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.

The nonlinear dynamic analysis of rotating composite boring round bar containing carbon nanotubes (CNTs) in cutting system was investigated. Firstly, simplify the boring bar to the model of non-extendable rotary cantilever structure. Both the Halpin-Tsai model and micro-mechanical layering theory were used to predict the material properties of the boring round bar. Then the equations for the composite boring bar based on Euler Bernoulli shaft theory, including von Karman geometric nonlinearity are derived. The nonlinear dynamic model of cutting system including periodic regenerative chatter cutting force, periodic control force, viscoelastic and process damping is established by using Hamilton principle. The analytical solution of the steady-state response of the cutting system was subsequently obtained by the Galerkin approximation and the perturbation method of multiple time scales. Finally, the influences of carbon nanotube-related parameters, fiber volume fraction, fiber orientations, stacking sequences, damping coefficient and geometry properties of the cutter edge on the stability of the cutting system are evaluated. The obtained results show that the incorporation of CNTs has significant effect on the dynamic behavior of the cutting process. Increasing the process damping and changing the cutter edge and bar's cross section can improve stability of the cutting process. Furthermore, the unstable cutting region is sensitive to multi-valued properties generated by jumping.