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研究生： 蔡毅瑋
Yi-Wei Tsai
論文名稱： 非軸對稱板材成形極限與翹曲現象之分析
Analysis of Forming Limit and Warpage Phenomenon in Non-Axisymmetric Sheet Metal Forming Processes
指導教授： 黃佑民
You-Min Huang
口試委員: 黃永茂
Yeong-Maw Hwang
李榮顯
Rong-Shean Lee
徐瑞坤
Ray-Quan Hsu
陳復國
Fuh-Kuo Chen
王國雄
Kuo-Shong Wang
林榮慶
Zone-Ching Lin
向四海
Su-Hai Hsiang
學位類別： 博士
Doctor
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2008
畢業學年度： 96
語文別： 中文
論文頁數： 143
中文關鍵詞： 橢圓杯引伸成形製程 、非軸對稱板材成形製程 、彈塑性有限元素法 、翹曲現象 、橢圓孔凸緣成形製程
外文關鍵詞： non-axisymmetric sheet metal forming processes, elliptical hole-flanging process, elasto-plastic finite element method, elliptical cup drawing process, warping phenomenon
相關次數： 點閱：216  下載：1 
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  •  上一筆

    • 本文採用Prandtl-Reuss塑流法則和Hill的降伏條件，結合有限變形理論及updated Lagrangian formulation (ULF)的觀念建立一增量型彈塑性大變形三維有限元素分析程式，並應用四邊形四節點退化殼元素(degenerated shell element)所推導之形狀函數偶合入剛性矩陣中，組成三維有限元素之分析模式，以及使用廣義r-min法處理板材成形時，元素降伏之判斷、最大容許應變增量、最大容許旋轉增量、料片與模具間節點之接觸或分離等問題。

    此外，本文亦利用拉伸試驗所量測之試片破裂厚度作為破裂的判斷準則，再將此準則應用到增量型彈塑性大變形三維有限元素分析程式以作為板材破裂與否之依據。本文以非軸對稱板材成形製程為例，如：橢圓孔凸緣成形製程、橢圓杯引伸成形製程和U型彎曲成形製程，分析結果包括沖頭負荷與衝程關係圖、工件厚度分佈圖、工件之應力分佈圖、工件之應變分佈圖和工件之成形履歷。同時，本文也設計實驗模具，並於液壓成形機上進行成形實驗，透過資料擷取系統得到實驗結果。

    本文首先將所發展出之三維CAE程式應用於橢圓孔凸緣成形製程，從分析結果可以得知，由於工件內孔長軸周緣處承受較大之拉伸應力，因此最大應力及最小厚度值皆集中於工件內孔長軸之區域。工件之最大沖頭負荷隨著沖頭圓弧半徑的增加而降低，也隨著初始橢圓內孔之減少而有增加的趨勢。

    於橢圓杯成形製程之分析，工件最小厚度集中在工件與沖頭長軸接觸之區域，係因料片在長軸處承受了最大拉伸應力。本文也比較不同沖模圓弧半徑對LDR的改善，發現當沖頭圓弧半徑與沖模圓弧半徑增加時，則極限引伸比將會增加。

    最後，本文於U型彎曲成形中，對於工件在U型彎曲成形中翹曲現象的形成提供了變形履歷之資料，此外，並探討如何從沖模圓弧半徑的變化中找尋較小的翹曲量，也就是翹曲現象的改善。從分析與實驗結果得知，增加沖頭圓弧半徑和降低沖模圓弧半徑所得到的翹曲量將比起原先的翹曲量為小，因此應用此CAE分析程式將可得到相當大的改善結果。

    本論文將所發展之彈塑性有限元素分析程式，即CAE模擬程式應用於非軸對稱金屬板材成形製程分析，由各製程之分析結果所得知其CAE程式之可靠性與信賴性，並能提供模具設計者與製程分析人員之需求，以為製造生產時的缺陷預估、製程改良及模具設計之依據。

