Rapid Stability Analysis of Variable Pitch and Helix End Mills Using a Non-Iterative Multi-Frequency Solution

Variable pitch and helix end mills disturb the regeneration mechanism that causes chatter vibrations, and as such, they enable stable, high-performance, and high material removal rate milling processes. The regeneration mechanism is altered by the non-uniform tool geometry that results in multiple or distributed delays between vibrations imprinted on the machined surface. The design procedure for these cutters needs characterization of the stability diagrams to decide the non-uniform geometry that improves the absolute minimum stable depth of cut as well as the changes in the size and location of stability pockets. This paper presents a unified method to rapidly analyze the stability of variable helix and pitch cutters with multiple or distributed delays using a non-iterative multi-frequency domain approach that uses the Nyquist criterion to check stability at every spindle speed and depth of cut tuple. Predictions are benchmarked with the established and widely used semi-discretization method and verified with previously published experimental data, which are further validated by our own experiments. The proposed method is as accurate as of the established one while offering computational savings of up to 94%. Since explorations of alternate and better designs were potentially precluded by the computational inefficiency of previous methods, and since the method proposed herein is fast and accurate, it can help to accelerate the design of improved variable helix and pitch end mills for their use in industrial settings.