Optimized grid structures for the characteristic diagram based estimation of thermo-elastic tool center point displacements in machine tools

It is a well-known problem of milling machines, that waste heat from motors, friction effects on guides and also the milling process itself greatly affect the positioning accuracy and thus the production quality. An economic and energy-efficient method of correcting this thermo-elastic positioning error is to gather sensor data from the machine tool and the process and to use that information to predict and correct the resulting tool center point displacement using high dimensional characteristic diagrams. The size of these characteristic diagrams depends on the number of input variables (sensors) and the fineness of the discretization of the grid. While the number of sensors can usually not be reduced without affecting the quality of the prediction, it is often possible to minimize the size of characteristic diagrams through the use of adaptive grid refinement. This ensures that the finest grid sections correspond with the load cases that have the largest local gradients. Through such adaptive refinement, it is possible to reduce storage capacity and computation time without significant loss of precision. The aim of this article is to examine, test and compare different methods of adaptive grid refinement. For this, simulation data from a machine tool is used.