    A methodology of formulating an elasto-plastic three-dimensional finite element model, which is based on Prandtl-Reuss flow rule and Hill’s yield criterion respectively, combined with an updated Lagrangian formulation, is developed to simulation sheet metal forming processes. An extended r-min algorithm is proposed to formulate the boundary conditions, such as the yield of the elements, maximum allowable strain increment, maximum allowable rotation increment, maximum allowable equivalent stress increment, and tolerance for nodes getting out of contact with tool.
    The fractured thickness of speciment in tension experiment is used as the criterion of fracture. That is, if the sheet thickness of the forming process is less than fractured thickness, then the fracture of material in this region will happen. This paper has analyzed the non-axisymmetric sheet metal forming processes. (e.g. elliptical hole-flanging process, the elliptical cup drawing process and U-bending process.) The simulation results include relationships between punch load and punch stroke, distribution of the thickness, distribution of the stress, distribution of the strain, deformation history. In addition, tools were designed to perform experiments for each process.
    In the elliptical hole-flanging process, the maximum stress and the minimum thickness are concentrated on the contact regions between workpiece and punch major axis. The maximum punch load decrease, as the profile radius of elliptical punch and initial hole of blank increase remarkably.
    In the elliptical cup drawing process, the minimum thickness are concentrated on the contact regions between workpiece and punch major axis. This thesis also compared the influence of different tool radii on LDR. The LDR increased as the punch radius and die radius become larger.
    This thesis introduced the production of warping phenomenon in the U-bending process, and investigates how to obtain improvement from the change of different punch radii and die radii. This thesis provides suggestion of a better punch radius and die radius to acquire the improvement of warpage.
    From the comparison between experimental and simulation results show that the finite element code can precisely analyze non-axisymmetric sheet metal forming processes. This thesis also provides model designers and program analyzers with a reference for the prediction of defects, improvement of the process and design of the model in times of manufacturing and production.

    摘 要............................................I ABSTRACT........................................III 誌 謝............................................V 目 錄...........................................VI 符號索引..........................................X 圖表索引........................................XVI 第一章 緒論......................................1 1.1 前言..........................................1 1.2 研究動機與目的................................3 1.3 文獻回顧......................................4 1.4 本論文之構成..................................8 第二章 基本理論.................................11 2.1 基本假設.....................................11 2.2 有限變形之應變與應變率.......................11 2.3 有限變形之應力與應力率.......................12 2.4 有限變形之updated Lagrangian formulation.....16 2.5 材料之彈塑性構成關係式.......................18 第三章 有限元素分析.............................25 3.1 簡介.........................................25 3.2 虛功原理之離散化.............................27 3.3 退化殼元素(degenerated shell element)........29 3.4 摩擦處理.....................................31 3.5 廣義r-min法之增量步驟的計算..................34 3.6 三維曲度修正方程式...........................38 3.7 除荷之設定...................................38 3.8 靜態顯函(static explicit)....................39 3.9 CAE程式之流程................................39 第四章 金屬板材橢圓孔凸緣成形極限之分析.........45 4.1 前言.........................................45 4.2 實驗設備與實驗步驟...........................47 4.3 橢圓孔凸緣成形製程之數值分析.................50 4.3.1 邊界條件...................................50 4.3.2 材料參數...................................51 4.4 數值分析與實驗結果之比較.....................52 4.4.1 橢圓孔凸緣成形之沖頭負荷之比較.............52 4.4.2 工件應力分佈之比較.........................53 4.4.3 工件主應變分佈之比較.......................53 4.4.4 工件擴孔周緣高度之變化.....................53 4.4.5 工件之成形履歷.............................54 4.4.6 工件厚度變化之比較.........................54 4.5 橢圓孔凸緣成形極限分析.......................55 4.6 沖頭圓弧半徑對於初始橢圓內孔成形之比較.......58 4.7 本章之結語...................................59 第五章 不鏽鋼板材之橢圓杯引伸成形極限之分析.....80 5.1 前言.........................................80 5.2實驗設備與實驗步驟............................82 5.3 橢圓杯引伸成形製程之數值分析.................83 5.4 數值分析與實驗結果之比較.....................83 5.4.1 橢圓杯引伸成形之沖頭負荷之比較.............83 5.4.2 工件應力分佈之比較.........................84 5.4.3 工件之成形履歷.............................85 5.4.4 工件厚度變化之比較.........................86 5.5 橢圓杯引伸成形極限分析.......................86 5.6 不同模具圓弧半徑之極限引伸比之比較...........88 5.7 本章之結語...................................89 第六章 金屬板材U型彎曲成形製程翹曲現象之分析...105 6.1 前言........................................105 6.2 實驗設備與實驗步驟..........................105 6.3 U型彎曲成形製程之數值分析...................105 6.3.1 邊界條件..................................106 6.3.2 材料參數..................................106 6.4 數值分析與實驗結果之比較....................107 6.4.1 U型彎曲成形之沖頭負荷之比較...............107 6.4.2 工件之應力分佈............................108 6.4.3 工件基本尺寸量測與厚度分佈圖..............108 6.5 翹曲現象之形成..............................109 6.6 翹曲現象之改善..............................110 6.7 本章之結語..................................112 第七章 結論....................................131 7.1 結論........................................131 7.2未來研究之展望...............................134 參考文獻........................................135 作者簡介........................................142

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