Abstract

The authors present an improved formulation for the axisymmetric solid harmonic finite element (FE) modeling of a flexible, spinning rotor. A thorough comparison of beam-type FE and axisymmetric solid FE rotor models is presented, indicating the errors that result from beam FE usage for various nondimensional rotor topologies. The axisymmetric rotor is meshed in only two dimensions: axial and radial, with both displacement fields being represented with Fourier series expansions. Centrifugal stress-stiffening and spin-softening effects are included in all elements and most importantly in modeling flexible disks. Beam FE and axisymmetric FE natural frequencies, mode shapes, and critical speeds are compared to identify shaft geometries where the beam model yields a significant error. Finally, limitations of beam FE models and guidance for utilizing axisymmetric solid FE models in rotor dynamic simulations are provided.

References

1.
Myklestad
,
N. O.
,
1944
, “
A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beams
,”
J. Aeronaut. Sci.
11
(
2
), pp.
153
162
.
2.
Pestel
,
E.
, and
Leckie
,
F.
,
1963
,
Matrix Methods in Elasto Mechanics
,
McGraw-Hill
,
New York
.
3.
Nelson
,
H. D.
, and
McVaugh
,
J. M.
,
1976
, “
The Dynamics of Rotor-Bearing Systems Using Finite Elements
,”
ASME J. Eng. Ind.
,
98
(
2
), pp.
593
600
.
4.
Nelson
,
H. D.
,
1980
, “
A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,”
ASME J. Mech. Des.
,
102
(
4
), pp.
793
803
.
5.
Thomas
,
D. L.
,
Wilson
,
J. M.
, and
Wilson
,
R. R.
,
1973
, “
Timoshenko Beam Finite Elements
,”
J. Sound Vib.
,
31
(
3
), pp.
315
330
.
6.
Rouch
,
K. E.
, and
Kao
,
J. S.
,
1979
, “
A Tapered Beam Finite Element for Rotor Dynamics Analysis
,”
J. Sound Vib.
,
66
(
1
), pp.
119
140
.
7.
Greenhill
,
L. M.
,
Bickford
,
W. B.
, and
Nelson
,
H. D.
,
1985
, “
A Conical Beam Finite Element for Rotor Dynamics Analysis
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
,
107
(
4
), pp.
421
430
.
8.
Stephenson
,
R. W.
,
Rouch
,
K. E.
, and
Arora
,
R.
,
1989
, “
Modelling of Rotors with Axisymmetric Solid Harmonic Elements
,”
J. Sound Vib.
,
131
(
3
), pp.
431
443
.
9.
Vest
,
T. A.
, and
Darlow
,
M. S.
,
1990
, “
A Modified Conical Beam Element Based on Finite Element Analysis: Experimental Correlations
,”
ASME J. Vib. Acoust.
,
112
(
3
), pp.
350
354
.
10.
Stephenson
,
R. W.
, and
Rouch
,
K. E.
,
1993
, “
Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements With Matrix Reduction
,”
ASME J. Vib. Acoust.
,
115
(
4
), pp.
484
489
.
11.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
,
2001
,
Concepts and Applications of Finite Element Analysis
,
Wiley
,
New York
.
12.
Geradin
,
M.
, and
Kill
,
N.
,
1984
, “
A New Approach to Finite Element Modelling of Flexible Rotors
,”
Eng. Comput.
,
1
(
1
), pp.
52
64
.
13.
Genta
,
G.
, and
Tonoli
,
A.
,
1996
, “
A Harmonic Finite Element for the Analysis of Flexural, Torsional and Axial Rotordynamic Behaviour of Discs
,”
J. Sound Vib.
,
196
(
1
), pp.
19
43
.
14.
Genta
,
G.
, and
Tonoli
,
A.
,
1997
, “
