本文乃探討金屬板材彎曲成形之模具外形最佳化設計。研究中，首先使用顯性動態有限元素法結合Barlat的異向性降伏準則模擬金屬板材彎曲成形，然後接續使用隱性有限元素法模擬回彈角度分析。此外，並利用適應性網路模糊推論系統(Adaptive Network Fuzzy Inference System, ANFIS)進行各種彎曲成形模具形狀最佳化設計。為求理論之驗證，利用方形與V形90度模具進行板材折邊彎曲成形(L形彎曲)、U形彎曲成形、方板對角線彎曲成形(V形彎曲)之實驗，並比較彎曲成形數值分析與實驗之沖頭負荷與衝程關係、變形歷程、成形後回彈角度，以驗證有限元素分析與最佳化之可信度。
    本文亦探討各彎曲製程參數對回彈角度之影響，當摩擦係數或板料厚度增加時則回彈角度減小；當彎曲半徑或模具間隙增加時，則回彈角度增大。最後，本文針對方板鋁合金對角線彎曲成形製程，利用ANFIS預測回彈後的成形角度為90度時，模具角度需為85.137度，並以一組V 形85.137度之最佳化模具來進行實驗，得到回彈後的成形角度為89.93度。經由數值模擬與實驗比較，顯示本文結合有限元素分析與ANFIS，可正確預測板材回彈的模具角度，使板金彎曲成形發生不可避免的回彈問題獲得改善。

The objective of this thesis is to explore the die shape optimal design of the sheet metal bending process. Firstly, the dynamic-explicit finite element method based on the Barlat’s anisotropic yield criterion is used to simulate the sheet metal bending process in this study. After bending process, the springback angle is then analyzed by static-implicit finite element method. Besides, the die shape optimal design is performed by Adaptive Network Fuzzy Inference System (ANFIS) in various bending processes of sheet metal. In order to verify the theories, the square and V-type dies are designed for several experiments of L-bending, U-bending, and V-bending to prove the reliability of finite element analysis and optimal design by comparison of the punch load versus punch stroke relationship, the deformation history, and the springback angle after bending process between numerical and experimental results.
    The present study also discusses the influence of design parameters on springback angle of the bending processes. The springback angle decreases as friction coefficient or blank thickness becomes larger. The springback angle increases as bending radius or gap of dies becomes larger. Finally, this study predicts the angle of V-type die to be 85.137 degrees by ANFIS when the formed angle is 90 degrees in V-bending process of aluminum alloy sheet. A set of V-type optimal die, which angle is 85.137 degrees, is used to carry on the experiment. The formed angle is 89.93 degrees after V-bending experiment. By comparison of numerical and experimental results, it shows that the die angle of bending process can be correctly predicted by finite element method with ANFIS in the thesis. The inevitable springback problem will obtain the improvement in the sheet metal bending process.

