Evaluation of temperature field and heat flux by inverse analysis during steel strip rolling

Knowledge of the temperature field in the roll is a critical factor of modern, high-speed rolling mills. In this paper, an inverse analytical method is developed to determine the temperature field and especially the temperature (and heat flux) at the surface of the roll by measuring the temperature with a thermocouple (fully embedded) at only one point inside the roll. Iterative methods are not studied because short computation times are desired. Some assumptions are done to resolve analytically the unsteady heat equation, taking into account the restrictions of the measurement system (e.g., measurement according to successive times). The solution is validated by comparing the outputs of the method and prescribed analytical temperature fields. Good agreement is obtained. Noise sensitivity is estimated by adding artificial random numbers to the inputs. Good accuracy is observed. A 10% error of the temperature sensor depth is also considered and does not compromise the method. On the other hand, the computation time (around 0.05 s by cycle) is studied to rapidly optimise the industrial parameters during the rolling process.