Unbalance of rotating parts is the main source of excitation of lateral oscillations of rotors, of increase of time varying forces transmitted to the rotor stationary part, and of energy losses generated in the support elements. The technological solution, which makes it possible to reduce these undesirable effects, consists in adding damping devices to the rotor supports. A simple dynamical analysis shows that to achieve their optimum performance their damping effect must be adaptable to the current operating speed. This is enabled by magnetorheological squeeze film dampers, the damping effect of which is controlled by the change of magnetic flux passing through the lubricating layer. The developed mathematical model of the magnetorheological squeeze film damper is based on assumptions of the classical theory of lubrication and on representing the magnetorheological oil by a bilinear material. The results of the carried out computational simulations show that the appropriate control of the damping force makes it possible to minimize the energy losses in a wide range of operating speeds. The development of a new mathematical model of the magnetorheological squeeze film damper, the extension of computational procedures, in which this model has been implemented, the confirmation that the magnetorheological dampers make it possible to reduce energy losses in the rotor supports, and learning more on influence of controllable dampers on behavior of rotor systems are the principal contributions of the presented paper. The carried out research highlights the possibility of reducing the energy losses by means of employing magnetorheological squeeze film dampers, which represents a new field of their prospective application.

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