Analysis of the energy laws of material destruction
Authors: Mishchuk Yevhen , Nazarenko Ivan 
Published: August 2023

The number of parameters that determine the process of destruction of materials in the crushing chamber is significant and difficult to describe by known mathematical laws. Most of the theories that describe the energy consumption of the destruction process are based on empirical indicators and are not supported by the theoretical foundations of the process. The paper provides an analysis of the latest research in the field of material destruction processes, on the basis of which it was established that modern methods of determining the energy of material destruction differ significantly from each other, are based on different energy hypotheses, both according to accepted assumptions and according to the obtained results. Thus, the lack of a generally accepted model of the grinding process and a single method of determining the energy consumption of the process of destruction of materials by crushing machines is the problem that needs to be solved. For this purpose, an analysis of the main classical laws of destruction of materials in the crushing chamber was carried out. Almost all classical laws are described by the use of proportionality coefficients, which take into account the physical properties of the material, friction costs in the machine nodes, heat losses, the amount of material in the crushing chamber and other parameters that affect the destruction process. This leads to the difficulty of determining the influence of individual parameters on the destruction process, in addition, the coefficients themselves do not have a calculation method and in most cases are determined experimentally. Bond's law has the largest number of variations. In which the work index parameter is used as a proportionality factor. However, the parameter of the Bond work index has a wide range of changes, as well as a large number of methods for its calculation. In general, the dependence itself describes well the processes between the zones of fine crushing and coarse grinding. In the work, the limits of the change of the proportionality coefficients for various energy laws were established for the corresponding destruction conditions. The wide limits of the change of the coefficients testify to the significant stochasticity of the process itself, and do not allow a true description of the picture of destruction. One of the options for the intensification of the destruction process is the application of a shock load. The paper considers the dependence for determining the energy consumption during the dynamic destruction of rocks, which makes it possible to assess the advantages and disadvantages of static destruction. The main parameters that have an impact on dynamic destruction are the speed of load application and the geometry of the surface of the working tool. Based on the analysis, it was established that a large number of parameters that influence the crushing process of machines for the production of building materials greatly complicate the creation of a single theory of destruction at this stage of human development. The further development of research on destruction processes in crushing machines is seen in the creation of a stochastic model for describing the kinetics of the destruction process, which will take into account the peculiarities of the destruction process at the micro and macro levels.