Issue 37

U. Muhin et alii, Frattura ed Integrità Strutturale, 37 (2016) 305-311; DOI: 10.3221/IGF-ESIS.37.40 306 from the upper surface of the strip, and the environment. Temperature monitoring of the end of the rolling and coiling by radiation pyrometers. The mathematical model of the thermal state of the metal in the collecting roller table is based on the definition of the space-time temperature field strip. The calculated field is found by solving one-dimensional unsteady heat conduction equation (1) the numerical method - the method of finite differences:          2 2 ( ) ( ) ( ) V T T T c T T q x (1) where: ρ - density of the metal, kg/m 3 ; c - specific heat of the metal J/(kg×K); λ - thermal conductivity of the metal, W/(m×K); T - temperature of the metal, K; τ – time, s; x - coordinate of the strip thickness, m; qv - power density heat sources, W/m 3 . Heat loss from strip cooling water, radiation, and interaction with the ambient air are described by the boundary conditions of the second and third kind, and for the difference scheme are given in the following form:           ср T q T T x where: Tsr - ambient temperature; q - heat flux, W/m 2 ; α - heat transfer coefficient, W/(m 2 ×K). The solution of the heat is carried by the sweep method. As a finite-difference scheme is used implicit scheme. The calculation of heat flow and heat transfer coefficient is performed on the dependence presented in [1-3] for the conditions of collecting roller table of continuous strip hot rolling mill (CSHRM). On cooling the strip to the collecting roller table mill hot rolling the metal undergoes a polymorphic transformation of γ → α, which is accompanied by significant heat release. The vast majority of mathematical models of the thermal state of the band on the collecting roller table, for example, [2-6], does not include a calculation of the polymorphic transformation as transportation for the band collecting roller table, which can lead to substantial error in the prediction of coiling temperature variation of process parameters in a wide range. To calculate the polymorphic transformation in the collecting roller table to know Ar3 transformation temperature of the beginning and end of the conversion of Ar1. These parameters depend on the chemical composition of steel, the cooling rate, the dislocation density in the crystal lattice, the grain size and strain rate prior to the metal. In constructing a mathematical model of calculation of the critical points Ar3 and Ar1 made only according to the chemical composition of the steel, cooling rate and, indirectly, on the grain size, by choosing for the calculation of thermokinetic decomposition diagrams of supercooled austenite with austenite temperature, similar to the conditions CSHRM. The density and thermal conductivity of the metal is given according to the reference data. Specific heat of the metal is calculated by the formula:        1 c Xc X c where: X - the share of the formed α-phase; c α - the heat capacity of α-phase; cγ - the heat capacity of γ-phase. The quantity of X is calculated as follows according to [7]:      1 exp n X by (2)    3 3 1 j Ar t y Ar Ar