The application of duffing's equation in predicting the emission characteristics of sawdust particles (2010)
"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 Two dimensional graphical representation of continuous time series of Duffing's dynamic system for sawdust particles was investigated with emphasis placed on application to sawdust particle motion and the saw machines. Pr~liminary 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 Runge-Kutta Algorithm. Linear transformation that guarantees non-negative values of time series was implemented. This was followed by the respective computation of the x- and y-components of the resulting time series values of the sawdust movement using a 21tmodulated 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 as emission from band saws was therefore demonstrated here, in approaches that thus advance knowledge of sawdust emission studies. "