Motion planning and numerical simulation of material deposition at corners in extrusion additive manufacturing

The material deposition along a toolpath with a sharp corner is simulated with a computational fluid dynamics model. We investigate the effects of smoothing the toolpath and material over-extrusion on the corner rounding and the corner swelling, for 90 degrees and 30 degrees turns. The toolpath motion is controlled with trapezoidal velocity profiles constrained by a maximal acceleration. The toolpath smoothing of the corner is parametrized by a blending acceleration factor. Analytical solutions for the deviation of the smoothed toolpath from the trajectory of the sharp corner, as well as the additional printing time required by the deceleration and acceleration phases in the vicinity of the turn are provided. Moreover, several scenarios with different blending acceleration factors are simulated, for the cases of a constant extrusion rate and an extrusion rate proportional to the printing head speed. The constant extrusion rate causes material over-extrusion during the deceleration and acceleration phases of the printing head. However, the toolpath smoothing reduces the corner swelling. The amount of underfill and overfill at the inside and outside of the corner are quantified, as compared to an ideal case where the printing head would instantaneously change its speed direction at the corner. The numerical results show that there is an optimal amount of toolpath smoothing where the over-extrusion compensates for the corner rounding; hence improving the quality of the corner. A uniform road width is obtained with the proportional extrusion rate.