Fused Deposition Modeling (FDM), an Additive Manufacturing (AM) technique, is widely used due to its low-cost and open source. Geometry accuracy and strength performance of the printed parts are closely related to inter-layer bonding between adjacent layers and inter-road bonding in the layer. Because of the limit of layer-based AM, the longitudinal tensile strength of the filaments is much higher than the bonding strength between adjacent filaments, which brings anisotropy of the printed part. While CLFDM is devoted to solve this problem and obtain better geometry accuracy and meanwhile decrease build time by virtue of high continuity of filament, reduced stair-step effect, and lesser number of layers, especially when manufacturing thin and curved parts (shells). However, to the best of our knowledge in the aspects of process modeling of CLFDM, available researches focus mainly on simple curved layer, instead of more intricate ones possessing tiny features, which are more common in manufacturing. Therefore, to realize Solid Freeform Fabrication (SFF), this paper researches CLFDM with VEF (simultaneously changing the direction and the dimension of extruded filament according to manufacturing demand of the curved layer), which would be a fundamental study and a foundation for Advanced Design for Additive Manufacturing (ADFAM), slicing and path planning (extruder path generation) in 3D space. To realize slicing and printing with homogeneous and inhomogeneous extruded filament between consecutive layers and within the layer (flat or curved), models of flat layer FDM and CLFDM with VEF are respectively established. Then, the relationships among key process parameters are analyzed. Finally, graphical simulation of the proposed strategy based on a vase is provided to verify its effectiveness and advantages from a theoretical point of view. In general, variable direction of extruded filament along tangential directions of part surface imparts smoother surfaces, instead of rough exterior appearance resulting from stair-step effects. And variable dimension of extruded filament maximizes material extruded to increase build speed wherever allowed and minimizes deposition size for resolution whenever needed, resulting in curved layer surfaces with uneven layer thickness and having tiny features.

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