Analysis of the vibration attenuation of rotors supported by magnetorheological squeeze film dampers as a multiphysical finite element problem

Placing damping devices between the rotor and its frame is a frequently used engineering solution for reducing excessive vibrations of rotating machines. Their damping effect must be controllable to achieve their optimum performance in a wide range of operating speeds. This is enabled by magnetorheological squeeze film dampers, the damping force of which can be controlled by changing magnetic flux passing through the lubricating layer. The magnetorheological oil is represented in the developed mathematical model by Bingham material. The magnetic induction in the damper gap is a significant parameter that directly influences resistance against the flow of the magnetorheological oil and generates the additional magnetic force acting on the rotor journal. Therefore, three approaches (1D, 2D, and 3D) to determination of the semi-analytical relations describing its distribution in the lubricating film were proposed, tested, and compared. The appropriate coefficients were determined by repeatedly solving 2D or 3D magnetostatic problems for the specified damper dimensions, design, and rising magnitude of the journal eccentricity utilizing the finite element and least square methods. In the developed computational model of the rotating machine, the rotor shaft is represented by a beam like-body that is discretised into finite elements. The magnetorheological dampers are implemented by springs and force couplings. The principal contribution of this article consists in the development of a methodology, based on three approaches, for the derivation of closed form formulas describing the distribution of magnetic induction in the damper gap as a function of the rotor journal eccentricity and angular position. The individual approaches give some differences in the results that are consequent upon the distinguishing level used for modelling the damping device. The extent of their applicability is discussed in the article. The developed computational models are intended for the investigation of the vibration attenuation of rotor systems in a wide range of rotational speeds.