| 摘要: | 本計畫的主要目的，是利用Yeh 和Yang[24]所提出之變分上界限法，來探討靜可容邊界條件對圓環鍛粗問題之上界限解的效應。變分上界限法係應用變分原理取代微分方法以最小化上界限能量方程式。於採用變分上界限方法求解時，在最小化上界限能量方程式前其速度場通常被假設為一隱函數（Implicit function）型態。因此除可獲得動可容邊界條件外亦可決定靜可容邊界條件，並應用於求得所假設之函數以及上界限解。其所獲得之結果已被[24,25]所證實較傳統上界限解為精確且合理，然而對於靜可容邊界條件的效應則仍需進一步研究。本計畫的另一個研究目的，則在探討中立面幾何形狀的效應，因為經由有限元素的結果發現圓環鍛粗之中立面，未如以往上界限解所假設係成圓柱形狀。為達此目的，因此本計畫將以往假設為常數的中立半徑視為一較高階的函數，以期待所獲得之上界限解會有所改進。在驗證VUB 解方面，將採用Hsiang 和Huang [6]，Lee and Altan [8]，以及Nagpal 等人[16]的實驗結果，並且亦與FEM 解做比較及討論。FEM 解的獲得則是使用商業套裝軟體MARC 或相當功能之軟體如DEFORM 及ABAQUS。 By using the Variational Upper-Bound (VUB) method developed by Yeh and Yang [24], one of the objective of this proposal research is to investigate the effect of the statically boundary condition on the upper-bound solution of the upset forging of ring. In stead of using ordinary calculus to minimize the upper-bound energy equation, the VUB method applies the method of variational calculus. Further, the velocity field is assumed as an implicit function in prior before the upper-bound energy equation is extremized (minimized) using the method of variational calculus. In addition to the kimematically boundary condition, the statically boundary condition can be derived and then imposed in determining the assumed function as well as the upper-bound solution as a result. The solution obtained in this manner has been shown to be more realistic and accurate, when compared with the experimental results [24, 25], than the traditional upper-bound solution, but the effect of the statically boundary condition still deserves further investigation. The other objective of the proposal research is to investigate the effect of the geometrical shape of the neutral surface, since the solution of FEM has shown that the neutral surface of the upset forging of ring is a not cylindrical shape as was assumed in the upper-bound solution. For this purpose, the radius of the neutral surface, which was assumed as a constant, will be assumed as a function of higher order in analysis. It is expected that the solution determined in this manner should be improved. In verification of the VUB solution, the experimental results of Hsiang and Huang [6], Lee and Altan [8], and Nagpal et al. [16] will be employed. The FEM solution obtained using a commercially software package, MARC or an equivalent such as DEFORM and ABAQUS, will be compared and discussed to closure. 研究期間：9308 ~ 9407 |
