Complex of Mathematical Models and Methods to Calculate Pressure Effect on Sulfide Distribution in Steel

Abstract

Primary objective is to develop computational method to analyze digital pictures of sulfide prints, helping obtain qualitative image characteristics, and to formulate mathematical model of the distribution of sulphide inclusions to determine specific features of the pressure effect on the macrostructure formation of carbon steel castings flooded into the uncooled mold.
 The research was carried out using images of sulfide prints of templates cut of steel cylindrical castings; L500 steel was applied. The castings result from industrial tests of a method of gas-dynamic effect on the fusion in the foundry forms under the conditions of a casthouse of Dnipropetrovsk aggregate plant PJSC. Digital pictures of sulfide prints, obtained in terms of the increased rate of gas pressure and maximum pressure, were binarized; defective fra gments were removed; and zoning took place. The developed computational method has been applied for fragments of images, representing different zones; data arrays have been received containing sizes and amounts of inclusions in the fragment.
 The developed computational method to analyze digital images of sulfide prints has been implemented. ASImprints software support has helped obtain qualitative characteristics of images; namely, distribution of amount of the certain-size sulfide inclusions. 
 The computational method to analyze digital images of sulfide prints has made it possible to study the set of patterns of sulfide prints. The dependences have been obtained, describing specific features of sulfide inclusion distribution while varying gas-dynamic pressure method in terms of fusion in the casting form. It has been demonstrated that the distribution describes effectively the power-series distribution to compare with the exponential one. Mathematical model of the power-series distribution parameter dependence upon pressure has been developed. Deviation of the distribution parameters in terms of the experimental values and the model values has been evaluated. 
 The research demonstrates the ways to apply an algorithm of simple recursive casting for quantitative analysis of digital images of sulfide prints. Use of ASImprints, being software implementation of the computational method to analyze digital images of sulfide prints making it possible to obtain qualitative characteristics of images, has helped identify that the increased pressure within a casting-device for gas injection system results in the increased specific amount of inclusions and the decreased specific zone of sulfide inclusions respectively. It has been defined that exponential function describes reliably the nature of sulfide inclusion distribution in the digital image of sulfide print. The research has demonstrated that fragments of a sulfide print, belonging to one zone, are statistically homogeneous. Thus, it is possible to analyze quantitively digital image zone of a sulfide print on its fragment. Mathematical model of dependence of sulfide inclusion distribution in carbon-steel castings in terms of gas-dynamic effect on fusion solidifying in a mold has been developed. The model may be applied to predict sulfide inclusion distribution within the selected zones of cross section of the cylindrical castings solidifying in the uncooled mold in terms of the preset mode of gas-dynamic effect.
 Keywords: gas-dynamic effect, pressure, solidification, casting, steel, 35 Л, mold, macrostructure, sulfides, inclusions, template, sulfide print, distribution, polynomial, parameters, prediction, software implementation, ASImprints