In this paper

the stability of milling in vertical machining center is predicted by numerical integration method. Firstly

the single-degree-of-freedom and two-degree-of-freedom milling dynamic models affected by chatter are represented by time-delay differential equation

and the delay period is discretized; Secondly

the time-delay differential equation is solved by numerical integral method

the milling stability is determined according to Floquet

and the stability lobe diagram is obtained. Finally

in order to verify the correctness of the numerical integration method

the milling force coefficient and modal parameters are obtained by parameter identification experiments

the machining parameters are selected from the obtained lobe diagram for experimental verification. The numerical simulation results show that the numerical integration method is superior to the 1st-SDM method and the 1st-FDM method in terms of computational efficiency and accuracy. The numerical integration method solution results are consistent with the experimental results

which can guide the selection of milling process parameters and ensure the stability of milling processing.