INVERSE METHOD FOR DETERMINING TEMPERATURE DISTRIBUTION IN MACHINING

Abstract

The high tool-chip interface temperature is the primary reason for rapid tool wear in machining. Thus, sensing and control of cutting temperature is important in achieving a desired tool performance. However, the interface temperature distribution is difficult to measure directly due to the smallness of scale and high speeds and temperatures involved. In the present project, the temperature distribution along the tool-chip interface is predicted by using the temperatures sensed at remote and accessible locations inside the cutting tool. The problem of estimating cutting temperatures will be simplified by only focusing on modelling the tool, not including the chip and the workpiece. The present problem is an inverse heat conduction problem which is much more difficult to solve than the direct one due to its ill-posed nature, that is, small changes in the measured interior temperatures will result in big errors in the estimated boundary temperatures.

The regularization method is used to make the present steady-state two-dimensional inverse heat conduction problem well-posed. The regularization method modifies the least squares approach by adding the regularization terms which are controlled by regularization parameters and have a smoothing effect on the solution, that is, reduce the fluctuations of the solution which are inherent in ill-posed inverse problems. A central issue in the regularization method is how to choose numerical values for the regularization parameters. In the present study three methods, mean squared residual error (MSRE) criterion, true mean squared error (TMSE) criterion, and generalized cross validation (GCV) criterion are introduced to determine the optimal regularization parameters. In these methods, the optimal regularization parameters are obtained by minimisation of the criterion function. Cubic interpolation is used to minimize the criterion function for the case that only one regularization parameter is chosen and multidimensional simplex minimization method is used for the case of multiple parameters.

An inverse finite element code is developed in the present study and its applicability is demonstrated through comparison with results obtained by direct numerical simulation and comparison with experimental data from the literature. The results show that the choice of the regularization parameter is critical to the present inverse analysis, and TMSE and GCV criteria are valid. The present study discussed the effect of the location and error level of the interior measurement temperatures and the order of regularization parameters to the inverse solution. The present inverse method is also applied to various geometries and used to predict the tool-chip interface heat flux.