Investigation on Cotes-formula-based prediction method and its experimental verification of milling stability

Abstract

Abstract Regenerative chatter is the main factor affecting the stability of milling process. The reasonable prediction of milling stability lobe diagram (SLD) is the core to controlling chatter and improving production efficiency. Therefore, a milling system with consideration of the regenerative effect is formulized as the delay differential equation (DDE). By uniformly discretizing the part of the forced vibration in the tooth passing period, the state transition matrix can be achieved by sophisticatedly adopting the Cotes formula for the fit value of the DDE at every discretized point. And then, the judgment criterion of milling stability that the eigenvalues of the state transition matrix are not more than 1 is suggested by using Floquet theory. Compared with the first-order semi-discretization method (SDM), the first-order full-discretization method (FDM) and second-order FDM, the results show that the proposed method has an advantage over the first-order SDM and the FDM whether in the computational accuracy or the computational efficiency. Finally, some group of milling experiments were done to validate the proposed method. The morphology of machined surface shows the predicted SLD results are highly consistent with the experimental values. Therefore, the proposed method has a good industrial application value in determining the optimal chatter-free cutting conditions.