Mathematical Model of the Layer-by-Layer FFF/FGF Polymer Extrusion Process for Use in the Algorithm of Numerical Implementation of Real-Time Thermal Cycle Control

Abstract

An approach for improving and maintaining a consistent weld quality of the deposited material during the FFF printing process is proposed. The approach is based on the analysis of the printing process thermal cycle and the real-time nozzle temperature control. The mathematical model of the FFF printing process has been developed with the use of real-time control in the algorithm of numerical implementation. The successful solution of the thermal conductivity problem made it possible to determine segment-wise heating settings for use during the printing process, resulting in a high and stable quality of welding. Comparison of the results of modeling with other well-known mathematical models of the FFF printing process and experimental results showed the adequacy of the proposed model. A maximum deviation of 17.7% between the simulation results and the thermography data was observed. The proposed model was verified using rectangular 3D polylactide shapes printed with and without regulation of the power of the heat source according to the previously estimated settings. The overall quality of regulation, stability of the system, and the PI coefficients of the controller were evaluated using a simulated model of the control system. The results of the experiment fully correspond with the modeling results.