One of the substantial topics in the forward extrusion process is using theoretical methods to predict the exit profile distortion due to the non-symmetry of sections or the off-centricity of die cavity. In this paper, a new approach based on the Riemann mapping theorem and upper bound method is developed to obtain the velocity field and the strain distribution. Then, the strain distribution is determined for the die with off-centered square sections. Afterwards, the exit profile curvature is calculated using an approach based on elastic–plastic bending of beams. Theoretical results are compared to the results yielded through experimental and finite element simulation and validated. Subsequently, the effect of various parameters such as relative die length and friction factor is examined on the amount of the exit profile distortion. The results show that the obtained theory can be used to predict the strain distribution and the exit profile distortion in addition to the process pressure.

中文翻译：

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使用黎曼映射定理和上限法预测正向挤压过程中的出口轮廓变形

正向挤压过程中的重要课题之一是使用理论方法来预测由于截面的非对称性或模腔的偏心而导致的出口轮廓变形。在本文中，开发了一种基于黎曼映射定理和上限方法的新方法来获得速度场和应变分布。然后，确定具有偏心方形截面的模具的应变分布。然后，使用基于梁的弹塑性弯曲的方法计算出口轮廓曲率。将理论结果与通过实验和有限元模拟得出的结果进行比较并进行验证。随后，检查了各种参数（例如相对模具长度和摩擦系数）对出口轮廓变形量的影响。