Purpose. The substantiation of the mathematical model of mechanical deformation of the elastic-plastic medium and the modeling of the transport process of the expansion assemblies. Methodology. Mathematical and theoretical studies were based on the fundamental theory of continuum mechanics and general positions of engineering mechanics. Analytical and graphical analysis of mathematical models carried out on a PC in a specialized software complex. Results. In the current conditions of economic development of the country, considerable attention should be paid to the development and modernization of certain sectors of the economy. Significant amounts of work, which are accompanied by the development of soil of different properties, which can be defined as an elastic-plastic material. These studies will solve a number of problems that are acute not only in agriculture but also in construction, in the open pit mining, reclamation, one of which is an imperfect process of loosening the soil during its cultivation. Therefore, the urgent problem is to establish rational parameters of the transport surface of the unit for loosening the elastic-plastic material. The developed mathematical model allows determining the emerging stress, which in turn determines the boundary of the destruction of the elastic-plastic material. In the design of lining assemblies, it is advisable to have a radius of the outlet section R = 0.18 m or more. Originality. The mathematical models for the process of destruction of elastic-plastic material and forecasting of optimal transport parameters for designing of expansion assemblies are obtained. Practical value. The developed mathematical model will provide an improvement in the process of loosening elastic-plastic material, and engineering calculations during the design of the rutter can prevent unwarranted increase in resistance, with displaced materials on the cutting surface. References 10, figures 8.

The scheme of vibration-centrifugal installation, providing the increase of productivity and efficiency of machine parts vibration treatment is presented in this paper. The influence of the treated environment on the technological vibration treatment process and determination of its optimal parameters is investigated on the basis of mathematical modeling. Graphical dependences of specific kinetic energy on the crank rotational velocity at different values of the fork rotational velocity are presented. Effective ways of technological process parameters optimization and new ways of its development are identified.

The paper presents an advanced complex mathematical model of centrifuge dynamics for the formation of tubular products made of concrete or any other plastic and viscous confining mixtures. In the two-dimensional (plane) formulation of the problem, the studied mechanical system consists of a framework form (hollow rotor) with a partial confining filling, its elastic-damping suspension and power drive. It is assumed that the rotor is rigid, of correct design, has a certain static imbalance and can be both horizontal and vertical. The used filling is a concrete or some other mixture as a quasi-homogeneous plastic and viscous rheological body, which spreads slowly and in a shear flow over the inner surface of the rotor under the action of gravity forces and transfer forces of inertia. The rotor suspension is a roller lever type, but can be of any design, with certain inertial, rigid and damping characteristics. The variable power drive provides application of a variable torque to the rotor. The general theorems and dynamics equations, including the theorem on the motion of the mass center and the differential equation of rotation at the plane motion of a body with a pole other than the mass center, are used to construct differential equations of rotor dynamics. This eliminates the shortcomings of the known mathematical models with the similar problem statement. The proposed mathematical model can be implemented according to the well-known algorithms for numerical integration and used to develop or adjust the appropriate software. This enables the centrifuge dynamics to be studied more fully, to take into account and optimize its important parameters and characteristics.

The review of vibration treatment is carried out in this paper. The workpiece vibration treatment is essential in ensuring the engineering products quality. The schemes of abrasive granule interaction with the workpiece surface during vibration and vibration-centrifugal treatment are considered. Process analysis is based on the nature of the abrasive pellet interaction with the workpiece surface. The whole process of roughness forming on VCP is divided into certain stages. The proposed models reveal the physical nature of the granules interaction with the workpiece surface.