鈑金成形加工在傳統上,產品的製造幾乎都憑藉試誤法和經驗來完成,但 精度及效率都不理想,故必須借助理論依據,預測工件成形時工件內部的 應力、應變分佈,藉以獲得可行的製造法,使鈑金成形的成功率獲得提升 。而本論文研究,係以有限元素法分析軸對稱鈑金在張伸(stretching)、 引伸(drawing)及液助成形(hydroforming)時,材料之應力、應變分佈及 各種參數(如摩擦係數、材料性質等)對鈑金成形性的影響。本研究採用 彈塑性大應變有限元素法進行軸對稱鈑金材料之張伸、引伸及液助成形等 製程分析,並引用平面應力假設,以簡化計算的複雜性,另以Total Lagrangian Formulation原理及虛功原理推導勁度方程式與位移應變關係 式,而構成方程式( Constitutive Equations)則由滿足Hill's rate- independent normal anisotropic relation之Von Mises Flow Rule推導 得之,胚料和衝頭間摩擦模式視為庫侖常數(Coulomb Friction),非線性 方程式之求解則利用Newton-Raphson Method。以上計算法係使用薄膜理 論做為模擬軸對稱鈑金張伸、引伸及及液助成形之理論依據。為驗證上述 計算法和計算機程式的正確性,程式的計算結果將與前人已探討過的例子 、實驗值做比較。經由數值運算所獲得的應變分佈與衝頭荷載,與實驗值 做比較,發現兩者間的差異不大,證明所採用之計算理論依據與計算機程 式,其正確性可有效模擬上述三種鈑金成形製程,另從引伸成形和液助成 形的應變分佈比較,很明顯的可以獲知,相對於引伸成形,運用液助成形 能提高鈑金的成形性。
A computational method for the simulation of axisymmettric sheet metal forming processes such as stretching, deep drawing and hydroforming is presented. The elastic-plastic finite element method with large strain formaulation is applied to simplify the procedure of the analysis. The total Lagrangian formulation and virtual work theory are used to derive the Von- Mises flow rule which satisfy Hill's rate-independent normal anisotropic relation is adopted. In the contact region, the relative motion between sheet and punch is governed by Coulomb friction law. Newton Raphson method is then used to solve the nonlinear problem. Some examples on stretching, drawing and hydroforming of sheet metal are considered, and the computed results are compared with experimental data and existing numerical solutions. Both the strains and the punch load obtained with above method agree well with the experimental results. From the comparison of strain distribution between deep drawing and hydroforming, it is favour to use hydroforming process to promote the formability of sheet metal.