugletekhizdat, 1952.
- Yu. V. Belyaev. On estimating the degree of utilization of impact energy in impact machines. Proceedings of VNIIstroydormash, issue No. 10, 1955.