Geometric Representation of the Swept Volume of a Generalized Cutter Using Implicit Surfaces

doi:10.3901/JME.2015.23.144

Abstract

Abstract: An implicit surface methodology for computing the swept volume of a generalized cutter in five-axis NC milling simulation is proposed. In order to improve efficiency of boolean subtraction operations, the implicit surface is adopted to determine spatial relationships between the swept volume and set of points representing a workpiece without a time-consuming intersection computation in the three-dimensional space. The geometry of a generalized cutter represented by implicit surfaces is defined. According to the rigid body motion theory in frames, the mapping from a cutter frame to a workpiece frame is built, and surface boundaries are determined via the inversely motion. Translations and rotational angles are interpolated linearly, and implicit functions of the swept volume are deduced in the workpiece frame. Solutions of implicit functions are analyzed, and can be used to generate the swept volume of a generalized cutter based on implicit surfaces. Examples show the approach developed is exact and efficient, and is applied to the material removal simulation in a CNC controller.

Key words: five-axis, implicit surfaces, NC simulation, swept volume

WANG Hongliang, GUO Ruifeng, PENG Jianjun, WANG Pin, LIU Xian. Geometric Representation of the Swept Volume of a Generalized Cutter Using Implicit Surfaces[J]. Journal of Mechanical Engineering, 2015, 51(23): 144-152.

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