In milling processes

chatter usually results in poor surface quality

tool wear and even shorten the life of machine tool. In order to build the dynamic model of milling process using regenerative theory

a new full-discretization method based on third-order Newton-Hermite interpolation method is proposed in this study. The dynamic milling process considering regenerative chatter can be expressed as delay differential equations

then the transition matrix is constructed by using third-order Newton and Hermite interpolation of the state item and the time-delay term

respectively. Finally

the stability of the system was determined based on the Floquet theory

and the corresponding stability lobe diagrams are obtained. The numerical results obtained utilizing extensive simulation indicate that the convergence rate of the proposed method is faster than that of the first full-discretization method (1stFDM) and the third-order updated full-discretization method (3rdUFDM)

and the discrete error of the proposed method is the smallest at the same of the discrete number. In addition

for single degree of freedom dynamic model

the proposed method is more efficient than the 1stFDM and the 3rdUFDM

and the computation accuracy of the proposed method is better than that of the 1stFDM and the 3rdUFDM. The experimental results show that the proposed method is effective for predicting the milling stability.