THE APPLICATION OF DUFFING'S EQUATION IN PREDICTING THE EMISSION CHARACTERISTICS OF SAWDUST PARTKLES

ABSTRACT

Sawdust particles soon after emission from the cutting machine usually move dynamically with transformation in some dimensions. This paper models the sawdust particle motion as a two dimensional transformation system of continuous time series. Cost could be saved using this approach instead of utilizing dynamic systems that depend on time history. TWP dimensional graphical representation of continuous time series of Duffing's dynamic system for sawdust particles was investigated with emphasis placed on application to sawdust pa* motion and the saw machines. Preliminary studies were made using the harmonic functions, F(t) = Cos(wt) and F(t) = Sin(wt), for their familiarity in both science and technology communities. The solution to Duffing's model equation for the sawdust particles was sought from displacement and velocity perspectives, using the RungeKu#a Algorithm. Linear transformation that guarantees non-negative values of time series was implemented. This was followed by the respectives computation of the x- and y-components of the resulting time series values of the sawdust movement using a 2% modulated time measured in radians. The graphical representations of the x- and y components compared well quantitatively and qualitatively with the corresponding phase plots. The feasibility of modelling sawdust dynamics 9s emission from band saws was therefore demonstrated here, in approaches that thus advance knowledge of sawdust emission studies.