JP2014206395A - Method of measuring deflection of diffusion layer and surface pressure value - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technology of accurately calculating the amount of deflection of a diffusion layer and a surface pressure value.SOLUTION: A method of measuring the amount of deflection of a diffusion layer of a fuel cell includes the steps of: (a) setting a stiffness matrix of the diffusion layer; (b) calculating strain; (c) calculating strain to be obtained when tensile load is applied to the diffusion layer; (d) comparing calculation results of the steps (b) and (c) with results of a compression test and a tensile test of the diffusion layer, to optimize the stiffness matrix; (e) calculating the amounts of deflection by means of a finite-element method, by use of the stiffness matrix optimized in the step (d), according to a preset experiment schedule; (f) forming a response curved surface on the basis of the amounts of deflection calculated in the step (e); and (g) creating a calculation formula for calculating the amount of deflection on the basis of the response curved surface.

Description

  The present invention relates to a diffusion layer of a fuel cell.

  The fuel cell includes a membrane electrode assembly and a gas diffusion layer (also simply referred to as “diffusion layer”) for diffusing gas. A plurality of fuel cells are stacked, and a predetermined compressive load is applied from both sides in the stacking direction to constitute a fuel cell stack.

  Here, in order to evaluate the performance and characteristics of the fuel cell, the amount of deflection of the diffusion layer may be used (for example, Patent Document 1).

JP 2008-201005 A

  In the technique of Patent Document 1, the amount of bending of a carbon fiber sheet used for a gas diffusion electrode of a fuel cell (corresponding to a “diffusion layer” in the present specification) is obtained as the amount of bending at the time of fracture at the time of bending strength measurement. .

  However, unlike a metal material or the like, the diffusion layer has anisotropy and is a porous member (foaming material), so that the amount of deflection cannot be accurately calculated by a method of measuring the amount of deflection using bending strength. There is a case.

  As described above, a technique that can accurately calculate the amount of deflection of the diffusion layer is desired. In addition, in order to evaluate the performance and characteristics of the fuel cell, there is a demand for a technique that can accurately calculate index values representing various physical property values and characteristics of the diffusion layer instead of the deflection amount of the diffusion layer. Examples of index values representing various physical property values and characteristics include surface pressure values applied to the diffusion layer when the diffusion layer is a constituent member of the fuel cell stack. Further, in the fuel cell, it has been desired to suppress the number of parts, simplify the manufacturing process, reduce the manufacturing cost, and the like.

  SUMMARY An advantage of some aspects of the invention is to solve at least a part of the problems described above, and the invention can be implemented as the following forms.

(1) According to one aspect of the present invention, a method for measuring the amount of deflection of a diffusion layer is provided. In this method, (a) a step of setting a rigidity matrix of the diffusion layer, and (b) a strain when a compressive load is applied to the diffusion layer is calculated using the rigidity matrix set in step (a). (C) a step of calculating strain when a tensile load is applied to the diffusion layer using the rigidity matrix set in step (a), (d) step (b) and step (c) ) And the results of compression test and tensile test of the diffusion layer to optimize the stiffness matrix, and (e) optimized by the step (d) according to a predetermined experimental plan Applying a plurality of the deflection amounts by applying the converted stiffness matrix to the finite element method, and (f) creating a response surface based on the plurality of deflection amounts calculated in the step (e). , (G) Based on the serial response surface, and a step of creating a formula for calculating the deflection amount. According to the method of this embodiment, the amount of deflection can be calculated more accurately using the created calculation formula.