目  錄
中文摘要 ------------------------------------------------------------------------ I
英文摘要 ------------------------------------------------------------------------ II
目    錄 ----------------------------------------------------------------------- IV
圖表索引 ---------------------------------------------------------------------- VII
第一章 緒論 ------------------------------------------------------------------- 01
1.1 前言 ------------------------------------------------------------------ 01
1.2 研究動機與目的 --------------------------------------------------- 02
1.3 文獻回顧 ------------------------------------------------------------ 03
1.4 論文之構成 --------------------------------------------------------- 05
第二章 基本理論 ------------------------------------------------------------- 07
2.1 顯性有限元素法 --------------------------------------------------- 07
2.2 隱性有限元素法 --------------------------------------------------- 12
2.3 異向性板材降伏方程式 ------------------------------------------ 13
2.4 適應性網路模糊控制理論 --------------------------------------- 15
2.4.1 模糊推論之架構 -------------------------------------------- 15
2.4.2 模糊化 -------------------------------------------------------- 15
2.4.3模糊規則庫 --------------------------------------------------- 17
2.4.4模糊推論機 --------------------------------------------------- 18
2.4.5解模糊化介面 ------------------------------------------------ 18
2.4.6適應性網路模糊推論系統之架構 ------------------------ 19
2.4.7複合式學習演算法 ------------------------------------------ 21
第三章 板材彎曲成形實驗與數值分析 ---------------------------------- 24
3.1 板材彎曲折邊成形(L形彎曲) ------------------------------------ 24
3.1.1成形模具之幾何尺寸與材料參數 ------------------------ 24
3.1.2有限元素分析 ------------------------------------------------ 25
3.1.2.1元素類型 ----------------------------------------------- 26
3.1.2.2接觸問題 ----------------------------------------------- 26
3.1.2.3材料模型 ----------------------------------------------- 27
3.1.2.4回彈分析與需要拘束 -------------------------------- 27
3.1.3實驗流程 ------------------------------------------------------ 29
3.1.4數值分析與實驗結果之比較 ------------------------------ 30
3.1.4.1彎曲過程中沖頭負荷之比較 ----------------------- 30
3.1.4.2彎曲之成形歷程 -------------------------------------- 31
3.1.4.3工件之應力分佈 -------------------------------------- 32
3.1.4.4回彈後之成形角度 ----------------------------------- 32
3.2 板材U形彎曲成形 ------------------------------------------------ 47
3.2.1有限元素分析 ------------------------------------------------ 47
3.2.2實驗流程 ------------------------------------------------------ 48
3.2.3數值分析與實驗結果之比較 ------------------------------ 49
3.2.3.1彎曲過程中沖頭負荷之比較 ----------------------- 49
3.2.3.2彎曲之成形歷程 -------------------------------------- 50
3.2.3.3工件之應力分佈 -------------------------------------- 51
3.2.3.4回彈後之成形角度 ----------------------------------- 51
3.3 方板對角線彎曲成形(V形彎曲) -------------------------------- 63
3.3.1成形模具之幾何尺寸與材料參數 ------------------------ 63
3.3.2有限元素分析 ------------------------------------------------ 63
3.3.3實驗流程 ------------------------------------------------------ 64
3.3.4數值分析與實驗結果之比較 ------------------------------ 65
3.3.4.1彎曲過程中沖頭負荷之比較 ----------------------- 66
3.3.4.2彎曲之成形歷程 -------------------------------------- 66
3.3.4.3工件之應力分佈 -------------------------------------- 67
3.3.4.4回彈後之成形角度 ----------------------------------- 67
3.4 影響回彈角度因素 ------------------------------------------------ 76
3.4.1材料厚度對回彈的影響 ------------------------------------ 76
3.4.2摩擦係數對回彈的影響 ------------------------------------ 76
3.4.3彎曲半徑對回彈的影響 ------------------------------------ 77
3.4.4模具間隙對回彈的影響 ------------------------------------ 77
3.4.5間隔環大小對回彈的影響 --------------------------------- 78
第四章 最佳化模具角度設計 ---------------------------------------------- 82
4.1 L形彎曲最佳化模具角度設計 ---------------------------------- 82
4.1.1 有限元素分析 ----------------------------------------------- 82
4.1.2 欲設計模具之彎曲成形分析 ----------------------------- 83
4.2 V形彎曲最佳化模具角度設計 ---------------------------------- 88
4.2.1 最佳化模具形狀設計 -------------------------------------- 88
4.2.2 欲設計模具之彎曲成形模擬分析與實驗之比較 ----- 88
4.2.2.1彎曲過程中沖頭負荷之比較 ----------------------- 89
4.2.2.2最佳化V形彎曲之成形歷程 ----------------------- 89
第五章 結論 ------------------------------------------------------------------- 98
5.1 結論 ------------------------------------------------------------------ 98
5.2 未來展望 ----------------------------------------------------------- 100
附錄 ---------------------------------------------------------------------------- 101
參考文獻 ---------------------------------------------------------------------- 107
符號索引 ---------------------------------------------------------------------- 110
 
