A CRITICAL ANALYSIS OF EMPIRICAL FORMULAS DESCRIBING THE PHENOMENON OF COMPACTION OF THE POWDERS

摘要

The starting point of the analysis was the observation of dimensional defects of some of the formulas of the mathematical models of phenomena compaction of powders. For this reason, the authors used dimensional analysis for the most known mathematical models of phenomena compacting powders. The dimensional analysis of these formula, shows that the main damage dimensional, consist, primarily, in arguments with physical dimension for the transcendental functions and, secondly, the equations are not dimensionally correct (the two members do not have the same physical size). Also, many equations of the mathematical models of the powder compaction processes violate the principle of dimensional homogeneity. In these situations, there are mathematical models of compacting powders named after their authors: Jones, Walker, Heckel, Kawakita-Ludde, Panella-Filho, Soonergaard, and others, a total of twenty-nine models. In twenty-five of the twenty-nine models examined, the authors propose corrected equations, which satisfy the principles of dimensional analysis. In one of these models is given even more options and corrected and introduce new variables in the model, which widens considerably the physical phenomenon - Nutting model. The results presented in this paper were obtained, imposing to the equations of the mathematical models of the phenomena compacting of the powders, only general principles of dimensional analysis. It remains, for another attempt, to apply the most important tool of dimensional analysis: Pi theorem. For the mathematical models, where it was possible, we offer modified variants, for the mathematical equations, that define the patterns analyzed. In each case, we have highlighted the benefits of reformulating the mathematical equations that define the models, in terms of dimensional analysis.