Robust prediction of chatter stability in micro milling comparing edge theorem and LMI

Machine tool chatter is detrimental to productivity and the overall quality of manufactured parts. Analytical stability models are used to predict the occurrence of chatter for a given set of machining conditions and improve productivity. Conventional chatter models typically assume that parameters are constant, which can lead to an unsuitable stability lobe prediction. System dynamics, including natural frequency and damping ratio, and cutting coefficients are the main parameters that can change during actual machining operations. Parameter variations can be taken into consideration using different robust control theory approaches. A frequency domain approach using Edge theorem, can analytically account for time invariant parameter uncertainty directly in the characteristic equation. Combined with the Zero Exclusion method, computation of stability regions can be checked graphically. Chatter stability can also be detected using a time domain approach involving Lyapunov stability theory subjected to linear matrix inequality (LMI) conditions. This paper presents two novel robust chatter stability models for predicting stability regions while accounting for three uncertain parameters. Robust stability lobes can be predicted and facilitate optimal machining parameter selection to achieve higher productivity.