Baguet, Sébastien

Dakel, M. Zaki

Dufour, Régis

English

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Prediction of the non-linear dynamic behavior of
on-board rotors under extreme solicitations
M. Zaki Dakel, Sébastien Baguet, Régis Dufour
To cite this version:
M. Zaki Dakel, Sébastien Baguet, Régis Dufour. Prediction of the non-linear dynamic behavior of
on-board rotors under extreme solicitations. CIRI-CMVA 2014 - 4th International Congress on the
Engineering of Industrial Risks - 32th Machinery Vibration Seminar, Oct 2014, Montréal, Québec,
Canada. 2014. ￿hal-01075978￿
4ème Congrès CIRI, 29-31 October 2014, Montréal, Québec
 The implicit Newmark time-step integration algorithm combined 
with the Newton-Raphson iterative technique is used to solve the 
equations of motion.
 When sinusoidal motions of the support lead to periodic 
(harmonic and sub-harmonic) responses of the rotor, the 
shooting method is optimized and employed to solve the 
equations of motion.
4. Dynamic analysis
6. Conclusions
M(t), C(t), G(t), K(t): Mass, damping, gyroscopic and stiffness 
matrices with periodic and time-varying parametric 
coefficients due to the geometric asymmetry of the rotor and 
the rotational motions of the support.
F(t): External force vector due to the mass unbalance and the 
rotational and translational motions of the support.
Fbe: External non-linear hydrodynamic force vector of the 
bearing.
2. Basic description
1. Introduction
3. Equations of motion
 Shape and magnitude of the orbits can be significantly 
affected by the amplitude of the support motion.
 Bifurcation in the dynamic response due to the motions of 
the support: periodic, quasi-periodic or chaotic motions.
 This behavior cannot be predicted with the linearized bearing 
model.
Problem statement: In the transportation domain and power 
plants, rotors in bending are subjected not only to rotating mass 
unbalance but also to several motions of their support.
Objective: Investigation of the dynamics of an on-board rotor 
mounted on hydrodynamic journal bearings in the presence of rigid 
support excitations.
Support-excited rotor systems in the literature:
Simple rotors (Jeffcott rotor, Rayleigh-Ritz method),
Rotors on flexible bearings with constant coefficients,
Rotors excited by simple motions of their support.
Improvements: Finite elements, Non-linear hydrodynamic 
bearings, Combined motions of the support.
Prediction of the non-linear dynamic behavior of on-board rotors under 
extreme solicitations
Mzaki Dakel, Sébastien Baguet, Régis Dufour (regis.dufour@insa-lyon.fr)
Université de Lyon, CNRS, INSA-Lyon, LaMCoS UMR5259, F-69621, France
5. Simulation results
Hydrodynamic bearings + Mass unbalance (Ω=20 Hz) + Harmonic 
translation of the support zO = ZO cos Ωz t, with Ωz = 80 Hz
 Influence of the bearing model (Linear/Non-Linear)
 Bifurcation diagram (control parameter: amplitude ZO)
 Bifurcation responses (orbits and Poincaré maps)
( ) ( ) ( )( ) ( ) ( ) ( ),bet t t t t+ + Ω + = +M δ C G δ K δ F F δ δɺɺ ɺ ɺ
Rotation of the support Translation of the support
Rotating parts (Disk and shaft)
Symmetric Asymmetric Symmetric Asymmetric
Parametric terms
(Instability sources)
Yes Yes No No
External terms Yes Yes Yes No
ZO = 0.73×10-4 m ZO = 0.95×10-4 m
C
h
a
o
ti
c
Q
u
a
s
i-p
e
rio
d
ic
ZO = 0.1×10-4 m ZO = 0.5×10-4 m
L
in
e
a
r 
b
e
a
ri
n
g
s
N
o
n
-l
in
e
a
r 
b
e
a
ri
n
g
s
≈
Period-
doubling 
orbit
≠
Amplitude of the support translation
R
o
to
r 
d
is
p
la
c
e
m
e
n
t
1τ-periodic
Quasi-periodic 
and chaotic
2τ, 4τ,…
Frames of reference of the 
on-board rotor
Euler angles for the transformation 
between the frames
Non-linear 
hydrodynamic bearing
Linearized bearing 
model


Prediction of the non-linear dynamic behavior of on-board rotors under extreme solicitations

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Prediction of the non-linear dynamic behavior of on-board rotors under extreme solicitations

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