A Harmonic Finite Element for the Analysis of Flexural, Torsional and Axial Rotordynamic Behavior of Blade Arrays
,”
J. Sound Vib.
,
207
(
5
), pp.
693
720
.
15.
Greenhill
,
L. M.
, and
Lease
,
V. J.
,
2007
, “
Additional Investigations Into the Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System
,”
ASME
Paper No. GT2007-28065, pp.
995
1003
.
16.
Genta
,
G.
,
2005
,
Dynamics of Rotating Systems
,
Springer
,
New York
.
17.
Genta
,
G.
,
2011
, “Dynamic Modeling of Rotors: A Modal Approach,”
IUTAM Symposium on Emerging Trends in Rotor Dynamics
, Vol.
1011
,
K.
Gupta
, ed.,
Springer
,
Dordrecht
.
18.
Datta
,
A.
,
2016
, “
X3D—A 3D Solid Finite Element Multibody Dynamic Analysis for Rotorcraft
,”
American Helicopter Society Technical Meeting on Aeromechanics Design for Vertical Lift
,
Francisco, CA
,
Jan. 20–22
.
19.
Tseng
,
C.-W.
,
Shen
,
J.-Y.
,
Kim
,
H.
, and
Shen
,
I. Y.
,
2005
, “
A Unified Approach to Analyze Vibration of Axisymmetric Rotating Structures With Flexible Stationary Parts
,”
ASME J. Vib. Acoust.
,
127
(
2
), pp.
125
138
.
20.
Kiesel
,
T.
, and
Marburg
,
S.
,
2016
, “
Simulation of Mode-Locking Phenomena in a Complex Nonlinear Rotor System Using 3D Solid Finite Elements
,”
Proc. Inst. Mech. Eng. C
,
230
(
6
), pp.
959
973
.
21.
Hu
,
L.
, and
Palazzolo
,
A.
,
2016
, “
Solid Element Rotordynamic Modeling of a Rotor on a Flexible Support Structure Utilizing Multiple-Input and Multiple-Output Support Transfer Functions
,”
ASME J. Eng. Gas Turbines Power
,
139
(
1
), p.
012503
.
22.
Combescure
,
D.
, and
Lazarus
,
A.
,
2008
, “
Refined Finite Element Modelling for the Vibration Analysis of Large Rotating Machines: Application to the Gas Turbine Modular Helium Reactor Power Conversion Unit
,”
J. Sound Vib.
,
318
(
4–5
), pp.
1262
1280
.
23.
Zienkiewicz
,
O. C.
,
Taylor
,
R. L.
, and
Zhu
,
J. Z.
,
2005
,
The Finite Element Method: Its Basis and Fundamentals
,
Butterworth-Heinemann
,
Boston
.
24.
Palazzolo
,
A.
,
2016
,
Vibration Theory and Applications with Finite Elements and Active Vibration Control
,
Wiley
,
UK
.
25.
Suh
,
J.
, and
Palazzolo
,
A.
,
2014
, “
Three-Dimensional Thermohydrodynamic Morton Effect Simulation—Part I: Theoretical Model
,”
ASME J. Tribol.
,
136
(
3
), p.
031706
.
26.
Suh
,
J.
, and
Palazzolo
,
A.
,
2014
, “
Three-Dimensional Thermohydrodynamic Morton Effect Analysis—Part II: Parametric Studies
,”
ASME J. Tribol.
,
136
(
3
), p.
031707
.
27.
Guyan
,
R. J.
,
1965
, “
Reduction of Stiffness and Mass Matrices
,”
AIAA J.
,
3
(
2
), pp.
380
380
.
28.
Kohnke
,
P. C.
,
1989
, “
ANSYS Engineering Analysis System Theoretical Manual
,”
Swanson Analysis System, Inc.
,
Houston, PA
.
29.
Vance
,
J. M.
,
Murphy
,
B. T.
, and
Tripp
,
H. A.
,
1987
, “
Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part I: The Rotor Mass-Elastic Model
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
,
109
(
1
), pp.
1
7
.
30.
Vance
,
J. M.
,
Murphy
,
B. T.
, and
Tripp
,
H. A.
,
1987
, “
Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
,
109
(
1
), pp.
8
14
.
You do not currently have access to this content.