Topilnytskyy Volodymyr – PhD, Associate Professor of the Department of Designing and Operation of Machines of the Lviv Polytechnic National University (S. Bandery str., 12, Lviv, Ukraine, 79013, e-mail: topilnvol@gmail.com).

Kusyi Yaroslav – PhD, Associate Professor of the Department of Mechanical Engineering Technologies of the Lviv Polytechnic National University (S. Bandery str., 12, Lviv, Ukraine, 79013, e-mail: jarkym@ukr.net).

Rebot Dariya – PhD, Assistant of the Department of Designing and Operation of Machines of the Lviv Polytechnic National University (S. Bandery str., 12, Lviv, Ukraine, 79013, e-mail: dasha_kotlyarova@ukr.net).

The article describes the methodology for the study of the dynamics of vibrating machines for surface processing of products by mathematical modeling, which is presented in four main stages. The first stage: analysis of classes of vibrating machines for surface treatment of products, choice of basic for solving the technological problem, project of a unified calculation scheme of the machine. The second stage: development of a nonlinear mathematical model for describing the dynamics of the vibration machine working body and its filling, development of elements of automated calculations of the machine. The third stage: the study of the influence of the parameters of the vibrating machine, product sets and tools (with their various combinations) on the factors of the intensity of products surface processing. The fourth stage: recommendations for choosing vibrating machine parameters and machining bodies that will maximize the processing performance of products with the selected intensity criterion. 

A mathematical model for describing the motion of a vibrating machine for surface treatment of articles by a set of unrelated bodies of small size is created. It has two unbalance units that generate oscillations of its working body and a spring suspension-mounting of the working chamber (container). The model is parametric and nonlinear, incorporating key dynamic, kinematic and geometric parameters of the vibrating machine in symbolic format. It is constructed by: descriptions of the plane-parallel movement of the mechanical system, the rotational motion of the material point and the body; second-order Lagrange equation; asymptotic (approximate) methods of nonlinear mechanics. With the help of the model it is possible: to describe the oscillatory movement of the working chamber (container) of the vibrating machine; to study the influence of the machine parameters on the efficiency of performance of the set technological task, the conditions of occurrence of non-stationary modes of operation of the vibrating machine and the ways of their regulation.

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