(2) According to another aspect of the present invention, a method for measuring a surface pressure value applied to a diffusion layer is provided. In this method, (a) a step of setting a rigidity matrix of the diffusion layer, and (b) a strain when a compressive load is applied to the diffusion layer is calculated using the rigidity matrix set in step (a). (C) a step of calculating strain when a tensile load is applied to the diffusion layer using the rigidity matrix set in step (a), (d) step (b) and step (c) ) And the results of compression test and tensile test of the diffusion layer to optimize the stiffness matrix, and (e) optimized by the step (d) according to a predetermined experimental plan A step of calculating a plurality of the surface pressure values by applying the converted stiffness matrix to a finite element method, and (f) generating a response surface based on the plurality of surface pressure values calculated in the step (e). Process (g) Based on the serial response surface, and a step of creating a formula for calculating the surface pressure value. According to the method of this embodiment, the surface pressure value can be calculated more accurately using the created calculation formula.

  The present invention can be realized in various forms, for example, a method for measuring physical property values and index values related to the diffusion layer such as the amount of deflection of the diffusion layer and the surface pressure applied to the diffusion layer, and the like. It can be realized in the form of a diffusion layer or a fuel cell designed by using the method.

It is a figure for demonstrating the deflection amount of a fuel cell. It is a creation flow of the relational expression (deflection relational expression) which calculates the amount of bending. It is a figure which shows the result of the tension calculation of a gas diffusion layer, and a tension test. It is a figure which shows the result of the compression calculation and compression test of a gas diffusion layer. It is a figure which shows the material characteristic of a gas diffusion layer. It is a figure which shows the experiment plan used by step S8. It is a figure for demonstrating the 1st application example. It is a figure utilized for a bending relational expression. It is a figure which shows the relationship between the coefficient X represented by the bending | flexion relational expression shown in FIG. 7, Young's modulus E11, and bending amount. It is the figure which showed the bending relational expression in the 2nd application example. It is a figure which shows the relationship between the coefficient X represented by the bending | flexion relational expression shown in FIG. 10, Young's modulus E11, and bending amount. It is the figure which showed the bending relational expression in the 3rd application example. It is a figure which shows the relationship between the coefficient X represented by the bending | flexion relational expression shown in FIG. 12, the Young's modulus E11, and bending amount.

Next, embodiments of the present invention will be described in the following order.
A. First Embodiment B. Variations:

A. First embodiment:
A-1. Fuel cell configuration and deflection:
FIG. 1 is a diagram for explaining a deflection amount Da of the fuel cell 10. The fuel cell 10 is configured by sandwiching the membrane electrode assembly 16 between the gas diffusion layers 14 and 15 and then sandwiching the membrane electrode assembly 16 between the anode side separator 12 and the cathode side separator 17.

  The membrane electrode assembly 16 is configured by joining an anode and a cathode as an electrode catalyst layer to both surfaces of an electrolyte membrane having proton conductivity. The anode and the cathode have a configuration in which carbon carrying a catalyst such as platinum or a platinum alloy is held by an ionomer (electrolyte resin).

  The gas diffusion layers 14 and 15 have anisotropy and are formed of a porous member (foaming material). The gas diffusion layers 14 and 15 are formed of a conductive member having gas permeability, for example, a carbon porous body such as carbon paper or carbon cloth, or a foam metal, and diffuse and transmit gas to the corresponding electrode.

  The anode-side separator 12 is disposed on the anode side of the membrane electrode assembly 16 and includes an in-cell fuel gas flow channel 13 for flowing a fuel gas containing hydrogen. The cathode side separator 17 is disposed on the cathode side of the membrane electrode assembly 16 and includes an in-cell oxidizing gas flow path 18 through which an oxidizing gas containing oxygen (air in the present embodiment) flows. The separators 12 and 17 are made of a gas-impermeable conductive member, for example, a dense carbon made of gas compressed by gas compression, baked carbon, or stainless steel.

  A plurality of fuel cells 10 are stacked in the stacking direction, and a predetermined compressive load F1 is applied from both sides in the stacking direction to form a fuel cell stack. When the compression load F1 is applied to the fuel cell 10, the gas diffusion layers 14 and 15 are compressed in the stacking direction by the separators 12 and 17. As a result, a part of the gas diffusion layers 14 and 15 bite into the in-cell fuel gas channel 13 and the in-cell oxidizing gas channel 18 and the gas diffusion layers 14 and 15 are deformed to be bent. This amount of biting is referred to as “bending amount Da”.

