Battery packs used in electrified vehicles exhibit high modal density due to their repeated cell substructures. If the excitation contains frequencies in the region of high modal density, small commonly occurring structural variations can lead to drastic changes in the vibration response. The battery pack fatigue life depends strongly on their vibration response; thus, a statistical analysis of the vibration response with structural variations is important from a design point of view. In this work, parametric reduced-order models (PROMs) are created to efficiently and accurately predict the vibration response in Monte Carlo calculations, which account for stochastic structural variations. Additionally, an efficient iterative approach to handle material nonlinearities used in battery packs is proposed to augment the PROMs. The nonlinear structural behavior is explored, and numerical results are provided to validate the proposed models against full-order finite element approaches.

References

References
1.
Lu
,
L.
,
Han
,
X.
,
Li
,
J.
,
Hua
,
J.
, and
Ouyang
,
M.
,
2013
, “
A Review on the Key Issues for Lithium-Ion Battery Management in Electric Vehicles
,”
J. Power Sources
,
226
, pp.
272
288
.
2.
Plett
,
G. L.
,
2004
, “
High-Performance Battery-Pack Power Estimation Using a Dynamic Cell Model
,”
IEEE Trans. Veh. Technol.
,
53
(
5
), pp.
1586
1593
.
3.
Einhorn
,
M.
,
Roessler
,
W.
, and
Fleig
,
J.
,
2011
, “
Improved Performance of Serially Connected Li-Ion Batteries With Active Cell Balancing in Electric Vehicles
,”
IEEE Trans. Veh. Technol.
,
60
(
6
), pp.
2448
2457
.
4.
Croce
,
F.
,
Focarete
,
M. L.
,
Hassoun
,
J.
,
Meschini
,
I.
, and
Scrosati
,
B.
,
2011
, “
A Safe, High-Rate and High-Energy Polymer Lithium-Ion Battery Based on Gelled Membranes Prepared by Electrospinning
,”
Energy Environ. Sci.
,
4
(
3
), pp.
921
927
.
5.
Hong
,
S.-K.
,
Epureanu
,
B. I.
, and
Castanier
,
M. P.
,
2014
, “
Parametric Reduced-Order Models of Battery Pack Vibration Including Structural Variation and Prestress Effects
,”
J. Power Sources
,
261
, pp.
101
111
.
6.
Bendiksen
,
O. O.
,
1987
, “
Mode Localization Phenomena in Large Space Structures
,”
AIAA J.
,
25
(
9
), pp.
1241
1248
.
7.
Ezvan
,
O.
,
Batou
,
A.
,
Soize
,
C.
, and
Gagliardini
,
L.
,
2017
, “
Multilevel Model Reduction for Uncertainty Quantification in Computational Structural Dynamics
,”
Comput. Mech.
,
59
(
2
), pp.
219
246
.
8.
Batou
,
A.
,
2015
, “
A Global/Local Probabilistic Approach for Reduced-Order Modeling Adapted to the Low- and Mid-Frequency Structural Dynamics
,”
Comput. Methods Appl. Mech. Eng.
,
294
, pp.
123
140
.
9.
Hodges
,
C.
,
1982
, “
Confinement of Vibration by Structural Irregularity
,”
J. Sound Vib.
,
82
(
3
), pp.
411
424
.
10.
Bendiksen
,
O.
,
2000
, “
Localization Phenomena in Structural Dynamics
,”
Chaos, Solitons Fractals
,
11
(
10
), pp.
1621
1660
.
11.
Hurty
,
W. C.
,
1965
, “
Dynamic Analysis of Structural Systems Using Component Modes
,”
AIAA J.
,
3
(
4
), pp.
678
685
.
12.
Rubin
,
S.
,
1975
, “
Improved Component-Mode Representation for Structural Dynamic Analysis
,”
AIAA J.
,
13
(
8
), pp.
995
1006
.
13.
Hintz
,
R. M.
,
1975
, “
Analytical Methods in Component Modal Synthesis
,”
AIAA J.
,
13
(
8
), pp.
1007
1016
.
14.
Craig
,
R.
, and
Chang
,
C. J.
,
1976
, “
Free-Interface Methods of Substructure Coupling for Dynamic Analysis
,”
AIAA J.
,
14
(
11
), pp.
1633
1635
.
15.
Shyu
,
W.-H.
,
Gu
,
J.
,
Hulbert
,
G. M.
, and
Ma
,
Z.-D.
,
2000
, “
On the Use of Multiple Quasi-Static Mode Compensation Sets for Component Mode Synthesis of Complex Structures
,”
Finite Elem. Anal. Des.
,
35
(
2
), pp.
119
140
.
16.
Craig
,
R. R.
, and
Bampton
,
M. C.
,
1968
, “
Coupling of Substructures for Dynamic Analysis
,”
AIAA J.
,
6
(
7
), pp.
1313
1319
.
17.
Castanier
,
M. P.
,
Tan
,
Y.-C.
