Inverse problem of estimating the heat flux at the roller/workpiece interface during a rolling process

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space-dependent heat flux at the roller/workpiece interface during rolling process from the knowledge of temperature measurements taken within the roller. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. The results show that an excellent estimation on the space-dependent heat flux can be obtained for the test cases considered in this study.