Positioning algorithm for 5-axis machining of ruled surfaces based on radius and angle offset

An analytical model for 5-axis flank milling ruled surfaces tolerance is built considering curvature of the baseline. A new concept angle offset is advanced based on studying the relationship between tool axis vector and generatrix, the offset angle evaluate equation is obtained. Radius and angle (R&A) offset algorithm is put forward and applied to calculate tool location data for 5-axis flank milling ruled surfaces to improve the error distribution of the whole milled surface and eliminate the tolerance caused by the different direction of the normal vector, which make sure two baseline of the surface machined precisely. The influences of parameters such as length of generatrix, angle of two normal vectors of generatrix end point to the error distribution are analyzed by an example. The error distribution index of radius offset algorithm and R&A offset algorithm is contrasted, and the result shows that the latter one has higher precision and sounder process technology.