Efficient computation of temperature fields using physics-informed neural networks to model the thermo-elastic machine tool behavior

• Applicants: Professor Dr.-Ing. Christian Brecher; Professor Dr. Michael Herty
• Subject Area: Production Automation and Assembly Technology ; Engineering Design, Machine Elements, Product Development ; Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 537928890

Sustainable manufacturing and high production quality significantly determine competitiveness in industry. Manufacturing defects, which occur largely due to thermo-elastic errors, must be reduced. To correct thermo-elastic machine tool errors, these must be known. Since the internal and external heat sources and sinks influence the temperature field and thus the thermo-elastic tool center point (TCP) error, the temperature field provides valuable information about the thermo-elastic machine tool behavior. In literature, temperature fields are often determined using the finite element method (FEM), which requires high computational power and is time-consuming due to the need to identify and model all boundary conditions. Inaccuracies in the calculated boundary conditions deteriorate the calculated temperature field as well as the corresponding displacements. Another approach is the direct determination of the thermo-elastic displacements using artificial neural networks. These do not require knowledge of the underlying physical phenomena. However, generation of training data is costly. Physics-informed neural networks (PINNs) combine the positive features of both approaches. They allow for accurately approximating the solution of complex partial differential equations (PDEs) using only little training data and do not require complete knowledge of the boundary conditions. Therefore, PINNs are used in this research project to determine the temperature field and the corresponding TCP displacement of a machine tool. The main goal of this research is the efficient computation of the machine tool temperature field based on small training data sets and without precise knowledge of boundary conditions using PINNs. Three success criteria are defined. First, an efficient generation of training data sets has to be enabled. Second, the temperature field is to be determined with a maximum deviation of 20 %. Third, the calculation is conducted in thermal real time. To achieve these goals, a demonstrator machine is equipped with temperature sensors and a displacement measurement system. In the next step, the internal and external heat flows of the machine tool are modeled and used to set up the thermo-elastic PDE of the entire machine tool using an FE model. Training data for the PINNs is generated using measurement data. This data is used to develop and implement the PINN to calculate the temperature field. The pose dependency of the thermo-elastic errors is taken into account. After successful development of the PINN, the training data sets are optimized with respect to their size and the acceptable inaccuracy of the boundary conditions. Afterwards, the PINN training is optimized regarding efficiency and reliable applicability of the PINN. After successful determination of the temperature field and optimization of the PINN, the displacement is calculated based on the temperature field. Finally, the model results are validated.

• DFG Programme: Research Grants