Parametric Reduced-Order Models of Battery Pack Vibration Including Structural Variation and Pre-stress Effects

The goal of this work is to develop an efficient numerical modeling method for the vibration of hybrid electric vehicle (HEV) battery packs to support probabilistic forced response simulations and fatigue life predictions. There are two important sources of variations in HEV battery packs that affect their structural dynamic response. One source is the uncertain level of pre-stress due to bolts or welds used for joining cells within a pack. The other source is small structural variations among the cells of a battery pack. The structural dynamics of HEV battery packs are known to feature very high modal density in many frequency bands. That is because packs are composed of nominally identical cells. The high modal density combined with small, random structural variations among the cells can lead to drastic variations in the dynamic response compared with those of the ideal nominal system. Therefore, it is important to perform probabilistic simulations of the structural response with pre-stress variations and cell-to-cell parameter variations in order to accurately predict the fatigue life of a pack. In this paper, a new parametric reduced-order model (PROM) formulation is derived for HEV battery pack vibration by employing several key observation; namely (1) the stiffness matrix can be parameterized for different levels of pre-stress, (2) the mode shapes of a battery pack with cell-to-cell variation can be represented as a linear combination of the mode shapes of the nominal system, and (3) the frame holding each cell has vibratory motion. These key observations are exploited to include the effects of pre-stress and cell-to-cell variations directly in the PROM formulation. A numerical example of an academic battery pack with pouch cells is presented to demonstrate that the PROMs capture the effects of both prestress and structural variation on HEV battery packs. The PROMs are validated numerically by comparing their forced response predictions with those from full-order finite element models (FEMs) of the same systems.