Method, apparatus, and program for determining casting state in continuous casting

Abstract

A determination apparatus of a casting state in continuous casting where there are a solidified shell, a mold flux layer, and a mold being respective thermal conductors between a molten steel and cooling water for the mold, the determination apparatus comprising an estimation unit, a calculation unit, and a determination unit. A computer program for causing a computer to determine a casting state in continuous casting where there are a solidified shell, a mold flux layer, and a mold being respective thermal conductors between a molten steel and cooling water for the mold.

1 . A determination apparatus of a casting state in continuous casting where there are a solidified shell, a mold flux layer, and a mold being respective thermal conductors between a molten steel and cooling water for the mold, the determination apparatus comprising:
 an estimation unit which finds a heat transfer coefficient α being a heat flux per a unit temperature difference between the solidified shell and the mold sandwiching the mold flux layer and a heat transfer coefficient β between the molten steel and the solidified shell by using data from a plurality of temperature sensing units which are embedded in the mold while shifting positions in a casting direction by solving an inverse problem, and estimates a solidified shell thickness and a solidified shell temperature from the heat transfer coefficient α and the heat transfer coefficient β;   a calculation unit which sets the heat transfer coefficient α, the heat transfer coefficient β, the solidified shell estimated thickness, and the solidified shell estimated temperature found by the estimation unit as solidified state in mold estimation amounts, and obtains solidified state in mold evaluation amounts from the solidified state in mold estimation amounts; and   a determination unit which determines whether a normal casting state or an abnormal casting state by comparing at least one or more kinds of amounts contained in the solidified state in mold estimation amounts and the solidified state in mold evaluation amounts obtained by the calculation unit with allowable limit values which are found based on at least one or more kinds of amounts contained in the solidified state in mold estimation amounts and the solidified state in mold evaluation amounts when the abnormal casting occurred in a past and stored in an allowable limit value storage unit,   wherein in the mold where widths in a horizontal direction of two planes which are not adjacent but face each other are equal from among four planes of mold surfaces which are in contact with a cast slab through the mold flux layer,   two planes whose widths in the horizontal direction are narrower than the other two planes are called as short sides,   a difference of the heat transfer coefficients β obtained at the short sides at the same mold height position is called as a short side β difference,   a difference of solidified shell thicknesses obtained at the short sides at the same mold height position is called as a short side shell thickness difference, and   the solidified state in mold evaluation amounts are calculated from at least either the short side β difference or the short side shell thickness difference.   
     
     
         2 . The determination apparatus of the casting state according to  claim 1 ,
 wherein an arbitrary position at 120 mm or more and 175 mm or less from an upper end of the mold is set to P 1 , an arbitrary position at 340 mm or more and 480 mm or less from the upper end of the mold is set to P 2 , and embedding positions of the temperature sensing units are provided at intervals of 120 mm or less within a range from P 1  to P 2 , and at least one point is provided at a position where a distance from a lower end of the mold is within 300 mm.   
     
     
         3 . The determination apparatus of the casting state according to  claim 1 ,
 wherein, in the determination unit, occurrence of a break-out is determined in order to determine whether the normal casting state or the abnormal casting state.   
     
     
         4 . The determination apparatus of the casting state according to  claim 1 , further comprising:
 a data storage unit, wherein time-series data obtained by setting at least one or more kinds of amounts contained in the solidified state in mold estimation amounts and the solidified state in mold evaluation amounts as a time-series data, is stored together with information of whether or not the abnormal casting occurred; and   wherein the allowable limit value storing unit stores information obtained by deciding allowable limit values defining a range regarded to be the normal casting state based on the time-series data when the abnormal casting occurred and statistic information including an average and a standard deviation of the time-series data.   
     
     
         5 . The determination apparatus of the casting state according to  claim 1 ,
 wherein the solidified state in mold evaluation amount is a moving average from one second to 15 minutes in the past of at least either the short side β difference or the short side shell thickness difference.   
     
     
         6 . The determination apparatus of the casting state according to  claim 1 ,
 wherein the solidified state in mold evaluation amount is a minimum value from one second to 15 minutes in the past of at least either an absolute value of the short side β difference or an absolute value of the short side shell thickness difference.   
     
     
         7 . The determination apparatus of the casting state according to  claim 4 ,
 wherein at least one or more kinds of amounts contained in the solidified state in mold estimation amounts and the solidified state in mold evaluation amounts are classified by layers in accordance with classifications for casting conditions and measurement values defined in advance, and the statistic information is at least either the average or the standard deviation in each group classified by layers.   
     
     
         8 . The determination apparatus of the casting state according to  claim 7 ,
 wherein the casting conditions and the measurement values are one or more kinds from among a casting speed, a casting width, a molten steel temperature, a difference between the molten steel temperature and a liquidus temperature, and a difference between the molten steel temperature and a solidus temperature.   
     
     
         9 . The determination apparatus of the casting state according to  claim 4 ,
 wherein a value where one time or more value of the standard deviation is added to the average and a value where one time or more value of the standard deviation is subtracted from the average are used as the allowable limit values.   
     
     
         10 . A computer program for causing a computer to determine a casting state in continuous casting where there are a solidified shell, a mold flux layer, and a mold being respective thermal conductors between a molten steel and cooling water for the mold, the computer program causing a computer to execute:
 a first process of finding a heat transfer coefficient α being a heat flux per a unit temperature difference between the solidified shell and the mold sandwiching the mold flux layer and a heat transfer coefficient β between the molten steel and the solidified shell by using data from a plurality of temperature sensing units which are embedded in the mold while shifting positions in a casting direction by solving an inverse problem, and estimating a solidified shell thickness and a solidified shell temperature from the heat transfer coefficient α and the heat transfer coefficient β;   a second process of setting the heat transfer coefficient α, the heat transfer coefficient β, the solidified shell estimated thickness, and the solidified shell estimated temperature found by the first process as solidified state in mold estimation amounts, and obtaining solidified state in mold evaluation amounts from the solidified state in mold estimation amounts; and   a third process of determining whether a normal casting state or an abnormal casting state by comparing at least one or more kinds of amounts contained in the solidified state in mold estimation amounts and the solidified state in mold evaluation amounts obtained by the second process with allowable limit values which are found based on at least one or more kinds of amounts contained in the solidified state in mold estimation amounts and the solidified state in mold evaluation amounts when the abnormal casting occurred in a past and stored in an allowable limit value storage unit,   wherein in the mold where widths in a horizontal direction of two planes which are not adjacent but face each other are equal from among four planes of mold surfaces which are in contact with a cast slab through the mold flux layer,   two planes whose widths in the horizontal direction are narrower than the other two planes are called as short sides,   a difference of the heat transfer coefficients β obtained at the short sides at the same mold height position is called as a short side β difference,   a difference of solidified shell thicknesses obtained at the short sides at the same mold height position is called as a short side shell thickness difference, and   the solidified state in mold evaluation amounts are calculated from at least either the short side β difference or the short side shell thickness difference.