Collaborative optimization of conical cutter sequence for efficient multi-axis machining of deep curved cavities

•A collaborative optimization method of conical tool sequence and machining ranges and cutting parameters aiming for the highest four-axis roughing efficiency of deep and narrow cavity.•An efficient method of finding characteristic points for computing all feasible conical cutters was proposed.•Considering the geometric and physical accessibility, the tool sequence domains were determined.•A model of best cutting performance of a weak conical ball-end cutter.•Experimental example of the proposed method show its effectiveness in improving roughing efficiency.