Control-Oriented Modeling of Electrode Material for Mechanical Notching and Stacking Processes of Battery Manufacturing

The processes of notching and stacking represent two crucial stages of battery cell manufacturing that have a significant influence on the quality of the produced cells from the perspective of lifetime. In addition, these stages are also crucial concerning safety, especially, when the production of cells with high energy density is concerned. This is due to the fact that imperfect cutting edge quality in notching (due to burr) may lead to sharp edges that cut through separator foils when stacking is executed. This may produce internal short circuits in produced cells that are possibly not detected during the formation stage but only show up during operation when internal pressure and temperature variations in battery cells lead to a gradual extension of this defect. The same is also true for mechanical deformations of electrodes during their transport within the stacking process which may lead to wrinkles as well as cracks. Therefore, this paper presents a control-oriented modeling procedure for flexible electrodes that can be used for forecasting deflections in elastic and plastic regimes during notching and stacking and therefore is inevitable for a model-based design of control strategies for both handling stages. The core of this modeling approach is the replacement of the governing partial differential equation for the material deformation by a model that is discretized in space and time. For that purpose, the Crank-Nicolson approach is employed due to its favorable property of preserving the stability properties when discretizing the underlying infinite-dimensional model.