Abstract: Progressive die is the most precise one of the important machine tool in manufacturing field. Concurrent engineering is an important research field of advanced manufacturing technology Concurrent design of life – oriented progressive die makes an alterpt to get a same life of the all die substructures in a progressive die. The lower cost of progressive die design and manufacturing can be obtained. With the help of the concepts of Lebesgue measure and Lebesgue integral in real function, the mathematics model of concurrent design of life – oriented progressive die is advanced. Which were the Lebesgue measure and Lebesgue integral of die substructures and a general mathematics model of the relation between progressive die structure and die substructures. Based on the mathematics model, the concurrent CAD software of life – oriented progressive die is developed. And it can be as a guide of die & mold CAD software development for knowledge.

Key words: Concurrent CAD of die & mold, Lebesgue integral, Life – oriented, Mathematics model