The main objectives of this research are to investigate analytical tools for optimizing a milling process that uses non-uniform pitch cutters, and to validate the analytical findings experimentally. The focus in the analytical investigation is primarily on the multiple time-delay effects on the chatter stability of the dynamics. The problem gives rise to transcendental characteristic equations with rationally unrelated time delays, which have to be resolved in the domain of the delays from the perspective of stability. Optimum cutter design will be investigated based on a trade-off between the chatter rejection ability and increased productivity. Corresponding optimum cutting conditions will also be derived. The approach will be based on a recent mathematical paradigm of the principal investigator , which is called the "Cluster Treatment of Characteristic Roots". This paradigm will create a display that is analogous to the conventional stability lobes, except for the complete set of pitch angle variations. Broad ranging experimental studies will be performed using various cutter geometries and the correspondence of the analytical and experimental findings will be investigated in each case.
If successfull, this research will yield a new analytical procedure that will be available to the machine tools science. This procedure will facilitate the selection of optimum cutting parameters to avoid chatter and increase productivity. Such optimized machining conditions will translate into a production cost advantage. The outcome of the research will also be used to train graduate students as well as the practicing manufacturing engineers through various channels of dissemination.
