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.
