On a Powder Consolidation Problem

On a Powder Consolidation Problem

The problem of the consolidation of an aerated fine powder under gravity is considered. The industrial relevance of the problem is discussed and a mathematical model is introduced. The mathematical structure is that of a coupled system for three unknowns, pressure, stress, and height of the powder in the (axisymmetric) bunker containing it. The system itself consists of a parabolic PDE, an ODE,...

Study on Laser Consolidation of Metal Powder

The layered manufacturing technique is one of the most effective processes for the manufacture of prototypes, tools and functional end products. Selective Laser Sintering (SLS) and Selective Laser Melting (SLM), in particular, are two of the most versatile techniques, able to cover a wide range of materials such as polymer, ceramic and metal powder. In this study, the monitoring method of proce...

Numerical Simulation of Aerated Powder Consolidation

When a fine powder is dumped into a silo, the gas trapped by the particles will slowly escape by diffusing through the material. The corresponding uneven gas pressure distribution creates a body force that is taken into account through Darcy’s law. By using spatial averaging, the formulation, even though essentially one-dimensional in space, includes effects due the geometry of the container. A...

Method for Improving Consolidation of Powder Resin

Approximation of a batch consolidation problem

In batch production systems, multiple items can be processed in the same batch if they share sufficiently similar production parameters. We consider the batch consolidation problem of minimizing the number of batches of a finite set of items. This article focuses on the case in which only one or two items can be processed in a single batch. The problem is NP-hard and cannot be approximated with...