The steady-state and transient dynamics of a flexible spinning shaft with eccentricity driven by a DC motor (i.e., non-ideal energy-source) with external and internal damping is studied in this paper. It is well established that the structural response of a vibratory system to which a non-ideal drive is connected may act as an energy sink under certain conditions such that a part of the energy supplied by the source is spent to vibrate the structure rather than to increase the drive speed. This phenomenon is formally known as the Sommerfeld effect. The Sommerfeld effect characterized by jump phenomena is studied through the steady state amplitude obtained by instantaneous power balance method and further verified through numerical simulation. Transient responses of non-dimensional amplitude and shaft speed wth time evolution through first mode resonance are also given. © Faculty of Mechanical Engineering, Belgrade.

Sovan Sundar Dasgupta

Department of Design and Automation

School of Mechanical Engineering

Vellore Campus

John Rajan A

Department of Manufacturing Engineering

Fulltext

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FME Transaction

Sommerfeld effect often causes dynamic instability in high speed rotors driven through energy source with limited power. As a result, the system dynamics changes in a very unusual manner while exceeding a critical value of input power with sudden nonlinear jump of rotor speed proximity to the system resonance. Such instability phenomena arising out of strong nonlinear rotor-drive interactions need to be attenuated to ensure smooth operation and industrial safety. A novel approach is presented here to study the attenuation of this kind of instability in an internally damped DC motor driven discrete rotor system with the adjustment of fractional order parameter in its external damping term. Using Lagrangian formulation, the equations of motion of the discrete rotor system are derived. The well-known Caputo model is adopted for the fractional order external damping modelling. Following, a characteristic equation in the form of a fifth order polynomial is obtained through steady-state energy balance approach which leads to obtain various amplitude frequency responses with a few values of fractional order of the external damping. As the fractional order increases gradually, the Sommerfeld effect is found to be attenuated accordingly. A few steady-state results are found to be in good agreement with some results reported earlier. Additionally, root-loci technique is employed to obtain a specific value of fractional order for which the complete disappearance of Sommerfeld effect is achieved through the merging of the break points. Finally, a transient analysis also confirms the steady-state results numerically. © 2019

European Journal of Mechanics - A/Solids

Suppression of Sommerfeld effect in a non-ideal discrete rotor system with fractional order external damping

Eccentric shaft-disk system with internal damping driven by a non-ideal power source exhibits Sommerfeld effect characterized by nonlinear jump phenomena of amplitude and rotor speed upon exceeding a critical power input around the critical speed. This effect causes instability in high speed rotors. So the diminution of such effect is extremely important in order to smooth running of the rotors at high speeds. The aim of this paper is to attenuate the Sommerfeld effect of an internally damped unbalanced flexible shaft-disk system via linearized active magnetic bearings. The shaft-disk system is excited through a brushed DC motor which acts as a non-ideal energy source. The characteristic equation of fifth order polynomial in rotor speed is obtained through energy balance of supplied power and the mechanical power dissipated at steady-state condition. Using MATLAB simulations, amplitude frequency responses are obtained close to system resonance for several values of bias current of active magnetic bearings. Thus the Sommerfeld effect is found to be attenuated as bias current increases gradually. The complete disappearance of Sommerfeld effect is also reported when the bias current reaches a specific value under certain conditions. A few numerical results are validated with established results when bias current is made to zero. © 2019, Springer Nature B.V.

Journal	FME Transaction
Publisher	Centre for Evaluation in Education and Science (CEON/CEES)
ISSN	1451-2092
Open Access	0