A frequency-domain solution for efficient stability prediction of variable helix cutters milling

The utilization of variable pitch or helix cutters is an effective means to prevent chatter vibration during milling. In this paper, a frequency-domain solution to efficiently predict the stability for variable helix cutters milling is presented. This method is based on the principles of variable pitch model developed by Altintas and only considers the zero-order approximation of time-varying directional cutting constants. After discretizing the axial depth of cut into finite elements and modeling each element as a variable pitch cutter, time-varying regenerative delays in the case of variable helix cutters are transformed into multiple constant regenerative times. The chatter free axial depth of cut is solved from a stability expression in which the regenerative delay terms are approximated by the Taylor series expansion, whereas the spindle speed is identified from regenerative phase delays. Compared with time-averaged semidiscretization method, the accuracy and efficiency of the proposed technique has been verified. The results show that the proposed method has high computational efficiency. It is suited to calculate optimal geometries of milling tools and beneficial for application.