https://hal-enpc.archives-ouvertes.fr/hal-00790209Weisz-Patrault, DanielDanielWeisz-Patraultmsa - Matériaux et Structures Architecturés - navier umr 8205 - Laboratoire Navier - IFSTTAR - Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche ScientifiqueInverse three-dimensional method for fast evaluation of temperature and heat flux fields during rolling processHAL CCSD2012[PHYS.MECA.THER] Physics [physics]/Mechanics [physics]/Thermics [physics.class-ph][SPI.MECA.THER] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Thermics [physics.class-ph]Weisz-Patrault, Daniel2013-02-19 16:14:172022-01-15 03:50:372013-02-19 16:26:58enConference papersapplication/pdf1Monitoring and controlling flatness during the rolling process becomes critical for ensuring the product quality. Flatness defects are due to highly three-dimensional phenomena. Indeed, strips with different widths are rolled during the same campaign and cooling systems are heterogeneous along the axial direction to modify the thermal expansion of the roll. Therefore this paper presents a fully three dimensional inverse analytical method to determine the temperature field and heat fluxes (especially at the surface of the roll) by interpreting measurements of temperature done with several thermocouples fully embedded in the roll body and aligned along the axial direction. Since the method is dedicated to on-line interpretation and designed as a tool for adapting the rolling parameters during the rolling process, iterative methods are not studied to avoid long computation times, which justify the development of an analytical solution of the problem. The computation time displayed by Scilab 5.3 with a quadcore 2.8 GHz is around 0.07 s/cycle. The 3D unsteady heat equation is solved analytically in the roll, managing only one assumption so that restrictions of the measurement system (i.e., successive times) are taken into account. The solution is validated by comparing the outputs (surface temperature) and a prescribed temperature field (corresponding to hot rolling conditions). A satisfying 1.1% error is obtained. The accuracy is therefore promising. Furthermore noise sensitivity is evaluated by adding random values to the inputs (temperature computed at a depth of 0.5 mm under the surface) and the accuracy has not bee compromised (1.8%). Therefore good noise robustness is demonstrated.