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Chatter is undesirable self-excited vibrations, which always lead to adverse effects during milling process. Selecting a reasonable combination of cutting parameters is an effective way to avoid chatter. Based on the mathematical model of milling process and the Floquet theory, the stable cutting area can be determined. The stability lobe diagrams (SLD) could be obtained by different interpolationmethods. To study the effect of higher order interpolation methods on the accuracy and efficiency of milling stability prediction, the state item, the time-delayed item, and the periodic-coefficient item of the state-space equation are approximated by different higher order interpolation methods, respectively. The calculations show that when the state item is approximated by the third-order Hermite interpolation polynomial, third-order Newton interpolation of the time-delayed item can improve the accuracy of SLD, while higher order interpolation of periodic-coefficient item has negative effect on improving effectiveness and efficiency compared to high-order interpolation of the state item and the time-delayed item. In order to obtain the SLD of milling process more accurately, an updated full-discretization milling stability prediction method which based on the third-order Hermite-Newton interpolation polynomial approximation is proposed in this paper. By dividing the tooth passing period equally into a finite set of time intervals, the third-order Hermite interpolation polynomial and the third-order Newton interpolation polynomial are utilized in each time interval to estimate the state item and the time-delayed item, respectively. The comparison of convergence rate of the critical eigenvalues and the SLD of the proposed method between the existing methods is carried out. The results indicate that the proposed method show a faster convergence rate than that of other methods, and its SLD is more close to the ideal ones with small number of time intervals. [ABSTRACT FROM AUTHOR]

• This article introduced the stiffness characteristics of the joint surface between the mechanical connection structures of the spindle-tool holder, tool holder-spring clamp, and spring clamp-tool of the spindle system in the robot machining system into the prediction of machining stability. • This paper proposed a method for establishing a tool tip frequency response prediction model for robot milling systems, which improves the accuracy of theoretical prediction of the tool tip dynamic characteristics of robot milling systems under different postures, Compared to the method of obtaining tool tip frequency response of robot milling system through experiments to support milling stability prediction, the method proposed in this paper effectively improves the efficiency of robot milling stability prediction. • The prediction results of the proposed tool tip frequency response prediction model were imported, and a two-degree-of-freedom chatter prediction model considering the regenerative effect is established, and the robot milling chatter is predicted considering redundant degrees of freedom. The accuracy of prediction results is verified by milling experiment. The change of tool tip frequency response caused by the posture dependence of robot dynamic is one of the key problems that make it difficult to accurately predict the milling stability of robot. In this paper, a tool tip frequency response prediction method considering the interface stiffness characteristics of spindle-tool system is proposed for stability prediction of robotic milling under the condition of posture variation. Firstly, the interface stiffness models of spindle-toolholder, toolholder-spring clip and spring clip-tool are established based on Yoshimura's unit area method. Then, The dynamics model for the robot body and the interface stiffness models for spindle-tool system are imported into the finite element analysis model of the spindle system, so that the prediction of the tool tip frequency response is realized by harmonic response analysis. Compared with the experimental results, the maximum error of the natural frequency was not more than 2 %, and the maximum error of the amplitude was not more than 12 %. Finally, the 2 DOF robot milling stability prediction model is established. Then the robot milling chatter is predicted considering redundant degrees of freedom from the perspective of regenerative chatter prediction theory, and the accuracy of prediction results is verified by milling experiment. [ABSTRACT FROM AUTHOR]