Dynamical Stability Analysis of Rotating Composite Cutter Bar with Nanocarbon Materials

Abstract

This paper studies the free vibration response of a spinning and variable cross-section composite cutter bar homogeneously enhanced with carbon nanomaterials. Based on the Rules of Mixture (ROM) and the Halpin–Tsai Model (HTM), we establish a motion model of the spinning and variable cross-section composite cutter bar by containing carbon nanomaterials, which combines the Euler–Bernoulli beam theory and Hamilton principle. In addition, the dynamic governing equations are solved by using the Galerkin method so as to obtain the characteristic equation. The curves of decay rate-rotating speed and natural frequency-rotating speed are obtained especially by numerical analysis, and the corresponding critical speed and instability threshold of the composite cutter bar are also calculated. By selecting different parameters such as length-to-diameter (or length-to-width-to-thickness) ratios and volume contents of carbon nanomaterials, cutter bar taper ratios, ply orientations, and stacking sequences, the relation between instability threshold and loss factor is obtained with respect to the composite cutter bar. The results obtained found that the cutter bar’s stiffness is increased by adding carbon nanomaterials into the carbon fiber-reinforced polymer composites. Its natural frequency and critical speed are increased, but the cutter bar’s damping decreases with the increasing content of carbon nanomaterials. The results of critical speed and fundamental natural frequency of composite cutter bar for high-speed machining are greatly meaningful.