臺灣博碩士論文加值系統

雙極板是質子交換膜燃料電池中關鍵組件之一，但傳統石墨雙極板成本昂貴且需要幾毫米厚度，所以金屬雙極板因而產生。本文使用有限元素分析程式模擬不銹鋼雙極板棋盤式微流道冲壓製程，材料為長與寬皆為15mm，厚度0.05mm 的不銹鋼薄板(SUS304)，以剛性沖頭對材料做微沖壓製程，在雙極板上沖出棋盤式6*6 顆圓形凸緣流道，流道寬度和深度分別為0.75mm 和0.5mm，探討冲壓製程最佳成形性及微觀尺寸效應影響。本文有限元素法是運用Prandtl-Reuss 之塑流法則，結合有限元素變形理論與updated Lagrangian formulation(ULF)觀念，建立一庫侖摩擦法則之增量型彈塑性變形有限元素分析程式以模擬金屬雙極板微流道之成形製程。本論文中亦運用選擇性減化積分法SRI (slective reduced integration)與四節點四
邊形退化殼元素所推導之形狀函數至剛性矩陣中。在處理彈塑性狀態及模具與板料間的接觸問題，則採用廣義的rmin方式處理，此方式可有效處理彈塑性狀態的計算上的問題，並且延伸到處理模具與板料之間的接觸問題。
本文研究重點在於藉由模擬與分析微冲壓成形製程之全部變形履歷資料、冲頭負荷與冲程之關係、應力與應變分布、厚度分布、截面深度及截面厚度，並選用SUS304 薄板進行微冲壓成形之實驗，與模擬結果作比對以驗證本分析程式之可靠性。另外，使用不同參數有：摩擦係數、模具倒角半徑、板料厚度、模具角度與柱體形狀 (梯柱、方柱、圓柱以及錐柱) 等做變化進行微冲壓製程分析。不同柱體形狀的成形性，經分析後得到梯柱具有較佳的成形性，其次是圓錐柱；在冲程方面，除了0.5mm 以外也實際做過其他冲程之模擬與實驗，在模擬時發現冲程只要高於0.5mm 就會有裂痕之情形，此情形與實際冲壓得出之成品相符合；越接近板材中央處所量測出的流道深度會越深，越外圍的流道深度受到板材翹曲的影響，流道深度會越淺。本文建立有限元素分析模式，亦比較傳統巨觀材料模型與比例因子修正後的材料模型，結果指出修正後的材料模型較能符合實際成形情況，該比例因子修正法亦可運用於SUS304 不銹鋼微觀任意厚度的修正，以省略繁複的拉伸試驗。
本論文所提出之方法能夠有效地模擬不銹鋼金屬雙極板之微流道冲壓製程。因此，可廣泛應用在各種流道形狀的冲壓製程上，建立完善分析數據及預估微冲壓過程中產生的各式問題，有利降低試誤損失及增進生產速率，進而使得燃料電池可朝向更精確微小化之發展。

The bipolar plate is one of key components of proton exchange membrane fuel cell.But the cost of using the graphite bipolar plate is more expensive and the thickness
needs to be increased a few millimeters. These reasons bring metal bipolar plate come into being. This paper is discussed the influence between the stamping process
formability and micro-size effect by using the finite element analysis system ,simulating stainless steel bipolar plate pin-type microfluidic stamping process. The length and
width of materials are both 15mm, stainless steel sheet (SUS304) 0.05mm in thickness.By micro-stamping process with the rigid punch which is punched pin-type channel as 6*6 circular convex, the width and depth of fluid channel is 0.75mm and 0.5mm. The finite element method in this paper is combined the plastic fluidic rule of Prandtl-Reuss with finite element deformed theory and updated Lagrangian formulation (ULF concept) which builds up the Coulomb law of friction by using the increasing volume-type and large elasto-plastic deformed finite element analysis system to simulate the process of forming metal bipolar board micro-fluid channel. It’s also used the selective reduced
integration method of SRI (selective reduced integration) and four-node quadrilateral degenerated shell element derived shape function into the stiffness matrix. In dealing
with the contact problem between the status of elastic plastic, mold and the sheet metal by adopting the board rmin way which not only could be effectively solved the
calculating problem of elasto-plastic state but extended to contact problem between processing mold and the sheet metal.
