Mathematical models of the temperature field in the filament-extruder system during 3D printing

• Main Authors: Zagirnyak, M., Kobilskaya, E., Lyashenko, V., Salenko, A.
• Format: Conference Proceeding
• Language: English
• Subjects: 3-D printers; Boundary conditions; Boundary value problems; Exact solutions; Extrusion; Fused deposition modeling; Heat sources; Laminates; Mathematical models; Melting points; Polymers; Process controls; Process parameters; Rapid prototyping; Temperature distribution; Thermodynamics; Three dimensional models; Three dimensional printing
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0033797

The paper presents mathematical models of the temperature field in the filament-extruder system during 3D printing according to the FDM (fused deposition modeling) technology. The molten polymer thread is extruded on a heated surface with gradual lamination of layers of material on top of each other, creating a finished part. Mathematical model of the temperature field in the filament-extruder system is considered as a boundary value problem for the heat equation with the addition of appropriate boundary conditions. The filament is heated in a limited area by external heat sources, and is transferred convectively or conductively to the melting point of the filament at the outlet of the heating zone of the extruder. The boundary value problem is solved by the numerical-analytical method. The temperature distributions of the polymer thread in the extruder and at the outlet of it for different conditions of 3D printing process of parts are constructed. The paper presents the relations for determining each of the 3-D printing process control parameters by the FDM method. These relations are obtained from analytical solutions of problems that describe the thermal process during 3-D printing.