Arrangement of Belleville Springs on Endplates Combined with Optimal Cross-Sectional Shape in PEMFC Stack Using Equivalent Beam Modeling and FEA

1. Introduction

Proton exchange membrane fuel cells (PEMFCs) are great alternative vehicle power source devices to the current existing internal combustion engine [ 1 3 ] and are critical for the carbon peak and carbon neutrality goals in the transportation field, as well as the sustainability of Earth’s energy. PEMFCs are potential energy devices that use hydrogen and oxygen to produce electricity by way of an electrochemical reaction for driving a hybrid fuel cell vehicle [ 4 6 ]. The efficiency of a PEMFC system is 50~60%, which is higher than the 10~16% efficiency of an internal combustion engine [ 1 ]. At present, PEMFCs have become one of the current focuses of research due to their advantages of having high efficiency, zero emissions, a low operating temperature and a quick start-up [ 7 10 ].

Since the output voltage of a single cell is limited, PEMFCs are usually composed of many cells and are compressed together by endplates to form fuel cell stacks [ 11 ]. However, since the fuel cell endplate deforms under the large clamping load applied by the steel belts, a non-uniform contact pressure distribution occurs on the multiple interfaces of the bipolar plate (BPP) and membrane electrolyte assembly (MEA) in the stack [ 12 ]. However, the contact pressure distribution in the fuel cell stack is a major factor that affects the fuel cell performance. Appropriate deformation of the fuel cell endplate is essential to reduce the ohmic resistance and prevent leakage of the reactant and coolant [ 13 ]. Furthermore, excessive compression of endplate deformation may reduce the porosity of the gas diffusion layer (GDL) and even cause damage [ 14 ]. Uniform deformation of the endplate is important in order to achieve a highly efficient PEMFC electrochemical reaction [ 15 ].

The design of the endplate under assembly force is of key importance to a uniform contact pressure distribution in a PEMFC stack [ 16 ]. Although increasing the endplate thickness is conducive to increasing the endplate bending stiffness and strength, the volume-specific power density of the fuel cell stack becomes less ideal [ 17 ]. Therefore, an appropriate cross-sectional endplate shape needs to achieve an optimal balance between increasing the endplate volume-specific power and reducing its deformation.

Moreover, it should be noted that the fuel cell endplate is not rigid, and it does not directly come into contact with the BPP; a set of Belleville springs can be integrated into the endplate and elastically connected to the BPP, which is used in order to make the applied assembly force smoother and to absorb the compressive load resulting from thermal expansion [ 18 19 ]. Fuel cell endplates with Belleville springs allow the support of a large load with small deformation and have numerous advantageous and excellent characteristics such as a long life, high energy storage capacity, low cost and greater security, being widely used in fuel cell stack design and application, particularly in fuel cell vehicles [ 20 ]. Since Belleville springs support large reaction forces as well as the endplate under the assembly force of the fuel cell stack using steel clamping belts, and these two forces are applied on the fuel cell endplate, the fuel cell endplate thus plays an important role in dual forces, resulting in complex endplate deformation. Studying the arrangement of Belleville springs on a fuel cell endplate with an optimal cross-sectional shape is essential to determine uniform endplate compression.

Many researchers have provided several valuable works on the optimization design of the endplate. Asghari et al. [ 18 ] utilized FEA to analyze the influence of the endplate thickness on pressure distribution uniformity inside the stack. The optimum thickness was 35 mm for their 5 kW PEMFC stack. Alizadeh et al. [ 21 ] established a PEMFC model and investigated the effect of the endplate thickness and material properties on the contact pressure distribution of an MEA. Zhang et al. [ 22 ] found that the endplate thickness has the strongest effect on both the maximum stress and contact pressure distribution of the MEA. Zhou et al. [ 23 ] developed a methodology based on a composite model and the equivalent material property to predict the mechanical behaviors in a PEMFC stack and found that the aluminum alloy endplate had a small deformation under the same compression ratio compared to an epoxy endplate.

