A new Steiner patch based file format for Additive Manufacturing processes

Abstract

Additive Manufacturing (AM) processes adopt a layering approach for building parts in continuous slices and use the Standard Tessellation Language (STL) file format as an input to generate the slices during part manufacturing. However, the current STL format uses planar triangular facets to approximate the surfaces of the parts. This approximation introduces errors in the part representation which leads to additional errors downstream in the parts produced by AM processes. Recently, another file format called Additive Manufacturing File (AMF) was introduced by ASTM which seeks to use curved triangles based on second degree Hermite curves. However, while generating the slices for manufacturing the part, the curved triangles are recursively sub-divided back to planar triangles which may lead to the same approximation error present in the STL file. This paper introduces a new file format which uses curved Steiner patches instead of planar triangles for not only approximating the part surfaces but also for generating the slices. Steiner patches are bounded Roman surfaces and can be parametrically represented by rational Bezier equations. Since Steiner surfaces are of higher order, this new Steiner file format will have a better accuracy than the traditional STL and AMF formats and will lead to lower Geometric Dimensioning and Tolerancing (GD&T) errors in parts manufactured by AM processes. Since the intersection of a plane and the Steiner patch is a closed form mathematical solution, the slicing of the Steiner format can be accomplished with very little computational complexity. The Steiner representation has been used to approximate the surfaces of two test parts and the chordal errors in the surfaces are calculated. The chordal errors in the Steiner format are compared with the STL and AMF formats of the test surfaces and the results have been presented. Further, an error based adaptive tessellation algorithm is developed for generating the Steiner representation which reduces the number of curved facets while still improving the accuracy of the Steiner format. The test parts are virtually manufactured using the adaptive Steiner, STL and AMF format representations and the GD&T errors of the manufactured parts are calculated and compared. The results demonstrate that the modified Steiner format is able to significantly reduce the chordal and profile errors as compared to the STL and AMF formats.