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级进冲模是制造业最精密的重要工艺装备之一，并行工程是先进制造技术领域的重要研究方向。面向寿命的级进冲模并行设计是力图使级进冲模各工序模具子结构的寿命趋于一致。实现最低成本条件下，使所设计的级进冲模达到要求的使用寿命。运用实变函数中的Ｌｅｂｅｓｇｕｅ测度和Ｌｅｂｅｓｇｕｅ积分的概念，结合面向寿命的级进冲模并行设计的特点，建立了面向寿命的级进冲模并行设计数学模型—模具子结构的Ｌｅｂｅｓｇｕｅ测度和Ｌｅｂｅｓｇｕｅ积分，提出了级进冲模结构与模具子结构关系的一般数学表达式。为面向寿命的级进冲模并行ＣＡＤ技术的开发提供了理论基础和指导思想。同时也为面向知识的模具ＣＡＤ技术开发提供了借鉴。
Progressive die is one of the most sophisticated and important manufacturing equipment in the manufacturing industry. Concurrent engineering is an important research direction in advanced manufacturing technology. The progressive design of life-oriented progressive dies is an attempt to bring the life of mold sub- To achieve the lowest cost conditions, the design of progressive die to achieve the required life. Using the concept of Lebesgue measure and Lebesgue integral in real variable function and combining with the characteristics of parallel design of progressive die facing life, a mathematic model of progressive die design with life span is established, Lebesgue measure and Lebesgue integral of die substructure, The general mathematical expression of the relationship between progressive die structure and die substructure. It provides a theoretical basis and guiding ideology for the development of life-oriented progressive die CAD technology. At the same time, it also provides a reference for the development of mold-oriented CAD technology.