經由連續退火線(Continuous Annealing Line，簡稱CAL)製程後的鋼帶於沖製成鋼片時，其邊緣會產生翹曲，其原因應與鋼帶在通過爐輥時，產生寬度與厚度方向不均勻塑性變形及溫度分佈有關。CAL內有許多工作區域，本論文著重在建立鋼帶於連續退火線的溫度與熱應力分析方法。
能量平衡法是將預熱爐區分為數個圍場，各圍場內受熱對流、熱輻射，以及鋼帶與爐輥間接觸熱傳等歷程，並假設爐內已為穩態。換言之，各圍場是以能量平衡和溫度單獨考量。能量平衡法最後可由反覆疊代計算求得鋼帶橫向和縱向的溫度分佈，所得爐內溫度參數，來作為有限元素分析初始邊界條件。
　　爐輥表面溫度與鋼帶溫度有直接關係是因彼此的接觸熱傳影響，使用有限元素來模擬分析爐輥3維暫態的溫度分佈，可精確得到爐輥表面溫度值。在模擬時發現減小到適當貝克勒數(Peclet number, PeR)值，可有效降低電腦運算時間，另外2維模型從結果中可看出，與3維模型中心有覆蓋鋼帶部份在溫度分佈上有很好的一致性，然而運算時間卻只須花費二十分之一左右，因此使用適當且較低貝克勒數值的2維模型來模擬，便可花費最少時間卻不失結果的精確度。
　　因熱─力耦合影響，其3維鋼帶溫度和應力的分佈是將熱或力學模型所求數值代入另一模型當初始條件，經反覆疊代後達數值解收斂便可獲得。模擬結果顯示，爐輥錐度造成鋼帶寬度方向溫度分佈不均勻，這會導致鋼帶寬度方向應力分佈不均的結果。

The cold-rolled steel sheets produced by continuous annealing line (CAL) exhibit a significant phenomenon of warping during punching process. The phenomenon of warping may result from the nonuniform temperature and nonuniform plastic deformation along both the width and the thickness of the strip when it passes through the rolls in CAL. In this study, the analyses of temperature and thermal stresses of the strip in CAL are established.
The space of the preheating furnace is divided into several enclosures in which the mechanisms of heat convection, heat radiation, and contact heat transfer between the strip and the rolls are taken into account. It is assumed that the furnace is already in the steady state. In other words, the energy remains balance within each enclosure and the temperature at each component is independent of time. The longitudinal and transverse temperature distributions of the strip are finally iteratively calculated by using the method of energy balance. 2-D temperature distributions of the steel strip are studied with the aid of finite element analysis.
3-D transient temperature distributions of taper rolls in a CAL are investigated by using finite element analysis. Since the temperature of strip is closely related to the surface temperature of rolls due to the effect of contact heat transfer between them, it is crucial to determine the accurate surface temperature of rolls in CAL. It is found that the computational time for the case with low Peclet number (PeR), however, can be significantly reduced. Moreover, it is seen that the results of 2-D model are in good agreement with 3-D model in the central region covered with strip, while the computational time of the former is about one twentieth of the latter. Consequently, a minimum computational cost can be achieved by using 2-D model with suitable lower value of Peclet number without sacrificing the accuracy of the simulation results.
3-D distributions of temperature and stress of the strip are then iteratively evaluated by thermal and mechanical models due to their coupling effect until a satisfied convergence in numerical solutions can be obtained. The results show that the taper rolls tend to introduce a significantly nonuniform distribution of temperature along the width. This temperature pattern might lead to an unfavorable consequence of enormously nonuniform distribution of stress along the width.

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