A numerical study of the calendering process is presented. The material to be calendered is modeled by using Giesekus constitutive equation. The flow equations are first presented in dimensionless forms and then simplified by incorporating the lubrication approximation theory. The resulting equations are analytically solved for the stream function. The pressure gradient, pressure, and other engineering parameters related to the calendering process, such as roll-separating force, power function, and entering sheet thickness, are numerically calculated by using Runge–Kutta algorithm. The influence of the Giesekus parameter and the Deborah number on the velocity profile, pressure gradient, pressure, power function, roll-separating force, and exiting sheet thickness are discussed in detail with the help of various graphs. The present analysis indicates that the pressure in the nip region decreases with increasing Giesekus parameter and Deborah number. The power function and the roll-separating force exhibit decreasing trends with increasing Deborah number. The exiting sheet thickness decreases up to a certain entering sheet thickness, as compared to the Newtonian case. Beyond this entering sheet thickness, the exiting sheet thickness increases with increasing entering sheet thickness.

中文翻译：

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基于Giesekus流体模型的压延过程数值分析

介绍了压延过程的数值研究。被压延的材料通过使用 Giesekus 本构方程建模。流动方程首先以无量纲形式呈现，然后通过结合润滑近似理论进行简化。得到的方程是针对流函数进行解析求解的。压力梯度、压力和其他与压延过程相关的工程参数，如分辊力、幂函数和输入板厚等，均采用 Runge-Kutta 算法进行数值计算。借助各种图表详细讨论了 Giesekus 参数和 Deborah 数对速度分布、压力梯度、压力、功率函数、辊分离力和退出板厚度的影响。目前的分析表明，辊隙区域的压力随着 Giesekus 参数和 Deborah 数的增加而降低。幂函数和辊分离力随着德博拉数的增加呈现下降趋势。与牛顿情况相比，退出板厚度减小到一定进入板厚度。超过该进入板厚度，退出板厚度随着进入板厚度的增加而增加。