Envelope surface formed by cutting edge under runout error in five-axis flank milling

This paper investigates the analytical envelope surface model formed by specially designed cutting edge under cutter runout error, including axis offset error and tilt error, in five-axis flank milling. This model, which is independent of the machine tool type, is determined by the tangency condition in envelope theory. First, the cutter runout is defined by four parameters, namely offset distance, offset direction angle, locating angle, and tilt angle. Then, the cutting edge represented by cubic B-spline curve is used as the generator of cutter rotation surface to formulate the closed-form envelope surface model. In particular, the runout error and feedrate are both integrated into the model. In addition, we study special cases of the analytical model and the runout effect on envelope surface. Finally, computer example validates the feasibility of the proposed model with runout. We find that envelope surface formed by cutter edge is different from each other at the existence of runout, and envelope surface dedicated to final machined surface is generated by the composition of some segments of cutter edges. The results can be applied to tool path optimization in five-axis flank milling and NC simulation with cutter runout.