本文係探討微小圓杯引伸成形與料片最佳化之模擬分析。為了驗證有限元素方法能有效分析微小圓杯引伸成形，本文首先模擬微小圓杯引伸凸緣，並與期刊論文之實驗比較，其結果一致。且本文亦探討間隔環大小對皺折產生的影響。其次模擬微小圓杯引伸貫穿，分析成形負荷、厚度分佈及成形杯高，藉由期刊論文之實驗比較，探討模擬分析與實驗結果之差異，並藉著模擬分析來預測實驗時模具間之摩擦係數。本文亦針對影響微小成形之重要因素(模具間摩擦係數、板材異向性及尺寸效應)作一系列之探討。在尺寸效應方面，本文將料片厚度及晶粒大小導入材料應力應變構成式，並利用適當之猜測值，以期使用單一式子就能準確預測不同料片厚度及晶粒大小之應力應變曲線，結果顯示，與單純應力應變構成式相比，導入尺寸效應因子的應力應變構成式差距皆在5%以內。本文亦探討模具Dp/t=20之極限引伸率，利用成形極限圖與對應成形狀況圖可以了解破裂的原因及趨勢，結果顯示模具Dp/t=20之極限引伸率為2.3。
本文為改善金屬板材異向性所導致微小圓杯引伸貫穿之耳緣現象，採用真應變法(true strain method)結合權重因子與ANFIS來預測無耳緣之最佳化料片輪廓。並探討板材異向性值分佈不同所造成真應變法之適用性。結果顯示料片45度異向性值較小時，可適用於真應變法來取得最佳化的效果。料片45度異向性值較大時，必須使用權重因子來修飾料片外徑並製成資料庫，再採用適當之規屬函數來進行ANFIS最佳化，結果顯示有相當好的耳緣修正成效，本文之研究成果可提供微小成形及料片最佳化相關研究之參考

This thesis discusses the simulation of micro cylindrical cup drawing and blank optimization. In order to prove that finite element method can effectively analyze the micro cylindrical cup drawing. The simulation of micro cylindrical flange cup drawing is firstly performed and compared with the experimental result in the journal paper. It shows that the result is the same. Besides, wrinkle dues to the improper gap of the blank holder is also discussed. Secondly, the simulation of micro cylindrical cup drawing is performed and compared with punch load, thickness distribution and cup height in the journal paper. Friction coefficient of the tools is predicted to verify the corresponding model in the experiments. This thesis also focus on the important factors of micro forming, which are friction coefficient, anisotropy of the sheet metal and size effect. In the discussion of size effect, this thesis combines the thickness and grain size into the stress-strain relation. A set of proper values is imported to predict the stress-strain curve by only one equation. The result of original stress-strain relation and stress-strain relation combines with the thickness and grain size is compared. The result shows the difference is within 5%. In the field of forming limit, this thesis uses the model that Dp/t=20 and check the limit drawing ratio (LDR) by the forming limit diagram (FLD).With the forming limit diagram, the reason and tendency of crack is realized and the result shows the limit drawing ratio is 2.3.
    In order to reduce the earing dues to anisotropy of sheet metal in the micro cylindrical cup drawing, true strain method combines weighting factor and Adaptive-Network-based Fuzzy Inference System (ANFIS) to predict the optimum blank with no earing. The distribution of the anisotropy of the sheet metal affects the applicability of true strain method. The result shows that if the anisotropic value in the 45 degree in the rolling direction is smaller, true strain method is suitable. If the anisotropic value in the 45 degree in the rolling direction is larger, weighting factor is used to modify the blank shape and sort the result into a data base as training data for ANFIS and a proper membership function is used. It shows good result of the modification. The research of this thesis can be the reference to the relative research in micro forming and blank optimization.

