About an exponential model of heating slabs in methodical furnaces

Introduction. In conditions of increasing requirements for the quality of metal heating before rolling, the task of creating and improving the algorithmic support of automated process control systems (ACS TP) of methodical furnaces is quite relevant. Aim. Consider the problem of physical conditioning and parametric tuning of the so-called exponential model, which is often used to describe the heating of slabs in rolling mill furnaces: the question arises of how much the exponential model corresponds to the physics of the heating process, and what accuracy of the description can be achieved. Materials and methods. A comparison is made of both the structures of the models - the physical model based on the heat equation and the exponential model, and the results of calculating the mass average temperature of the metal using these models. Results. It is shown that the exponential model exactly corresponds to the physics of the heating process only for thermally thin bodies. A differential equation is obtained for the error in calculating the mass-average temperature of thermally massive bodies. In this case, three heating modes are analyzed: at a constant temperature of the working space and with a linear and exponential increase in this temperature. The solution of the equation for the calculation error during heating at a constant temperature of the working space is given. It is established that the exponential model satisfactorily describes the process, as a rule, only for the heating mode at a constant temperature of the working space. The rational value of the tunable parameter of the exponential model is found. A rather simple scheme of the transition from the parameters of the model, the core of which is the differential heat equation, to the parameters of the simplified exponential model for the mass-average temperature, is indicated. Conclusion. The results of the work can be used in the development and improvement of the algorithmic support of automated process control systems of methodological furnaces.