A nonlinear inverse problem in estimating the heat generation in rotary friction welding

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat generation at the interface of cylindrical bars during rotary friction welding process from the knowledge of temperature measurements taken within the stationary bar. In the direct problem, the heat capacity and thermal conductivity are functions of temperature; hence, this is a nonlinear inverse problem. 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. Results show that an excellent estimation on the time-dependent heat generation can be obtained for the test cases considered in this study. The current methodology can be applied to the prediction of heat generation in rotary friction welding.