目      錄	
    摘要....................................................................................................I
目錄..................................................................................................IV
圖目錄.............................................................................................VII
表目錄.............................................................................................XII
符號索引.......................................................................................XIII
第一章	緒論......................................................................................1
1.1	前言..................................................................................1
1.2	文獻回顧..........................................................................1
1.3	研究動機與目的..............................................................6
1.4	論文之構成......................................................................7
第二章	基本理論..............................................................................8
    2.1 動態顯性有限元素.............................................................8
    2.2 ..Hill板材異向性降伏理論................................................13
    2.3 殼元素理論.......................................................................17
            2.3.1共旋坐標 (co-rotational coordinates).....................17
            2.3.2速度-應變 位移關係..............................................18
            2.3.3應力合成與節點力..................................................20
        2.4 真應變法理論...................................................................21
        2.5 適應性網路模糊控制理論...............................................22
第三章 數值模擬與料片最佳化....................................................27
    3.1有限元素分析....................................................................27
        3.1.1 元素類型................................................................27
        3.1.2 接觸與負載設定....................................................28
    3.2 微小圓杯引伸凸緣...........................................................29
        3.2.1 模具幾何尺寸........................................................29
        3.2.2 料片材料參數........................................................30
        3.2.3 邊界條件與網格規劃............................................30
        3.2.4 電腦輔助分析步驟................................................34
3.3 微小圓杯引伸貫穿...........................................................34
        3.3.1 模具幾何尺寸........................................................34
        3.3.2 料片材料參數........................................................36
        3.3.3 邊界條件與網格規劃............................................36
        3.3.4 電腦輔助分析步驟................................................46
    3.4 杯高最佳化.......................................................................46
第四章 結果與討論........................................................................49
    4.1 微小圓杯引伸凸緣模擬...................................................49
        4.1.1 料片成形歷程........................................................49
        4.1.2 成形分析結果........................................................50
        4.1.3 皺折原因探討........................................................52
    4.2微小圓杯引伸貫穿模擬....................................................57
        4.2.1 成形負荷比較........................................................57
        4.2.2 厚度分佈比較........................................................57
        4.2.3 杯高比較................................................................59
            4.2.4 模具間摩擦係數對成形影響探討........................60
        4.2.5 板材異向性r值對成形影響探討.........................63
    4.3 杯高最佳化.......................................................................66
    4.4厚度與晶粒大小效應探討................................................71
        4.4.1 厚度與晶粒大小效應對流動應力影響................71
        4.4.2 成形結果探討........................................................79
    4.5 成形極限探討...................................................................84
第五章 結論與未來發展................................................................91
    5.1 結論...................................................................................91
    5.2未來展望............................................................................93
參考文獻..........................................................................................94