, and
Pierre
,
C.
,
2001
, “
Characteristic Constraint Modes for Component Mode Synthesis
,”
AIAA J.
,
39
(
6
), pp.
1182
1187
.
18.
Balmés
,
E.
,
1996
, “
Parametric Families of Reduced Finite Element Models: Theory and Applications
,”
Mech. Syst. Signal Process.
,
10
(
4
), pp.
381
394
.
19.
Hong
,
S.-K.
,
Epureanu
,
B. I.
,
Castanier
,
M. P.
, and
Gorsich
,
D. J.
,
2011
, “
Parametric Reduced-Order Models for Predicting the Vibration Response of Complex Structures With Component Damage and Uncertainties
,”
J. Sound Vib.
,
330
(
6
), pp.
1091
1110
.
20.
Hong
,
S.-K.
,
Epureanu
,
B. I.
, and
Castanier
,
M. P.
,
2013
, “
Next-Generation Parametric Reduced-Order Models
,”
Mech. Syst. Signal Process.
,
37
(
12
), pp.
403
421
.
21.
Lim
,
S.-H.
,
Bladh
,
R.
,
Castanier
,
M. P.
, and
Pierre
,
C.
,
2007
, “
Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration
,”
AIAA J.
,
45
(
9
), pp.
2285
2298
.
22.
Cannarella
,
J.
, and
Arnold
,
C. B.
,
2014
, “
Stress Evolution and Capacity Fade in Constrained Lithium-Ion Pouch Cells
,”
J. Power Sources
,
245
, pp.
745
751
.
23.
Oh
,
K.-Y.
,
Samad
,
N. A.
,
Kim
,
Y.
,
Siegel
,
J. B.
,
Stefanopoulou
,
A. G.
, and
Epureanu
,
B. I.
,
2016
, “
A Novel Phenomenological Multi-Physics Model of Li-Ion Battery Cells
,”
J. Power Sources
,
326
, pp.
447
458
.
24.
Kenney
,
B.
,
Darcovich
,
K.
,
MacNeil
,
D. D.
, and
Davidson
,
I. J.
,
2012
, “
Modelling the Impact of Variations in Electrode Manufacturing on Lithium-Ion Battery Modules
,”
J. Power Sources
,
213
, pp.
391
401
.
25.
Schuster
,
S. F.
,
Brand
,
M. J.
,
Berg
,
P.
,
Gleissenberger
,
M.
, and
Jossen
,
A.
,
2015
, “
Lithium-Ion Cell-to-Cell Variation During Battery Electric Vehicle Operation
,”
J. Power Sources
,
297
, pp.
242
251
.
26.
Yang
,
M.-T.
, and
Griffin
,
J. H.
,
1999
, “
A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes
,”
ASME J. Eng. Gas Turbines Power
,
123
(
4
), pp.
893
900
.
27.
Lai
,
W.-J.
,
Ali
,
M. Y.
, and
Pan
,
J.
,
2014
, “
Mechanical Behavior of Representative Volume Elements of Lithium-Ion Battery Cells Under Compressive Loading Conditions
,”
J. Power Sources
,
245
, pp.
609
623
.
28.
Sahraei
,
E.
,
Hill
,
R.
, and
Wierzbicki
,
T.
,
2012
, “
Calibration and Finite Element Simulation of Pouch Lithium-Ion Batteries for Mechanical Integrity
,”
J. Power Sources
,
201
, pp.
307
321
.
29.
Yazami
,
R.
, and
Reynier
,
Y.
,
2006
, “
Thermodynamics and Crystal Structure Anomalies in Lithium-Intercalated Graphite
,”
J. Power Sources
,
153
(
2
), pp.
312
318
.
30.
Fu
,
R.
,
Xiao
,
M.
, and
Choe
,
S.-Y.
,
2013
, “
Modeling, Validation and Analysis of Mechanical Stress Generation and Dimension Changes of a Pouch Type High Power Li-Ion Battery
,”
J. Power Sources
,
224
, pp.
211
224
.
31.
Oh
,
K.-Y.
,
Siegel
,
J. B.
,
Secondo
,
L.
,
Kim
,
S. U.
,
Samad
,
N. A.
,
Qin
,
J.
,
Anderson
,
D.
,
Garikipati
,
K.
,
Knobloch
,
A.
,
Epureanu
,
B. I.
,
Monroe
,
C. W.
, and
Stefanopoulou
,
A.
,
2014
, “
Rate Dependence of Swelling in Lithium-Ion Cells
,”
J. Power Sources
,
267
, pp.
197
202
.
32.
Oh
,
K.-Y.
,
Epureanu
,
B. I.
,
Siegel
,
J. B.
, and
Stefanopoulou
,
A. G.
,
2016
, “
Phenomenological Force and Swelling Models for Rechargeable Lithium-Ion Battery Cells
,”
J. Power Sources
,
310
, pp.
118
129
.
You do not currently have access to this content.