The main point of the research in this paper would be emphasized that proceeding the micro-punching experiment by selecting SUS304 stainless steel, simulating and analyzing the entire deformed data of micro-punching forming process, the relation between punch load and stroke, the distribution of stress and strain, the distribution of
thickness, cross-section depth and section thickness which test and verify the validity of this formula. So far, proceeding the micro-forming process with the different parameter from the variation of friction coeifficent, chamfering mold radius, sheet thickness, the angle of mold and the shape of prism(ladder prism, Rectangular prism, cylinder and Pyramid...etc.) Through analyzing the formability of the different shape of prism finally
be concluded the better formability in ladder prism, Pyramid is in second. While forming process, we also proceeded and simulated the experiment using other depth, not only with 0.5mm, but we found that there would have cracks if the depth is deeper than 0.5mm. The depth of fluid channel which is closer to the central of the plate would be deeper and deeper, on the other hand, the fluid channel of the outer plate would be swallow due to warped plate. In this paper, it is to establish finite element analysis model and to compare the model between the traditional material and scale-factor material. The results indicate that the modified material model is closer to real forming condition. This ratio correction could be also adopted SUS304 stainless steel in any micro-thickness to skip the complicated tensile experiment.
The methods which are proposed to in this paper could be effectively simulated stainless steel bipolar plate of the micro-stamping process fluid. Therefore, it could be
adopted widely in all kinds of channel shape for stamping process, established the completed analysis data, improved all kinds of problems by forecasting the process of
micro-punching in order to lower down the missing of test and increase the production efficiency. Furthermore, fuel cell could be moved forward on more accurate miniaturized development.

致 謝 --------------------------------------------------- I
中 文 摘 要 --------------------------------------------- II
英 文 摘 要 --------------------------------------------- IV
目 錄 -------------------------------------------------- VII
表 目 錄 ------------------------------------------------- X
圖 目 錄 ------------------------------------------------- XI
符 號 說 明 --------------------------------------------- XIV
第 一 章 緒論--------------------------------------------- 1
1.1 前言------------------------------------------------- 1
1.2 研究動機---------------------------------------------- 2
1.3 研究方法---------------------------------------------- 4
1.4 燃料電池簡介------------------------------------------ 5
1.5 文獻回顧--------------------------------------------- 12
1.6 論文架構--------------------------------------------- 21
第 二 章 基礎理論----------------------------------------- 24
2.1 基本假設--------------------------------------------- 24
2.2 有限變形之應力與應力率--------------------------------- 23
2.3 有限變形之應變與應變率--------------------------------- 29
2.4 有限變形之update Lagrangian formulation-------------- 30
2.5 材料之彈塑性構成關係式-------------------------------- 33
第 三 章 有限元素分析理論--------------------------------- 38
3.1 剛性統制方程式--------------------------------------- 38
3.2 虛功原理之離散化---------------------------------------40
3.3 摩擦處理--------------------------------------------- 41
3.4 三維曲度修正方程式-------------------------------------45
3.5 退化殼元素Degenerated Shell Element-------------------47
3.6 不同積分法則推導退化殼元素之剛性矩陣--------------------- 49
3.7 除荷之設定---------------------------------------------51
3.8 靜態顯函Static Explicit--------------------------------51
