Doubly shrink fitted dies: optimisation by analytical and FEM calculations

In some powder metallurgy part forming, when high compacting loads would require a too large single shrink fitted die, or the inner die diameter is very large but the compaction area is modest, twice shrink fitted dies, which are relatively expensive and complex to build, should be used. In both cases, at any given compacting load, the design should minimise dimensions and stresses. The design targets are minimum die size, optimum intermediate diameter and optimum interference, with maximum stresses on each die item lower than those allowable for the selected materials. In dual mode, for fixed overall dimension, intermediate diameters and shrink fitting interference should enable to maximise the compacting load without exceeding the allowable maximum stresses. In the first part of this work, for cylindrical shapes (circular profile dies) and axisymmetric plane stress problems, dimensions, interferences and stress–strain states have been analytically calculated to optimise doubly shrink fitted dies in the abovementioned sense. In the second part, the same evaluations for axisymmetric generic problems have been carried out by finite element method (FEM) approach integrated in an optimisation procedure. The minimum overall dimensions of the die are presented as a function of the ratio between applied load and maximum allowable stress. Corresponding interferences and optimum diameters have been calculated. Some approximate equations for a quick and handy optimisation are presented. The differences between analytical and numerical results obviously depend on the consideration of the actually stressed length, or compact height, and total die height. The comparison indicates that FEM analyses are needed since analytical calculations generally give low approximations, especially for some die geometries.