Model order reduction via substructuring for a nonlinear, differential‐algebraic machine tool model with moving loads

Abstract

Machine tools are permanently exposed to complex static, dynamic and thermic loads. This often results in an undesired displacement of the tool center point (TCP), causing errors in the production process and thus limiting the achievable workpiece quality. Recent research efforts try to counter these effects by process-parallel solutions utilizing machine internal data. Therefore, fast simulation models are a fundamental requirement. Here, model order reduction (MOR) becomes crucial. The resulting low-dimensional models are required for various applications, e.g., in digital twins, the correction of thermally induced errors at the TCP during the production process as well as for lifetime calculations in predictive maintenance. In this contribution, we present a strategy of MOR for a coupled thermo-mechanical model with a nonlinear subsystem and moving loads, using the example of a feed axis with nonlinear machine components. Applying tailored substructuring techniques, we are able to separate the linear and nonlinear system components. This allows to apply classic linear MOR methods to the much larger linear part, whereas the small nonlinear part is kept, and thus enables drastically reduced computing times. The relative movement is considered by a switched system approach. Transient thermo-mechanical interactions of the feed axis are calculated in a final investigation, comparing the performance of the resulting reduced-order model and the original one.