Circular Layout in Thermal Deburring

Balanced circular layout with a prohibited zone is considered. The problem is motivated by thermal deburring, the modern technology of removing burrs from machine parts by detonating gas mixtures in a cylindrical deburring chamber. To achieve a uniform distribution of thermal and pressure effects, the chamber zone with extremely high temperature/pressure has to be excluded from the feasible layout thus giving rise to the layout with the prohibited zone. Cylindrical parts have to be placed as distant as possible one from another, as well as from the border of the cylindrical container and from the prohibited cylindrical zone. Mechanical stability of the layout is assured by introducing balancing conditions. The overall problem is then reduced to the two-dimensional sparsest circular packing problem subject to the prohibited circular zone and the balancing conditions. Using ANSYS CFX software, a numerical simulation for the temperature/pressure distribution in the chamber is presented. Three cases are considered: the sparsest balanced and unbalanced layouts, as well as the sparsest balanced layout with the prohibited zone. The latter layout is considered to be the most promising for the uniform thermal processing.