A unit sphere discretization and search approach to optimize building direction with minimized volumetric error for rapid prototyping

Abstract

As a material-additive process, rapid prototyping (RP) has shown its capability in creating complex geometries that traditional material-removal processes cannot accomplish. However, its layer manufacturing nature still subjects itself to undesired staircase effects. It has been shown that staircase effects have relationship with the building orientation in RP processes. In order to minimize staircase effects, the building orientation has to be properly selected prior to the implementation of RP processes. This paper presents a method to select the optimal building direction in RP processes that leads to the minimized volumetric error. In order to explore the global directional space, a unit sphere is uniformly discretized first to represent the potential directions in a 3-dimensional (3-D) space. Following that, each facet comprising the STL geometric model is mapped onto the discretized unit sphere as a great circle individually, which represents the optimal directions for that facet. In order to find the globally optimal solution, both an exhaustive search and a genetic algorithm (GA)-based searching strategy are presented to identify the globally optimal direction for building the 3-D geometry. At the end of the paper, examples are presented to show the effectiveness of the method.