Read Vibration Analysis for Polymer Electrolyte Fuel Cell Stack Assembly text version

Vibration Analysis for Polymer Electrolyte Fuel Cell Stack Assembly

Takayuki KOIZUMI, Nobutaka TSUJIUCHI, Shun OHNO Department of Engineering, Doshisha University, 1-3, Tataramiyakodani, Kyotanabe, Kyoto, 610-0321, Japan

ABSTRACT A fuel cell stack is laminated with a number of plate-type cells, and the latest model is assembled by compression from both ends of plates. When this structure is exposed to external vibration, it is possible that there will be lateral transition of cells or leakage of fuel gas and coolant water. Consequently, this research aims to understand the vibration characteristics of a fuel cell stack and to evaluate their seismic resistance under a vibration environment. We study two sizes of stack assemblies of polymer electrolyte fuel cell (PEFC) for cogeneration systems. First we acquired the vibration characteristics of the small-size stack (1-kw type) by experimental modal analysis and conducted a seismic test. Next we constructed the finite element model of the small-size fuel cell stack and conducted an eigen value analysis. In modeling the stack, coupling and translational stiffness between cells are determined so that the analytical results of the natural frequency and mode shape correspond with the experimental results. Finally, the large-size stack (10-kw type) finite element model was constructed by scaling the small-size stack model, and the modal parameters of the large-size stack were predicted. We found that the 1kW stack has its first bending mode at 168 Hz and adequate seismic resistance. We predict that the 10-kW stack has first mode at approximately 80 Hz.

1. INTRODUCTION Recently, fuel cells have attracted attention as new power resources and are used in fuel-cell vehicles and stationary cogeneration systems. The fuel cell stack in the power generation parts of inside these appliances has structures laminated with a number of plate-type cells. Currently, the method of assembling the stack is changing from fastening laminated parts using stud bolts to holding them by compression from both ends of plates. This is due to design like expanding cell surface area, structural simplification, and reduction of the parts count. But stack assembled by the latter method has low strength in the shear direction and bends under its own weight. Also, the stack is mounted on system frames keeping the laminating direction horizontal. Therefore, a transition of lamination or fuel gas leakage may occur when the stack is excited by an external force like an earthquake vibration. While seismic analysis for the large size of fuel cell plant has conducted [1], but research focusing on the vibration problem of the laminated structure of fuel cell stack has not been carried out. Therefore, vibration analysis and evaluation of seismic resistance are conducted in this research. The subjects of this research are two sizes of stack assemblies of polymer electrolyte fuel cell (PEFC) for cogeneration systems. One has a generation capacity of 1-kW. The stack has a width of about 200 mm, a length of about 350 mm, and a weight of about 100 mm, weight about 13 kg and is shown in Fig. 1. The other stack has a generation capacity of 10-kW and has a width of about 300 mm, a length of about 1000 mm, a height of about 300 mm, and a weight of about 130 kg and is shown in Fig. 2.

Fig.1 Appearance of 1kw Fuel-Cell Stack

Fig.2 Appearance of 10kw Fuel-Cell Stack

2. VIBRATION TEST OF 1-KW STACK First the modal property of the 1-kW stack was acquired by experimental modal analysis. The experiment was conducted using the LMS Test.Lab. Then a leak test under vibration was carried out for evaluation of seismic resistance. 2.1. Experimental modal analysis An impact test of the 1-kW stack was conducted using a general-purpose impact hammer (made by PCB) for acquisition of frequency response functions. A free-free condition was simulated by hanging up test pieces at four points on pressure plates. As shown in Fig. 3, a total of 3 input points were set on each surface of stack, and a total of 36 response points were set on each side. Single input-multi output type measuring displanting response point was took on. Measurements were averaged over 8 times. Triaxial responses were measured using a triaxial acceleration pickup (made by TEAC).

Pressure Plate

End Plate Laminated Part

End Plate

Pressure Plate


Input Response Points

Fig.3 Input and response points on stack surface

An estimation of modal parameters from frequency response functions acquired by experiment was conducted by applying the POLYMAX method on the Test.Lab [2]. Calculated mode shapes of the 1-kW stack are shown in Fig. 4. As the figure shows the first mode is vertical bending at 168.9 Hz, and both ends of pressure plates are vibrating commonly with the bending of the laminated part. The second mode is the parallel swing of pressure plates, which mainly vibrate at 240.4 Hz. The third mode is the lateral bending of the laminated part only at 316.5 Hz. The fourth mode is the torsion of the entire stack at 336.4 Hz.