A-2. Relational expression creation flow:
FIG. 2 is a flow of creating a relational expression (deflection relational expression) for calculating the deflection amount Da. FIG. 3 is a diagram showing the results of the tensile calculation and the tensile test of the gas diffusion layers 14 and 15. FIG. 4 is a diagram showing the compression calculation and compression test results of the gas diffusion layers 14 and 15. FIG. 5 is a diagram showing material characteristics of the gas diffusion layers 14 and 15. FIG. 6 is a diagram showing an experimental design used in step S8. Here, the tensile calculation calculates the elongation of the diffusion layers 14 and 15 when stress is applied in a direction orthogonal to the thickness direction of the gas diffusion layers 14 and 15. In the compression calculation, the thickness of the diffusion layers 14 and 15 when a compression load (surface pressure) is applied in the thickness direction of the diffusion layers 14 and 15 is calculated. A method of creating a relational expression for calculating the deflection amount Da with high accuracy will be described with reference to FIGS.

  As shown in FIG. 2, the stiffness matrix of the diffusion layers 14 and 15 is optimized by performing the steps S2 to S6. Specifically, by performing steps S2 to S5, among the nine variables of the anisotropic elastic properties of the diffusion layers 14 and 15, the four variables E11, E22, G12, and ν13 and the foaming elastic characteristics are expressed by a cubic function. A total of seven variables of three variables, which are coefficients for definition, are optimized. That is, by performing the processes of steps S2 to S6, the above seven variables that best represent the characteristics of the diffusion layers 14 and 15 are specified.

・ Three variables related to foam elastic properties:
The cubic function of the foam elastic property is represented by the following formula (1).
(Formula 1)
σ = X × (A1 × ε ³ −A2 × ε ² + A3 × ε) (1)
Here, σ is stress, X is a coefficient, A1 to A3 are variables, and ε is strain.

  In the above equation (1), X × A1, X × A2, and X × A3 are three variables. Here, in the above formula (1), X is 1.0 when the diffusion layers 14 and 15 having standard foaming elastic characteristics as a reference are used. That is, the coefficient X of the diffusion layers 14 and 15 used to create the relational expression for calculating the deflection amount Da is set to 1.0. The coefficient X has different values due to the different foaming elastic characteristics of the diffusion layers 14 and 15. For example, the value is smaller than 1.0 or larger than 1.0 depending on the degree of distortion.

  First, the above seven variables of the stiffness matrix of the diffusion layers 14 and 16 are set (step S2). Next, tensile calculation and compression calculation are performed (steps S3 and S4). Specifically, in step S3, the strain of the diffusion layers 14 and 15 when a tensile load is applied to the diffusion layers 14 and 15 is calculated using the stiffness matrix set in step S2. In step S4, the strain of the diffusion layers 14 and 15 when a compressive load is applied to the diffusion layers 14 and 15 is calculated using the stiffness matrix set in step S2.

  Next, the calculation result obtained in steps S3 and S4 is compared with the test result obtained by actually performing the tensile test and the compression test using the diffusion layers 14 and 15, and the difference between the test result and the calculation result is sufficiently small. Is determined (step S5). For example, whether the difference between the calculation result of the tensile calculation and the test result of the tensile test is a predetermined value (for example, 5%) or less, and the difference between the calculation result of the compression calculation and the test result of the compression test is It is determined whether or not it is a predetermined value (for example, 5%) or less. For example, a graph plotting the results of the tensile calculation and the tensile test as shown in FIG. 3 and a graph plotting the compression calculation and the results of the compression test as shown in FIG. 4 are created. It is determined by comparing.

