Development of a model order reduction method for the direct generation of time-discrete, low-dimensional models of machine tools

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The development of modern machine tools is under great innovation, time and cost pressure. With continuous growth of productivity demands, also the complexity of machine tools increases. There is a high demand for innovative methods of developing and testing, to handle with these challenges. It results in preventing expensive design- or development-failures of a physical prototype as well as reducing commissioning times at a later point in time. Therefore time-deterministic models are needed, on the one hand having a high model quality and on the other hand a solution at a predetermined time step. Due to the model size of typical finite element models, these time steps are not suitable for real-time computations. Consequently, there is a demand for adapted model order reduction to solve real time problems. Currently, no such automated procedure for the creation of real-time computable systems exists applicable for complex finite-element models. The subject of this research project is to develop a model order reduction method for the direct generation of time-discrete, low-dimensional models of machine tools. The main goal of the project is the automated and customized application specific provision of discrete-time, deterministic, reduced systems to real-time capable models of the dynamic behavior of machine tools. For this purpose an innovative model order reduction method will be developed, which provides a low-dimensional approximation for a fixed time step of an original model along with the associated error estimate and retaining inherent system properties (such as passivity, steady-state accuracy). The method is based on high-dimensional ordinary differential equations and differential-algebraic equations, which are provided by finite element models of machine tools or rather machine modules. Furthermore, the method allows for the consideration of the time step for real-time calculations. In addition, the error estimation serves as abort criterion allowing the automatic model order reduction. Through interdisciplinary cooperation of production engineering and mathematics to support this innovative process and shorten the development of mechatronic systems and as machine tool is provided. This method is used in the early stage of the development process as far as to the point of virtual commissioning. The method makes a major contribution to the creation of structural models and to the increase of the accuracy of these models.