MATHEMATICAL DESCRIPTION OF TWO-DIMENSIONAL PERIODIC CIRCULAR MOVEMENT OF WORK-PIECE BEING TURNED IN MODERNIZED SAWING UNIT

Abstract

The paper presents a theoretical investigation on nature of two-dimensional periodic circular movement of a work-piece attached to the end of a modernized sawing unit boom. The boom oscillation axis is established on an elastic suspension that makes forced oscillations along a horizontal axis. The paper provides a calculation model of an oscillatory system of a boom swing block for mathematical description of the point movement trajectory that belongs to the work-piece. The model permits to obtain a system of two connected equations describing this movement. Numerical solution of these equations permits to establish that the work-piece makes a two-dimensional periodic circular movement and it has an elliptical trajectory. The paper gives data that reveal influence of elastic and inertial and dissipative characteristics of the oscillatory system on the elliptical trajectory parameters of the work-piece movement. The paper demonstrates that the regulation of the forced oscillation frequency transferred to the boom swing block of the sawing unit is considered as. the simplest in realization and the most efficient method that makes it possible to control the required parameters.