  If the difference between the test result and the calculation result is larger than the predetermined value (step S5: NO), the seven variables of the stiffness matrix are set again in step S2. On the other hand, when the difference between the test result and the calculation result is equal to or less than the predetermined value (step S5: YES), the seven variables that satisfy the condition of step S5 are specified as the seven variables that most representatively represent the characteristics of the diffusion layers 14 and 15. (Step S6).

  FIG. 5 shows the anisotropic elastic properties specified in step S6. Of the anisotropic elastic properties shown in FIG. 5, E11, E22, and E33 represent Young's moduli in three directions orthogonal to each other. E22 is the Young's modulus in the thickness direction (Y-axis direction) of the diffusion layers 14 and 15. Of the anisotropic elastic properties, ν12, ν13, and ν23 represent Poisson's ratios in three directions orthogonal to each other. ν13 is the Poisson's ratio in the thickness direction of the diffusion layers 14 and 15. Of the anisotropic elastic properties, G12, G13, and G23 represent shear rigidity (rigidity) in three directions orthogonal to each other. G13 is the Poisson's ratio in the thickness direction of the diffusion layers 14 and 15. FIG. 5 shows the relationship between stress and strain calculated by applying Expression (1) expressed using optimized three variables.

  As shown in FIG. 2, after step S6, a plurality of deflection amounts Da by a finite element method (FEM) are calculated using a specified (optimized) stiffness matrix according to a predetermined experimental plan (step S6). S8). Specifically, as shown in FIG. 6, the four variables of the anisotropic elastic properties specified in step S6 and the coefficient X of the cubic equation (the above equation (1)) simulating foaming elastic properties are set at three levels. By shaking as described above, the deflection amount Da by the finite element method is calculated. For example, in this embodiment, as shown in FIG. 6, an experimental design table in which each factor is shaken by five levels is used. In the experimental design table shown in FIG. 6, E11 (a) to E11 (e) are set to different values, E22 (a) to E22 (e) are set to different values, and G12 (a) to Different values are set for G12 (e), different values are set for ν13 (a) to ν13 (e), and different values are set for X (a) to X (e).

Next, as shown in FIG. 1-No. A response curved surface is created based on the deflection amount Da calculated for each of 43 (step S10). Specifically, a response surface representing a deflection amount Da with respect to a parameter (E11, X, X ² , Co in this embodiment) generated based on the elements of the stiffness matrix is created. Next, “a”, “b”, “c”, and “Co” in Expression (2) are determined so that the deflection relational expression of Expression (2) below most represents the response surface created in Step S10. (Step S12). In the present embodiment, the deflection relational expression is approximated by a function of four terms. As the experimental design method, any one of a central composite design, a D optimal design, an orthogonal table, and the like can be used. In the present embodiment, the central composite design is used as the experiment design method.

(Formula 2)
Da = a × E11 + b × X + c × X ² + Co (2)
Here, Da is the amount of deflection, a, b, and c are coefficients, respectively, and Co is a constant term.

  In step S12, the coefficients a, b, c and the constant term Co are determined, so that a deflection relational expression is created.

A-3. effect:
In the above embodiment, the four variables of anisotropic elastic properties and the three variables as coefficients for defining the foam elastic properties by a cubic function are optimized, and the optimized variables are shaken by three or more levels according to the experimental plan. A response curved surface is created (steps S2 to S10). Then, a bending relational expression is created based on the response curved surface (step S12). Thereby, the bending amount Da of the diffusion layers 14 and 15 can be calculated more accurately using the created bending relational expression.

A-4. Examples of applications using flexural relations:
An application example using the bending relational expression created by obtaining the flow of steps S2 to S12 will be described below. As shown below, by using a deflection relational expression, it is possible to calculate the deflection amount Da for each characteristic of the diffusion layers 14 and 15 (coefficient X serving as an index of foaming elastic characteristics and Young's modulus). Thereby, the diffusion layers 14 and 15 in which the deflection amount Da is suppressed to a predetermined value or less can be easily designed.

