Three-dimensional solid element models often with a great number of degrees-of-freedom (DOFs) are now widely used for rotor dynamic analysis. While without reduction, it will cost considerable calculating resources and time to solve the equations of motion, especially when Monte Carlo simulation (MCS) is needed for stochastic analysis. To improve the analysis efficiency, the DOFs are partly reduced to modal spaces, and the stochastic results (critical speeds or unbalance response) are expanded to polynomial spaces. First, a reduced rotor model is got by component mode synthesis (CMS), and the stochastic results are expanded by polynomial chaos basis with unknown coefficients. Then, the reduced rotor model is used to calculate the sample results to obtain the coefficients. At last, the expressions of the result by polynomial chaos basis are used as surrogate models for MCS. An aero-engine rotor system with uncertain parameters is analyzed. The accuracy of the method is validated by direct MCS, and the high efficiency makes it possible for stochastic dynamic analysis of complex engine rotor systems modeled by 3D solid element.

References

References
1.
Rao
,
J. S.
, and
Sreenivas
,
R.
,
2003
, “
Dynamics of a Three Level Rotor System Using Solid Elements
,”
ASME
Paper No. GT2003-38783.
2.
Nandi
,
A.
, and
Neogy
,
S.
,
2001
, “
Modelling of Rotors With Three-Dimensional Solid Finite Elements
,”
J. Strain Anal. Eng. Des.
,
36
(
4
), pp.
359
371
.
3.
Ma
,
W. M.
, and
Wang
,
J. J.
,
2012
, “
3D Solid Finite Element Modeling and Rotordynamics of Large Rotating Machines: Application to an Industrial Turbo Engine
,”
Adv. Mater. Res.
,
591–593
, pp.
1879
1885
.
4.
Rao
,
J. S.
,
2011
,
History of Rotating Machinery Dynamics
, Vol.
20
,
Springer Science & Business Media
,
Berlin
.
5.
Geradin
,
M.
, and
Kill
,
N.
,
1986
, “
A Three Dimensional Approach to Dynamic Analysis of Rotating Shaft Disc Flexible Systems
,”
2nd IFToMM International Conference on Rotordynamics
, Tokyo, Japan, Sept., pp.
87
93
.
6.
Rao
,
J. S.
,
Sreenivas
,
R.
, and
Veeresh
,
C. V.
,
2002
, “
Solid Rotor Dynamics
,” Fourteenth US National Congress of Theoretical and Applied Mechanics, Blacksburg, VA, pp.
23
28
.
7.
Chaudhry
,
J. A.
,
2011
, “
3-D Finite Element Analysis of Rotors in Gas Turbines, Steam Turbines and Axial Pumps Including Blade Vibrations
,” Ph.D. thesis, University of Virginia, Charlottesville, VA.
8.
Guyan
,
R. J.
,
1965
, “
Reduction of Stiffness and Mass Matrices
,”
AIAA J.
,
3
(
2
), p.
380
.
9.
Craig
,
R. R.
,
1968
, “
Coupling of Substructures for Dynamic Analyses
,”
AIAA J.
,
6
(
7
), pp.
1313
1319
.
10.
Zuo
,
Y.
, and
Wang
,
J.
,
2015
, “
A Component Mode Synthesis Method for 3-D Finite Element Models of Aero-Engines
,”
J. Mech. Sci. Technol.
,
29
(
12
), pp.
5157
5166
.
11.
Seguí
,
B.
,
Faverjon
,
B.
, and
Jacquet-Richardet
,
G.
,
2013
, “
Effects of Random Stiffness Variations in Multistage Rotors Using the Polynomial Chaos Expansion
,”
J. Sound Vib.
,
332
(
18
), pp.
4178
4192
.
12.
Ma
,
Y. H.
,
Liang
,
Z. C.
,
Chen
,
M.
, and
Hong
,
J.
,
2013
, “
Interval Analysis of Rotor Dynamic Response With Uncertain Parameters
,”
J. Sound Vib.
,
332
(
16
), pp.
3869
3880
.
13.
Didier
,
J.
,
Sinou
,
J. J.
, and
Faverjon
,
B.
,
2012
, “
Study of the Non-Linear Dynamic Response of a Rotor System With Faults and Uncertainties
,”
J. Sound Vib.
,
331
(
3
), pp.
671
703
.
14.
Didier
,
J.
,
Faverjon
,
B.
, and
Sinou
,
J. J.
,
2011
, “
Analyzing the Dynamic Response of a Rotor System Under Uncertain Parameters by Polynomial Chaos Expansion
,”
J. Vib. Control
,
18
(
5
), pp.
587
607
.
15.
Genta
,
G.
,
2007
,
Dynamics of Rotating Systems
,
Springer Science & Business Media
,
Berlin
.
You do not currently have access to this content.