Thermal cutting of steel plates:modelling, simulation and optimal control of preheating strategies

Resumo

Steel is commonly delivered as coils, sheets or plates at the final stages of production. The plates have to be cut to the right dimensions and this is usually done by means of thermal cutting. Flame cutting is a common and versatile method to produce steel plates but it can cause undesired side effects. Till date, the flame cutting process has not been thoroughly studied using mathematical modelling and numerical simulations. The present work describes a 3D quasi-stationary state (QSS) model to understand the distribution of the heat in a steel plate including solid-solid and solid-liquid transitions during the flame cutting process. Simulations are carried out employing the finite element method. They are able to predict the size of the kerf and the heat affected zone. Recent experimental research has proved that slower speed and adding a preheating stage helps reducing the side effects of flame cutting. The current practice of preheating consists in globally preheating the plates uniformly. We study an alternative preheating method wherein, local induction is applied just before flame cutting. The method involves using an induction coil on top of the cutting line to preheat the area of the plate to be affected by the flame. In induction, heating is done by electromagnetic fields. Due to the ferromagnetic nature of steel, induced eddy currents are generated directly in the workpiece which then cause heating by the Joule effect. We use a 3D eddy currents model in the harmonic regime coupled with the QSS heat equation. The simulations showcase that the heating is concentrated in the surface due to the skin effect. This heat is transported by conduction to the bottom and some time after the position of the coil, uniform temperature is achieved in the cutting line. The setting described has been replicated in a laboratory for experimental validation and the measurements show similar trends to the numerical simulation results. The induction preheating concept is influenced by many parameters which makes finding the optimal setting an unfeasible task. To overcome this, the flame cutting system was decoupled from the electromagnetic problem. The electromagnetic joule heat source was substituted by a parametric heat source and was optimised by an optimal control approach. Analysis of this system has been done to prove the existence, uniqueness and regularity of the solutions of the partial differential equation system. A difficulty of the system is that it includes a quasilinear elliptic heat equation coupled to QSS phase fraction equations. First order optimality conditions are derived for the nonlinear elliptic system. A steepest descent algorithm is implemented to solve the optimal control problem. The algorithm provides promising results to match the cutting speed and thicknesses that require different levels of preheating. Moreover, the control is forced to have a similar distribution as the dissipated power that can be obtained by induction heating. The results of the thesis show that the employment of induction preheating in a real industrial process is indeed feasible. This could lead to the integration of this novel method of preheating in the manufacturing chain, influencing positively on the production rate and energy efficiency of the steel plates production.