Abstract:

Based on the theories of thick-walled cylinder, the mechanical characteristics of integral die under working conditions were analyzed and the  calculation  results  show  that it  is  difficult to increase the die strength only by increasing the wall thickness. In order to improve the load supporting capacity of the die, the scheme of prestressed multilayer the die was discussed. Based on the fourth failure criteria,a mathematical expression of n-layer combinatorial die under internal pressure was deduced. Lagrange multiplier method was used to obtain the optimum design parameters of combinatorial die. The design formulas of optimum diameter ratio of each layer, the limit loading pressure，the residual pressure in shrinkage interface and optimum radial magnitude of interference were investigated. Through the optimum design of three-layer combinatorial die, the derived formulas was verified using two methods of theoretical analysis and numerical simulation.The investigation shows that the simulation results are consistent with the theoretical ones.

Key words: extrusion die;strength design, structure optimization, Lagrange multiplier method

摘要：

基于厚壁圆筒理论,分析了整体式凹模工作载荷特点，讨论了单纯通过增加壁厚来提高模具强度的局限性。为提高承载能力，探讨了多层预应力组合凹模方案。基于第四强度理论，推导了n层组合凹模承受内压的数学表达式。采用Lagrange乘子法对组合凹模参数进行了优化设计,推导了n层组合凹模各层最佳径比分配、凹模极限内压、套缩界面残余压力及最优过盈量等设计变量的计算式。以三层组合凹模为算例，运用理论分析和数值模拟相结合的方法，对上述n层组合凹模的各设计变量计算式进行了验证，结果表明两者的结果吻合较好。

关键词: 挤压凹模, 强度设计, 结构优化, Lagrange乘子法