ABOUT THE EXPONENTER METHOD IN PROBLEMS OF SIMULATING METAL HEATING IN FURNACES

Abstract

Introduction. In the context of increasing requirements for the quality and efficiency of heating metal before rolling, the task of creating and improving algorithmic support for automated process control systems (APCS) for heating furnaces is quite relevant. Purpose of the study. To study the features of using the exponential method proposed in the scientific literature to describe the temperature fields of workpieces when heated in furnaces: the question of how well this approach corresponds to the physics of the heating process is clarified, and what accuracy of description can be achieved. It should be emphasized that this method is interesting, first of all, for the implementation of real-time mode in the process control system of heating furnaces. Materials and methods. It is noted that the reasonableness and attractiveness of the approach under consideration is explained both by the simplicity of the description and by the small number of parameters characterizing the exponent used. A physical and mathematical analysis of the ques- tion of how well the method satisfies the well-known mathematical description of the heating process is car- ried out, the core of which, as is well known, is the heat conduction equation. Results. It is shown that the model structure proposed in the literature satisfies the thermal conductivity equation only for the heating mode at a constant temperature of the workpiece surface. It has also been established that the condition de- scribing the absence of heat flow at the corresponding boundary is satisfied quite approximately for the initial moments of time, and absolutely accurately only for an infinitely long time. Methods for finding the initial condition for the time function included in the structure of the exponential under consideration are consi- dered. Numerical experiments were carried out to evaluate the influence of the method of determining the noted initial condition on the results of calculating temperature fields. It is shown that in the general case, the exponential method represents the temperature distribution over the cross section of the workpiece to be almost uniform. This allows us to conclude that the approach under consideration allows us to essen- tially track the dynamics of the mass-average temperature of the workpiece. Conclusion. The results of the work can be used in the development and improvement of algorithmic support for automated process control systems of methodical furnaces.