Mathematical Statistics for Measuring Steel Temperature in Steel-Teeming Ladle and Tundish at Continuous Steel Teeming

Abstract The article considers the temperature distribution in steel at its continuous teeming. The temperatures were measured sequentially in the steel-teeming ladle (one measurement) and the tundish (two measurements) using a platinum-platinum-rhodium thermocouple with an accuracy of ±4°C. This work analyzes the results of 170 casts of grade 5SP and 35GS steels. The type of temperature set distribution was checked against three goodness-of-fit criteria: Pearson χ-square test, Kolmogorov–Smirnov test λ and Shapiro–Wilk test W. It is shown that the temperatures in the steel-teeming ladle for various kinds of steel fit within the normal distribution model. The results obtained are consistent with the physics of steel casting. The metal in the steel-teeming ladle is practically stable and subject only to natural cooling through the lining, top and body of the ladle. However, in case of analyzing a sample of temperatures in the tundish at the first and second measurement, the normal distribution hypothesis should be rejected. Here, the steel temperature depends on a number of parameters, including the feed rate, casting rate, feed time, composition of slag-forming and heat-insulating mixtures, and others. The attempts to establish the relationship between the steel temperatures in the steel-teeming ladle and in the tundish were unsuccessful. Considering the temperature measurements in the tundish as two sequential data arrays, the first of which is an argument, and the second is a function, a linear relationship between the arrays is established. This relationship can be used to estimate the final steel temperature at the dropout of thermocouple readings, including in the event of a failure. The results of the work can be used in developing a mathematical model of steel teeming.