Volume decomposition for multi-axis support-free and gouging-free printing based on ellipsoidal slicing

Continuous multi-axis printing has drawn more and more attention owing to its unique advantages of eliminating the need of support (at least in theory) when printing complex models with overhang features and significantly reducing the stair-step effect of the conventional three-axis printing. For continuous multi-axis printing, the printing layers are typically not planar but curved, so to capitalize the extra DOFs provided by the rotary axes of the printer. When a printing layer is concave (i.e., its curvature vector points inward at the printing point), the potential nozzle-layer local gouging becomes a serious concern, which is especially problematic for metal printing wherein the size of the nozzle head is usually large. Unfortunately, this convexity issue has received little attention in the existing curved slicing algorithms, making them prone to the local gouging quandary. In this paper, we propose a novel curved layer decomposition algorithm based on the use of (only the positive sides of) ellipsoidal surfaces. To facilitate the generation of ellipsoidal printing layers for an arbitrary freeform solid model with a complex topology (e.g., having a non-zero genus number), the powerful algebraic technique of skeletonization is employed by our algorithm to first decompose the model into a suitable set of sub-entities, for each of which a series of ellipsoidal printing layers are then generated, wherein the parameters of ellipsoidal layers are adaptively adjusted to satisfy the necessary constraints such as support-free and other requirements. Preliminary experiments in both computer simulation and physical printing of the proposed algorithm are conducted, and the results give a positive validation on the effectiveness and feasibility of the proposed methodology.