Abstract
A nonlinear dynamic analysis of the cutting process of a nonextensible composite cutting bar is presented. The cutting bar is simplified as a cantilever with plane bending. The nonlinearity is mainly originated from the nonextensible assumption, and the material of cutting bar is assumed to be viscoelastic composite, which is described by the Kelvin–Voigt equation. The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. The steady forced response of the cutting system under periodically varying cutting force is approximately solved by the multiscale method. Meanwhile, the effects of parameters such as the geometry of the cutting bar (including length and diameter), damping, the cutting coefficient, the cutting depth, the number of the cutting teeth, the amplitude of the cutting force, and the ply angle on nonlinear lobes and primary resonance curves during the cutting process are investigated using numerical calculations. The results demonstrate that the critical cutting depth is inversely proportional to the aspect ratio of the cutting bar and the cutting force coefficient. Meanwhile, the chatter stability in the milling process can be significantly enhanced by increasing the structural damping. The peak of the primary resonance curve is bent toward the right side. Due to the cubic nonlinearity in the cutting system, primary resonance curves show the characteristics of typical Duffing’s vibrator with hard spring, and jump and multivalue regions appear.
Highlights
Cutting is an indispensable key step in processing and manufacturing of mechanical parts
Induced by dynamic instability in closed-loop systems consisting of cutting tools and workpieces, chatter can be categorized as regenerative chatter and mode-coupling chatter. e regenerative chatter is the one with most severe hazard. e occurrence of chatter can lead to the reduction of cutting specification and processing quality and even seriously cause damage to the cutting tools. erefore, an accurate model for chatter analysis is of great significance to effective chatter control
Previous studies demonstrated that the critical cutting depth is proportional to the dynamic stiffness of the boring bar [1]. erefore, passive control methods such as various dynamic vibration absorbers [2, 3] and impact dampers [4] have been proposed to reduce the chatter of the boring bar and enhance the cutting stability. ese control methods are highly effective under certain conditions
Summary
Cutting is an indispensable key step in processing and manufacturing of mechanical parts. By taking cutting force and structural nonlinearity into account, Moradi and Movahhedy [19] investigated internal resonance and regenerative chatter in milling process.
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