Methodological Aspects of Modeling and Calculation of Thermal Processes in Multi-Seat Chill Molds

Abstract

Calculation of the hardening kinetics of cast iron castings in multi-place molds is of great practical importance. The results of such a study can help optimize casting technology while ensuring high quality of cast products.

The article considers some aspects of simplified numerical modeling of thermal processes in multi-seat casting   molds, in particular, the solidification of castings iron grinding balls.

The first aspect of modeling concerns the reduction of the computational complexity of the process by moving from a multi-cavity casting mold to a single-cavity spherical model by introducing vertical mid-planes of symmetry in the multi-cavity chill mold with the condition of zero heat flux. This allowed us to analyze only a segment of the mold with one ball casting, free from heat exchange through conditional boundaries, with cooling through open outer surfaces that do not border on adjacent mold segments and are in contact with the surrounding air. To ensure a correct transition to a spherical model of the chill mold, a method is proposed for equating its volume to the volume of a selected segment of the casting mold with an adjustment of the convection heat transfer coefficient to ensure equality of heat flows from the external surfaces of such bodies.

The second aspect is devoted to the description of phase transitions in casting without explicitly introducing boundary conditions between phases. Using a numerical finite difference method, it is proposed to exclude interphase boundaries from consideration, retaining only the near-boundary nodes (volumes). This allows recurrently calculating the temperature fields within each phase, changing the thermal conductivity coefficient during the transition between phases.

The central issue of the work was a numerical study of the reduction of heat transfer rate of heat transfer by a gap with a gas layer, due to thermal expansion of the  chill mold material, and of casting shrinkage, and its effect on the kinetics of solidification and the structure of the cast product. To do this, a fictitious layer (volume) is introduced between the metal and the mold wall, which allows describing the effect of the gas gap on heat transfer without the need to adapt the mesh or model geometry.

Computer calculations indicate a distribution of the solidification rate across the cross-section of the ball casting (0.5-0.8 mm/s), at which a white cast iron structure is formed across the entire cross-section of the cast product. Based on the calculated data, graphical dependencies were constructed for changes in the casting surface layer temperature and gas gap over time. The calculations were performed for various casting regimes (painted chill mold, lined chill mold, unpainted chill mold).

When the thickness of the chill mold wall increased from 40 to 70 mm, the kinetics of curing, due to the small size of the casting and rapid cooling, did not change qualitatively or quantitatively. At the same time, the cooling time of the solidified casting in the chill mold to the knockout temperature was somewhat reduced (~14%), which can be explained by the greater accumulation of heat in the more massive casting mold.

In general, Ø40 mm cast iron balls receive significantly lower dynamic loads when operated in mills compared to Ø100-120 mm grinding bodies, and white cast iron may be an economically viable material for their production.