Development of a generalized extended harmonic solution for analyzing the combination of chatter suppression techniques in milling

In this paper a comprehensive and structured analysis of the stabilizing properties linked to the combination of different chatter suppression techniques in milling was carried out. Specifically, the spindle speed variation, the stiffness variation and the usage of tools with variable pitch and variable helixangles were considered. For this purpose, a unique, general and efficient frequency domain formulation (extended harmonic solution) was developed. It is suitable for dealing with differential delayed equations characterized by multiple and distributed time dependent delays and time periodic dynamics. It was demonstrated that the developed solution converges to the reference cases, which were studied in literature through semi-discretization and its extensions. Moreover, by selecting a proper number of considered harmonics, the computation time was reduced of one order of magnitude, in the face of a slight reduction of accuracy with respect to time domain approaches. The computed stability lobe diagrams demonstrated that the combination of multi-chatter suppression techniques allows exploiting the best features of each methodology. The simultaneous use of the spindle speed variation and the stiffness variation was studied for the first time. The absolute limit of stability increased up to 204%, much more than by adopting the techniques in a separate manner. If the enlargement of the stability region is considered as the reference target, the best results were granted by the combination of all the three strategies. Indeed, the improvement with respect to the use of only two techniques was at least 10%.