一种椭圆模的建模及其拉拔力的解析研究

目的设计一种能提高产品成材率、降低能量消耗的拉拔模具,并对其进行工艺优化。方法在求解内部塑性变形功率过程中,利用线性的EA(平均面积)屈服准则,克服了非线性的Mises屈服准则积分困难的问题,得到了拉拔时内部塑性变形功率的解析表达式;通过对入口径向速度积分,得到了入口剪切功率的解析表达式;通过对速度场的曲线积分并利用积分中值定理,得到了摩擦功率的解析表达式;最终,基于上界法得到了拉拔力的解析表达式。结果通过有限元模拟,验证了拉拔力解析式的正确性,并与传统锥模进行了比较,最大应力降幅达到17.5%。结论利用椭圆曲线设计得到的椭圆模能够降低应力集中,提高拉拔制品的质量,减少拉拔时的能量消耗,可以为相关工程人员提供科学指导。

Modeling of an Elliptical Die and Analytical Research of Its Drawing Force

The paper aims to design an elliptical drawing die and optimize its process to improve the yield rate and reduce energy consumption of product. In solving the internal plastic deformation energy rate, the difficulty of nonlinear specific plastic energy rate integration was overcome with the yield criterion of EA, and the analytical expression of internal plastic deformation energy rate was obtained. The analytical expression of the entrance shear power was obtained by integrating the entrance radial velocity. The analytical expression of friction energy rate was obtained by integrating the velocity field and using the mean value theorem of integral. Furthermore, the analytical expression of drawing force was obtained based on the upper bound method. The correctness of the analytical expression of drawing force was verified by finite element modeling. Compared traditional conical dies, its maximum stress decrease reached 17.5%. The elliptical obtained with the elliptical curve design could reduce the stress concentration, improve the quality of drawing product, reduce the energy consumption of drawing and provide the scientific guidance for relevant engineers.