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., , , , and , 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.

中文翻译：

---

考虑复合刀具高阶变形的切削过程非线性动力学

本文对复合刀具切削过程进行非线性动力学分析。刀具简化为非平面弯曲旋转轴。考虑了刀具的高阶弯曲变形、结构阻尼和陀螺效应。假设刀具受到包含一次和二次谐波分量的再生二维切削力。基于哈密顿原理，推导出切削系统非线性颤振运动方程。广义坐标系中的非线性常微分方程由伽辽金法求得。为了分析切削过程的非线性动态响应，多尺度方法用于推导出周期性切削力作用下切削系统受迫响应的解析近似解。在受迫响应分析中，包括一次共振和超谐波共振四种情况，即，, , ，和，被考虑。研究了长径比、结构阻尼、切削力和层板角度对一次共振和超谐波共振的影响。结果表明，由高阶弯曲变形引起的非线性显着影响铣削过程的动态行为，并且切削系统的有效非线性是硬型的。呈现多值共振曲线和跳跃现象。详细讨论了各种因素的影响，例如长径比、帘布层角度、结构阻尼、切削力和转速。