Abstract
Based on the observation that the boundary surface of a rotary milling cutter can be represented as the envelope of a one-parameter family of spheres,the analytical expression of the surface swept by a milling cutter undergoing a general spatial motion is derived in a very simple way by using the envelope theory of two-parameter family of spheres.For a toroidal cutter,two methods for determining the effective patch of the obtained envelope surface are proposed.The results can be applied to multi-axis numerical control machining simulation and verification,tool collision check,accuracy evaluation,row spacing optimization and tool path generation.The simulation results show that the proposed method has high precision and high stability.
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