Aim. Developing an approach for determining the modes of jet treatment for the curved surfaces of products to ensure uniform processing, which is achieved by maintaining a constant distance from the nozzle end to the surface and maintaining the perpendicularity of the nozzle axis to the curved surface at the point of processing during movement and changing the nozzle inclination. Method. The basic principles of analytical geometry on the plane are used to describe the processed curved surface. Kinematic equations of a material point motion as the basic principles of theoretical mechanics were used to research the motion of the processed curved surface. Graphical dependences and analysis of the obtained results were carried out by using the mathematical editor. Results. The result is the complex of the mathematical models, the use of which in control systems of technological equipment will ensure uniform processing by adjusting the linear velocity of the product surface and the angular velocity of the jet nozzle, and thus ensure the required accuracy and quality of products. Scientific novelty. The approach for modeling jet treatment of products with curved surfaces is improved, namely the method of determining processing modes under conditions of constant distance from the nozzle end to the surface and perpendicularity of the nozzle axis to the tangent at the processing point is proposed. Analytically, expressions for mathematical description of curved surfaces depending on their shape and character of motion are obtained. Practical significance. The proposed approach is recommended to be used in technological processes of jet treating for the products of complex configuration, when designing units of technological equipment or devices designed to ensure the movement of the product or the tool. Mathematical models can be the basis for ensuring the quality of curved surfaces of products obtained by jet treating. Key words: jet treatment, process equipment, processing modes, curved surface, product movement.
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