The calculation diagrams of oscillating systems and operation features of vibratory finishing machines are considered. The mathematical models of three-mass and four-mass oscillating systems are presented. The amplitude values of the oscillating masses displacements are derived. The functions of inertial and stiffness parameters optimization are formed. The optimization problems are solved with a help of MathCAD software. On the basis of synthesized inertial and stiffness parameters, the amplitude-frequency characteristics of the oscillating systems of vibratory finishing machines are formed and analyzed. In order to verify the validity of the proposed theoretical approaches, the simulation of the mathematical model of the oscillating system motion is carried out by means of numerical solving of the system of differential equations of the oscillating masses motion. The proposed structural diagrams and the operation schemes of the vibratory finishing machine, as well as the derived analytical formulas may be used by designers, researchers and technologists while improving existent and developing new equipment for vibro-finishing treatment.

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