MATHEMATICAL MODELING OF THE INTERACTION OF MACHINE ELEMENTS AND MECHANISMS WITH THE DISCRETE ENVIRONMENT

Abstract

When creating machines (diggers, road, agricultural, construction) and mechanisms (transporting, dosing) of a certain class, as well as containers for transporting and storing discrete materials, there is a need to determine some power, kinematic and energy parameters at the design stage. For the normal functioning of existing equipment samples, it is necessary to reliably assess the possible operating conditions. All this can be done using mathematical modeling of the interaction of the machine or mechanism with the technological environment.

The disadvantage of existing interaction models of individual machines’ elements and mechanisms with various bulk materials is that they do not fully take into account the characteristic features of deformation of bulk materials. They, as a rule, describe the behavior of the material in the near-limit and limit states by unrelated relations. In addition, the representation of physical dependencies in integral form requires the determination of coefficients and parameters of these dependencies from natural studies.

The model of interaction of machine elements with a technological discrete environment must take into account the characteristic features of its deformation: the dependence of the ultimate resistance  on the magnitude of compressive stresses ; the dependence of shear deformations  on normal compressive stresses м; the dependence of volumetric deformations  on shear deformations .

A mathematical model of the interaction of machine elements and mechanisms of a certain class with a discrete environment is described, the features of which are that: the model takes into account the influence of normal compressive stresses on the magnitude of shear deformations; experimental parameters that are included in the physical relations of the model are determined by conducting laboratory studies of a specific material.