Layered Manufacturing of Thin-walled Parts

We describe a new algorithm we have developed for making partially hollow layered parts with thin, dense walls of approximately uniform thickness, for faster build times and reduced material usage. We have implemented our algorithm on a fused deposition modeling (FDM) machine, using separate build volumes for a loosely filled interior and a thin, solid, exterior wall. The build volumes are derived as simple boolean combinations of slice contours and their offsets. We make use of an efficient algorithm for computing the Voronoi diagram of a general polygon as part of the process of creating offset contours. Our algorithm guarantees that the surface of the final part will be dense while still allowing an efficient build. INTRODUCTION Designers who want to make prototypes of solid threedimensional parts directly from CAD descriptions are increasingly turning to a class of technologies collectively referred to as layered manufacturing or solid freeform fabrication (SFF). These technologies include stereolithography (SLA), 3-D printing, fused deposition modeling (FDM), selective laser sintering (SLS), and laminated object manufacturing (LOM)(4). In all these processes, a triangulated boundary representation (b-rep) of the CAD model of the part in STL format (1) is sliced into horizontal, 2.5-D layers of uniform thickness. Each cross sectional layer is successively deposited, hardened, fused, or cut, depending on the particular process, and attached to the layer beneath it. (For technologies such as SLA and FDM, a sacrificial support structure must also be built to support overhanging geometry.) The stacked layers form the final part. With most additive layered SFF processes, build time is roughly proportional to the solid volume of the final part. With FDM, it is proportional to the amount of material deposited (for the part and for supports). With SLS or SLA, it is proportional to the scan and dwell time of the laser solidifying the build material. When making a model of a solid part with a low surface area to volume ratio, using a process such as (FDM), we can complete the build considerably faster if we don’t fill the interior of the part densely. For a fairly sturdy final part, we can fill the interior with a loose cross-hatched pattern for support, with a solid wall several layers thick at the surface. The QuickSlice 6.2 software (19) that currently ships with the Stratasys FDM machine includes a fast buildoption. The software identifies slices that are “hidden” by slices above and below, and for these it builds a dense shell consisting of three concentric “roads” inside the perimeter, and fills the interior (the hidden part) with a looser fill pattern, as shown in figure 1. The drawback of this straight-forward approach is that if the slice intersects any part surfaces that approach horizontal, the software will just do a solid fill on the entire slice because the concentric outer roads might not entirely hide the loose fill pattern in adjacent layers. For large layers whose interiors would be almost entirely hidden, this is a waste of time and material. Experienced 1 Copyright 2000 by ASME Figure 1. FOR A SIMPLE RECTANGULAR BLOCK, ALL OF THE INTERIOR SLICES ARE “HIDDEN” AND THUS CAN BE BUILT USING THE FAST BUILD STYLE PICTURED ON THE LEFT. FOR CONTRAST, THE REGULAR BUILD STYLE USED ON THE TOP AND BOTTOM SLICES IS PICTURED ON THE RIGHT, WITH DENSELY SPACED PARALLEL ROADS IN THE INTERIOR. IN AREAS WHERE A PART SURFACE SHOWS A SHALLOW SLOPE WITH RESPECT TO THE BUILD PLANE, THE BUILD STYLE ON THE LEFT CANNOT BE USED. users of FDM machines may manually re-assign such layers to be built with the fast build option and change the number of concentric roads, but if they are too aggressive the result is a part such as the one pictured in figure 2. Ideally, we would like to divide the part into a thin outer wall region (for the solid fill) and interior region(s) (for the loose fill). This division could be accomplished by finding the exact interior offset surface in 3D and then slicing this offset surface along with the original part; unfortunately, calculating a 3D offset is slow, difficult to program, and subject to failures caused by numerical accuracy limitations in floating point calculations. Since the wall need not be of perfectly uniform thickness, we can use a