Stability analysis of milling with irregular pitch tools by the implicit subspace iteration method

Abstract

Irregular pitch tools have been used since a long time ago to avoid chatter in milling processes. Optimal design of these mills was studied by some researchers. The method used is based in the frequency domain, and there were some practical examples showing that the process gives good results. Nevertheless, for high order lobes the method was not verified analytically, one of the difficulties being the large size of the matrices involved in the analysis. A recent method for obtaining stability diagrams is based in the use of implicit subspace iteration method, giving rise to much shorter calculation times than the already known discretized time domain methods. Use of this method allowed assessing the stability of processes with irregular pitch mills in both high and medium order lobes regions. The method of subspace iteration was compared with the more conventional semi-discretization method in low order lobes region, with good agreement. Afterwards, the stability of milling processes with irregular pitch tools designed after previous proposals was assessed in both medium and high order lobes regions. As a conclusion, in the examples analyzed the angles selection shows to be an optimal solution, although for high order lobes the regular pitch tools provides better stability. As a further research topic, other possible angle distributions to improve the behavior at low velocities should be analyzed.