A coupled thermo-mechanical framework for modeling and compensating workspace-dependent thermal errors in gantry-type FDM printers

Thermal errors in fused deposition modeling (FDM) machines can reduce dimensional accuracy by altering the nozzle position due to non-uniform heating of the nozzle and the build platform. While previous studies have mainly emphasized part distortion, the workspace-dependent thermal deformation of the printer structure has received less attention. This study develops a coupled thermo-mechanical framework to model, validate, and compensate position-dependent thermal errors in a gantry-type FDM 3D printer. A finite element model was used to predict the temperature field and the resulting Z-direction nozzle displacement at 27 locations distributed over three measurement planes within the build volume. Experimental validation was carried out using a laser displacement sensor. The simulated and experimental results agree well, with deviations generally within 3%–5%, confirming the reliability of the proposed model. The model achieved an MAE of 2.51 µm and an RMSE of 2.54 µm. Linear regression between the numerical predictions and experimental measurements yielded an R 2 value of 0.992, indicating excellent agreement between the simulation and experimental results. Furthermore, the 95% confidence interval of the mean prediction error was 2.34 to 2.67 µm, demonstrating the robustness and consistency of the proposed model. The sensitivity analysis reveals that the heat bed temperature is the dominant factor influencing thermal deformation, with a sensitivity of 4.091 µm/°C. In comparison, the nozzle temperature exhibits moderate sensitivity (0.85 µm/°C), while the convection coefficient (20–40 W/m 2 K) shows a limited influence within the investigated range. These findings highlight that precise control of the heated bed temperature is essential for minimizing thermal deformation and improving printing accuracy. Based on the validated deformation field, a position-dependent compensation strategy is proposed to improve dimensional accuracy and support future real-time thermal error correction in FDM systems.