Nonlinear Dyn DOI 10.1007/s11071-017-3329-0 ORIGINAL PAPER Sommerfeld effect in a gyroscopic overhung rotor-disk system Alfa Bisoi · A. K. Samantaray · R. Bhattacharyya Received: 23 March 2016 / Accepted: 1 January 2017 © Springer Science+Business Media Dordrecht 2017 Abstract Deflection of a rotor-disk at the free end of a flexible overhung rotor-shaft causes rotation about diametral axis and consequently leads to a strong gyro- scopic coupling in a spinning overhung rotor system. When the rotor is spun up about its axis, the unbalance in the rotor-disk causes transverse and rotational vibra- tions to increase as the spin speed approaches the crit- ical speed of the rotor. These transverse and rotational vibrations dissipate a lot of energy, and if the rotor is driven through a non-ideal drive, i.e., a motor which can supply a limited amount of power, then the entire motor power may be spent to account for the energy dis- sipation. As a result, the rotor speed may get stuck in resonance at the critical speed or jump through the crit- ical speed to a much higher speed with lower transverse and rotational vibration levels. These symptoms, nor- mally referred to as the Sommerfeld effect, occur due to the intrinsic energetic coupling between the drive and the driven systems and are important design consider- ations for development of various rotating machinery with flexible rotor-shafts or supports (bearings). Som- merfeld effect in a strongly gyroscopic rotor dynamic system is studied in this article. The dynamics of an A. Bisoi · A. K. Samantaray (B ) · R. Bhattacharyya Systems, Dynamics and Control Laboratory, Department of Mechanical Engineering, Indian Institute of Technology-Kharagpur, Kharagpur 721302, India e-mail: samantaray@mech.iitkgp.ernet.in overhung rotor system near the regimes of Sommer- feld effect is studied by using a discrete and a contin- uous shaft-rotor model coupled with the model of the non-ideal motor drive. The models are developed using multi-energy domain modeling approach in bond graph model form. A steady-state analysis of power transfer mechanism is used to postulate the ideal characteris- tics of Sommerfeld effect in the neighborhood of the critical speed, and thereafter, full transient analysis is performed with aid of the bond graph model-generated coupled equations of motion to validate the postulated characteristics of the Sommerfeld effect. Keywords Gyroscopic rotor system · Non-ideal source · Sommerfeld effect · Multi-energy domain modeling · Bond graph 1 Introduction Overhung rotors are used in many industrial and domestic applications, for example in washing machines, helicopter rotors, wind turbines, centrifuges, and impeller pumps. In some applications with over- hung rotors, rotor-shafts are designed with long and thin geometry to provide space for components such as impellers and seals [1]. With increased length and reduced cross section of the rotor-shaft, its bending and torsional flexibilities increase. A flexible rotor-shaft has lower critical speeds. Moreover, rotating machines require high-speed operation to maximize power out- 123