Ruhl thesis 3

page 3

© Dr. Des. Volker Ruhl

topological information other than the orientation of each facet (i.e. which side of the facet is the material-side). The simplification of a part’s surface in a set of small triangles 9 still is a relict from the first day’s of Rapid Prototyping which very much was determined by limited computer power, and by the lack of more sophisticated slicing algorithms (see paragraph 3). Further, tessellation has been an already well known first-order approximation of complex geometry. Ray tracing, and Finite Element methods have applied this approximation technique before. Today, appropriate 3D-modeling software products provide surface tessellation as a standard feature as the STL format became the industry standard for all commercial RP systems. Nevertheless, the drawbacks of this format are obvious: Highly non-linear surfaces, must be tessellated into a large number of small facets, resulting in very large data files. The accuracy is low, because of the inherent chordal deviation of the planar triangle to the mathematically correct curve (see figure). The maximum chordal deviation is determined by the CAD operator before creating the STL file. This resolution in the STL-file is fixed, which means that for improved resolution the whole STL-file must be recalculated from the original geometric model. In many cases, the tessellation operation itself introduces errors to the CAD model such as gaps or holes along the intersection of trimmed surfaces or the edges of the part model (see figure). A solution to these problems is to exchange the STL format with higher order geometric entities, preferably the source geometry with which a part is designed. Several research institutes and commercial vendors of RP equipment work on direct, NURBS-based slicing techniques that will allow users of solid modeling software to directly slice the 3D model without the need of employing the intermediary STL format. Files containing higher order information will be smaller and more accurate than comparable faceted geometry files, however, the geometric input and the algorithms for processing the geometry are more complex. Finally, interchange standards must be developed for higher order geometric descriptions. While these standards are under development, they are still subject to change until agreed upon.

Downloading - Downloading of the STL file to the workstation of the RP apparatus

Preprocessing - Preprocessing the tessellated file comprises retrieving, viewing and verifying with SFF vendors proprietory or specialized 3rd party software10. Verifying the part file comprehends the finite element mesh - a predecessor of the STL format

CAD-resolution - cordal deviation of the STL -facet from the more accurate polynomial curve

Each surface facet is defined by 12 coordinates (x, y and z) of 3 vertices and a unit normal. The direction of the unit vector as well as the way the vertices are listed (counterclockwise when looking from the outside) determines the inside and the outside face of the facet

Irregular surface triangulation leads to flaws in the final part or even to build failures. Particularly prone to those irregularities are complex part features such a round-offs or fillets on double curved surfaces patches.

Cracks or holes in surface tessellation are introduced by CAD systems’ tessellation algorithms. These gaps particularly occur at trimmed intersections of double curved surfaces. Missing surface facets wouldcertainly lead to build failures as no tool-path can be defined in those areas. CAD surface models with gaps are referred to as not „water-tide“.