Low-dimensional time-discrete models for high dynamic machine tools

The coupling of real and virtual machine tool components in a hardware-in-the-loop environment is commonly used by state-of-the-art engineering tools as well as automated test procedures to verify the system behaviour. Time deterministic models are necessary to provide simulation results in a predictable time frame. This leads to efficient development procedures. This article presents a method and results of an automated engineering tool that uses time discrete deterministic order-reduced systems for the calculation of the dynamic machine tool behaviour. An innovative model-order-reduction (MOR) procedure was developed that provides a low-dimensional approximation of the original model with associated error estimation as well as inherent system characteristics, like passivity and steady-state accuracy, for a defined time step width. The validation of the calculation model, based on the new MOR procedure, was carried out on a three-axes test stand. It is representative f or high dynamic machine tools and equipped with an integrated real-time control environment. The real-time settings as well as stiffness K, damping D, and mass M can be adjusted. Various low-dimensional time discrete models were implemented for demonstrative application and experimental validation of the MOR procedure. The results show high potential for the use in engineering processes. A reduction from a secondary order system with 19, 932 unknowns to a first order system with 80 unknowns was realized. Furthermore, the difference between calculated and measured deviation of the test stand's x-axes was achieved with a value of eXMax = 750 nm.