Robust stability of milling operations based on pseudospectral approach

Abstract

The prediction of chatter-free machining parameters is not reliable for industrial applications without guaranteed robustness against modeling uncertainties. Measurement inaccuracies, fitting uncertainties, simplifications and modeling errors typically lead to a mismatch between the mathematical model and the real physical system. This paper presents the robust stability analysis of milling operations based on a pseudospectral approach to take into account the effect of bounded parametric uncertainties both in the cutting coefficients and in the modal parameters. In order to make the predictions more accurate, the operational modal analysis of the spindle during rotation was conducted. The natural frequencies and damping ratios of the dominant vibration modes were identified from the impact tests of the rotating tool at different spindle speeds. The uncertainties of the fitted parameters were included in the computation of the pseudospectral radius of the monodromy operator of the time-periodic system. The solver is tested in a case study and experimental chatter tests are also included for demonstration purposes.