Generation of swept volumes of toroidal endmills in five-axis motion using space curves

Abstract

Accurate prediction of the swept volume of a cutting tool is essential in NC verification algorithms for detecting deficiencies in a proposed tool path, such as gouging, undercutting and interference. This paper explores a new technique for generating the swept volume of a toroidal endmill, and analyzes the results obtained for two test cases. For a given tool location along a path, a curve on the cutting surface of the tool is identified that rs:presents the imprint of the tool on the machined surface. This curve will be designated a space curve as it is defined in 3D spa.ce. The method relies on forward difference information obtained from a G-code or cutter location data file in order to compute the space curves. Once several su.ccessive space curves have been identified, a facetted surface model of the footprint of the tool along a pass may be readily calculated and compared with the design surface. The method has b,een verified for two test cases: a) 5-axis tool path on a hemispherical cavity and b) a 5-axis tool path on the complex surface of a turbine blade. Results from the new method are compared with the slow, but dependable my-casting technique. It is concluded that the new technique offers al fast and accurate method of verifying multi-axis tool paths. In the future, it is hoped that the simulation can be extended to all cutter shapes, and not be limited to toroidal cutters.