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-
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