Research Papers

Nonlinear Parametric Reduced-Order Model for the Structural Dynamics of Hybrid Electric Vehicle Batteries

[+] Author and Article Information
Jauching Lu

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48105
e-mail: jauching@umich.com

Kiran D'Souza

Department of Mechanical and Aerospace
The Ohio State University,
Columbus, OH 43235
e-mail: dsouza.60@osu.edu

Matthew P. Castanier

U.S. Army Tank Automotive Research,
Development, and Engineering Center (TARDEC),
6501 E. 11 Mile Road,
Warren, MI 48397-5000
e-mail: matthew.p.castanier.civ@mail.mil

Bogdan I. Epureanu

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48105
e-mail: epureanu@umich.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 23, 2017; final manuscript received October 4, 2017; published online December 12, 2017. Assoc. Editor: Stefano Gonella.This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Vib. Acoust 140(2), 021018 (Dec 12, 2017) (9 pages) Paper No: VIB-17-1278; doi: 10.1115/1.4038302 History: Received June 23, 2017; Revised October 04, 2017

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.

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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. [CrossRef]
Plett, G. L. , 2004, “ High-Performance Battery-Pack Power Estimation Using a Dynamic Cell Model,” IEEE Trans. Veh. Technol., 53(5), pp. 1586–1593. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Bendiksen, O. O. , 1987, “ Mode Localization Phenomena in Large Space Structures,” AIAA J., 25(9), pp. 1241–1248. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Hodges, C. , 1982, “ Confinement of Vibration by Structural Irregularity,” J. Sound Vib., 82(3), pp. 411–424. [CrossRef]
Bendiksen, O. , 2000, “ Localization Phenomena in Structural Dynamics,” Chaos, Solitons Fractals, 11(10), pp. 1621–1660. [CrossRef]
Hurty, W. C. , 1965, “ Dynamic Analysis of Structural Systems Using Component Modes,” AIAA J., 3(4), pp. 678–685. [CrossRef]
Rubin, S. , 1975, “ Improved Component-Mode Representation for Structural Dynamic Analysis,” AIAA J., 13(8), pp. 995–1006. [CrossRef]
Hintz, R. M. , 1975, “ Analytical Methods in Component Modal Synthesis,” AIAA J., 13(8), pp. 1007–1016. [CrossRef]
Craig, R. , and Chang, C. J. , 1976, “ Free-Interface Methods of Substructure Coupling for Dynamic Analysis,” AIAA J., 14(11), pp. 1633–1635. [CrossRef]
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. [CrossRef]
Craig, R. R. , and Bampton, M. C. , 1968, “ Coupling of Substructures for Dynamic Analysis,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Castanier, M. P. , Tan, Y.-C. , and Pierre, C. , 2001, “ Characteristic Constraint Modes for Component Mode Synthesis,” AIAA J., 39(6), pp. 1182–1187. [CrossRef]
Balmés, E. , 1996, “ Parametric Families of Reduced Finite Element Models: Theory and Applications,” Mech. Syst. Signal Process., 10(4), pp. 381–394. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Yazami, R. , and Reynier, Y. , 2006, “ Thermodynamics and Crystal Structure Anomalies in Lithium-Intercalated Graphite,” J. Power Sources, 153(2), pp. 312–318. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]


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Fig. 1

Natural frequency simulation results of the academic battery pack model with repeated substructures

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Fig. 2

Structural variations: (a) prestress variation and (b) cell-to-cell variation

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Fig. 3

(a) Vibration response of the battery pack, (b) the amplitude at the center of each cell is the largest, and (c) the stiffness of cell varies with strain

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Fig. 4

Relation between states of charge and swelling

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Fig. 5

(a) Simplified battery pack model with 20 nominally identical cells and (b) each cell is comprised of several components

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Fig. 6

The vibration responses at the center of cell 10 affected by (a) prestress variations due to changes in clamping, (b) prestress variations due to changes in temperature, (c) cell-to-cell variations, and (d) nonlinearity in material

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Fig. 7

Validation results: (a) linear, cell 10, 3% prestress variation and case 1 cell-to-cell variation, (b) linear, cell 10, 3% prestress variation and case 2 cell-to-cell variation, and (c) nonlinear, cell 7, 3% prestress variation and case 2 cell-to-cell variation

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Fig. 8

(a) Linear and (b) nonlinear statistical analyses for 1000 cell-to-cell variation cases



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