Fig 1.
(a) Schematic diagram of Jeffcott rotor with stator. (b) Schematic diagram of the rubbing forces.
Fig 2.
Sigmoid function sigm(R) under the different control parameter .
Fig 3.
Bifurcation diagrams of the rotor/stator rubbing system with ,
,
and
obtained from (a) the piecewise smooth governing equation, (b) the smoothening governing equation with
.
Fig 4.
Experimental results of the rotor/stator testing system.
(a) Bifurcation diagram. (b) Orbit with . (c) Orbit with
. (d) Orbit with
. (e) Orbit with
. In Figs 4(b) to 4(e), the clearance between the rotor and the stator is represented by the red dashed cycle with the rotor orbit of blue curves.
Fig 5.
Orbits and full spectra of the rotor with ,
,
,
and
. (a) Periodic motion with
. (b) Quasi-periodic motion with
. (c) Quasi-periodic motion with
. (d) Periodic motion with
. In the orbits, the rotor/stator clearance is represented by the red dashed cycle.
Table 1.
and
for partial rub with
.
Fig 6.
Poincaré sections of the rotor/stator rubbing system with ,
,
,
and
. (a) Periodic motion with
. (b) Quasi-periodic motion with
. (c) Quasi-periodic motion with
. (d) Periodic motion with
.
Fig 7.
Bifurcation diagrams of the smoothening rotor/stator rubbing system with and
, during (a)
,
,
, (b)
,
,
, (c)
,
,
, (d)
,
,
.
Fig 8.
Behaviors of eigenvalues with the variation of from 0 to 4 with
in the smoothening rotor/stator rubbing system with
,
,
,
and
.
The red dashed line represented the stability boundary with .
Fig 9.
Lines HP1 and HP2 are the Hopf bifurcation boundaries of periodic motion.
Fig 10.
Bifurcation characteristics under different rotating speed of the rotor in the rotor/stator rubbing system with ,
,
,
and
. (a)
versus
. (b)
versus
.
HP1 and HP2 represent the Hopf bifurcation boundaries. SN1, SN2, SN3 and SN4 represent the saddle-node bifurcation boundaries.
Fig 11.
Rotor response characteristics on the plane of , where
,
,
and
. Curves HP1 and HP2 indicate the rotating speed where the ‘jump’ phenomena between periodic motion and quasi-periodic motion occur.
Lines SN1, SN2, SN3 and SN4 represent the saddle-node bifurcation boundaries. ZHP is Zero-Hopf bifurcation point.