CHOOSING A MATHEMATICAL MODEL OF THE INTERACTION OF MACHINES ELEMENTS AND MECHANISMS WITH A GRANULAR TECHNOLOGICAL ENVIRONMENT - DOROFIEIEV, YURII (Herald of Khmelnytskyi National University. Technical sciences, 2025)
Existing models are analyzed to assess the effectiveness of their use for mathematical modeling of the interaction of elements of transporting machines and mechanisms with a granular technological environment.Logical-mathematical class models require field tests to determine empirical coefficients.The non-deformability of limit state models makes it impossible to use them for modeling the entire technological process.The use of integral-type models is limited by the need to determine model parameters from field studies and the inability to use them to model the process of material destruction when it comes into contact with transporting elements.Models that use the physical relations of the nonlinear theory of elasticity and the theory of plasticity open up the fundamental possibility of detailed modeling of the entire process of interaction between machine elements and the environment.In our opinion, the most promising for modeling the interaction of elements of a conveying machine with a granular technological medium are models based on physical relations of the deformation type. They reflect the influence of internal friction on the laws of deformation and fracture of materials and, in principle, allow us to implement the modeling procedure based on the methods of the theory of a deformable solid. To be able to use these models, it is necessary to: clearly describe the features of deformation and fracture of discrete materials; formulate a mathematical model that reflects these features; substantiate and develop algorithms and computational procedures that allow us to obtain a solution to the problem. In addition, modeling specific problems requires the development of methods and laboratory equipment to determine the values of the calculated parameters of the model.
Keywords: granular medium; mathematical model; internal friction