WAVELET-BASED MULTIRESOLUTION REPRESENTATION OF A GEOMETRIC MODEL FOR FREE-FORM SURFACE MACHINING

Hiroaki Date, Satoshi Kanai and Takeshi KishinamiGraduate School of Engineering, Hokkaido UniversitySapporo 060-8628, JAPANABSTRACTIn a 3D free-form CAM system, a series of intermediateshape models for machining are required as the references ofNC programming. The safety and efficiency of the machininggreatly depend on the geometric relation between theseintermediate shape models. However current CAM systems lackthe function of automatic generation of the appropriate series ofthese shape models.In this paper, a new wavelet-based multiresolutionrepresentation (MRR) of a series of intermediate shape modelsfor machining is proposed. The proposed MRR enables verycompact data representation for these models. In this MRR,geometric relations between each resolution model can becontrolled so as to avoid overcut and to level the cutting loads.Two new control methods for MRR based on the lifting schemeand wavelet coefficient modification are proposed to supportthe contour line and scan line milling. The effectiveness of theMRR was verified through simulation.KEYWORDS: Computer Aided Manufacturing, GeometricModel, Wavelet Transform, Multiresolution Representation,Free-form Surface Machining, Tool Path Generation1. INTRODUCTION1.1 Background Recently, mold and die manufacturing requires faster andmore efficient free-form surface machining processes. Ingeneral, in free-form surface machining, a geometric model ofthe free-form surface of the final product shape is first designedusing a 3D CAD system. The NC data of the tool path for themachining process must be programmed using a 3D CAMsystem. Generally, a free-form machining process for one finalproduct shape can not be performed by a single machiningoperation but requires a series of several machining operations:roughing, semi-finishing and finishing operations. In a 3D CAMsystem, tool path generation for each of these machiningoperations requires a series of geometric models of theintermediate shapes as references. The safety and efficiency ofthe machining operations greatly depend on the geometricrelation between the intermediate shapes. However, currently,the geometric models required for the tool path generation aremostly designed by using the following two methods: 1) Only one geometric model for a final product shape is usedas a reference for all of the machining operations. 2) The series of intermediate shape models for each machiningoperation is manually designed by a production engineer inadvance, and each model is used a reference for themachining operations.In the first case, since the tool cutting ability and removalvolume are disregarded, it is difficult to achieve safe andefficient machining. In the second case, the geometric relationsbetween each model are designed with consideration of the toolcutting ability and removal volume; however, this is a difficulttask and can only be performed by a very experienced operator.Moreover, redesign of the models may be needed if the tools orproduct shape are modified. The amount of model data mayalso be very large due to the necessity to preserve all of theintermediate shape models. From a technical point of view, theradius of a tool is large in roughing and gradually becomessmaller with the progress of the machining operation, becausethe given tolerance of the milling must be strictly satisfied in thefinishing operation. It is therefore desirable to generate a series of intermediateshape models in which the cutting ability and removal volumecan be automatically considered, the amount of model data canbe compressed, and the resolution of the models can bechanged.1.2 Motivation and purpose Wavelet transform (WT) has recently been widely used incomputer graphic studies as a powerful tool for datacompression, simplification and fast transmission of 2D imagesand 3D models [1]. By using WT, the original object can berepresented by Multiresolution Representation (MRR), whichconsists of both the approximation of a given object and thedetails that are lost in approximation. Approximation shows thelow-frequency components and the details show the series ofhigh-frequency components.