Dynamic and Stability Analysis of the Machine Hydrostatic Slide with Magnetorheological Damper

Abstract

Tangential dynamic behaviors of the machine hydrostatic slide with a magnetorheological (MR) fluid damper are studied, and the effect of the MR damper to control the vibration of the hydrostatic slide is discussed. The dynamic model of the hydrostatic slide with the MR damper is established, and the tangential vibration equation of linear and nonlinear is derived. The multidimensional incremental harmonic balance method (MIHBM) with discrete Fourier transform (DFT) is derived by which the nonlinear response and stability of the system are studied. The resonance response of the Duffing equation under the combined action of harmonic excitation and constant excitation is obtained. In order to investigate the vibration response of the hydrostatic slide with the MR damper in detail, the bifurcation diagram, phase diagram, and Poincaré map are given. Finally, the dynamic response of the machine hydrostatic slide with the MR damper is discussed, and it is verified that the MR damper can suppress the tangential vibration of the hydrostatic slide effectively and the constant controller can control the chaotic behavior of the system well.