Modelling of magnetorheological squeeze film dampers for vibration suppression of rigid rotors

Abstract

The magnetorheological squeeze film damping devices for vibration suppression of rigid rotors are studied in this article. The development of their mathematical model is based on assumptions of the classical theory of lubrication with the exception of lubricant. Because the magnetorheological fluids affected by a magnetic field belong to the class of liquids with a yielding shear stress, the lubricant is represented by bilinear theoretical material. The pressure distribution in the full oil film is then described by a modified Reynolds equation. In addition, the influence of cavitation and of the magnetic forces, by which the damping device acts on the rotor journal, were taken into account. The advantage of the developed mathematical model is that, unlike the Bingham or Herschel-Bulkley materials, the flow curve of the bilinear liquid is continuous. It reduces the nonlinear character of the damping forces and thus raises the numerical stability of the computational procedures. The solution convergence is reached also in cases when the procedures based on modelling the magnetorheological fluid by Bingham or Herschel-Bulkley materials fail. Application of bilinear material provides a better description of physical behavior of magnetorheological oils affected by a magnetic field during the damping process. The simulations show that changing magnetic induction in the lubricating film makes it possible to achieve optimum performance of the damping device in a wide range of the rotor operating speeds and confirms increased numerical stability of the computational procedures.