Frequency domain stability analysis of milling processes with variable helix tools

An analytical approach for the stability analysis of milling with variable pitch and variable helix tools is presented. An important parameter, which affects the occurrence of unstable regenerative chatter vibrations, is the time delay between two subsequent cuts. For variable pitch or variable helix tools a distributed time delay arises in the model equations, which can suppress chatter vibrations in comparison to uniform pitch and uniform helix tools with a single point wise time delay. For the stability analysis in the frequency domain the well-known multifrequency approach is extended to variable helix angles with continuously distributed delays. The results of the zeroth-order approximation with time-averaged coefficient matrices and the more precise results of the multifrequency solution with higher harmonics of the chatter signal are verified by known results from the literature. The frequency domain approach is suited to calculate optimal geometries of milling tools and beneficial for application with many structural degrees of freedom