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Estimation of tool/chip interface temperatures for on-line tool monitoring: an inverse problem approach

We examine a steady inverse heat transfer problem that arises in online machine tool monitoring: identifying tool/chip interface temperatures from remote sensor measurements. The matrix equations relating the sensor temperatures and sensor fluxes to the prediction surface (tool/chip interface) temperatures are obtained by finite element methods. Truncated singular value decomposition, a standard inverse technique, is used as a baseline for comparing the inverse solutions. We also develop a new set of inverse approaches, vector projection inverse methods, specifically for this problem. Inverse solutions are computed with all methods for two temperature profiles and various noise levels. Because of the extreme ill-conditioning of the problem, only two coefficients can be obtained reliably for all of the inverse approaches examined. Truncated singular value decomposition does not perform well, but two of the new methods are robust and give reasonable accuracy. Combining data from temperature and flux sensors (data fusion) is far more effective than using temperature sensors alone, and with data fusion the inverse can be computed robustly with information from only four sensor locations.