圖表索引
圖2-1	連續物體於卡氏座標系統變形 --------------------------------- 22
圖2-2	模糊理論推論系統 ------------------------------------------------ 22
圖2-3	適應性網路模糊推論系統之架構示意圖 --------------------- 23
圖3-1	L形彎曲之模具配置及相關尺寸圖----------------------------- 33
圖3-2	L形彎曲之沖頭網格規劃圖--------------------------------------- 36
圖3-3	L形彎曲之沖模網格規劃圖--------------------------------------- 37
圖3-4	L形彎曲之壓料板網格規劃圖------------------------------------ 38
圖3-5	L形彎曲之料片網格規劃圖--------------------------------------- 38
圖3-6	回彈全模型約束節點之位置 ------------------------------------ 39
圖3-7	回彈對稱模型約束節點之位置 --------------------------------- 39
圖3-8	SPCC軟鋼於L形彎曲實驗與數值模擬之沖頭負荷與衝程  比較-------40   
圖3-9	6061鋁合金於L形彎曲實驗與數值模擬之沖頭負荷與衝程 比較-------40
圖3-10	SPCC軟鋼於L形彎曲之成形歷程------------------------------- 41
圖3-11	6061鋁合金於L形彎曲之成形歷程----------------------------- 42
圖3-12	SPCC軟鋼於L形彎曲之應力分佈圖---------------------------- 43
圖3-13	6061鋁合金於L形彎曲之應力分佈圖-------------------------- 43
圖3-14	L形彎曲之回彈後成形角度計算之參考點---------------------44
圖3-15	6061鋁合金於L形彎曲數值分析與實驗之最終成形工件比較-------46
圖3-16	U形彎曲之模具配置及相關尺寸圖----------------------------- 53
圖3-17	U形彎曲之沖頭網格規劃圖-------------------------------------- 54
圖3-18	U形彎曲之沖模網格規劃圖-------------------------------------- 55
圖3-19	U形彎曲之壓料板網格規劃圖----------------------------------- 56
圖3-20	料片於U形彎曲之網格分割與邊界條件設定----------------- 56
圖3-21	SPCC軟鋼於U形彎曲實驗與模擬之沖頭負荷與衝程比較--------------57
圖3-22	6061鋁合金於U形彎曲實驗與模擬之沖頭負荷與衝程比較------------57
圖3-23	SPCC軟鋼於U形彎曲之成形歷程------------------------------ 58
圖3-24	6061鋁合金於U形彎曲之成形歷程----------------------------- 59
圖3-25	SPCC軟鋼於U形彎曲之應力分佈圖--------------------------- 60
圖3-26	6061鋁合金於U形彎曲之應力分佈圖-------------------------- 60
圖3-27	U形彎曲回彈後成形角度計算之參考點----------------------- 61
圖3-28	6061鋁合金於U形彎曲數值分析與實驗之最終成形工件  比較-------62
圖3-29	V形彎曲之模具與料片配置圖----------------------------------- 70
圖3-30	V形彎曲之沖頭網格圖------------------------------------------70
圖3-31	V形彎曲之沖模網格圖------------------------------------------71
圖3-32	料片於V形彎曲之網格分割與邊界條件設定----------------- 71
圖3-33	6061鋁合金於U形彎曲實驗與模擬之沖頭負荷與衝程比較------------72
圖3-34	6061鋁合金於V形彎曲之成形歷程----------------------------- 73
圖3-35	V形彎曲之應力分佈圖-------------------------------------------74
圖3-36	V形彎曲回彈後成形角度計算之參考點----------------------- 74
圖3-37	6061鋁合金於V形彎曲數值分析與實驗之最終成形工件  比較--------75
圖3-38	厚度對回彈的影響 ------------------------------------------------ 79
圖3-39	摩擦係數對回彈的影響 ------------------------------------------ 79
圖3-40	彎曲半徑對回彈的影響 ------------------------------------------ 80
圖3-41	模具間隙對回彈的影響 ------------------------------------------ 80
圖3-42	間隔環對回彈的影響 --------------------------------------------- 81
圖4-1	L形彎曲之沖頭角度93.751度網格圖--------------------------- 85
圖4-2	L形彎曲之沖模角度93.751度網格圖--------------------------- 86
圖4-3	6061鋁合金於L形彎曲之成形歷程----------------------------- 87
圖4-4	V形彎曲之沖頭角度85.137度網格圖--------------------------- 93
圖4-5	V形彎曲之沖模角度85.137度網格圖--------------------------- 93
圖4-6	最佳化V形彎曲實驗與數值模擬之沖頭負荷與衝程比較---94
圖4-7	最佳化V形彎曲之成形歷程------------------------------------95
 
表4-1	L形彎曲之模具角度與回彈的成形角度資料庫--------------- 84
表4-2	V形彎曲之模具角度與回彈的成形角度資料庫-------------- 89
表4-3	於V形彎曲中未最佳化模具與最佳化模具角度之數值與實驗分析-------97
照片3-1	L形彎曲之沖頭---------------------------------------------------34
照片3-2	L形彎曲之壓料板------------------------------------------------34
照片3-3	L形彎曲之沖模--------------------------------------------------35
照片3-4	L形彎曲之鋁板與鋼板------------------------------------------ 35
照片3-5	SPCC軟鋼於L形彎曲實驗最終成形之工件-----------------44
照片3-6	6061鋁合金於L形彎曲實驗最終成形之工件---------------45
照片3-7	L形工件外形投影於螢幕--------------------------------------- 45
照片3-8	SPCC軟鋼於U形彎曲實驗最終成形後之工件------------- 61
照片3-9	6061鋁合金於U形彎曲實驗最終成形後之件-------------- 62
照片3-10	V形彎曲90度沖頭----------------------------------------------- 69
照片3-11	V形彎曲90度沖模------------------------------------------------69
照片3-12	6061鋁合金於V形彎曲實驗最終成形後之工件------------75
照片4-1	V形彎曲之85.137度沖頭--------------------------------------- 92
照片4-2	V形彎曲之85.137度沖頭--------------------------------------- 92
照片4-3	最佳化V形彎曲實驗最終成形後之工件--------------------- 96
照片4-4	最佳化V形彎曲實驗成形後之工件置於直角規上--------- 96

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