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., Ω ¯ = ω 1 , Ω ¯ = ω 2 , 2 Ω ¯ = ω 1 , and 2 Ω ¯ = ω 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.
Highlights
As a high-efficiency, high-quality, low-cost machining method, high-speed cutting technology has been widely used in aerospace and mold manufacturing
E passive chatter control methods are mainly based on various types of dynamic vibration absorbers [1, 2] and impact dampers [3]
If the empirical method is used to establish the model of the tool structure, a large number of repetitive tests are needed to obtain the dynamic parameters of the tool structure of different sizes, geometries, and materials, which is very time consuming and of low effectiveness. erefore, as a more effective modeling method for cutting tool, the continuous parameter dynamics modeling of cutting tool based on analytical method, has received great attention [23,24,25,26,27,28,29,30,31,32,33]
Summary
As a high-efficiency, high-quality, low-cost machining method, high-speed cutting technology has been widely used in aerospace and mold manufacturing. Moradi et al [22] investigated the internal resonance and regenerative chatter of the milling process considering both the cutting force and the structural nonlinearity. In order to investigate the dynamic characteristics of cutting system and the stability mechanism of machining process, it is necessary to conduct a comprehensive analysis on various influencing factors. In this case, if the empirical method is used to establish the model of the tool structure, a large number of repetitive tests are needed to obtain the dynamic parameters of the tool structure of different sizes, geometries, and materials, which is very time consuming and of low effectiveness. Nonlinear dynamics of the system are studied for four cases of primary and superharmonic resonances; i.e., Ω ω1, Ω ω2, 2Ω ω1, and 2Ω ω2 are studied. e numerical calculation is conducted to investigate the effect of various parameters on the frequency response of the cutting system
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