A new multigrid based method for characteristic diagram based correction of thermo-elastic deformations in machine tools

It is a well-known problem of milling machines, that waste heat from motors, friction effects on guides, environmental variations and the milling process itself greatly affect positioning accuracy and thus production quality. An economic and energy-efficient method of correcting this thermo-elastic positioning error is to gather sensor data (temperatures, axis positions, etc.) 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 computation of these characteristic diagrams leads to very large sparse linear systems of equations which require a vast memory and computation time to solve. This is particularly problematic for complex machines and varying production conditions which require characteristic diagrams with many input variables. To solve this issue, a new multigrid based method for the computation of characteristic diagrams will be presented, tested and compared to the previously used smoothed grid regression method.