Sensitivity analysis by the adjoint variable method for optimization of the die compaction process in particulate materials processing

Nonuniform shrinkage during sintering results from the nonuniform green density distribution in a compacted powder body and this creates a severe problem in net-shape forming. Therefore, proper selection of the process parameters, such as compaction die design, upper and lower punch displacements, and sequential tool motion, is very important for the optimum design of die compaction processing. Previously, these were guess-estimated based on experience. As a first step in developing a more scientific design technique in powder metallurgy, the equations for the adjoint variable method (AVM) for the non-steady-state uniaxial powder compaction process are derived in detail. The accuracy of the AVM is verified through the comparison of the design sensitivity with calculations performed using the finite difference method.