Rotors are often coupled with a stationary part by rolling element bearings. To suppress their excessive vibration, the bearings are inserted in squeeze film dampers. The control of damping in the support elements offers the possibility to minimize the oscillation amplitude of accelerating or decelerating rotors, passing the regions of critical speeds. The controllable damping effect can be achieved if the squeeze film dampers are lubricated with magnetorheological oil. The change in the applied current feeding the electric coil changes magnetic induction in the damper gap, which changes the oil damping properties. The minimum vibration amplitude of the rotor running up or down through the resonance area is accomplished if the current increase or decrease is not sudden, but if it is distributed in some time interval. This article concentrates on determination of the optimum parameters of this manipulation. The developed procedure leads to solving an unconstrained optimization problem with the implicit objective function. The evolution method was used for its solving. In the investigated case, the proposed procedure made it possible to reduce maximum vibration amplitude by about 40% compared with the uncontrolled current decrease. The main contribution of the conducted research work is presentation of a new and original procedure for controlling the damping effect in the rotor supports. It provides a new idea to the designers and engineers regarding how to minimize amplitude of the rotor vibration when passing the critical speed. In addition, the article points to a new area of utilization of controllable magnetorheological squeeze film dampers.

Adding damping devices to the rotor supports is a frequently used technological solution for reducing vibrations of rotating machines. To achieve their optimum performance, their damping effect must be adaptable to the current operating speed. This is offered by magnetorheological squeeze film dampers. The magnetorheological oils are liquids sensitive to magnetic induction and belong to the class of fluids with a yielding shear stress. Their response to the change of a magnetic field is not instantaneous, but it is a process called the delayed yielding. The developed mathematical model of the magnetorheological squeeze film damper is based on the assumptions of the classical theory of lubrication. The lubricant is represented by a bilinear material, the yielding shear stress of which depends on magnetic induction. The delayed yielding process is described by a convolution integral with an exponential kernel. The developed mathematical model of the damper was implemented in the computational procedures for transient analysis of rotors working at variable operating speed. The carried-out simulations showed that the delayed yielding effect could have a significant influence on performance of magnetorheological damping devices. The development of a novel mathematical model of a magnetorheological squeeze film damper, the representation of the magnetorheological oil by bilinear material, taking the delayed yielding phenomenon into consideration, increased numerical stability of the computational procedures for transient analysis of flexible rotors, and extension of knowledge on behavior of rotor systems damped by magnetorheological squeeze film dampers are the principal contributions of this paper.