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 mac hine tool monitoring: identifying tool/chip interface temperatures from rem ote sensor measurements. The matrix equations relating the sensor temperatu res and sensor fluxes to the prediction surface (tool/chip interface) tempe ratures are obtained by finite element methods. Truncated singular value de composition, a standard inverse technique, is used as a baseline for compar ing 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 va rious noise levels. Because of the extreme ill-conditioning of the problem, only two coefficients can be obtained reliably for all of the inverse appr oaches examined. Truncated singular value decomposition does not perform we t, but two of the new methods are robust and give reasonable accuracy. Comb ining data from temperature and flux sensors (data fusion) is far more effe ctive than using temperature sensors alone, and with data fusion the invers e can be computed robustly with information from only four sensor locations .