拔长过程有限元模拟的新方法

New Method for Finite Element Simulation of Stretch Forming

拔长工序通常包含多个道次且每个道次中包含多次压下,采用常规有限元法模拟拔长过程的计算时间往往很长,限制了有限元模拟在拔长工艺优化设计中的应用。为提高拔长过程有限元模拟的计算效率,根据坯料局部变形的特点,提出一种刚性端自由度缩减方法:通过有限元总体平衡方程组的变换,分别对各组刚性端自由度进行缩减,以减少平衡方程组的阶数。同时还提出选取刚性端自由度的算法,并通过数值试验给出算法关键参数的取值。将此方法应用于自主开发的三维热力耦合刚粘塑性有限元程序中。分别采用此方法和常规有限元法对正八角形截面坯料的一个拔长道次进行模拟,预测拔长过程中的载荷以及道次结束后坯料的等效应变和温度分布,比较分别采用两种方法进行模拟所需的计算时间。计算结果验证了此方法的有效性。

Stretch forming process usually consists of multiple passes and each pass consists of multiple reductions,so it is time-consuming to run simulations of the process by using the conventional finite element method（FEM）.This problem is an obstacle to the use of FE simulations in optimal design of stretch forming process.In order to improve the computational efficiency of the FE simulations,a rigid-end degree-of-freedom（DOF） reduction method is presented based on the characteristic of local deformation of billet.In this method,through transformation of the FE equilibrium equations,the number of DOFs of each rigid end and the order of the equilibrium equations are reduced.An algorithm to select the rigid-end DOFs is proposed and an important parameter of the algorithm is suggested through numerical tests.The presented method is applied into a self-developed three-dimensional thermo-mechanical coupling rigid-viscoplastic FE program.A stretch pass of an octagonal cross-section billet is simulated by using this method and by using the conventional FEM.The load during the stretch process and the equivalent strain and temperature distribution after the pass are predicted.The computation time by using this method is compared with that by using the conventional FEM.The effectiveness of this method is verified by the computational results.