Determination of damping coefficient of shock impulse for rocks grinding process

Abstract

Introduction. The physical properties of rocks, which determine the choice of the type of mill, as well as its operating parameters, are considered. The importance of studying the damping properties of the crushed material and their influence on the energy intensity of the grinding process is noted. Research methods and materials. The differential equation of motion of the crack wall, previously obtained by the authors of the article, is applied when it is exposed to a shock wave with amplitude σ and duration τ. The classical theory of damped oscillations of the system is used to determine the damping decrement of the shock pulse amplitude. A series of experimental studies was carried out on a laboratory sample of a drum mill to determine the magnitude of the shock pulse damping coefficient. Rocks from various deposits in Russia with strictly defined strength characteristics were used as the crushed material. Research results. Dependences of the amplitude of the shock pulse on time are constructed for the grinding of granite raw materials, carbonate rocks and soft rocks (gypsum) in a drum mill. The following conclusions were drawn: 1. When grinding strong and very hard rocks in a drum mill, a strong impact occurs (with a large amplitude and duration of the shock pulse) and with its weak damping when propagating in the rock. 2. When grinding carbonate rocks, doubling the angular velocity of rotation of the grinding chamber leads to an increase in the amplitude of the shock pulse by about 1.5 times. 3. The duration of shock wave propagation in both cases is approximately equal. 4. The frequency of grinding media collisions increases significantly. This indicates a sharp increase in the energy intensity of the grinding process. 5. When grinding soft rocks in a drum mill, almost half of the input energy is spent on overcoming the damping properties of the material, and small, frequent pulses, which consume half of all energy, are not able to grind the material to the desired size. Discussion. Based on the conducted studies, graphs of dependencies between the main parameters of the drum mill were constructed. The dependences of the duration of the shock pulse on the average diameter of the particles of the crushed material are constructed. The analysis of these dependences made it possible to conclude that the duration of the shock pulse is in a parabolic dependence on the value of the average particle diameter of the crushed material. The dependences of the damping coefficient on the damping decrement of the shock pulse amplitude are constructed. The analysis of these dependences allowed us to conclude that the shock pulse damping coefficient increases almost linearly with an increase in the damping decrement of the shock pulse amplitude. The dependences of the damping coefficient of the shock pulse on the average diameter of the particles of the crushed material are constructed. The analysis of these dependences allowed us to conclude that the shock pulse damping coefficient is in a quadratic dependence on the value of the average particle diameter of the crushed material. Conclusion. In this article, based on the classical theory of damped oscillations of such system, the principle of determining the damping coefficient of the shock pulse propagating from the grinding body deep into the grinding load of the drum mill is scientifically substantiated. Resume. Experimental determination of the value of the damping factor of the shock pulse, along with the use of the energy criterion for the destruction of the rock, makes it possible to calculate the amount of energy required to destroy the rock particles to a given size. Suggestions for practical application and direction for future research: The results of the research can be used at the enterprises of the mining sector of the industry to improve the efficiency of processing mineral resources and reduce the energy intensity of the process of grinding rocks in drum mills.