Five-Axis Manufacturing Simulation Based on Normal Arc Mapping and Offset Volume Computation

This paper presents a general manufacturing simulation method for 5-axis manufacturing processes including both numerical controlled (NC) machining and additive manufacturing (AM). The method is based on three major steps: (1) normal arc mapping that is general for computing critical curves, (2) computing the cutter swept volume (SCV) along a 5-axis tool paths based on the critical curves, and (3) computation of simulation results based on a set of sampling points from the cutter swept volume. The first two steps are discussed in details. Based on the properties of the envelop theory, we first present a normal arc mapping method that is general and intuitive. Accordingly the critical curves can be computed for any position and orientation of a tool on a 5-axis tool path. We test various tool shapes including three typical cutters in NC machining and a laser ellipsoid tool in Stereolithography apparatus (SLA). Based on the critical curves, the envelope surfaces of the cutter swept volume related to given tool motions can be determined. We compute a closed continuous surface to approximate the cutter swept volume. The approximation error in computed result has been analyzed. Finally we use a discrete representation, layered depth normal images (LDNIs), to convert a set of cutter swept volumes into a booleaned solid model. The discrete computation based on LDNIs enables us to compute the simulation result robustly and effectively. We demonstrate our method for both NC machining and additive manufacturing processes. Five-axis tool paths can also be given in both curves and surfaces. Various test cases have been presented to illustrate the effectiveness of our method.