Nonlinear Dynamics of Cutting Process considering Higher-Order Deformation of Composite Cutting Tool

Abstract

In this paper, the nonlinear dynamic analysis of the cutting process of composite cutting tool is performed. The cutting tool is simplified to a nonplanar bending rotating shaft. The higher-order bending deformation, structural damping, and gyroscopic effect of cutting tool are considered. It is assumed that cutting tool is subjected to a regenerative two-dimensional cutting force containing the first and second harmonic components. Based on the Hamilton principle, the motion equation of nonlinear chatter of the cutting system is derived. The nonlinear ordinary differential equations in the generalized coordinates are obtained by Galerkin method. In order to analyze the nonlinear dynamic response of cutting process, the multiscale method is used to derive the analytical approximate solution of the forced response for the cutting system under periodic cutting forces. In the forced response analysis, four cases including primary resonance and superharmonic resonance, i.e., $\overline{\mathrm{\Omega }}={\omega }_1$ , $\overline{\mathrm{\Omega }}={\omega }_2$ , $2\overline{\mathrm{\Omega }}={\omega }_1$ , and $2\overline{\mathrm{\Omega }}={\omega }_2$ , are considered. The influences of ratio of length to diameter, structural damping, cutting force, and ply angle on primary resonance and superharmonic resonance are investigated. The results show that nonlinearity due to higher-order bending deformation significantly affects the dynamic behavior of the milling process and that the effective nonlinearity of the cutting system is of hard type. Multivalued resonance curves and jump phenomenon are presented. The influences of various factors, such as ratio of length to diameter, ply angle, structural damping, cutting force, and rotating speed, are thoroughly discussed.