Abstract

Modeling of the dynamic behavior of the rotating system when subject to misaligned shafts is an interesting subject, aiming either the selection of appropriate couplings from early stages of project or the monitoring and model-based diagnosis of such machines. This research is focused on the dynamics of the system when angular misalignment is induced. The methodology to take into account this fault is based on the structural analysis of the flexible coupling, with the consequent use of cyclic restoring forces and moments exerted by this component on the coupled shafts. Structural analysis of metallic disc coupling is conducted by means of the finite element method, in which the flexible disc component is modeled using thin shell formulation. Once misalignments are applied, the cyclic nature of coupling efforts is captured by the application of consecutive shaft spin angles. Steady-state response is simulated and then displacements spectrum are analyzed in order to highlight harmonic components rising due to misalignment. Test rig measurements are performed, and the theoretical model is discussed in terms of locus, frequency response function (FRF), orbit shape, and spectrum information. Disc coupling is regarded, as limited literature in vibration spectrums is available for this type of coupling.

References

References
1.
Muszynska
,
A.
,
2005
,
Rotordynamics
,
CRC Press
,
New York
.
2.
Piotrowski
,
J.
,
2006
,
Shaft Alignment Handbook
,
CRC Press
,
New York
.
3.
Patel
,
H.
, and
Darpe
,
A.
,
2009
, “
Vibration Response of Misaligned Rotors
,”
J. Sound Vib.
,
325
(
3
), pp.
609
628
. 10.1016/j.jsv.2009.03.024
4.
Xu
,
M.
, and
Marangoni
,
R. D.
,
1994
, “
Vibration Analysis of a Motor-Flexible Coupling-Rotor System Subject to Misalignment and Unbalance, Part I—Theoretical Model and Analysis
,”
J. Sound Vib.
,
176
(
5
), pp.
663
679
. 10.1006/jsvi.1994.1405
5.
Dewell
,
D. L.
, and
Mitchell
,
L. D.
,
1984
, “
Detection of a Misaligned Disc Coupling Using Spectrum Analysis
,”
Trans ASME J. Vib. Acoust. Stress Reliab. Design
,
106
(
1
), pp.
9
15
. 10.1115/1.3269161
6.
Al-Hussain
,
K. M.
, and
Redmond
,
I.
,
2002
, “
Dynamic Response of Two Rotors Connected by Rigid Mechanical Coupling With Parallel Misalignment
,”
J. Sound Vib.
,
249
(
3
), pp.
483
498
. 10.1006/jsvi.2001.3866
7.
Sudhakar
,
G.
, and
Sekhar
,
A. S.
,
2009
, “
Coupling Misalignment in Rotating Machines—Modelling, Effects and Monitoring
,”
Noise Vib. Worldwide
,
40
(
1
), pp.
17
39
. 10.1260/0957-4565.40.1.17
8.
Prabhu
,
B. S.
,
1997
, “
An Experimental Investigation on the Misalignment Effects in Journal Bearings
,”
Tribol. Trans.
,
40
(
2
), pp.
235
242
. 10.1080/10402009708983650
9.
Bou-Said
,
B.
, and
Nicolas
,
D.
,
1992
, “
Effect of Misalignment on Static and Dynamic Characteristics of Hybrid Bearing
,”
Tribol. Trans.
,
35
(
2
), pp.
325
331
. 10.1080/10402009208982124
10.
Pennacchi
,
P.
,
Vania
,
A.
, and
Chatterton
,
S.
,
2012
, “
Nonlinear Effects Caused by Coupling Misalignment in Rotors Equipped With Journal Bearings
,”
Mech. Syst. Signal Process.
,
30
, pp.
306
322
. 10.1016/j.ymssp.2011.11.020
11.
Dal
,
A.
, and
Karaçay
,
T.
,
2017
, “
Effects of Angular Misalignment on the Performance of Rotor-Bearings Systems Supported by Externally Pressurized Air Bearing
,”
Tribol. Int.
,
111
, pp.
276
288
. 10.1016/j.triboint.2017.03.018
12.
Tadeo
,
A. T.
, and
Cavalca
,
K. L.
,
2003
, “
A Comparison of Flexible Coupling Models for Updating in Rotating Machinery Response
,”
J. Braz. Soc. Mech. Sci. Eng.
,
25
(
3
), pp.
235
246
. 10.1590/S1678-58782003000300004
13.
Simon
,
G.