3.9 廣義min r 法之增量步驟的計算--------------------------- 52
第 四 章 棋盤式微流道雙極板沖壓實驗與數值分析----------------- 56
4.1 棋盤式雙極板微流道沖壓實驗與模擬之簡介------------------ 56
4.2 研究步驟--------------------------------------------- 58
4.3 實驗設備與微沖壓模具建構------------------------------- 59
4.3.1 實驗設備------------------------------------------- 59
4.3.2 微沖壓模具建構-------------------------------------- 62
4.4 胚料拉伸試驗------------------------------------------ 64
4.4.1 拉伸試驗------------------------------------------- 64
4.4.2 試驗結果------------------------------------------- 65
4.5 比例因子修正之微觀彈塑性材料模型------------------------ 66
4.6 材料參數--------------------------------------------- 69
4.7 不同冲程實驗成品比較----------------------------------- 71
4.8 棋盤式雙極板微流道沖壓製程之數值分析--------------------- 73
4.8.1 有限元素網格化處理----------------------------------- 73
4.8.2 邊界條件-------------------------------------------- 75
4.8.3 彈塑性與接觸問題之處理------------------------------- 75
4.8.4 除荷處理-------------------------------------------- 76
4.9 不銹鋼雙極板微流道沖壓實驗與模擬結果之分析------------ 76
4.10 棋盤式微流道成品金相實驗分析-------------------------- 84
第 五 章 棋盤式微流道雙極板冲壓製程參數分析------------------- 87
5.1 摩擦係數對沖壓金屬雙極板影響---------------------------- 87
5.1.1 變化摩擦係數對方柱模擬分析---------------------------- 87
5.1.2 變化摩擦係數與圓柱模擬分析---------------------------- 88
5.2 板料厚度對沖壓金屬雙極板影響---------------------------- 94
5.2.1 變化板料厚度對方柱模擬分析---------------------------- 94
5.2.2 變化板料厚度對圓柱模擬分析---------------------------- 95
5.3 模具倒角半徑對沖壓金屬雙極板影響------------------------ 100
5.3.1 變化模具倒角半徑對方柱模擬分析----------------------- 100
5.3.2 變化模具倒角半徑對圓柱模擬分析----------------------- 101
5.4 模具角度對沖壓金屬雙極板影響--------------------------- 107
5.4.1 變化模具角度對方柱模擬分析--------------------------- 107
5.4.2 變化模具角度對圓柱模擬分析--------------------------- 108
5.5 不同柱體形狀之影響------------------------------------ 113
5.6 流道數量對於冲壓金屬雙極板之影響------------------------ 121
第 六 章 結果與討論--------------------------------------- 122
6.1 結論------------------------------------------------ 122
6.2 未來展望--------------------------------------------- 124
參 考 文 獻 --------------------------------------------- 125

[1] M. Koç and S. Mahabunphachai, “Feasibility investigations on a novel micro-manufacturing process for fabrication of fuel cell bipolar plates: Internal pressure-assisted embossing of microchannels with in-die
mechanical bonding,” J. Power Sources, Vol. 172, n. 2, pp. 725-733, 2007.
[2] S. Mahabunphachai and M. Koç, “Fabrication of micro-channel arrays on thin metallic sheet using internal fluid pressure: Investigations on size effects and development of design guidelines,” J. Power Sources, Vol.175, n. 1, pp. 363-371, 2008.
[3] T.E. Lipman, J.L. Edwards, D.M. Kammen,"Fuel cell system economics:comparing the costs of generating power with stationary and motor vehicle PEM fuel cell systems," Energy Policy, v.32, pp. 101-125,2004.
[4] T. Matsuura, M. Kato, M. Hori, “Study on metallic bipolar plate for proton exchange membrane fuel cell,” Journal of Power Sources, v.161, pp. 74-78, 2006.
[5] http://www.Ballard.com (Last retrieved on March, 2004)
[6] 林益樟，“高分子複合型燃料電池雙極板射出成型製程與流道配置對
碳纖分佈之研究”，中原大學 機械工程研究所 碩士論文，新竹。
[7] Toshihiko Kanezaki , Xianguo Li , J.J. Baschuk,“Cross-leakage flow between adjacent flow channels in PEM fuel cells”, Journal of Power Sources, v.162, pp. 415-425, 2006.
[8] Wei-Mon Yan, Ching-Hung Yang, Chyi-Yeou Soong, Falin Chen, Sheng-Chin Mei,“Experimental studies on optimal operating conditions for different flow field designs of PEM fuel cells”, Journal of Power Sources,v. 160, pp.284-292, 2006.
[9] U.Engel and R.Eckstein, “Microforming-From Basic Reaearch to Its Realization,” Journal of Materials Processing Technology, Vol.125-126, pp.35-44,2002.
[10] M.Geiger, M.Kleiner, R.Eckstein, N.Tiesler and U.Engel, “Microforming”, CIRP Annals-Manufacturing Technology, Vol.50, pp.445-462, 2001.
