Geometric Research And Application On Additive And Subtractive Manufacturing

Manufacturing industry is the mainstay industry of a country,which can directly reflect a country's productivity level,including "additive manufacturing","subtractive manufacturing" and molding manufacturing distinguished by different fabricating technologies.Manufacturing industry is a typical interdisciplinary field involving materials,machinery,control,communication and many other aspects.A large number of geometric problems are involved in the model designing process(CAD),the mechanical simulation analysis(CAE),the final process planning(CAM).This dissertation focuses on the geometry and application problems in the intelligent manufacturing.We pay attention to the space filling curves used in additive and subtractive manufacturing,domain decomposition problems during the setup planning for fiully closed freeform surfaces.Regarding to the application problems,we propose a creative modeling method of perforated lampshades for continuous projective images.Main contributions of this dissertation are presented as follows:1.A globally continuous and low-curvature tool path for additive manufacturingWe introduce Fermat spirals to "space-filling" curves and develop a new kind of"space-filling" curves,connected Fermat spirals,and show their compelling properties as a tool path fill pattern for layered fabrication.Unlike classical space-filling curves such as the Peano or Hilbert curves,which constantly wind and bind to preserve locality,connected Fermat spirals are formed mostly by long,low-curvature paths.This geometric property,along with continuity,influences the quality and efficiency of layered fabrication.We demonstrate that printing 2D layers following tool paths as connected Fermat spirals leads to efficient and quality fabrication,compared to conventional fill patterns.2.An iso-scallop tool path for subtractive manufacturingWe generate a continuous,space-filling,and iso-scallop tool path which conforms to the machining patch boundary,enabling efficient carving with high-quality surface finishing.The tool path is generated in the form of connected Fermat spirals,which have been generalized from a 2D fill pattern for layered manufacturing to work for curved surfaces.Furthermore,we develop a novel method to control the spacing of Fermat spirals based on directional surface curvature and adapt the heat method to obtain iso-scallop tool path.We demonstrate iso-scallop Fermat spiral carving paths for freeform 3D patches.Comparisons are made to tool paths generated by commercial software in terms of real machining time and surface quality.3.Setup planning of fully closed freeform surfaces in CNCSetup planning methods from the CAD and manufacturing literature have mainly focused on CAD models.We present an automatic setup planning algorithm for subtractive manufacturing of freeform 3D objects.Our method decomposes the input object's surface into a small number of patches each of which is fully accessible and machinable by the CNC machine,in continuous fashion,under a fixed cutter-object setup configuration.This is achieved by covering the input surface with a minimum number of accessible regions and then extracting a set of machinable patches from each accessible region.4.Fabricated perforated lampshades for continuous projective imagesWe present a new halftoning technique for designing fabricated perforated lampshades that project continuous grayscale images onto the surrounding walls.Given the geometry of the lampshade and a target grayscale image,our method computes a distribution of tiny holes over the shell,such that the combined footprints of the light emanating through the holes form the target image on a nearby diffuse surface.Our objective is to approximate the continuous tones and the spatial detail of the target image,to the extent possible within the constraints of the fabrication process.