The application of fractal box dimensions in predicting the emission characteristics of colliding sawdust particles for sustainable sawmilling

Abstract

The prediction of emission characteristics of sawdust particles immediately after the cutting operation from the interaction of band saw’s blade and plank is a growing research area. Still, a wide gap exists with respect to understanding the behaviour of sawdust particles as they collide with one another. Previous efforts have focused on non-collision states of sawdust particles. However, in real life, collision of particles must occur, with several particles colliding after the cutting operation. This paper establishes a new perspective of the fractal properties of sawdust particles in motion as a motivation to understanding how to control its toxicity of effects on sawmill workers and maintain sustainable sawmilling activities. In particular, the possibility of predicting the fractal dimension of the randomly moving sawdust particles in sawmills that is generated as fractal curves using the combination of probabilities and theoretical fractal dimensions is investigated for the first time. Cases were established on the possible representations of the theory and practice. As an example, four cases were designed around varied number of fractal pattern combinations drawn out of five and fifty different probabilities combinations, ten different random number generating seed values and maximum of four fractal curves generation iterations as driven parameters. Preliminary study of the differences between theoretical fractal box dimension recorded a maximum absolute percentage error of 7.24% for fractal curve associated with fractal pattern five (i.e. Koch 5). In all the cases studied, average absolute percentage error decreases between 3.52 ± 1.18 and 1.51 ± 1.14 while the correlation coefficient (R2) decreases between 0.9315 and 0.7365 from case 1 to case 4, respectively. It is concluded that the model is a good predictor of sawdust particle emission at colliding states from cutting operation. This is reflected in the fact that the higher the number of fractal patterns (generators) in a study case, the smaller the correlation coefficient between average estimated fractal box dimension and predicted fractal dimension of the sawdust particles in motion in the sawmill.