Equivalent stiffness model of a proton exchange membrane fuel cell stack including hygrothermal effects and dimensional tolerances

Proton exchange membrane fuel cells (PEMFCs) require mechanical compression to ensure structural integrity, prevent leakage, and to minimize the electrical contact resistance. The mechanical properties and dimensions of the fuel cell vary during assembly due to manufacturing tolerances and during operation due to both temperature and humidity. Variation in stack compression affects the interfacial contact pressures between components and hence fuel cell performance. This paper presents a one-dimensional equivalent stiffness model of a PEMFC stack capable of predicting independent membrane and gasket contact pressures for an applied external load. The model accounts for nonlinear component compression behavior, thickness variation due to manufacturing tolerances, thermal expansion, membrane expansion due to water uptake, and stack dimensional change due to clamping mechanism stiffness. The equivalent stiffness model is compared to a three-dimensional (3D) finite element model, showing good agreement for multicell stacks. Results demonstrate that the correct specification of gasket thickness and stiffness is essential in ensuring a predictable membrane contact pressure, adequate sealing, and avoiding excessive stresses in the bi-polar plate (BPP). Increase in membrane contact pressure due to membrane water uptake is shown to be significantly greater than the increase due to component thermal expansion in the PEMFC operating range. The predicted increase in membrane contact pressure due to thermal and hydration effects is 18% for a stack containing fully hydrated Nafion® 117 membranes at 80 °C, 90% relative humidity (RH) using an eight bolt clamping design and a nominal 1.2 MPa assembly pressure.