Theoretical-Numerical Investigation of a New Approach to Reconstruct the Temperature Field in PBF-LB/M Using Multispectral Process Monitoring

The monitoring of additive manufacturing processes such as powder bed fusion enables the detection of several process quantities important to the quality of the built part. In this context, radiation-based monitoring techniques have been used to obtain information about the melt pool and the general temperature distribution on the surface of the powder bed. High temporal and spatial resolution have been achieved at the cost of large storage requirements. This contribution aims to offer an alternative strategy of gaining information about the powder bed’s temperature field with sufficient resolution but with an economical amount of data. The investigated measurement setup uses a spectrometer to detect the spectral radiation intensities emitted by an area enclosing the melt pool and part of its surroundings. An analytical description of this process is presented, which shows that the measured spectral entities can be reconstructed by the Ritz method. It is also shown that the corresponding weighting factors can be physically interpreted as subdomains of constant temperature within the measurement area. Two different test cases are numerically analyzed, showing that the methodology allows for an approximation of the melt pool size while further assumptions remain necessary to reconstruct the actual temperature distribution.