This paper presents a numerical study of the calendering mechanism. The calendered material is represented using the Carreau-Yasuda fluid model. The governing flow equations in the calendering process are made first dimensionless then the lubrication approximation theory (LAT) is used to simplify them. The simplified flow equations are transformed into stream function and then are numerically solved. A numerical method is constructed with Matlab’s built-in-bvp4c routine to find the stream function and pressure gradient. We use the Runge-Kutta algorithm to calculate the pressure and mechanical quantities related to the calendering process. In this analysis the pressure distribution increases with increasing Weissenberg number, however the pressure domain length decreases as the Weissenberg number increases. The pressure inside the nip region decreases from its Newtonian value when the power law index is less than one (shear thinning), and the pressure profile increases from its Newtonian pressure when the power law index is greater than one(shear thickening). How the Carreau-Yasuda fluid model parameters influence the velocity and related calendering process quantities are also discussed via graphs.

本文提出了压延机理的数值研究。压延后的材料使用Carreau-Yasuda流体模型表示。首先使压延过程中的控制流方程无量纲化，然后使用润滑近似理论（LAT）对其进行简化。简化的流动方程被转换成流函数，然后进行数值求解。使用Matlab的内置bvp4c例程构造了一种数值方法，以查找流函数和压力梯度。我们使用Runge-Kutta算法来计算与压延过程有关的压力和机械量。在此分析中，压力分布随魏森伯格数的增加而增加，但是压力域长度随魏森伯格数的增加而减小。当幂律指数小于1时，辊隙区域内的压力从其牛顿值减小（剪切变稀）；当幂律指数大于1时，压区曲线从其牛顿压力增加（剪切变厚）。还通过图形讨论了Carreau-Yasuda流体模型参数如何影响速度和相关的压延过程量。