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在全量理论的基础上,引入增量思想,构建了多步正成形算法。其基本原理是在一步正成形的基础上,适当增加了若干个中间步,依次计算各中间步之间的应变改变量,并以分量形式累加到当前步的总应变,基于全量理论进行Newton-Raphson迭代计算,并将计算结果以应变分量的形式累加到下个中间步计算中,计算对应的弹塑性本构矩阵,从而在计算过程中体现加载历史的影响,提高了最终的模拟结果精度。设计了方盒件多行程实验方案,采用电腐蚀方法在初始坯料上刻上圆形网格,进行了10 mm、20 mm、30 mm、40 mm、50 mm五个不同行程的方盒件成形实验。利用光学方法测量网格变形量并推算出网格应变量,使用超声测厚仪测量板料不同行程的厚度变化量。通过几种不同算法在计算精度和计算效率上的对比,证明了多步正成形算法的有效性。
Based on the theory of full quantity, this paper introduces incremental thought and constructs multi-step positive forming algorithm. The basic principle is that on the basis of one-step forward, some intermediate steps are added appropriately, and then the amount of the change of the strain between the intermediate steps is calculated in turn, and the total strain of the current step is accumulated in the form of components. Based on the total amount theory, the Newton- Raphson iterative calculation, and the calculation results are added in the form of strain components to the calculation of the next intermediate step, and the corresponding elastic-plastic constitutive matrices are calculated. Thus, the influence of loading history is reflected in the calculation process, and the precision of the final simulation result is improved. The multi-stroke program of square box was designed. A circular grid was carved on the initial blank by electric erosion method. The square box was formed by five different travels of 10 mm, 20 mm, 30 mm, 40 mm and 50 mm experiment. Optical method was used to measure the amount of grid deformation and calculate the amount of grid strain. Ultrasonic thickness gauge was used to measure the thickness variation of different travels of sheet metal. The comparison between the computational accuracy and computational efficiency of several different algorithms proves the effectiveness of the multi-step forward algorithm.