TY - JOUR
T1 - Nonlinear dynamic behaviour of a rotor-foundation system coupled through passive magnetic bearings with magnetic anisotropy - Theory and experiment
AU - Enemark, Søren
AU - Santos, Ilmar F.
PY - 2016
Y1 - 2016
N2 - In this work, the nonlinear dynamic behaviour of a
vertical rigid rotor interacting with a flexible foundation by means of
two passive magnetic bearings is quantified and evaluated. The
quantification is based on theoretical and experimental investigation of
the non-uniformity (anisotropy) of the magnetic field and the weak
nonlinearity of the magnetic forces. Through mathematical modelling the
nonlinear equations of motion are established for describing the shaft
and bearing housing lateral dynamics coupled via the nonlinear and
non-uniform magnetic forces. The equations of motion are solved in the
frequency domain by the methods of Finite Difference and
pseudo-arclength continuation. The theoretical findings are validated
against experiments carried out using a dedicated test-rig and a special
device for characterisation of the magnetic anisotropy.The
characterisation of the magnetic anisotropy shows that it can be
quantified as magnetic eccentricities having an amplitude and a phase,
which result in linear and parametric excitation. The magnetic
eccentricities are also determined using the steady-state response of
the rotor–bearing system due to forcing from the magnetic anisotropies
and several levels of mass imbalance. Discrepancies in the results from
the two methods in terms of magnetic eccentricity magnitude are due to
additional geometric eccentricities in the shaft. The steady-state
system response shows clear nonlinear phenomena, e.g. bent resonance
peaks, jump phenomena and nonlinear cross-coupling between the two
orthogonal directions, especially during counter-phase motion between
shaft and bearings. The clear nonlinear behaviour is facilitated by the
lack of damping resulting in relatively large vibrations. The overall
nonlinear dynamic behaviour is well captured by the theoretical model,
thereby validating the modelling approach.
AB - In this work, the nonlinear dynamic behaviour of a
vertical rigid rotor interacting with a flexible foundation by means of
two passive magnetic bearings is quantified and evaluated. The
quantification is based on theoretical and experimental investigation of
the non-uniformity (anisotropy) of the magnetic field and the weak
nonlinearity of the magnetic forces. Through mathematical modelling the
nonlinear equations of motion are established for describing the shaft
and bearing housing lateral dynamics coupled via the nonlinear and
non-uniform magnetic forces. The equations of motion are solved in the
frequency domain by the methods of Finite Difference and
pseudo-arclength continuation. The theoretical findings are validated
against experiments carried out using a dedicated test-rig and a special
device for characterisation of the magnetic anisotropy.The
characterisation of the magnetic anisotropy shows that it can be
quantified as magnetic eccentricities having an amplitude and a phase,
which result in linear and parametric excitation. The magnetic
eccentricities are also determined using the steady-state response of
the rotor–bearing system due to forcing from the magnetic anisotropies
and several levels of mass imbalance. Discrepancies in the results from
the two methods in terms of magnetic eccentricity magnitude are due to
additional geometric eccentricities in the shaft. The steady-state
system response shows clear nonlinear phenomena, e.g. bent resonance
peaks, jump phenomena and nonlinear cross-coupling between the two
orthogonal directions, especially during counter-phase motion between
shaft and bearings. The clear nonlinear behaviour is facilitated by the
lack of damping resulting in relatively large vibrations. The overall
nonlinear dynamic behaviour is well captured by the theoretical model,
thereby validating the modelling approach.
U2 - 10.1016/j.jsv.2015.10.007
DO - 10.1016/j.jsv.2015.10.007
M3 - Journal article
SN - 0022-460X
VL - 363
SP - 407
EP - 427
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
ER -