Five-axis CNC machining presents high efficiency and unparallel flexibility in the machining of complex curved surfaces. However, generation of gouge-free CNC tool path and cutter orientation in 5-axis CNC machining remains a challenge due to the complex nature of the geometry problem encountered and the wide variations of surface geometry. In particular, curvature gouge is the biggest obstacle that hinders the advantages of 5-axis CNC machining. At present to avoid curvature gouge. a ball mill cutter with simple cutter geometry is mostly used in machining complex curved surfaces, although this either leads to lengthy machining time or poor surface finish with larger cusps which require extensive amount of hand polishing later on. An end and/or torus mill cutters with better cutter-surface curvature match can considerably improve the efficiency of the machining and the quality of the machined surface. But generation of appropriate tool paths and orientations for the more complex cutter geometry in gouge-free 5-axis CNC machining of curved surface requires a better understanding and a rigorous model of cutter-surface interaction, which do not exist at present.

In this work, a rigorous mathematical model of cutter-surface geometry that facilitate better understanding on the interactions between various mill cutters. including ball. torus and end mills. and curved surface is introduced. The model is based on the new Euler-Meusnier Sphere (EMS) concept from a generic mathematical and geometric model of the cutter and surface geometry. The EMS model determines the curvature gouge constraints with varying cutter size and maximum cutter tilting angle for any given surfaces. A generic. global curvature gouge detection and avoidance method for the 5-axis CNC machining of concave, curved surfaces has been introduced. The method also improves curvature match between the cutter and the machined surface by facilitating the use of torus and end mill cutters.

Computer simulation tests and real part machining have been carried out to assess the effectiveness of the new theory and newly introduced curvature gouge detection and avoidance criteria. Five-axis CNC machining experiments on curved surface, e.g. ellipse and exponent surfaces, are carried out. The machined surfaces following different tool path and cutter orientation strategies are measured using a CMM to appraise the real benefit of the introduced approach. The method has been applied to all three types of commonly used mill cutters:​ end. torus and sphere, for concave curved surfaces with limited curvature variation. The machining experiments have demonstrated the superior capability of the new method in providing guaranteed gouge elimination. better surface quality, and simple implementation. in comparing with 5-axis tool path and cutter orientation planning methods.

The new EMS concept and curvature gouge detection/elimination method form the foundation for generating highly efficient, high quality surface producing 5-axis CNC tool path. and cutter orientation planning, programming and optimization for machining curved surfaces.