The paper presents validation tests for method which is used for the evaluation of the statistical distribution parameters for 3D particles’ diameters. The tested method, as source data, uses chord sets which are registered from a random cutting plane placed inside a sample space. In the sample space, there were individually generated three sets containing 3D virtual spheres. Each set had different Cumulative Distribution Function (CDF3) of the sphere diameters, namely: constant radius, normal distribution and bimodal distribution as a superposition of two normal distributions. It has been shown that having only a chord set it is possible, by using the tested method, to calculate the mean value of the outer sphere areas. For the sets of data, a chord method generates quite large errors for around 10% of the smallest nodules in the analysed population. With the increase of the nodule radii, the estimation errors decrease. The tested method may be applied to foundry issues e.g. for the estimation of gas pore sizes in castings or for the estimation of nodule graphite sizes in ductile cast iron.

The determination of the form of a probability density function (PDF3) of diameters for nodular particles by using a probability density function (PDF2), which form is empirically estimated from cross-sections of these nodules in a metallographic specimen, can be regarded as a special case of Wicksell's corpuscle problem (WCP). The estimation of the PDF3 for the nodular particles provides information about the kinetics of these particles nucleation, and so about the kinetics of their growth. This information is essential for building more accurate mathematical models of the alloy crystallization. In the paper there are presented two derivations of the methods used for the estimation of the PDF3 form. The first method bases on diameters received from a planar cross-section. The second one uses also data from the planar cross-section but not the diameters only chords. Both methods provide practical rules for the analysis of the empirical diameters’ and chord’s size distribution and allow to estimate the mean value of the external surface area of the particles.

This article is a description of the progress of research and development in the area of massive large-scale castings - slag ladles implemented in cooperation with the Faculty of Foundry Engineering of UST in Krakow. Slag ladles are the one of the major castings that has been developed by the Krakodlew (massive castings foundry) for many years. Quality requirements are constantly increasing in relation to the slag ladles. Slag ladles are an integral tool in the logistics of enterprises in the metallurgical industry in the process of well-organized slag management and other by-products and input materials. The need to increase the volume of slag ladles is still growing. Metallurgical production is expected to be achieved in Poland by 2022 at the level of 9.4 million Mg/year for the baseline scenario - 2016 - 9 million Mg/year. This article describes the research work carried out to date in the field of technology for the production of massive slag ladles of ductile cast iron and cast steel.