Modeling the Ultrasonic Micro-Injection Molding Process Using the Buckingham Pi Theorem.

Dimensional analysis through the Buckingham Pi theorem was confirmed as an efficient mathematical tool to model the otherwise non-linear high order ultrasonic micro-injection molding process (UMIM). Several combinations of processing conditions were evaluated to obtain experimental measurements and validate the derived equations. UMIM processing parameters, output variable energy consumption, and final specimen's Young modulus were arranged in dimensionless groups and formulated as functional relationships, which lead to dimensionless equations that predict output variables as a function of the user-specified processing parameters and known material properties.