A High-Accuracy Tool Path Generation (HATPG) Method for 5-Axis Flank Milling of Ruled Surfaces with a Conical Cutter Based on Instantaneous Envelope Surface Modelling

In this paper, a novel framework of generating high-accuracy tool path for 5-axis flank milling of ruled surfaces with a conical cutter is developed by designing the instantaneous envelope surface of each planned cutter location (CL). Based on the analysis of the envelope theory, the instantaneous envelope profile of a selected cutter is only affected by the first-order derivation of the cutter’s motion, i.e. tangent vectors of the tool path. This property reveals an interesting fact that characteristic points on an envelope surface can be controlled via path tangents, thus laying the foundation for accurately evaluating the machining error at a single cutter location. On this basis, a simple yet robust method, called rotations for three-point offset (RTPO) method is first proposed to position a conical cutter to have at least three contact points with a ruled surface. Path tangents optimization is then performed to minimize the geometric deviation between the characteristic points and the ruled surface, followed by fine-tuning of the tool axis with a differential rigid motion. Both path tangent optimization and tool axis tuning are formulated as linear program problems, and the optimal cutter location with path tangents is determined by solving them repetitively. Finally, accurate tool path for conical cutter flank milling is generated with curve registration algorithms that interpolate the planned points and tangents. Examples are provided to validate the proposed method, and one can see high-accuracy flank milling paths can be planned point-by-point without subsequent optimization. •A simple and robust cutter positioning method called RTPO is proposed to locate a cutter with at least three contact points.•Path tangents are optimized with a linear model so that the characteristic point at a single CL is determined.•The optimal cutter position with minimum machining error is obtained via applying differential motions to the tool axis.•Tool path is formulated with the planned machining errors maintained at sampled CLs.