Model Order Reduction Strategies for the Computation of Compact Machine Tool Models

Abstract

The deviation of the tool center point (TCP) of a machine tool from its desired location needs to be assessed correctly to ensure an accurate and safe operation of the machine. A major source of TCP deviation are thermal loads, which are constantly changing during operation. Numerical simulation models help predicting these loads, but are typically large and expensive to solve. Especially in (real-time feedback) control settings, but also to ensure an efficient design phase of machine tools, it is inevitable to use compact reduced-order surrogate models which approximate the behavior of the original system but are much less computationally expensive to evaluate. Model order reduction (MOR) methods generate computationally efficient surrogates. Classic intrusive methods require explicit access to the assembled system matrices. However, commercial software packages, which are typically used for the design of machine tools, do not always allow an unrestricted access to the required matrices. Non-intrusive data-driven methods compute surrogates requiring only input and output data of a dynamical system and are therefore independent of the discretization method. We evaluate the performance of such data-driven approaches to compute cheap-to-evaluate surrogate models of machine tools and compare their efficacy to intrusive MOR strategies. A focus is put on modeling the machine tool via individual substructures, which can be reduced independently of each other.