1. Effect Of Vibration On The Performance Of
PEMFC
J AY D E E P D E S H PA N D E * , TA P O B R ATA D E Y ^ , P. C . G H O S H ^
* - P U N E V I D YA RT H I G R I H A’ S C O L L E G E O F E N G I N E E R I N G A N D
T E C H N O L O G Y, P U N E
^ - D E PA RT M E N T O F E N E R G Y S C I E N C E A N D E N G I N E E R I N G , I I T B O M B AY

2. Agenda
1.
Problem Definition
2.
Modelling
3.
Setup
4.
Results and Discussion
5.
Conclusion
6.
Future Scope

3. Problem Definition
Vibrating body experiences two forces which reduce the vibrations,
spring force and damping force given by;
The force acting body is given by,
The external excitation force is give by,
Fig. 1
External excitation force produces the case of forced vibrations

4. Problem Definition
Thus, by D’Alembert's principle, the motion of equation is given by,
On solving the equation for the boundary conditions, the
steady state solution is obtained as,
The steady state amplitude of vibration is given by,
Fig. 1

5. Problem Definition
ANSYS solves the equation in the matrix form by finite element discretization
For damping ratio ( ratio of damping coefficient to critical damping coefficient)
Vibrations are transferred from one component to other by the transmissibility relation;

6. Modelling
• The model is created in
SOLIDWORKS
• Endplates x2 – SS316
• Current Collectors x2 – Copper
• Graphite Plates x2 – Graphite
• Gaskets x2 – PTFE
• Membrane x1 – Nafion®
• GDL x2 – Carbon Paper
Fig. 2

7. Setup
Initially a modal analysis of the entire cell is performed to evaluate the natural frequencies
The bottom plate fixed and all modes are scanned up to 1KHz frequency
Using the obtained frequencies the model is exported for harmonic analysis with acceleration at
4g for 1 hour
The bottom plate is fixed
Deformations are noted
Final step of the analysis takes into account the loosening of bolts due to vibrations
Bottom plate is fixed for structural analysis
Change in bolting torques is applied to bolts and changes in contact pressure profiles is plotted

8. Results and Discussions
Modal Analysis:
Fig. 3
Zones with maximum modal displacements are indicated in the Fig. 3

9. Results and Discussions
Frequencies
Mode Frequency [Hz]
1
474.71
2
476.48
3
476.88
4
793.39
5
796.01
6
839.25
7
844.47
Table. 1

10. Results and Discussion
Fig. 4

11. Results and Discussion
Estimation of Hydrogen Leakage Rate
Operation at natural frequencies will result into large displacements at the zones shown in Fig. 3
Thus ,
From harmonic analysis displacement at resonance point=1.0338e-08 m
Area of the micro-pore= max. Displacement * width of the micro-pore
Area of the micro-pore = (1.0338e-08 * 0.003)
A= 3.1014e-11 m2

12. Results and Discussion
Estimation of Hydrogen Leakage Rate
Now considering the Hydrogen side pressure 2 bar and atmospheric pressure 1 bar, applying basic Bernoulli’s theo
rem we get,
(P1 / dg) = (P2 / dg) + (V2 / 2g);
(Neglecting change in Enthalpy, Internal Energy of Hydrogen)
Where,
P1 - Pressure at Hydrogen side
P2- Atmospheric Pressure
d- Density of Hydrogen = 0.08988 g/L
g- Acceleration due to gravity
V- Velocity of leaking Hydrogen
On substituting the values and solving we get, V= 1502.853 m/s
Thus, leakage Hydrogen flow rate = A*V= 0.16778 L/ hr

13. Conclusion
The paper outlines natural frequencies which should be avoided during the operation of fuel
cells
It also points out reduction in the contact pressure due to reduction in the bolting torque under
vibration. This will directly reflect on the performance of the fuel cell through increases losses
and leakages.
Study calculates the hydrogen leakage rate after vibration. Although the estimation is crude, it
gives some idea on the volume loss of hydrogen after and during the operation under vibrating
conditions.

14. Future Scope
Detailed hydrogen leakage estimation by consideration thermodynamic parameters
Safety framework for fuel cell design for mobile applications for safer operation in vibration
environment

15. References
References
1.
Boscolo, M. "Analytical Solution for Free Vibration Analysis of Composite Plates with Layer-wise Displacement Assumption." Composite Structu
res, 2013: 493-510.
2.
H.E.U. Ahmed, R. Banan, J.W.Yu, A.Bazylak. "Free Vibration Analysis of a Polymer Electrolye Membrane Fuel Cell." Jr. Power Sources, 2011: 5520
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3.
J. Tseng, D. R. Hsaio, B. W. Huang. "Dynamic Analysis of the Proton Exchange Membrane Fuel Cell." Applied Mechanics and Materials 284-287 (
2013): 718-722.
4.
M.K.Rao, Y.M. Desai. "Analytical Solution of Laminated and Sandwich Plates Using Mixed Theory." Composite Structures, 2004: 361-373.
5.
N. Rajalakshmi, S. Pandian, K.S. Dathathreyan. "Vibration Tests on a PEM Fuel Cell Stack Usable in Transport Application ." Intl. Jr. Hydrogen Ene
rgy, 2009: 3383-3387.
6.
T. Kouzomi, N. Tsujichi, S. Onho. Vibration Analysis of Polymer Eelectrolyte Stack Assembly. Kyoto: Department of Engineering, Doshisha Univer
sity, n.d.
7.
V Rouss, P. Lesage, S. Begot, D. Candusso, W. Charon, F. Harel, X. Francois, V. Selinger, C. Schilo, S. Yen-Andersen. "Mechanical Behavior of a Fue
l Cell Stack Under Vibrating Conditions Linked to Aircraft Applications Part I: Experimental." Intl. Jr. Hydrogen Energy, 2008: 6755-6765.
8.
V. Rouss, D. Candusso, W. Charon. "Mechanical Behavior of Fuel Cell Stack Under Vibrating Conditions Linked to Aircraft Applications part II:
Three-Dimensional Modelling." Intl. Jr. Hydrogen Energy , 2008: 6281-628

16. Transmissibility Ratio