The reliable estimation of a flexible foundation model and the state of unbalance (both amplitude and phase) of a turbogenerator from machine rundown measured vibration data is an active research area. Earlier studies on the estimation of both these quantities used the whole frequency range of the rundown as a single band. However, such an identification may be inaccurate for large flexible foundations having many modes in the rundown frequency range. For reliable identification, the whole frequency range has to be divided into a number of frequency bands and the frequency-dependent foundation models have to be estimated together with the unbalance. This paper combines the unbalance estimation with the split frequency range for the foundation model, and the highlights the limitations observed during estimation of foundation models and the state of unbalance. It is shown that the accuracy of the method may be enhanced by judicious choice of a weighting function. Having established the method in simulation, experimental data from a 3-m long test rig, with four journal bearings, is used to test the method. The approach seems to give reliable estimates of the machine unbalance.

Issue Section:
Gas Turbines: Structures and Dynamics
Keywords:
turbogenerators, vibration measurement, parameter estimation, state estimation, machine bearings
Topics:
Bearings, Machinery, Rotors, Errors, Noise (Sound), Modeling, Turbogenerators, Stiffness, Parameter estimation
1.
Adams, M. L., and McLosky, T. H., 1984, “Large Unbalance Vibration in Steam Turbine Generator Sets,” I.Mech.E., Conference, Vibrations in Rotating Machinery, York, UK, Sept. 11–13.
2.
Davies, W. G. R., Lees, A. W., Mayes, I. W., and Worsfold J. H., 1976, “Vibration Problems in Power Stations,” I.Mech.E., Conference Vibrations in Rotating Machinery, Cambridge, UK. Sept.
3.
Mayes, I. W., and Davies, G. W. R., 1980, “A Method of Calculating the Vibrational Behavior of Coupled Rotating Shafts Containing a Transverse Crack,” I.Mech.E., Conference, Vibrations in Rotating Machinery, Cambridge, UK, Sept. 2–4.
4.
Kellenburger
,
W.
,
1972
, “
Should a Flexible Rotor be Balanced in N or N+2 Planes?
”
J. Eng. Ind.
,
94
, pp.
548
–
560
.
5.
Nicholas
,
J. C.
,
Gunter
,
E. J.
, and
Allaire
,
P. E.
,
1976
, “
Effect of Residual Shaft Bow on Unbalance Response and Balancing of a Single Mass Flexible Rotor: Part I—Unbalance Response
,”
J. Eng. Power
,
98
, pp.
171
–
181
.
6.
Nicholas
,
J. C.
,
Gunter
,
E. J.
, and
Allaire
,
P. E.
,
1976
, “
Effect of Residual Shaft Bow on Unbalance Response and Balancing of a Single Mass Flexible Rotor: Part II—Balancing
,”
ASME J. Eng. Gas Turbines Power
,
98, pp.
182
–
189
.
7.
Parkinson
,
A. G.
,
Darlow
,
M. S.
, and
Smalley
,
A. J.
,
1984
, “
Balancing Flexible Rotating Shafts With an Initial Bend
,”
AIAA J.
,
22
(
5
), pp.
686
–
689
.
8.
Parkinson
,
A. G.
,
1991
, “
Balancing of Rotating Machinery
,”
J. Mech. Eng. Sci.
,
205
, pp.
53
–
66
.
9.
Foiles
,
W. C.
,
Allaire
,
P. E.
, and
Gunter
,
E. J.
,
1998
, “
Review: Rotor Balancing
,”
Shock and Vibration
,
5
, pp.
325
–
336
.
10.
Edwards
,
S.
,
Lees
,
A. W.
, and
Friswell
,
M. I.
,
1998
, “
Fault Diagnosis of Rotating Machinery
,”
Shock Vib. Dig.
,
30
(
1
), pp.
4
–
13
.
11.
Maslen, E. H., Vazquez, J. A., and Sortore, C. K., 2000, “Reconciliation of Rotordynamic Models With Experimental Data,” ASME Paper No. 2000-GT-0395.
12.
Vazquez
,
J. A.
,
Maslen
,
E. H.
,
Ahn
,
H.-J.
and
Han
,
D.-C.
,
2001
, “
Model Identification of a Rotor With Magnetic Bearings
,”
ASME J. Eng. Gas Turbines Power
,
125
, pp.
148
–
155
.
13.
Lees, A. W., and Simpson, I. C., 1983, “The Dynamics of Turbo-Alternator Foundations,” IMechE Conference Paper C6/83, Feb., London, UK.
14.
Lees, A. W., 1988, “The Least Squares Method Applied to Identify Rotor/Foundation Parameters,” I.Mech.E, Conference, Vibrations in Rotating Machinery, Edinburgh, UK, Sept. 13–15.
15.
Provassi
,
R.
,
Zanetta
,
G. A.
, and
Vania
,
A.
,
2000
, “
The Extended Kalman Filter in the Frequency Domain for the Identification of Mechanical Structure Excited by Multiple Sinusoidal Inputs
,”
Mech. Syst. Signal Process.
,
14
(
3
), pp.
327
–
341
.
16.
Zanetta, G. A., 1992, “Identification Methods in the Dynamics of Turbogenerator Rotors,” I.Mech.E. Conference, Vibrations in Rotating Machinery, Bath, UK, pp. 173–182.
17.
Vania, A., 2000, “On the Identification of the Foundation of a Large Turbogenerator Unit by the Analysis of Transient Vibrations,” I.Mech.E. Conference, Vibrations in Rotating Machinery, Nottingham, UK., Sept. 12–14.
18.
Feng
,
N. S.
, and
Hahn
,
E. J.
,
1995
, “
Including Foundation Effects on the Vibration Behavior of Rotating Machinery
,”
Mech. Syst. Signal Process.
,
9
(
3
), pp.
243
–
256
.
19.
Smart
,
M. G.
,
Friswell
,
M. I.
, and
Lees
,
A. W.
,
2000
, “
Estimating Turbogenerator Foundation Parameters—Model Selection and Regularisation
,”
Proc. R. Soc. London, Ser. A
,
456
, pp.
1583
–
1607
.
20.
Lees, A. W., and Friswell, M. I., 1996, “Estimation of Forces Exerted on Machine Foundations,” International Conference Identification in Engineering Systems, University of Wales, Swansea, UK, pp. 793–803.
21.
Lees
,
A. W.
, and
Friswell
,
M. I.
,
1997
, “
The Evaluation of Rotor Imbalance in Flexibly Mounted Machines
,”
J. Sound Vib.
,
208
(
5
), pp.
671
–
683
.
22.
Edwards
,
S.
,
Lees
,
A. W.
, and
Friswell
,
M. I.
,
2000
, “
Experimental Identification of Excitation and Support Parameters of a Flexible Rotor-Bearing-Foundation System From a Single Run-Down
,”
J. Sound Vib.
,
232pp.
(
5
),
963
–
992
.
23.
Hamrock, B. J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, Englewood Cliffs, NJ.
24.
Lawson, C. L., and Hanson, R. J., Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, NJ.
25.
Golub, G. H., and Van Loan, C. F., 1990, Matrix Computations, John Hopkins, Baltimore, MD.
26.
Hansen
,
P. C.
,
1994
, “
Regularisation Tools: A MATLAB Package for Analysis and Solution of Discrete Ill-Posed Problems
,”
Numer. Algorithms
,
6
, pp.
1
–
35
.
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