Extended unit arc length increment interpolation for generalized NURBS curves in multi-axis EDM

Multi-axis electrical discharging machining (EDM) is the main manufacturing approach for shrouded blisks. To maintain a stable discharging, the feedrate of an electrode must be regulated appropriately with respect to a workpiece. The feedrate control in multi-axis EDM is a challenge due to two facts. The first is that the feedrate fluctuations occur at line segment junctions along the feeding trajectory which is expressed in G01 codes. The second is that, with involvement of rotary axes, the feedrate control must consider the nonlinear mapping between the workpiece frame and the machine frame. This paper proposes an extended unit arc length increment interpolation (UALII) for generalized NURBS curves. Given the point coordinates in the machine frame, the coordinates in the workpiece frame can be obtained by the forward kinematics. By using the UALII, the curve parameter is first obtained. To achieve synchronization among involved axes, the curve parameter is substituted into the generalized NURBS curve. Due to the nonlinear mapping, each interpolation of one basic length unit (BLU) can give the axial increments which are more than one BLU. Digital differential analyzer (DDA) is used for a finer interpolation for each axial increment. Machining tests show that the use of UALII for generalized NURBS curves can decrease the machining time by 42.19%, 29.65% and 26.42%, respectively, as compared with the cases of no feedrate planning, the weighted average movement ratio algorithm (WAMRA) and the feedrate post-processing algorithm (FPPA). The extended UALII algorithm can also reduce the electrode wear.