Abstract

The current level of technological development is characterized by the constant complexity of the products. For its production requires processing a large number of parts of complex shape. Mathematical modeling is an effective and economical way to solve many technical problems. There are various ways to ensure the necessary cleanliness of machine parts or reduce the negative effects of technological pollution. Existing methods of finishing and cleaning parts on the physical-chemical effects on the material during processing are divided into several groups. The most widespread are both mechanical methods in which the removal of defects is carried out by mechanical action on machined parts of tools and chemical and mechanical methods in which there is a simultaneous mechanical effect of the tool and the chemical action of the external. The gas-dynamic method of removing defects that occur after the preliminary metalworking of parts of aircraft objects seems to be very effective. The mathematical model of this process is the system of laws for the conservation of the dynamics of a viscous heat-conducting gas, the physicochemical characteristics of which are established in an experimental way. The construction of a gas-dynamic model of the physical process of finishing parts as an arbitrary spatial form and the material of manufacture is presented. On the basis of the general laws of conservation of the dynamics of a viscous heat-conducting gas, analytical forms of solutions for the kinematic and dynamic characteristics of a high-temperature flow are obtained using the example of a flat channel simulating the surface of a part being cleaned. It is shown that in the flat case the conservation laws have a linear form, which provided exact solutions for the kinematic characteristics, such as the velocity and vorticity of a viscous gas flow, which play a major role in calculating the dynamic and thermal characteristics of the flow. The use of a generalized apparatus of vector-tensor analysis is fundamentally important in order to obtain integral representations of the solutions of differential forms of the laws of conservation of momentum and energy in the control region. Control of gas dynamic and thermodynamic parameters of the flow is able to provide a high-quality surface.

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