(a) Mode 1 168.9Hz 2.06% Vertical-Bending

(c)Mode 3 316.5Hz 2.65% Lateral-Bending

(b) Mode 2 240.4Hz 1.53% Parallel-Swinging

(d) Mode 4 336.4Hz 2.39% Torsion

Fig.4 Mode shapes of 1kW stack 2.2. Seismic evaluation test Next, sine-wave and earthquake-wave shaking tests were conducted for evaluation of the seismic resistance of the stack. Stack was fixed directly to the biaxial shaking table shown in Fig. 5. Test conditions were determined according to the JIS C0055 [3]. Swept sine waves from 1 Hz to 30 Hz with 3 stages of floor acceleration levels were used in the shaking tests: level 1 is horizontal: 6 m/s2, vertical: 3 m/s2; level 2 is horizontal: 9 m/s2, vertical: 4.5 m/s2; level 3 is horizontal: 15 m/s2, vertical: 7.5 m/s2. Sine wave shaking tests were conducted with uniaxial excitation for each direction (X,Y,Z). Also, earthquake-wave (KOBE, EL CENTRO) shaking tests were conducted with biaxial excitation. Then pressures of fuel gas and coolant water inside the stack were measured after each of the excitation steps. Damage and external leakage of the coolant water were checked concurrently. The pressure drop in the gas and coolant lines after each excitation steps is shown in Fig. 6. This shows that leakage of fuel gas and coolant water maintained a roughly constant rate. Variation in the measured pressure is within the error tolerance level and it originates the temperature changes during the excitation steps. An appearance check found that neither transition of cells nor leakage of water had occurred. Therefore, we conclude that 1-kW stack maintains seal performance under vibrations of earthquake levels.

Fig.5 Experiment condition of seismic test of 1kw stack

Fig.6 Pressure drop after each vibration test steps 3. FINITE ELEMENT ANALYSIS The finite element model of the 1-kW stack for an eigen value analysis was constructed. Contact stiffness between cells was determined in such a way that the modal properties of the experimental and analytical values were identical. Then the modal property of the 10-kw stack was predicted by scaling up the 1-kW stack model. 3.1. Contact state of cell surface Before modeling of the 1-kW stack, it is necessary to determine the contact state of the cell surface. Some research has reported that the contact stiffness between two compressed materials with smooth surfaces transits to the non-linear area from the linear area with increase of the compression bordering a fully contacted state [4][6]. Pressure at the nick point is called the critical surface pressure. Furthermore, it is known that two contacting materials are in the same state of rigidly connection and that bending frequency decreases when surface pressure reaches the critical point. In the case of fuel cell stack, it is difficult to determine contact stiffness between cell surfaces with theoretical formulae for smooth surfaces because channels for coolant water are carved on the cell surface and seal for leakage protection is placed around the cell. It is possible however, to evaluate whether the cells of the stack fully contact each other by measuring whether the pressure addition to the stack is over critical pressure. Then the contact state of the stack can be determined by measuring the compression displacement of the laminated part and the lateral bending frequency when pressure is varied.

Cell Surface (Carbon) Seal

Fig.7 Pattern diagram of cell surface

Fig.8 Shift of displacement by compression and bending natural frequency

Figure 8 shows compression displacement and lateral bending frequency when pressure addition changes from 1 kgf/cm2 to 6 kgf/cm2. Here, compression displacement follows a non linear curve and that bending frequency rises with pressure rises. Therefore, we conclude that the surface pressure of the stack is under critical pressure within the range of 1 6 kgf/cm2 and the cells do not connect rigidly. Consequently, we decided that the contact surfaces of the cells are connected by equivalent springs on the model. 3.2. Modeling of 1kW stack A finite element model of the 1-kW stack was constructed in such a way that the modal properties of the experimental and analytical values were identical. For the modeling, cells, end plates, and parts for pressure addition were all constructed independently. The numbers of node points and elements are 8838 and 5346, respectively. Cell parts and other parts used a hexahedral mesh and a tetrahedral mesh, respectively. The contact state of cells is expressed by connecting a pair of node points on every laminated cell surface by equivalent normal and translational springs. These equivalent spring stiffnesses are determined by parameter analysis in such a way that the natural frequencies (1st ­ 4th) of the experimental and analytical values were identical. The contact part between end plates and pressure plates is high-pressure zone due to line contact, so this part is expressed by the merger of the paired nodes on both contacting parts. General-purpose simulation software I-DEAS11 was used for modeling. The constructed finite element model of the is shown in Fig. 9.