,
1992
, “
Prediction of Vibration Behavior of Large Turbomachinery on Elastic Foundations due to Unbalance and Coupling Misalignment
,”
Proc. Inst. Mech. Eng. (IMechE)
,
206
(
1
), pp.
29
39
. 10.1243/PIME_PROC_1992_206_092_02
14.
Gibbons
,
C. B.
,
1976
, “
Coupling Misalignment Forces
,”
Proceedings of the Fifth Turbomachinery Symposium
,
College Station, TX
,
Oct. 12–14
, pp.
111
116
.
15.
Sekhar
,
A. S.
, and
Prabhu
,
B. S.
,
1995
, “
Effects of Coupling Misalignment on Vibrations of Rotating Machinery
,”
J. Sound Vib.
,
185
(
4
), pp.
655
671
. 10.1006/jsvi.1995.0407
16.
Prabhakar
,
S.
,
Sekhar
,
A.
, and
Mohanty
,
A.
,
2002
, “
Crack Versus Coupling Misalignment in a Transient Rotor System
,”
J. Sound Vib.
,
256
(
4
), pp.
773
789
. 10.1006/jsvi.2001.4225
17.
Lee
,
Y.
, and
Lee
,
C.
,
1999
, “
Modelling and Vibration Analysis of Misaligned Rotor-Ball Bearing Systems
,”
J. Sound Vib.
,
224
(
1
), pp.
17
32
. 10.1006/jsvi.1997.1301
18.
Jalan
,
A. K.
, and
Mohanty
,
A. R.
,
2009
, “
Model Based Fault Diagnosis of a Rotor-Bearing System for Misalignment and Unbalance Under Steady-State Condition
,”
J. Sound Vib.
,
327
(
3–5
), pp.
604
622
. 10.1016/j.jsv.2009.07.014
19.
Chandra
,
N. H.
, and
Sekhar
,
A. S.
,
2016
, “
Fault Detection in Rotor Bearing Systems Using Time Frequency Techniques
,”
Mech. Syst. Signal Process.
,
72–73
, pp.
105
133
. 10.1016/j.ymssp.2015.11.013
20.
Saavedra
,
P.
, and
Ramirez
,
D.
,
2004
, “
Vibration Analysis of Rotors for the Identification of Shaft Misalignment—Part I: Theoretical Analysis
,”
Proc. Inst. Mech. Eng. (IMechE)
,
218
(
9
), pp.
971
985
. 10.1243/0954406041991297
21.
Patel
,
H.
, and
Darpe
,
A.
,
2009
, “
Experimental Investigations on Vibration Response of Misaligned Rotors
,”
Mech. Syst. Signal Process.
,
23
(
7
), pp.
2236
2252
. 10.1016/j.ymssp.2009.04.004
22.
Rao
,
J.
, and
Sreenivas
,
R.
,
2003
, “
Dynamic Analysis of Misaligned Rotor Systems, Advances in Vibration Engineering
,”
J. Vib. Inst. India
,
2
(
1
), p.
1
.
23.
Zachwieja
,
J.
,
2011
, “
The Analysis of the Rotor’s Longitudinal Vibrations With Large Misalignment of Shafts and Rotex Type Coupling
,”
Diagn. Struct. Health Monit.
,
2
(
58
), pp.
19
23
.
24.
Hariharan
,
V.
, and
Srinivasan
,
P.
,
2009
, “
Vibration Analysis of Misaligned Shaft-Ball Bearing System
,”
Indian J. Sci Technol.
,
2
(
9
), pp.
45
50
.
25.
Cura
,
F.
, and
Mura
,
A.
,
2014
, “
Experimental and Theoretical Investigation About Reaction Moments in Misaligned Splined Couplings
,”
Mech. Syst. Signal Process.
,
45
(
2
), pp.
504
512
. 10.1016/j.ymssp.2013.12.005
26.
Guo
,
Y.
,
Lambert
,
S.
,
Wallen
,
R.
,
Errichello
,
R.
, and
Keller
,
J.
,
2016
, “
Theoretical and Experimental Study on Gear-Coupling Contact and Loads Considering Misalignment, Torque, and Friction Influences
,”
Mech. Mach. Theory
,
98
, pp.
242
262
. 10.1016/j.mechmachtheory.2015.11.015
27.
Kumar
,
S.
,
2015
, “
Vibration Signature Analysis of 4 Jaw Flexible Coupling Considering Misalignment in Two Planes
,”
Int. Res. J. Eng. Technol.
,
2
(
1
), pp.
73
84
.
28.
