Simulation of hot-end temperature field under closed-loop heating for material extrusion

In fused filament fabrication, the actual nozzle temperature can differ substantially from the commanded setpoint, introducing uncertainty into the thermal state of the extruded material and limiting process repeatability and transferability. This study develops a transient finite element framework for predicting the temperature field and control response of an FFF hot-end. The model couples a proportional-integral-derivative algorithm with pulse-density modulation to achieve closed-loop control of heating. Validation against infrared thermography and thermocouple measurements shows that the model captures the transient heating response and the spatial characteristics of the steady-state temperature field over the investigated setpoints. The validated model reveals the internal temperature field distribution and the underlying mechanisms of nozzle temperature deviation. At a setpoint of 430 °C, the thermal contact resistance at the interface between the nozzle and liquefier results in a temperature drop of 19.2 °C and the temperature of the inner wall of the flow channel drops by 34.2 °C from the hottest point to the nozzle outlet. The deviation increases with setpoint because greater external heat loss, combined with the limited thermal conductivity of the components and interfacial conductance, produces larger internal temperature differences. Increasing material thermal conductivity, suppressing radiative heat loss, and reducing the thermal resistance at the flow-channel interface effectively decrease the deviation. Increasing the thermal resistance between the liquefier heating surface and thermocouple causes controller overcompensation and internal overheating. The proposed model provides a tool for predicting nozzle temperature and optimizing the hot-end.