A temperature predicting model for manufacturing processes requiring coiling

摘要

A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars is presented. Although the method is of a general nature, the presentation in this work refers to themanufacturing of steel plates in hot rolling mills. The predicting strategy is based on a mathematical model of the evolution of temperature in a coiling and uncoiling bar and is presented in the form of a parabolic partial differential equation for ashape changing domain.. The mathematical model is solved numerically by a space discretization via geometrically adaptive finite elements which accomodate the change in shape of the domain, using a computationally novel treatment of the resulting thermalcontact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme Since the actual physical process may take less time than the time required by the process controlling computer to solve the full mathematical model a specialpredictive device was developed, in the form of a set of least squares plynomials, based on the numerical solution of the mathematical model.