• 作者： 林貫中; 周榮源
• 作者服務機構： 國立中興大學應用數學研究所
• 中文摘要： 本文主旨在分析黏彈性流體從非軸對稱噴嘴擠出後之擠出成型。採用對自由流斷面面積積分之方法，可推導得已含自由流邊界界面條件在內之一維非軸對稱自由流控制方程式。且為了簡化三維問題之複雜性，假設分析之流體為一細長噴流，其軸向長度遠大於橫向長度。則可將速度場展成此細長比因子之冪級數，在此本文僅取第零階問題來分析，其誤差可由高階問題來修正。同時對彈性力、慣性力、表面張力、黏滯力、重力、鬆弛時間和遲滯時間等物理效應皆已包含在本文所推導之公式內。 對各種不同擠出成型之自由流斷面面積與外形，在不同大小之物理效應影響下具有三種不同型態之變化，分別為：只有脹縮無扭曲變形；只有扭曲變形無脹縮；兼具扭曲變形和脹縮等三種不同變形型態。在剖面外形只有脹縮而無扭曲變形之型態中，剖面外形在不同之初始條件下只會均勻膨脹或縮小而不會產生扭曲變形。故面積比會沿Z軸增大或減小但縱橫比則保持定值。在流體剖面外形只會扭曲變形之型態中，因橫軸與縱軸之動量相互交替變化使得流體剖面外形產生扭曲變形之作用。但是斷面積始終保持為一。最後，本文探討流體剖面外形會脹縮與變形之情況。此時不但斷面積會改變剖面外形亦會沿Z軸方向變化，兼具了前述兩種變化型態。在所有三種不同變形型態斷面外形大多具有圓角，此與Han之實驗相互一致。
• 英文摘要： This paper analyzes the extrusion of viscoelastic liquids through nonaxisymmetric dies. Adopting asimplification scheme, an exact one dimensional nonaxisymmetric free jet model which incorporated the inter-facial conditions of the free surface is derived by integrating the three dimensional field equations over thejet cross section. To simplify the model, a small physical scale, the slenderness ratio, is introduced. The vonKarman assumption of velocity components can then be expanded in powers of this small scale. The truncatederror of expanded higher order terms can be traced. The physical effects of elasticity, inertia, surface tension,viscosity, gravity, relaxation time and retardation time are included in the three dimensional boundary valueproblem. For various nonaxisymmetric cross sections of extrusion, the cross section of extrudate can have thebehaviors of swell with no distortion, distortion without swell or distortion with swell. These behaviorsdepend on the order of each physical effect in the model. In regime of swell with no distortion, where theleading order effect is elasticity, all extrudates swell with similar shapes. In regimes of distortion withoutswell and distortion with swell, the distortion is due to the redistribution of transverse momentum. In allregimes, the extrudate cross section with rounded corners is consistent with Han's experimental results.
• 中文關鍵字： viscoelastic liquids; nonaxisymmetric extrusion; free surface; distortion; extrudate sewll
• 英文關鍵字： --