On the dependency of the extent of multiple solution zone around stability lobes on cutting law nonlinearity

Abstract

In machining vibrations analyses, regenerative chatter stability boundaries aka stability lobes are known to be often accompanied by a multiple solution zone in process parameters space. In that zone the stable steady response coexists with a finite-amplitude oscillatory solution preceding cut interruption. Exploration of the oscillatory behavior requires accounting for finite nominal cut thickness and the condition of the tool exit from cut. In the present work we explore these conditions via a harmonic balancing framework, bringing forward the dependency of the extent of the unstable post-critical chatter domain on the cutting law nonlinearity.