Towards the identification of heat induction in chip removing processes via an optimal control approach

Abstract

This paper presents a linear-quadratic regulator (LQR) approach for solving inverse heat conduction problems (IHCPs) arising in production processes like chip removing or drilling. The inaccessibility of the processed area does not allow the measuring of the induced temperature. Hence the reconstruction of the heat source based on given measurements at accessible regions becomes necessary. Therefore, a short insight into the standard treatment of an IHCP and the related LQR design is provided. The main challenge in applying LQR control to the IHCP is to solve the differential Riccati equation. Here, a model order reduction approach is used in order to reduce the system dimension. The numerical results will show the accuracy of the approach for a problem based on data given by practical measurements.In many production fields, a certain heat load is induced during a machining process, as e.g., drilling or milling procedures. These thermal loads affect the material properties and hence, cause deformations of the processed workpiece and the processing tool. Therefore, it is necessary to forecast the corresponding temperature field. However, in order to perform a simulation over the entire time horizon, the trajectories of the induced heat loads are required. Therefore, the modeling of chip removing processes and the associated determination of the actual induced amount of heat into the workpiece to be considered is a highly active research topic, see e.g., [20,[24][25][26] and references therein. Since the chip removing process already requires a high accuracy model in order to identify the amount of heat entering the workpiece of interest, here we aim at reconstructing the heat inputs to the workpiece from observations of the temperature at accessible regions of the workpiece. The procedure investigated here in fact tries to avoid the sophisticated modeling of the entire chip removing process. Instead of performing a direct simulation of the heat creation and transfer process, we solve an inverse heat conduction problem (IHCP) [18] for the induced heat. Still the reconstruction requires a good knowledge of the heat transfer coefficients used in our boundary conditions and thus can heavily benefit from the investigation of the forward process.