The purpose of the paper. Substantiation of structure (design), parameters and operation modes of the improved vibratory finishing machine. Analysis of dynamical processes which occur during “lap over lap” dressing. Investigation methodology. Mathematical model of motion of the mechanical system of vibratory finishing machine was developed on the basis of Lagrange differential equations of the second order. For the purpose of describing friction between the working surfaces of the laps, the Coulomb friction model was used.
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.