Analysis of directional factors in milling: importance of multi-frequency calculation and of the inclusion of the effect of the helix angle

Abstract

The concept of directional factor for chatter stability analysis has been used from a long time ago. The analysis of its evolution for different feed directions in milling processes provides a good way of selecting the best cutting conditions. For very stable cutting directions, corresponding to very low directional factors, the single frequency analysis gives unacceptable results and multi-frequency, or alternative solutions as semi-discretisation must be used. It is found also that the period doubling lobes extend at both sides of the tooth pass frequency equivalent to twice the natural frequency. In these cases, helix angle has a very important effect on the stability. For end milling processes, where the mill axial pitch can be of the order of the stable limit depth of cut, a very stable situation is found except in those areas corresponding to period doubling, where instability islands are found. Besides, a graphical construction for accurate estimation of the stable limit depth of cut and starting rotational speed of the period doubling lobes is proposed.