Stability analysis of 2-DOF milling dynamics for simultaneously varying tooth pitch and spindle speed with helix angle effect

Suppression of self-excited vibrations in their design and incipient stages is vital for assuring surface finish and machining efficiency in the precision machining process. Various cutting vibration suppression methods (e.g., variable tooth pitch and variable spindle speed) have been designed for suppressing regenerative chatter. However, variable parameter-based cutting vibration suppression models have mostly been developed separately with the other parameter assumed to be constant. In addition, these methods failed to provide detailed helix angle information required by a machining practitioner to determine which helix angle degree or group of helix angle degrees would have matched the stability of milling cutters. Moreover, only a single degree of freedom (1-DOF) milling system was adopted; thus, these methods cannot account for two degrees of freedom (2-DOF) and higher milling system. This study proposes a helix angle-based 2-DOF milling model with simultaneous tooth pitch and spindle speed variation to deal with these aforementioned problems. Experimental results showed that the proposed model can be effectively and efficiently applied to the prediction of the regenerative chatter stability for not only 1-DOF but also 2-DOF milling system. Empirical comparisons indicated that the proposed model outperformed the existing methods in stability prediction, while also offering stable area enlargement capability that facilitates cutting vibration suppression. A numerical example is presented to illustrate the usage of the proposed model.