Chatter stability of milling in frequency and discrete time domain

Chatter stability of milling operations has been gaining significant attention with a view to improving the material removal rates in high speed machining of aluminum alloys and low speed milling of difficult to cut, thermal resistant alloys. This paper presents frequency and discrete time domain chatter stability laws for milling operations in a unified manner. The time periodic dynamics of the milling process are modelled. By averaging time varying directional factors at cutter pitch intervals, the stability lobes are solved directly and analytically. When the process is highly intermittent, which occurs at high speeds and low radial depth of cuts, the stability lobes are more accurately solved either by taking higher harmonics of directional factors in frequency domain, or by using semi-discretization method. This paper compares the stability solutions against the numerical solutions and experiments, and provides comprehensive mathematical details of both fundamental stability solutions.