A new mathematical model of a short magnetorheological squeeze film damper for rotordynamic applications based on a bilinear oil representation - derivation of the governing equations

A technological solution frequently used to suppress vibrations in rotating machines consists in adding damping devices to the rotor supports. To achieve their optimum performance, their damping effect must be adaptable to the current operating conditions. This is offered by magnetorheological squeeze film dampers. Magnetorheological oils are usually modelled as Bingham or Herschel–Bulkley fluids with discontinuous stress versus shear rate curves. However, the flow curves of real magnetorheological oils consist of two almost linear parts of different slopes so that their character is closer to a bilinear theoretical material. Magnetorheological dampers are usually implemented in the mathematical models of rotor systems by force couplings, which produce highly nonlinear equations of motion governing their oscillations, and in some cases with a discontinuous flow curve, have solution convergence problems. This paper proposes the use of a bilinear material to model the magnetorheological fluid with a continuous flow curve reducing the nonlinear nature of the governing equations. The expected assets are reaching a more plausible description of the physical behaviour of rotor systems and increase in the stability of the computational procedures for analysis of their lateral vibrations.