A-4-1. First application example:
FIG. 7 is a diagram for explaining the first application example. FIG. 8 is a diagram used for a bending relational expression. Here, the bending relational expression shown in FIG. 7 is a relational expression when the number of terms of the polynomial is four. That is, the bending relational expression shown in FIG. 7 is the same as the expression (2). FIG. 7 also shows a table in which the coefficients a, b, and c and the numerical values substituted into the constant term Co are described.

  FIG. 8 shows a change in thickness when a predetermined surface pressure is applied to the thickness direction of the diffusion layers 14 and 15. The reference samples shown in FIG. 8 are the diffusion layers 14 and 15 used when determining the bending relational expression using the flow shown in FIG. The actual sample is a sample for actually calculating the deflection amount Da. The relationship between the surface pressure and the thickness shown in FIG. 8 is obtained for the reference sample and the actual sample, and how many times (X times) the actual sample is the reference sample is calculated. That is, when the reference sample and the actual sample are represented by the above equation (1), the coefficient X in the actual sample becomes the coefficient X of the relational expression shown in FIG.

  FIG. 9 is a diagram showing the relationship between the coefficient X and Young's modulus E11 represented by the deflection relational expression shown in FIG. 7 and the deflection amount Da. Here, in FIG. 9, the deflection amount Da is represented by the type of hatching. Specifically, a different hatching is applied each time the deflection amount Da changes, and the deflection amount Da decreases each time it moves from the hatching in the lower left region to the hatching in the upper right region in FIG. By obtaining the deflection relational expression, as shown in FIG. 9, the relationship between the coefficient X, the Young's modulus E11, and the deflection amount Da can be easily calculated.

A-4-2. Second application example:
FIG. 10 is a diagram showing a bending relational expression in the second application example. Here, FIG. 10 shows a relational expression when the number of terms of the bending relational expression is eight. FIG. 10 also shows the coefficients (a1 to g1) of each term and the values of constant terms. The deflection relational expression shown in FIG. 10 is created by approximating the response surface with a function of 8 terms (step S12 in FIG. 2). By increasing the number of terms in the bending relational expression, it is possible to create a bending relational expression for calculating the bending amount Da more accurately. It should be noted that the number of terms in the deflection relational expression is preferably 5-8 terms.

  FIG. 11 is a diagram showing the relationship between the coefficient X and Young's modulus E11 represented by the deflection relational expression shown in FIG. 10 and the deflection amount Da. Here, in FIG. 11, similarly to FIG. 9, the deflection amount Da is represented by the type of hatching. Specifically, a different hatching is applied every time the deflection amount Da changes, and the deflection amount Da decreases each time it moves from the hatching in the lower left region to the hatching in the upper right region in FIG. By using the diagram shown in FIG. 11, for example, in which range of diffusion layers 14 and 15 the coefficient X and the Young's modulus E11 can determine whether the deflection amount Da can be a predetermined value or less. For example, when it is desired to suppress the deflection amount Da of the diffusion layers 14 and 15 to 70 μm or less, the diffusion layers 14 and 15 that take the coefficient X and the Young's modulus E11 on the side indicated by the arrow from the boundary shown in FIG. good.

A-4-3. Third application example:
FIG. 12 is a diagram showing a bending relational expression in the third application example. Here, FIG. 12 shows a relational expression when the number of terms in the bending relational expression shown in FIG. FIG. 12 also shows the coefficients (a2 to j2) of each term and the values of constant terms. The bending relational expression shown in FIG. 12 is created by approximating the response curved surface with a function of 11 terms (step S12 in FIG. 2).

