Polynomial Chaos-Kriging approaches for an efficient probabilistic chatter prediction in milling

After more that 60 years of investigation, chatter vibrations in metal cutting are still a major cause for poor surface finish and machine tool damage. In order to avoid undesired machining conditions, chatter prediction algorithms may be applied to draw stability charts that allow a preliminary identification of the safe areas. Nevertheless, the stability boundaries are sensitive to the variations and uncertainties of the dynamic milling model coefficients. Thus, the accuracy and reliability of the obtained predictions can be inadequate for many industrial applications. For solving this problem, robust methods were recently devised that are fast but usually too conservative. On the other side, probabilistic approaches were also developed to estimate the probability of instability for a given combination of cutting parameters, by taking into account the statistical distributions of model coefficients. Probabilistic approaches allow a less conservative, risk-aware selection of stable cutting conditions. Unfortunately, their application is still very limited due to the required large amount of computational power and time. In this work, three novel probabilistic methods based on Polynomial Chaos and Kriging metamodels (PCE, KRI and PCK) were compared to state of the art probabilistic algorithms (MC, MC-SPA, DRM-SPA, RCPM). The numerical analysis and the experimental validation proved that MC-SPA, DRM-SPA, RCPM and PCE are too rough and thus needless for industrial applications. On the contrary, KRI and in some cases also PCK showed an excellent accuracy together with significantly shorter elaboration time than that required by the reference Monte Carlo (MC) technique.