In the paper dynamic electromechanical coupling between the structural model of the rotating machine drive system and the circuit model of the asynchronous motor has been investigated. By means of the computer model of the rotating machine drive system the results of experimental testing have been confirmed. From the obtained results of computations and measurements it follows that the coupling between the considered rotating system and the installed rotary dampers with the magneto-rheological fluid (MRF) results in effective energy dissipation leading to significant reduction of undesired torsional vibrations.