Positioning of a conical cutter for centrifugal blades finish machining based on the best uniform approximation (BUA) method

Abstract

To demonstrate the closeness between the tool and nominal surfaces during the flank milling of centrifugal blades, discrete points on the conical cutter tool axis are projected in the nominal surface normal direction, and a mapping curve on the conical surface is obtained. On this basis, a novel toolpath planning method, under hub surface constraints, is proposed for flank milling centrifugal blades using a conical cutter based on the BUA method. This is a nonlinear optimisation problem, therefore the programming linearisation method is provided. The effectiveness of the proposed BUA method is verified via numerical example of a ruled surface and compared with the least square (LS) and two-point offset (DPO) methods. The influence of the conical cutter cone angle on the planning error is also analysed. The proposed BUA method is also applied to a centrifugal blade flank milling numerical example and its feasibility is verified.