# Analysis on Free Vibration and Stability of Rotating Composite Milling Bar with Large Aspect Ratio
###### Abstract  
The free vibration behavior and stability of composite milling bar with large aspect ratio are analyzed. Specifically, the free vibration equations are derived based on Euler Bernoulli beam theory and [PERSON]'s principle and solved by Galerkin method. In addition, to investigate the stability of the cutting system with a rotating composite milling bar, this study develops an analytical model for regeneration and cutting force fluttering, in which the internal damping, external damping, gyroscopic effect, and inertial effect are considered. The subsequent stability lobes are obtained by the time domain method. Then, the stability of composite and conventional metal milling bar is compared. The effects of internal damping, external viscous damping, py angle, gyroscopic effect, and inertial effect on cutting stability are analyzed. m 20202019 May 20202019 May 20202020 May 20202019 May 2020202019 May 2020202019 May 2020202019 May 202020202019 May 202020202020202020202020202020202020202020  
performance of composite materials is better than the raw materials and can meet various requirements. In addition, the composite has the advantages of designable mechanical properties. Owing to their high specific strength, specific stiffness, lightweight and anti-fatigue properties, composite materials have been widely applied in aerospace, military industry and mechanical engineering. The composite material offers the possibility to simultaneously enhance the dynamic stiffness and fundamental natural frequency of milling bars with large aspect ratio. Chatter can be divided into two categories based on their self-excited vibration mechanisms, i.e., regenerative chatter and mode-coupling chatter. Regenerative chatter occurs due to the regeneration of surface corrugation generated by the previous cutting [8]. [PERSON] and [PERSON] [9] analyzed the stability limit of regenerative chatter in an orthogonal cutting. [PERSON] et al. [10; 11; 12] obtained the stability lobe diagram of a milling system in frequency domain by the frequency analysis method. This method has a high computational efficiency, and the gyroscopic effects activated by the rotation of milling bar is included in the analysis. On the other hand, in other literature [13; 14; 15; 16], the stability lobe diagrams of the chatter system were obtained in time domain. [PERSON] et al. [17; 18; 19] conducted a series of research on cutting issues, including the milling stability analysis considering the flexibility of cutter and workpiece, the influence of the tilting machining of circular segment end mills on the surface roughness of workpiece, the influence of the tilting machining of the barrel milling cutter on the stability, etc. In Literature [20], the first-order modal frequency domain method and the Chebyshev collocation method were used to analyze the cutting stability of large horizontal lathe. Based on comparison, the Chebyshev polynomial method was found to have higher calculation accuracy, while the first-order modal method had faster calculation speed. [PERSON] et al. [21] used finite element model to analyze milling chatter under gyroscopic effect. The iteration method was used to calculate the stability lobe diagram. Firstly, an initial spindle speed was set to solve the characteristic equation. Then the solved equation was used to determine the flutter frequency, critical cutting width and spindle speed. The next iteration of updating the equation and parameters was determined according to the convergence of spindle speed. [PERSON] et al. [22] and [PERSON] et al. [23; 24] established a cutting process model of rotary two-degree-of-freedom drill pipe and used the frequency domain method to study the stability of the cutting process. Due to the particularity of the drilling force model, it is not necessary to solve the characteristic equation. Instead, the cutting depth expression can be directly derived; this is the stability analysis of isotropic cutting bar, including rotation speed.