Research on Viscoelastic Nonlinear Energy Sink of Magnetorheological Elastomer for Chatter Suppression in Milling

Owing to the low stiffness of thin-walled workpieces, disturbances can readily arise during milling, severely compromising machining accuracy and surface quality. This study proposes a new viscoelastic model of a magnetorheological elastomer (MRE) and analyzes its vibration reduction performance under dynamic cutting forces. First, the governing equations of the system are derived from Newton’s second law, and the amplitude-frequency response curves are obtained using the harmonic balance method. The analytical results are then validated by Runge–Kutta numerical integration, with good agreement between the two approaches. Next, the vibration reduction performance of the MRE-based viscoelastic nonlinear energy sink (MNES) and the effects of its parameters are analyzed. Finally, the nonlinear stiffness coefficient and damping ratio are varied simultaneously at different mass ratios to identify the optimal parameter ranges for the MRE-based viscoelastic nonlinear energy sink of magnetorheological elastomer. The results show that the maximum amplitude of the main system first decreases and then increases as the nonlinear stiffness increases. With appropriate parameter selection, the MRE-based viscoelastic nonlinear energy sink of magnetorheological elastomer provides better vibration reduction performance than the traditional nonlinear energy sink. In addition, as the mass ratio increases, the minimum attainable value of the main-system amplitude initially decreases and then approaches a constant, while the optimal ranges of the nonlinear stiffness coefficient and damping ratio widen slightly. By combining a set of calculated parameters with the differential constitutive equation of the magnetorheological elastomer, the corresponding stress–strain curve is obtained. This provides guidance for the fabrication of magnetorheological elastomers with favorable vibration-damping performance. The stability of milling chatter is also analyzed. The calculated stability lobe diagram and supplementary time-domain verification results show that a milling system with the MNES can effectively suppress chatter and allow a greater depth of cut.