[11] A. Messner, U. Engel, R. Kals and F.vollertsen, “Size Effect in The FE-Simulation of Micro-Forming Processes.” Journal of Materials Processing Technology. (485): 371-376.,1994
[12] L. V. Raulea, A. M. Goijacrts, L. E. Govaert, F. P. T. Baaijens, “Size effects in the processing of thin metal sheets.”, Journal of Materials Processing Technology, (115), 44-48.,2001
[13] J. F. Michel, P. Picart, “Size effects on the constitutive behaviour for brass in sheet metal forming”, Journal of Materials Processing Technology, Vol.141, pp.439-446, 2003.
[14] Y. Saotome, K. Yasuda and H. Kaga, “Micro deep drawability of very thin sheet steels.” Journal of Materials Processing Technology. (113): 641-647, 2001
[15] F. Vollertsen, Z. Hu, H. Schulze Niehoff, C. Theiler, “State of the art in micro forming and investigations into micro deep drawing. Journal of
Materials Processing Technology. (151): 70-79, 2004
[16] N.Tiesler, “Microforming-Size Effect in Friction and Their in Fluence on Extrusion Porcesses,” Wire, Vol.52, n1 , pp.34-38 (2002).
[17] T. J. R. Hughes, “Generalization of selective integration procedures to anisotropic and nonlinear media,” International Journal of Numerical Methods in Engineering, Vol.15, pp.1413-1418, 1980
[18] A. Makinouchi and M. Kawka, “Process simulation in sheet metal forming,” Journal of Materials Processing Technology, Vol.46, pp.291-307, 1994
[19] M. Kawka and A. Makinouchi, “Shell-element Formulation in the static explicit FEM code for the simulation of sheet stamping,” Journal of Materials Processing Technology, Vol.50, pp.105-115, 1995
[20] Y. M. Huang and J. W Chen, “Influence of the die arc on formability in cylindrical cup-drawing,” Journal of Materials Processing Technology, Vol.55, pp.360-369, 1995
[21] Y. M. Huang and D. K. Leu, “Finite element analysis of contact problems for a sheet metal bending process,” Int. J. Computers and Structures, Vol.57, pp.15-27, 1996
[22] M. Kawka and A. Makinouchi, “Plastic Anisotropy in FEM Analysis Using Degenerated Solid Element,” Journal of Materials Processing Technology, Vol.60, pp.239-242, 1996
[23] D.K. Leu,“Finite-element simulation of the lateral compression of aluminium tube between rigid plates,” Int. J. of Mech. Sci., Vol.41, pp.621-638, 1999
[24] J. C. Wang, p. Hu and Y. Q. Liu, “Numerical study of the flange eaeeing of deep-drawing sheets with stronger anisotropy,” International Journal of Mechanical Sciences, Vol.43, pp.279-296, 2001
[25] Y. M. Huang and T. C. Chen, “Influence of blank profile on the V-Die bending camber process of sheet metal,” Int. J. Adv. Manuf. Technol., Vol.25, pp.668-667, 2005
[26] M. Banua, M. Takamura, T. Hama and O. Naidim, “Simulation of
springback and wrinkling in stamping of a dual phase steel rail-shaped part,” Journal of Materials Processing Technology, Vol.l73, pp.178-184 , 2006
[27] J.S. Kim,W.H.A. Pelen, K. Hemmes, R.C. Makkus,“Effect of alloying elements on the contact resistance and the passivation behaviour of stainless steels”, Corrosion Science, Vol. 44 ,pp.635-655,2002.
[28] R.J. Tian, J.C. Sun, L. Wang,“Effect of plasma nitriding on behavior of austenitic stainless steel 304L bipolar plate in proton exchange membrane fuel cell”, Journal of Power Sources,Vol. 163,pp. 719–724, 2006.
[29] Yan, W.M.; Soong, C.Y.; Chen, Falin; Chu, H.S, “Effects of flow distributor geometry and diffusion layer porosity on reactant gas transport and performance of proton exchangemembrane fuel cells”, J. Power Sources, 125, pp. 27-39, 2004
[30] He, W., Yi, J. S. and Nguyen, T. V., “Two-phase Flow Model of the Cathode of PEM Fuel Cell Using Interdigitated Flow Fields,” AICHE Journal, 46(10), pp. 2053-2064, 2000
[31] Lan Sun, Patrick H. Oosthuizen, Kim B. McAuley,“A numerical study of channel-to-channel flow cross-over through the gas diffusion layer in a PEM-fuel-cell flow system using a serpentine channel with a trapezoidal
cross-sectional shape”, International Journal of Thermal Sciences,Vol.45, pp. 1021–1026,2006.
