Fig. 1
Asymmetric rotor system supported horizontally: (a) Jeffcott-rotor system, (b) symmetric rotating disk, (c) asymmetric rotating disk.
Fig. 2
Asymmetrical horizontally supported rotor system with 4-pole active magnetic bearings
Fig. 3
Symmetric rotor system response curve at and: (a) oscillation amplitudes and at the horizontal and vertical directions, and (b) the corresponding phase-Angles.
Fig. 4
Symmetric rotor system temporal oscillations according to
Fig. 3 when
at different initial conditions: (a, b) the system steady-state temporal oscillations, and the corresponding whirling orbit at
, and (c, d) the system steady-state temporal oscillations, and the corresponding whirling orbit at
.
Fig. 5
Symmetric rotor system response curves at and: (a) oscillation amplitude in the horizontal direction, (b) oscillation amplitude in the vertical direction, and (c) the corresponding phase-Angles.
Fig. 6
Asymmetric rotor system temporal oscillations according to
Fig. 5 when
at different initial conditions: (a, b) the system steady-state temporal oscillations, and the corresponding whirling orbit at
, (c, d) the system steady-state temporal oscillations, and the corresponding whirling orbit at
, and (e, f) the system steady-state temporal oscillations, and the corresponding whirling orbit at
.
Fig. 7
Asymmetric rotor system response curves at and: (a) oscillation amplitude in the horizontal direction, (b) oscillation amplitude in the vertical direction, and (c) the corresponding phase-Angles.
Fig. 8
Asymmetric rotor system response curves at and: (a) oscillation amplitude in the horizontal direction, (b) oscillation amplitude in the vertical direction, and (c) the corresponding phase-Angles.
Fig. 9
Controlled asymmetric rotor system response curves at different values of the proportional gain at, and: (a, b) oscillation amplitudes and at the horizontal and vertical directions at , (c, d) oscillation amplitudes and at the horizontal and vertical directions at , and (e, f) oscillation amplitudes and at the horizontal and vertical directions at .
Fig. 10
Controlled asymmetric rotor system temporal oscillations according to
Fig. 9 at
when changing the proportional control gain
from
to
: (a, b) the system temporal oscillations in the horizontal and vertical directions at
, and (c) and the corresponding phase plane.
Fig. 11
Controlled asymmetric rotor system temporal oscillations according to
Fig. 9 at
when changing the proportional control gain
from
to
: (a, b) the system temporal oscillations in the horizontal and vertical directions at
, and (c) and the corresponding phase plane.
Fig. 12
Controlled asymmetric rotor system response curves at different values of the derivative gain at: (a, b) oscillation amplitudes and at the horizontal and vertical directions at, and (c, d) oscillation amplitudes and at the horizontal and vertical directions at .
Fig. 13
Controlled asymmetric rotor system response curves at different values of the asymmetric linear asymmetric stiffness coefficient at: (a, b) oscillation amplitudes and at the horizontal and vertical directions atand, and (c, d) oscillation amplitudes and at the horizontal and vertical directions atand.
Fig. 14
Controlled asymmetric rotor system response curves at different values of the asymmetric nonlinear asymmetric stiffness coefficient at: (a, b) oscillation amplitudes and at the horizontal and vertical directions atand, and (c, d) oscillation amplitudes and at the horizontal and vertical directions atand.
Fig. 15
Asymmetric rotor system response curves at and: (a, b) oscillation amplitudes in the horizontal and vertical directions, and (c, d) the corresponding phase-Angles.
Fig. 16
Controlled asymmetric rotor system response curves at, and: (a, b) oscillation amplitudes in the horizontal and vertical directions at , and (c, d) the corresponding phase-Angles.
Fig. 17
Temporal oscillations, the corresponding phase plane, and whirling orbit of the asymmetric rotor system before and after control at initial conditions
when
according to
Figs. 15 and
16: (a, c) the system temporal oscillations in the horizontal and vertical directions, (b) the phase plane, and (d) the steady-state whirling orbit.
Fig. 18
Temporal oscillations, the corresponding phase plane, and whirling orbit of the asymmetric rotor system before and after control at initial conditions
when
according to
Figs. 15 and
16: (a, c) the system temporal oscillations in the horizontal and vertical directions, (b) the phase plane, and (d) the steady-state whirling orbit.
Fig. 19
Asymmetric rotor system -amplitude response-curves atand: (a) oscillation amplitude in the horizontal direction, and (b) oscillation amplitude in the vertical direction.
Fig. 20
Controlled asymmetric rotor system -amplitude response-curves atand: (a) oscillation amplitude in the horizontal direction, and (b) oscillation amplitude in the vertical direction.