弹性模具冷弯成形中薄板的力学建模

MECHANICAL MODELING OF COLD METAL SHEET FORMING PROCESS ON ELASTIC DEFORMABLE DIE

提出了一个弹性模具薄板冷弯成形力学模型和相应的解法，并作了实例的数值分析。根据薄板与弹性体和椭圆冲头的接触情况，薄板可分成三部分。应用薄板的大挠度和接触力学理论，分别推出了各部分相应控制方程的解析解；然后根据对应的协调关系，用迭代法求出薄板的内力和接触应力的分布。该力学模型的主要优点是前提假定较少和整个求解过程物理意义明确。计算分析表明，本模型预测弹性模具上冷弯成形薄板的内力和接触应力十分有效。

A mechanical model and its solution for the cold metal sheet forming with rigid elliptical punch and deformable die is proposed to study these problems in details, some practical forming examples are investigated. According to interactive states of the forming sheet with the foundation and the punch, the sheet may be devided into three parts, and corresponding equlibrium equations analytical solutions are derived by large deflection plate theory and contact mechanics. Numerical efforts is made for distributions of internal forces and contact stresses of the sheet by relative compatibility conditions and interation approach. The present model is featured with less assumptions and computational effort the others.