  FIG. 13 is a diagram showing the relationship between the coefficient X and Young's modulus E11 represented by the deflection relational expression shown in FIG. 12, and the amount of deflection. Here, in FIG. 13, similarly to FIG. 9, the deflection amount Da is represented by the type of hatching. Specifically, a different hatching is applied every time the deflection amount Da changes, and the deflection amount Da decreases each time it moves from the hatching in the lower left region to the hatching in the upper right region in FIG. By using the diagram shown in FIG. 13, for example, in which range of diffusion layers 14 and 15 the coefficient X and the Young's modulus E11 can determine easily whether the deflection amount Da can be a predetermined value or less. For example, when it is desired to suppress the deflection amount Da of the diffusion layers 14 and 15 to 70 μm or less, the diffusion layers 14 and 15 that take the coefficient X and the Young's modulus E11 on the side indicated by the arrow from the boundary shown in FIG. good.

B. Variations:
B-1. First modification:
In the above embodiment, the relational expression for obtaining the deflection amount Da was created using the flow shown in FIG. 2, but the surface pressure when the diffusion layers 14 and 15 are assembled to the fuel cell stack using the flow shown in FIG. You may create the relational expression which calculates | requires a value. When creating the relational expression for obtaining the surface pressure value, the surface pressure value is calculated instead of calculating the deflection amount in step S8 shown in FIG. Then, based on the response curved surface created in step S10, a relational expression of surface pressure values is created in step S12. In this manner, by creating a relational expression for calculating the surface pressure value applied to the diffusion layers 14 and 15 according to the flow of FIG. 2, the surface pressure value can be calculated more accurately using the created calculation formula. .

  The present invention is not limited to the above-described embodiments, examples, and modifications, and can be realized with various configurations without departing from the spirit thereof. For example, the technical features in the embodiments, examples, and modifications corresponding to the technical features in each embodiment described in the summary section of the invention are to solve some or all of the above-described problems, or In order to achieve part or all of the above effects, replacement or combination can be performed as appropriate. Further, if the technical feature is not described as essential in the present specification, it can be deleted as appropriate.

DESCRIPTION OF SYMBOLS 10 ... Fuel cell 12 ... Anode side separator 13 ... Intra-cell fuel gas flow path 14, 15 ... Gas diffusion layer 16 ... Membrane electrode assembly 17 ... Cathode side separator 18 ... In-cell oxidizing gas flow path

Claims (2)

A method for measuring the amount of deflection of a diffusion layer of a fuel cell,
(A) setting a stiffness matrix of the diffusion layer;
(B) using the rigidity matrix set in step (a), calculating a strain when a compressive load is applied to the diffusion layer;
(C) using the rigidity matrix set in step (a), calculating a strain when a tensile load is applied to the diffusion layer;
(D) comparing the calculation results of step (b) and step (c) with the test results of the compression test and tensile test of the diffusion layer to optimize the stiffness matrix;
(E) calculating a plurality of deflection amounts by the finite element method using the stiffness matrix optimized in the step (d) according to a predetermined experimental plan;
(F) creating a response surface representing the amount of deflection for a parameter generated based on an element of the stiffness matrix based on the plurality of amounts of deflection calculated in step (e);
(G) A step of creating a calculation formula for calculating the deflection amount based on the response curved surface. A method for measuring a surface pressure value applied to a diffusion layer of a fuel cell,
(A) setting a stiffness matrix of the diffusion layer;
(B) using the rigidity matrix set in step (a), calculating a strain when a compressive load is applied to the diffusion layer;
(C) using the rigidity matrix set in step (a), calculating a strain when a tensile load is applied to the diffusion layer;
(D) comparing the calculation results of step (b) and step (c) with the test results of the compression test and tensile test of the diffusion layer to optimize the stiffness matrix;
(E) calculating a plurality of the surface pressure values by the finite element method using the stiffness matrix optimized in the step (d) according to a predetermined experimental plan;
(F) creating a response surface representing the amount of deflection with respect to a parameter generated based on an element of the stiffness matrix based on the plurality of surface pressure values calculated in the step (e);
(G) A step of creating a calculation formula for calculating the surface pressure value based on the response curved surface.

Images