Determiantion of energy characteristics of material destruction in the crushing chamber of the vibration crusher

Abstract

The crushing equipment is characterized by a significant energy-consuming system during the crushing workflow. The current trend in the development of such processes puts forward requirements for the development of new or improvement of existing energy-saving equipment. The essence of the solution to the problem in this work is determined by using resonant modes, which are inherently the most effective. The practical implementation of the resonance mode has been achieved taking into account the conditions for the interaction of the resonant vibration crusher with the material at the stages of its destruction. The degree of the stress-strain state of the material is taken into account, which was a prerequisite for identifying the potential for the development of a vibration load. Composed equations of motion based on a substantiated discrete-continuous model of a vibration crusher and processing material. An approach is applied to determine the stepwise destruction of the material with the determination of the required degree of energy. This methodological approach made it possible to reveal the nature of the process of material destruction, where energy costs at the stages of crack formation, their development and final destruction are taken into account. It was revealed that the greatest energy consumption during the operation of crushers goes into the kinetic energy of the crushing plates and the potential energy of deformation of the springs. The proposed model is common for any design of a vibration machine and its operating modes. The stable resonance mode has made it possible to significantly reduce the energy consumption for the course of the technological process of material grinding. The results obtained are used to improve the calculation methods for vibratory jaw and cone crushers that implement the corresponding energy-saving stable zones of the working process.

Research of processes of producing materials by technical power loading systems

“…To solve the problem, let's use the displacement method. Combining equations (2.15)-(2.17) by alternate substitution, and performing some mathematical transformations, let's obtain the equation of elastic balance of the body in displacements [4]:…”

“…Therefore, to solve this problem, it is necessary to find the displacement functions. These functions must satisfy three main conditions [4]:…”

“…The solution to this problem is complex and very voluminous, due to the use of biharmonic functions. Therefore, for further research, let's use the technique proposed for solving the stressstrain state of a body near the rupture zone, which has the shape of an ellipse [3,4].…”

“…To solve the problem, the gravitational potential outside a homogeneous elliptical plate of the following form was used [4]:…”

“…Constant A is found by the following formula [4]: After some transformations and calculations, the displacements from the action of normal forces through the elliptical coordinates will have the following form [4]:…”