Stability analysis in milling process based on updated numerical integration method. (March 2020) - Dong, Xinfeng; Qiu, Zhongzhu
Highlights: Numerical integration based on Hermite interpolation polynomial is constructed. Stability analysis based on Hermite numerical integration is proposed, and the rate of convergence and calculation accuracy of proposed method are analyzed and compared. Validity of proposed method is verified by milling experiment. Abstract: With the purpose of fast and accurately predicting the stable lobes of milling system, an updated numerical integration method (UNIM) is proposed to analyze the stability of delay-differential equation (DDE) established based on milling process. Firstly, the solution of DDE is transformed into integral expression which consists of homogeneous and particular terms. The tooth passing period of milling cutter is divided into two sub-periods, including free and forced vibrations. The state map of free vibration between the end and the beginning of time is established. Secondly, the period of forced vibration is divided into several equal time intervals, and the particular term of solution of DDE is approximated based on Hermite numerical integration within the discrete interval. The map of transition matrix is constructed between the current state and the state before the tooth passing period. The stability is analyzed according to the modulus of eigenvalue of transition matrix. Then, the convergence rate of stability analysis based on the UNIM is compared with that respectively based on the zeroth-order SDM, the first-order SDM, the first-order FDM, the second-order FDM, and numerical integration method. The stable lobes of the single and two DOF milling dynamic models are compared respectively based on UNIM and the second-order FDM. Finally, the milling experiment is carried out to verify the effectiveness of the proposed method, and the results show that the stability analysis based on UNIM has high calculation accuracy and speed.