Numerical Analysis of Load Capacity and Friction Torque of Eccentric Magnetorheological Fluid Seals

This paper presents the results of numerical calculation of steady-state magnetorheological fluid flow in the gap of an eccentric seal subjected to an external radial magnetic field. A coupled problem combining magnetic field analysis and laminar viscoplastic flow with Bingham rheology is solved to obtain pressure and velocity distributions within the seal gap, from which the hydrodynamic reaction forces of the fluid film and the rotor friction torque are determined. A parametric study was conducted in the ranges of rotor angular velocity ω = 100–400 rad/s, relative eccentricity ε = 0–0.9, and magnetic flux density B0 = 0–0.5 T at the pressure differential Δp = 2 atm. Analysis of the results shows that increasing the magnetic flux density from 0 to 0.5 T leads to an increase in the seal reaction force from 12 N to 642 N and the friction torque from 0.35 N·m to 11.23 N·m. The most intensive growth of both characteristics is observed in the range B0 = 0–0.3 T, beyond which saturation occurs as the MRF yield stress reaches its plateau value. An optimal control range of B0 = 0.1–0.2 T was determined, ensuring maximum seal energetic efficiency as quantified by the load capacity-to-friction torque ratio, which is maximized at 70 N/(N·m). Based on the obtained results, the consequences of using magnetorheological seals on the performance of the rotor system are discussed, including the analysis of the sealing effect on rotor-dynamic stability. Within the proposed optimal range, it is shown that an increase in magnetic flux density leads to a sign reversal of the horizontal reaction F2, while the monotonic growth of the ratio |F2|/F1 indicates an intensification of cross-coupling and a corresponding reduction in the rotordynamic stability margin at higher values of B0.