Sawalhi
,
N.
,
Ganeriwala
,
S.
, and
Tóth
,
M.
,
2019
, “
Parallel Misalignment Modeling and Coupling Bending Stiffness Measurement of a Rotor-Bearing System
,”
Appl. Acoust.
,
144
, pp.
124
141
.
29.
Arebi
,
L.
,
Gu
,
F.
, and
Ball
,
A.
,
2012
, “
A Comparative Study of Misalignment Detection Using a Novel Wireless Sensor With Conventional Wired Sensors
,”
J. Phys. Conference Series
,
364
(
1
), pp.
1
11
.
30.
Chacon
,
J.
,
Andicoberry
,
E. A.
,
Kappatos
,
V.
,
Asfis
,
G.
,
Gan
,
T.
, and
Balachandran
,
W.
,
2014
, “
Shaft Angular Misalignment Using Acoustic Emission
,”
Appl. Acoust.
,
85
, pp.
12
22
. 10.1016/j.apacoust.2014.03.018
31.
Reddy
,
M. C.
, and
Sekhar
,
A. S.
,
2015
, “
Detection and Monitoring of Coupling Misalignment in Rotors Using Torque Measurements
,”
Measurement
,
61
, pp.
111
122
. 10.1016/j.measurement.2014.10.031
32.
Verucchi
,
C.
,
Bossio
,
J.
,
Bossio
,
G.
, and
Acosta
,
G.
,
2016
, “
Misalignment Detection in Induction Motors With Flexible Coupling by Means of Estimated Torque Analysis and MCSA
,”
Mech. Syst. Signal Process.
,
80
, pp.
570
581
. 10.1016/j.ymssp.2016.04.035
33.
Redmond
,
I.
,
2010
, “
Study of a Misaligned Flexibly Coupled Shaft System Having Nonlinear Bearings and Cyclic Coupling Stiffness—Theoretical Model and Analysis
,”
J. Sound Vib.
,
329
(
6
), pp.
700
720
. 10.1016/j.jsv.2009.09.039
34.
Tuckmantel
,
F. W. S.
, and
Cavalca
,
K. L.
,
2019
, “
Vibration Signatures of a Rotor-Coupling-Bearing System Under Angular Misalignment
,”
Mech. Mach. Theory
,
133
, pp.
559
583
. 10.1016/j.mechmachtheory.2018.12.014
35.
Nelson
,
H.
, and
McVaugh
,
J.
,
1976
, “
The Dynamics of Rotor-Bearing Systems Using Finite Elements
,”
ASME J. Eng. Ind.
,
98
(
2
), pp.
593
600
. 10.1115/1.3438942
36.
Nelson
,
H.
,
1980
, “
A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,”
ASME J. Mech. Des.
,
102
(
4
), pp.
793
803
. 10.1115/1.3254824
37.
Lallane
,
M.
, and
Ferraris
,
G.
,
1998
,
Rotordynamics Prediction in Engineering
,
John Wiley and Sons
,
London
.
38.
Reynolds
,
O.
,
1886
, “
On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive oil
,”
Philos. Trans. R. Soc. London
,
177
, pp.
157
234
. 10.1098/rstl.1886.0005
39.
Pinkus
,
O.
, and
Sternlicht
,
S. A.
,
1961
,
Theory of Hydrodynamic Lubrication
,
McGraw-Hill
,
New York
.
40.
Machado
,
T.
, and
Cavalca
,
K.
,
2011
, “
Dynamic Analysis of Cylindrical Hydrodynamic Bearings With Geometric Discontinuities
,”
International Conference on Vibration Problems (ICOVP)
,
Prague, Czech Republic
,
Sept. 5–8
, pp.
352
358
.
41.
Lund
,
J. W.
,
1987
, “
Review of the Concept of Dynamic Coefficients for Fluid Film Journal Bearings
,”
ASME J. Tribol.
,
109
(
1
), pp.
37
41
. 10.1115/1.3261324
42.
Ventsel
,
E.
, and
Krauthammer
,
T.
,
2001
,
Thin Plates and Shells—Theory, Analysis and Applications
,
CTC Press
,
New York
.
43.
Kramer
,
E.
,
1993
,
Dynamics of Rotors and Foundations
,
Springer-Verlag
,
Berlin
.
44.
ISO 1940-1: 2003(E)
,
2003
,
Mechanical Vibration—Balance Quality Requirement for Rotors in a Constant (Rigid) State—Part 1: Specification and Verification of Balance Tolerances
.
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