Semianalytic stability algorithm in the frequency domain for interrupted milling

Abstract

The construction of stability diagrams of interrupted milling cases is generally carried out by means of time-consuming numerical methods in either frequency or time domain, since the period doubling lobes arising under interrupted cutting are omitted by the time-averaged parametric scan of the traditional zeroth order approximation. This paper presents a novel seminalytic method in the frequency domain for interrupted milling. Taking advantage of their analytical chatter frequency distribution, this method adds the period doubling lobes calculated in a single frequency scan to the existing Hopf limits of the zeroth order solution. This, together with intelligent selection of scanning frequency ranges and truncation to the minimum set of harmonics, allows very fast calculation of the stability charts of interrupted milling cases while retaining the analytical basis and advantages of the zeroth order algorithm. The method accurately describes the stability limits at period doubling dominated zones and improves the existing zeroth order solution, but exhibits slight inaccuracies in the prediction of Hopf boundaries due to mode interaction and harmonic truncation effects.