robust, easier-to-compute approximation while still obtaining full coverage at the part’s surface. RELATED WORK Yu et al (22) describe applying Rossignac’s solid offset algorithm for 3D constructive solid geometry (CSG) solids (16) in order to obtain offset surfaces for faster rapid prototyping. For input described with a b-rep, they suggest offsetting each slice contour individually in 2D, an approach that is clearly inadequate at Figure 2. A PART BUILT WITH AN OVER-AGGRESSIVE MANUAL EXTENSION OF THE QUICKSLICE SOFTWARE’S FAST BUILD REGION. NOTE THE GAPS IN THE SURFACE ON THE NEAR-HORIZONTAL FACES. horizontal and near-horizontal faces. The implementation of the CSG solid offset algorithm applied to SLA is described in Li et al (10). In Lam et al (8), they expand upon this work by describing how to derive an explicit representation for the FDM interior support geometry using an octree. Allen and Dutta have studied the related problem of minimizing the need for supports in FDM by selectively thickening different wall areas. In (2) they describe their algorithm for building a subset of thin shell surfaces without any supports, and minimizing supports for more general surfaces and solids. The original implementation was for surfaces and solids of revolution. In (3) they detail an extension of the algorithm to general closed surfaces. This algorithm discretizes each layer to a grid, reclassifies cells inside each original contour to be solid or support cells depending on the propagation of information from neighboring cells, and then derives new contours around connected groups of solid and support cells for input to the FDM machine. This algorithm is not designed to produce walls of uniform thickness. OUR THIN-WALLED ALGORITHM Our algorithm uses internal 2D offset contours and regularized boolean set operations to approximate the true internal 3D offset surface. We generate the thin-walled region, one layer at a time, based only on the 2D slice information of the current slice and a few slices above and below. We use regularized boolean set operations to ensure that our resulting contours are closed and have non-zero area. A regularized boolean operation is defined as the closure of the interior of the result of the corresponding standard boolean operation (15). For each layer, at the least we want the solid fill pattern in the region between the boundary of the slice and its 2D inner offset. We will refer to this region as the “slice offset region.” For the inner layers in the part shown in figure 3, the only region where 2 Copyright 2000 by ASME we need a solid fill is the slice offset region. Call this slice offset region Region 1. Figure 3. FOR THIS CENTRAL SLICE, THE AREA WE WANT TO FILL DENSELY WITH THE BUILD MATERIAL (A SOLID FILL) IS SIMPLY THE SLICE OFFSET REGION (REGION 1). THE INTERIOR REGION OF THIS LAYER WILL BE FILLED WITH A LOOSER CROSS-HATCHED PATTERN FOR SUPPORT. But not all of our slices will be through vertical faces. At horizontal faces, we want a solid fill pattern not only in the slice offset region but also in the whole horizontal region, since it will be visible from the exterior of the part, as shown in figure 4. At anFigure 4. WE USE A SOLID FILL IN THE SLICES DIRECTLY ABOVE OR BELOW HORIZONTAL FACES (REGION 2). gled faces, we want a solid fill pattern in the region of the current slice that is not covered by the two adjacent slices, since this will also be visible from the exterior of the part, as shown in figure 5. For near-vertical faces, this region will be a subset of Region 1, but we will need to explicitly calculate it for nearhorizontal faces. Both these cases – horizontal faces and angled, Figure 5. WE ALSO USE A SOLID FILL AT ANGLED FACES ANYWHERE THE CURRENT SLICE IS NOT COVERED BY THE SLICE ABOVE OR BELOW (REGION 2). near-horizontal faces – are taken care of by doing a solid fill (in addition to inside Region 1) inside any part of the current slice that doesn’t appear in the slice below or above it. We subtract the slice above and the slice below from the current slice to find this region. Call this Region 2. This will give us a solid fill at the visible surface of the part, but we won’t have a very good approximation of a thin wall yet. Where horizontal or near horizontal faces meet vertical faces, for example, we’ll get “gaps” in the interior boundary of the wall as shown in figure 6.