Machine tool simulation based on reduced order FE models

Numerical simulations of the behavior of machine tools are usually based on a finite element (FE) discretization of their mechanical structure. In order to capture all necessary details FE models are in general very large and sparse. Hence the computation of the simulation takes an unacceptable long time and requires much memory space. To calculate the results in reasonable time typically modal reduction is used to obtain a model of lower order. This method has the disadvantage that the reduced system only contains information of the modes chosen to generate the reduced system. Moreover, the choice of the essential modes is usually based on a heuristic and cannot be fully automated. Therefore, there is a need for alternate reduction methods which can be fully automated. In the last years new methods to reduce large and sparse dynamical systems were presented. The two most important ones are balanced truncation approximations (BTA) and Krylov subspace methods. Here the main focus is on the reduction of the special FE systems with Krylov subspace methods. The main goal of this work is to discuss whether these methods are suitable for this type of application, not on the derivation of a new reduction technique. Several Krylov subspace methods for first or second order systems based on the Interpolation-Rational-Krylov-Algorithm (IRKA) were implemented. The reduced systems are compared with reduced systems obtained by modal reduction and BTA.