Study on a 2D field-based multi-objective tool-axis optimization algorithm based on covariant field theory for five-axis tool path generation

In five-axis machining, drastic change of tool axis has negative effects on machining efficiency and quality. Our published work proposed a unified mathematical framework to generate smooth tool-axis field and implemented in 1D domain (Yan et al., J Manuf Syst 48:30–37, 2018). In this paper, we extend the mathematical framework to 2D domain and the framework is an integral functional problem converting diverse machining requirements, such as gouge and collision free, smoothness, into mathematical expressions. A tool-axis vector field (TAVF) defined on the freeform surface is calculated by optimizing the integral functional problem. The surface is discrete into triangular mesh, and the discrete TAVF calculation problem is solved by a numeric 2D finite element method (FEM). Subsequently, the proposed algorithm is implemented to generate field-generated tool path (FGTP). The tool path has been used in machining hub of blade disk (blisk). The blisk is a complex workpiece that impellers should be gouge avoided. Machining experiments indicate that tool path generated by the proposed algorithm can avoid collision and improve smoothness on the whole surface. The freeform surface machining quality is highly improved compared with that machined by region-partitioned tool path (RPTP).