[32] Linfa Peng , Xinmin Lai , Dong’an Liu a, Peng Hua and Jun Ni,“Flow channel shape optimum design for hydroformed metal bipolar plate in PEM fuel cell,” Journal of Power Sources, Vol.178, pp.223-230, 2008.
[33] Muammer Koc,Omer Necati Cora ,Sasawat Mahabunphachai,“Effect of manufacturing processes on formability and surface topography proton exchange membrane fuel cell metallic bipolar plates”, Journal of Power
Sources ,Vol. 195,pp. 725-733, 2007.
[34] Linfa Peng , Peng Hu, Xinmin Lai , Deqing Mei , Jun Ni ,“Investigation of micro/meso sheet soft punch stamping process – simulation and experiments”, Materials and Design ,Vol. 30,pp. 783–790,2009.
[35] Bo Zhang, Yufeng Zhang,∗, Hong He, Jianmin Li , Zhenyu Yuan, Chaoran Na, Xiaowei Liua,“Development and performance analysis of a metallic micro-direct methanol fuel cell for high-performance applications ” ,
Journal of Power Sources , Vol. 195 , pp. 7338–7348, 2010.
[36] 陳顯智，2007，金屬板材帽形引伸成形製程模擬分析，國立勤益科技
大學，碩士論文。
[37] 蔡宗勳，2006，金屬擠製製程之側向壓力分析，國立台灣科技大學，
碩士論文。
[38] 蔡毅瑋，2008，非軸對稱板材成形極限與翹曲現象之分析，國立台灣
科技大學，博士論文。
[39] R.M. McMeeking and J.R. Rice, “Finite element formulations for problems of large elastic-plastic deformation,” Int. J. Solids Structures, Vol.11, pp.601-606, 1975
[40] B.M. Irons and O.C. Zienkiewicz, “Analysis of Thick and Thin Shell Structures by Curved Finite Element,” International Journal for Numerical Methods in Engineering, Vol.2, No.3, pp.419-451, 1970
[41] T.J.R. Hughes and W.K. Liu, “Nonlinear Finite Element Analysis of Shells: Part I. Three-Dimensional Shells,” Computer Methods in Applied Mechanics and Engineering, Vol.26, No.3, pp.331-362, 1981
[42] T.J.R. Hughes, M. Cohen and M. Haroun, “Reduced and Selective Integration Techniques in the Finite Element Analysis of Plates,” Nuclear Engineering and Design, Vol.46, pp.203-222, 1978
[43] A. Makinouchi, C. Teodosiu and T. Nakagawa, “Advance in FEM Simulation and its Related Technologies in Sheet Metal Forming,” CIRPAnnals-Manufacturing Technology, Vol.47, No.2, pp.641-649, 1998
[44] Y. Yamada, N. Yoshimura and T. Sakurai, “Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method,” Int. J. of Mech. Sci., Vol.10, pp.343-354, 1968
[45] J.F.Michel and P.Picart,“ Modelling the constitutive behavior of thin metal sheet using strain gradient theory, ” Journal of Materials Processing Technology,125-126,164-169,2002
[46] 劉芳，2006，微成形製程關鍵技術研究，上海交通大學，博士後研究
論文。
[47] J.T. Oden and E.B. Pries, “Nonlocal and nonlinear friction law and variational principles for contact problems in elasticity,” Trans. ASME: Journal of Applied Mechanics, Vol.50, pp.67-76, 1983
[48] M.J. Saran and R.H. Wagoner, “A consistent implicit formulation for nonlinear finite element modeling with contact and friction. Part I. Theory,” Trans. ASME: Journal of Applied Mechanics, Vol.58, pp.499-506, 1991
[49] A. Kumar and G.reddy, “Effect of channel dimensions and shape in the flow-field distributor on the performance of polymer electrolyte membrane fuel cells,” Journal of Power Sources,Vol.113, pp.11-18, 2003