A multi-objective tool-axis optimization algorithm based on covariant field functional

In multi-axis machining, sudden change of tool-axis orientation has adverse effects on the machining quality and efficiency. In this paper, we proposed a mathematical framework to generate smooth tool-axis variation even on part surfaces lacking G2 and/or G1 continuities. An integral functional is formulated as the object function to represent the measurement of the rate of tool-axis change. The functional is covariant so that the result is independent of surface parameterization and applicable to non-Euclidean geometry. The minimization of the integral functional ensures minimal fluctuation of tool-axis. Other machining requirements, such as gouging-free, preferred (or greedy) direction, are incorporated into this optimization problem as constraints. The unified optimization problem is solved by a Finite Element Method (FEM) numerical method. The proposed algorithm is implemented in the planar sections of blade rough machining to produce tool path with smooth tool-axis variation. Machining results indicate that the presented algorithm can improve machining quality/efficiency and avoid gouging.