Efficient Volume-Generation During the Simulation of NC−Milling

This paper presents an efficient and robust algorithm for the geometric determination of swept volumes during the simulation of NC−milling (three-axis machining and five-axis machining). The boundary Ψ of the volume swept by a cutter Φ is represented polygonally by using instantaneous helical motions to exactly determine the line of contact between Φ and Ψ. Applying concepts of differential geometry allows a better and more efficient approximation of tool paths. Tool paths are explicitly calculated when a design surface Γ is to be milled along prescribed curves. We also describe how to quickly determine a polygonized representation of the truncated material during the milling process by means of „Γ−buffering“. This polygon-oriented algorithm is perfectly suitable for Boolean subtractions and error assessment. Index Terms – computer aided manufacturing, NC−milling, NC−verification, sweeps, solid modeling, Γ−Buffer. −−−−−−−−−−−−−−−−− s −−−−−−−−−−−−−−−−−