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Carbon fiber-reinforced silicon carbide matrix (C/SiC) composites are typical difficult-to-cut materials due to high hardness and brittleness. Aiming at the problem of the serious high cutting force and poor surface quality in conventional milling (CM) C/SiC composite process, ultrasonic vibration-assisted milling (UVAM) and conventional milling tests with a diamond-coated milling cutter were conducted. The results showed that reducing the feed per tooth, cutting depth, or increasing the cutting speed can reduce the average cutting force, and increasing the ultrasonic amplitude, the average cutting force decreases first and then increases. With the assistance of ultrasonic vibration, the maximum reduction rates of average cutting forces Fx, Fy, and Fz were 43.7%, 29.16%, and 68.09%.The ultrasonic vibration assisting effect does not significantly improve the damage of materials such as fiber breakage during processing. The ultrasonic vibration assisting effect improves the quality of processing edges. It is found that reducing feed per tooth, cutting depth, or increasing cutting speed can reduce surface roughness and increasing the ultrasonic amplitude reduces the surface roughness first and then increases. On the whole, the surface roughness of C/SiC ultrasonic vibration milling is slightly smaller than that of conventional machining. [ABSTRACT FROM AUTHOR]

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]

We present several matrix Kantorovich-type inequalities, which improve the results obtained in Liu and Neudecker (1996). Elementary methods suffice to prove the inequalities. [ABSTRACT FROM AUTHOR]