Fig.9 FE model of 1kW stack 3.3. Results of Eigen Value Analysis Eigen value analysis of the 1-kW stack model was conducted using the general-purpose structural analysis program NX NASTRAN. Natural modes of the 1-kW stack acquired by calculation are shown in Fig. 10. In addition, Table 1 compares the analytical natural frequencies with the experimental values. These results shows that the natural frequencies and natural modes closely correspond.

(a) Mode 1 164.6[Hz]

(b) Mode 2 240.5[Hz]

(c)Mode 3 322.9[Hz] Fig.10 Natural modes of 1kW stack

(d) Mode 4 336.5[Hz]

Table.1 Comparison of analytical natural frequencies with experimental value Mode No. 1 2 3 4 Experiment Freq.[Hz] 168.9 240.4 316.5 336.4 Analysis Freq.[Hz] 164.6 240.5 322.9 336.5 Error [%] 2.5 0.04 2.0 0.03 Mode Shape Vertical-Bending Parallel-Swing Lateral-Bending Torsion

3.4. Prediction of 10-kW Stack Modal Parameter The 10-kW stack model was constructed by using the contact stiffness identified on the 1-kW stack model. Contact stiffness on the unit contact area is identical to that of the 1-kW stack model because pressure addition and the contact state of the 10-kW stack correspond to those of the 1-kW. Figure 11 shows natural modes of the 10-kW stack acquired by eigen value analysis. We predict that 10-kW stack has its first bending mode at 83.3 Hz and second bending mode at 86.4 Hz. These results show that the10-kW stack doesn't resonate under earthquake excitation.

(a)Mode 1 83.3[Hz] Vertical-Bending

(b) Mode 2 86.4[Hz] Lateral-Bending

Fig.11 Analytical Mode Shape of 10kW Stack

4. CONCLUSIONS This research focused on the seismic resistance of laminated fuel cell stack. First a vibration test of a 1-kW stack was conducted. Then modal properties of a 10-kW stack were predicted by finite element analysis. As a result, the following conclusions were obtained: 1. The first mode of a 1-kW stack is at approximately 160 Hz, and seismic resistance was established by a pressure leak test under vibration. A finite element model of 10-kW stack was constructed using contact stiffness identified on the 1-kW stack model. As a result of eigen value analysis, we predicted that a 10-kW stack has its first bending mode at approximately 80[Hz].


Acknowledgements This work was supported by Energy Device Technology Department, Advanced Technology R&D Center, Mitsubishi Electric Corporation, Japan. We would like to acknowledge them for research cooperation.

REFERENCES [1] Y.Gocho, S.Watanabe, H.Kimura, T.Nasuda, Evaluation of Earthquake Resistance for 200kW On-site Phosphoric Acid Fuel Cell Stack Assembly, Proceedings of Annual Conference of Power & Energy Society of IEEJ, Vol. 9 No. 2, pp112-113, (1998) B.Peeters, G.Lowet, H.Van Der Auweraer, J.Leuridan, A New Procedure for Modal Parameter Estimation, Sound and Vibration, Vol. 38, No. 1, pp24-29, (2004) JIS C0055, Environmental Testing-Part3:Guidance Seismic Test Method for Equipments, (2000) H.Yamashita, T.Nakada, Powerplant Vibration Analysis on Considering the Compornent Joint Characteristics, Proceedings of 72th Annual Conference of JSME, vol. 3, pp416-418, (1994) K.Semba, K.Takahashi, Y.Sato, Powerplant Resonance Estimation by Finite Element Analysis, HONDA R&D Technical Review, Vol. 1, pp30-37, (1989) L.Shuo-jen, H. Chen-de, H.Ching-han, Analyses of the fuel cell stack assembly pressure, Journal of Power Sources, Vol. 145,No. 2, pp353-361 (2005)

[2] [3] [4] [5] [6]


Vibration Analysis for Polymer Electrolyte Fuel Cell Stack Assembly

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