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. after linearization one obtains a second-order system of ordinary differential equations. in order to capture all necessary details the system that inevitable arises is too complex to meet the expediency requirements of real time simulation and control. in commercial fe simulation software often modal reduction is used to obtain a model of lower order which allows for faster simulation. in recent years new methods to reduce large and sparse dynamical systems emerged. this work concentrates on the reduction of certain fe systems arising in machine tool simulation with krylov subspace methods. the main goal of this work is to discuss whether these methods are suitable for the type of application considered here. several krylov subspace methods for first or second-order systems were tested. numerical examples comparing our results to modal reduction are presented.