Математичне моделювання взаємодії елементів машин та механізмів з дискретним середовищем
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Дата
2025
Назва журналу
Номер ISSN
Назва тому
Видавець
Хмельницький національний університет
Анотація
Описується математична модель взаємодії елементів машин та механізмів певного класу з дискретним
середовищем. Особливостями запропонованої моделі є те, що: модель враховує вплив нормальних стискуючих
напружень на величину деформацій зсуву; експериментальні параметри, які входять у фізичні співвідношення
моделі, визначаються шляхом проведення лабораторних досліджень конкретного матеріалу
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 𝜏гр on the magnitude of compressive stresses 𝜎0; the dependence of shear deformations 𝛾0 on normal compressive stresses м; the dependence of volumetric deformations 𝜀0 on shear deformations 𝛾0. 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.
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 𝜏гр on the magnitude of compressive stresses 𝜎0; the dependence of shear deformations 𝛾0 on normal compressive stresses м; the dependence of volumetric deformations 𝜀0 on shear deformations 𝛾0. 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.
Опис
Ключові слова
дискретне середовище, внутрішнє кулонове тертя, дилатансія, discrete medium, internal Coulomb friction, dilatancy
Бібліографічний опис
Дорофєєв О. Математичне моделювання взаємодії елементів машин та механізмів з дискретним середовищем / О. Дорофєєв, О. Багрій, Ю. Дорофєєв // Вісник Хмельницького національного університету. Технічні науки. – 2025. – № 2. – С. 144-149.