圖  目  錄
圖1-1 Theiler[1]傳統大型與微小凸緣圓杯實驗比較圖.................2
圖1-2 Jian Cao[5]不同晶粒大小所對應之應力應變曲線圖...........3
圖1-3 Michel[6]一定的晶粒大小下，厚度與流動應力之關係......3
圖1-4 Kals[7] 一定的晶粒大小下，厚度與流動應力之關係.......4
圖1-5早乙女[10]使用後方擠製所製成的微齒輪軸.......................5
圖2-1 殼元素座標系統[17]............................................................17圖2-2 真應變法示意圖..................................................................22
圖2-3 模糊推論系統流程方塊圖..................................................24
圖2-4 適應性網路模糊推論系統之架構示意圖..........................25
圖3-1 殼元素示意圖......................................................................27
圖3-2 罰函數法修正節點穿透示意圖..........................................28
圖3-3 微小圓杯引伸凸緣之模具尺寸示意圖..............................29
圖3-4微小圓杯引伸凸緣之料片尺寸示意圖...............................30
圖3-5 衝頭之網格規劃圖 (上視圖與前視圖)............................31
圖3-6 母模之網格規劃圖 (上視圖與前視圖)............................32
圖3-7 壓料板之網格規劃圖 (上視圖)........................................33
圖3-8 料片之網格規劃圖 (上視圖)............................................33
圖3-9 微小圓杯引伸貫穿之模具尺寸示意圖..............................35
圖3-10 微小圓杯引伸貫穿之料片尺寸示意圖............................35
圖3-11 料片邊界條件示意圖........................................................36
圖3-12 料片之網格規劃圖 (上視圖)..........................................37
圖3-13 Dp/t=10衝頭之網格規劃圖 (上視圖與前視圖).............38
圖3-14 Dp/t=10母模之網格規劃圖 (上視圖與前視圖).............39
圖3-15 Dp/t=10壓料板之網格規劃圖 (上視圖).........................40
圖3-16 Dp/t=15衝頭之網格規劃圖 (上視圖與前視圖).............41
圖3-17 Dp/t=15母模之網格規劃圖 (上視圖與前視圖).............42
圖3-18 Dp/t=15壓料板之網格規劃圖 (上視圖).........................43
圖3-19 Dp/t=20衝頭之網格規劃圖 (上視圖與前視圖).............44
圖3-20 Dp/t=20母模之網格規劃圖 (上視圖與前視圖).............45
圖3-21 Dp/t=20壓料板之網格規劃圖 (上視圖).........................46
圖4-1 微小圓杯引伸凸緣之變形歷程圖......................................49
圖4-2 微小圓杯凸緣分析成形圖..................................................50
圖4-3 Theiler[1]傳統大型與微小圓杯凸緣實驗比較圖...............51
圖4-4 微小圓杯凸緣成形負荷圖..................................................51
圖4-5 微小圓杯凸緣成形厚度分佈圖..........................................51
圖4-6 微小圓杯凸緣應力分佈圖..................................................52
圖4-7 壓料板間隙為0.024mm之分析成形圖.............................53
圖4-8 壓料板間隙為0.03mm之分析成形圖...............................53
圖4-9 壓料板間隙為0.04mm之分析成形圖...............................53
圖4-10 壓料板間隙為0.05mm之分析成形圖.............................54
圖4-11 壓料板間隙為0.07mm之分析成形圖.............................54
圖4-12 不同壓料板間隙之成形負荷圖........................................54
圖4-13 壓料板間隔為0.024mm之厚度(左)及應力分佈圖(右)
..........................................................................................................55
圖4-14 壓料板間隔為0.03mm之厚度(左)及應力分佈圖(右)
..........................................................................................................55
圖4-15 壓料板間隔為0.04mm之厚度(左)及應力分佈圖(右)
..........................................................................................................55
圖4-16 壓料板間隔為0.05mm之厚度(左)及應力分佈圖(右)
..........................................................................................................56
圖4-17 壓料板間隔為0.07mm之厚度(左)及應力分佈圖(右)
..........................................................................................................56
圖4-18 成形負荷比較圖................................................................57
圖4-19 Dp/t=10的成形厚度分佈圖...............................................58
圖4-20 Dp/t=15的成形厚度分佈圖...............................................58
圖4-21 Dp/t=20的成形厚度分佈圖...............................................59
圖4-22 杯高比較圖........................................................................59
圖4-23 模具Dp/t=10不同模具間摩擦係數之成形負荷比較.....61
圖4-24 模具Dp/t=15不同模具間摩擦係數之成形負荷比較.....61
圖4-25 模具Dp/t=20不同模具間摩擦係數之成形負荷比較.....62
圖4-26 各模具之不同摩擦係數與早乙女[2]實驗之成形負荷之比較圖..................................................................................................62
圖4-27 各種異向性值狀況之成形負荷圖....................................64
圖4-28  、 及 之成形側視圖..............64
圖4-29 三個方向異向性值皆為1之成形側視圖........................65
圖4-30 三個方向異向性值皆為 之成形側視圖..........65
圖4-31利用真應變法修正至第三次之料片外徑 、   .........................................................................67
圖4-32利用真應變法修正至第三次之成形杯高 、   .........................................................................67
圖4-33利用真應變法修正至第三次之料片外徑 、   .........................................................................68
圖4-34利用真應變法修正至第三次之成形杯高 、   .........................................................................68
圖4-35使用權重因子修正之成形杯高.........................................69
圖4-36使用權重因子修正之效果.................................................69
圖4-37使用三個歸屬函數所求之成形杯高..................................70
圖4-38 使用權重因子與ANFIS最佳化方法之效果比較圖........70
圖4-39 厚度為0.1mm時各晶粒大小之應力應變曲線................72
圖4-40 厚度為0.2mm時各晶粒大小之應力應變曲線................73
圖4-41 厚度為0.5mm時各晶粒大小之應力應變曲線................73
圖4-42 晶粒大小為23 時各厚度之應力應變曲線.................74
圖4-43 晶粒大小為70 時各厚度之應力應變曲線.................74
圖4-44 晶粒大小為113 時各厚度之應力應變曲線...............75
    圖4-45 料片厚度為0.1mm，(4-4)式與 之應力
應變比較圖......................................................................................76
圖4-46 料片厚度為0.2mm，(4-4)式與 之應力
應變比較圖......................................................................................76
圖4-47 料片厚度為0.5mm，(4-4)式與 之應力
應變比較圖......................................................................................77
圖4-48晶粒大小為23 ，(4-4)式與 之應力
應變比較圖......................................................................................77
圖4-49晶粒大小為70 ，(4-4)式與 之應力應變比較圖......................................................................................78
圖4-50晶粒大小為113 ，(4-4)式與 之應力
應變比較圖......................................................................................78圖4-51 Dp/t=10時各晶粒大小之成形負荷圖( )
..........................................................................................................80
圖4-52 Dp/t=15時各晶粒大小之成形負荷圖( )
    ..........................................................................................................80
圖4-53 Dp/t=20時各晶粒大小之成形負荷圖( )
..........................................................................................................81
圖4-54 Dp/t=10時各晶粒大小之成形負荷圖((4-4)式)..............81
圖4-55 Dp/t=15時各晶粒大小之成形負荷圖((4-4)式)..............82
圖4-56 Dp/t=20時各晶粒大小之成形負荷圖((4-4)式)..............82
圖4-57 DR=2.0之成形極限圖及對應成形狀況............................84
圖4-58 DR=2.1之成形極限圖及對應成形狀況............................85
圖4-59 DR=2.2之成形極限圖及對應成形狀況............................86
圖4-60 DR=2.3之成形極限圖及對應成形狀況............................87
圖4-61 DR=2.4之成形極限圖及對應成形狀況............................88
圖4-62 DR=2.35之成形極限圖及對應成形狀況..........................89
圖4-63 DR=2.31之成形極限圖及對應成形狀況..........................90

表  目  錄
表3-1 微小圓杯引伸凸緣之模具尺寸...........................................30
表3-2 微小圓杯凸緣製程之模具尺寸...........................................36
表4-1 成形杯高比較表...................................................................61
表4-2各厚度及晶粒大小的k(強度係數)、n(應變硬化指數).....73
表4-3 (4-4)式中各係數之猜測值..................................................76
表4-4  與(4-4)式之最高成形負荷比較表.....79

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