Models for compaction and ejection of powder metal parts

by Khambekar, Jayant Vijay.

We focus on single punch compaction of powder metals in hollow cylindrical geometries, and pay special attention to the effects of non-uniform initial density distribution on final green densities, the effects of density-dependent powder properties and pressure dependent coefficients of friction on the evolution of the pressure and density profiles during compaction, and the time variations of the force required for ejection after the compaction pressure is removed. In studying the effects of non-uniform initial density distribution, we extend the work of Richman and Gaboriault [1999] to allow for fill densities that vary with initial location in the die. The process is modeled using equations of equilibrium in the axial and radial directions, a constitutive relation that relates the axial pressure to the radial pressure at any point in the specimen, and a plausible equation of state that relates local density to the local pressure. Coulomb friction is assumed to act at the interfaces between the specimen and both the die wall and core rod. In this manner, we determine the axial and radial variations of the final density, the axial, radial and tangential pressures, and the shear stress. Of special interest are the inverse problems, in which we find the required non-uniform initial density distribution that, in principle, will yield no variation in the final green density. For incorporating the effect of pressure and density dependent powder properties, we employ a one-dimensional model that predicts the axial variations of the pressure and density. In this model, however, we incorporate the density dependence of the radial-toaxial pressure ratio, as well as the pressure-dependence of the coefficients of friction at the die wall and core rod. The density-dependence of the pressure ratio is based on the i experimental measurements of Trassoras [1998], and the pressure dependence of the friction coefficients is based on the measurements of Sinka [2000] and Solimanjad et. al [2001]. In the course of this study, we focus attention on a Distalloy AE powder, and establish the relation between its compressibility and its radial-to-axial pressure ratio. Finally, we employ linear elasticity theory to model the ejection of the green compact. In the first phase, we model relaxation of the compact after removal of the compaction pressure as a misfit of three cylinders, representing the core rod, the compact and the die wall. The known input is radial pressure distribution at the conclusion of compaction, and the output is the corresponding radial pressure distributions that prevail after the compaction pressures are removed. In the second phase, we determine the variations with punch displacement of the ejection forces required to overcome friction at the core rod and die wall. The model includes additions to the friction forces due to the radial expansion (i.e. the Poisson effect) that occurs during ejection. Predictions of the model compare well to the experimental results of Gethin et.al. [1994]. ii