基于增量理论的板材轴对称成形直接积分解法  

Direct Integral Method for Solving Axisymmetric Sheet Forming Problem Based on Incremental Theory

作　　者：秦泗吉[1] 孔晓华[1] 杨莉[1] QIN Siji;KONG Xiaohua;YANG Li(Key Laboratory of Advanced Forging&Stamping Technology and Science of Ministry of Education of China,Yanshan University,Qinhuangdao,Hebei,066004)

机构地区：[1]燕山大学先进成形技术与科学教育部重点实验室

出　　处：《中国机械工程》2019年第21期2622-2628,共7页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(51675466,51175451);河北省自然科学基金资助项目(2018203373)

摘　　要：对一般轴对称曲面零件成形,在平面应力假设和增量理论等条件下,以初始构形为参考构形,采用参数分析方法,得到了等效应变增量的微分方程.由于该微分方程包含了等效应变增量和等效应变增量的一阶导数项,一般情况下,等效应变增量的一阶导数以隐函数的形式存在,难以采用理论方法进行求解,因此,将等效应变增量的一阶导数表示成其自身、等效应变增量以及参变量的函数,根据泰勒级数展开式和积分的定义给出了逐步积分解法,可用于求解轴对称胀形、翻边、拉深等板材成形问题.以圆筒形件和圆锥形件的拉深成形为例,采用增量理论,将总变形分成若干个增量步,逐步加载,跟踪变形质点,累加应变,求解得到了法兰区和凹模圆角区等的应变分布.对分别采用比例加载条件、增量理论计算得到的结果与实验值进行了比较,结果表明,采用增量理论得到的结果更接近实验值.By taking the initial configuration as reference,a differential equation of equivalent strain increment was obtained on the basis of plane stress assumption,incremental deformation theory using parametric analysis method.The differential equation was generally difficult to solve using theoretical methods because the first derivative terms of the equivalent strain increment of curved parts also existed as an implicit function.So,the first derivative of the equivalent strain increment was expressed as a function of the equivalent strain increment,parameter and itself.According to Taylor series expansion and the definition of the integral,a stepwise integral solution method was given to solve sheet metal forming problems such as bulging,flanging and deep drawing for axisymmetric parts.Taking the deep drawings of cylindrical parts and conical parts as examples,the total deformation was divided into several incremental steps and gradually loaded.Incremental theory solution was used to track the deformation particles and strain was added,and the strain distributions in the flange and the die radius regions were obtained.The analyzing results obtained by using the method under proportional loading condition and incremental theory respectively were compared with experiments.It is shown that the calculation results by incremental theory are closer to the experimental ones than those under the proportional loading conditions.

关 键 词：板材成形 增量理论 比例加载 平面应力 初始构形 直接积分解法 

分 类 号：TG386.1[金属学及工艺—金属压力加工]