A temperature predicting model for manufacturing processes requiring coiling

Abstract

A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars in the transfer table is presented. Although the method is of a general nature, the presentation in this work refers to the manufacturing 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 a shape 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 thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Since the actual physical process takes less time than the time required by the process controlling computer to solve the full mathematical model, a special predictive device was developed, in the form of a set of least squares polynomials, based on the off-line numerical solution of the mathematical model

Numerical modeling of thermal evolution in hot metal coiling

“…Figures (3)(4)(5) indicate important sources of non uniform temperature that result from bar heat loss and coiling of the bar. These sources are, essentially, the initial distribution of temperature at the exit of the roughing stands, the loss of heat to the environment, the longitudinal edge (widthwise) loss of heat and the loss of heat at the tail edge and head edge of the bar.…”

Modelling the Temperature Evolution During Hot Reversing Strip Rolling of Magnesium Alloys

“…Coil Geometry. The heat transfer problem is considered in the Cartesian coordinates instead of the more usual the cylindrical coordinates [7,8,9,10]. However, the 3-D domain Ω is still a cylinder in the formal mathematical sense, i.e.…”

Practical finite element heat transfer modelling for hot rolling of steels

“…In more recent times, digital computers have allowed wholesale numerical calculations to be made very quickly, resulting in the solution of problems using whole theorems [1][2][3][4] that had hitherto only been capable of solution by introducing a simplifying regime into the calculation. Over the last 20 years or so, many finite difference [5][6][7][8][9] and finite element [10][11][12][13][14][15][16][17][18][19][20][21][22][23] hot rolling process models have been developed. These range from two dimensional finite difference investigations on discrete process components, to large online process control codes.…”