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In the article considers the effect of surface roughness on the functioning of a specific mechanism. In case of proven dependence of the studied functional property of surface microgeometry, a process of optimization of the sought parameter is carried out, in which the methods of mathematical analysis and theoretic foundations of technology of appliance and mechanical engineering are used for the basis of the theoretical studies. As control parameters of the specified optimal microgeometry, deciding the given task, the so-called non-parametric criteria are used, namely graphical of certain surface-profile functions.

In the article, studies of the kinematics and dynamics of interaction of the elements of the vibration system "slug-cut disk" are made. A mathematical model describing the trajectory of a cutting arm has been created and the technological parameters of the system at which the phenomenon of resonance occurs have been determined.