Some studies on topology optimization have proposed the optimization of the endplate for the high power density of fuel cells. Lin et al. [ 24 ] established a multi-objective topology optimization model of the endplates in a PEMFC stack with nonlinear contact boundary conditions to obtain the optimized material distribution (topology) of the endplate in a specific allowable design space. Not only was the endplate weight reduced by over 25%, but also the contact pressure distribution uniformity in the fuel cell stack was improved by over 65%. Liu et al. [ 25 ] proposed a multi-objective stepwise optimization method for the endplate of a PEMFC stack clamped with steel belts. They divided the 2D optimization problem into shape optimization and topology optimization and used the annealing algorithm to carry out cross-sectional shape optimization. The mass of the optimized endplate was decreased by 39.50%, and the uniformity of the contact pressure distribution was increased by 11.5%. Yang et al. [ 16 ] redesigned a ribbed PEMFC endplate with the topology optimization method. The weight of the endplate was reduced by 14%, and the standard deviation of the contact pressure distribution was reduced by 16.6%, compared to the original endplate. Similarly, Zhang et al. [ 26 ] proposed a lightweight endplate with the topology optimization method for uniform endplate deformation. The weight of the designed endplate was reduced by 35%, and the uniformity of the contact pressure distribution remain unchanged.

In endplate design, some novel cross-sectional shapes have also been studied. Yu et al. [ 27 ] presented a new design of asymmetric composite sandwich endplates that are made of a reinforced carbon and glass fiber composite with a pre-curved cross-sectional shape generated by the residual thermal deformation. Similarly, Yu et al. [ 28 ] continued to employ an insulating foam–core composite sandwich structure with a pre-curved compliant pressure for the fuel cell endplate to achieve both high insulation and a uniform contact pressure distribution inside the stack. The experimental results showed that the new endplate cross-sectional shape design achieved a uniform contact pressure distribution and sufficient safety margins. Alizadeh et al. [ 29 ] designed a novel cross-sectional endplate with a pneumatic pressure chamber, which is composed of two endplates and an O-ring gasket. This structure can achieve a more uniform contact pressure distribution by transmitting the air pressure inside the pocket to the PEMFC stack. However, this structure is complex and not suitable for fuel cell vehicles. In their recent research, Barzegari et al. [ 30 ] developed a central composite design method with FEA models to optimize the cross-sectional geometric parameters of a pneumatic clamping system. The experiment showed that the weight and the contact pressure distribution of the optimized pneumatic endplate were significantly better than those of conventional endplates. Chung et al. [ 31 ] proposed a novel clamping structure to generate a uniform contact pressure distribution and designed a ribbed endplate to decrease its weight. The new design uses levers to move the clamping force from the tire bolts to the optimal positions, which is better after optimization.

Based on previous studies on endplates with steel clamping belts in a PEMFC stack, Belleville springs are generally installed under the endplate, which can absorb the impact of the vibration from the fuel cell vehicle on the road and also adjust the uniform contact pressure distribution caused by thermal expansion. The number and position of Belleville springs and the cross-sectional shape of the endplate will have a critical impact on the deformation of the endplate as well as the uniformity of the contact pressure distribution inside the stack and the efficiency of the PEMFC stack.

Therefore, as mentioned previously, it is essential to study endplates with Belleville springs combined with the optimal cross-sectional shape of the fuel cell endplates for a uniform contact pressure distribution and even high fuel cell performance. A numerical model of an endplate combined with Belleville springs clamped by four steel belts is proposed using the equivalent beam method, and then the numbers and positions of Belleville springs are optimized to achieve minimum deformation of the endplate in the fuel cell stack. Based on this, the cross-sectional shape of the endplate is optimized through FEA for the high-volume-specific power density. This work presents a practical method and provides a design direction for fuel cell stack assembly with an endplate and Belleville springs.