Mathematical modeling of ultrasonic micro injection molding using dimensional analysis for manufacturing polymeric parts

Abstract

Ultrasonic micro injection molding is a novel processing method to produce micro-scaled specimens at low production volumes that overcomes the material degradation originated by high residence times, and reduces material waste compared to conventional injection molding. Ultrasonic micro injection molding deals with ultrasonic energy and polymers under cyclic loads which experience a phase-change from solid to a non-Newtonian fluid flowing to fill a mold. Attempts have been made to study each of the steps of the process, all of them needing powerful FEM software and the establishment of several assumptions to simplify the calculus on the otherwise thermomechanical coupled problem with different time scales. This research work presents a methodology to reduce the mathematical complexity of the process while preserving the physics of the system through the usage of dimensional analysis. A correct relationship of processing parameters and energy consumption values was obtained using four different polypropylenes with distinct mechanical properties, all of them fitting adequately in the proposed formulation composed of dimensionless groups obtained through the Buckingham-Pi Theorem. A mathematical expression capable of quantitatively predict energy consumption from processing parameters was obtained. Additionally, a relationship between the processing parameters and the Young’s Modulus of the produced specimens was found, and a mathematical expression to calculate this property using processing parameters was stablished.