Michael Beitelschmidt

Model order reduction of finite element models: improved component mode synthesis

The finite element (FE) approach constitutes an essential methodology when modelling the elastic properties of structures in various research disciplines such as structural mechanics, engine dynamics and so on. Because of increased accuracy requirements, the FE method results in discretized models, which are described by higher order ordinary differential equations, or, in FE terms, by a large number of degrees of freedom (DoF). In this regard, the application of an additional methodology, referred to as the model order reduction (MOR) or DoF condensation, is rather compulsory. Herein, a reduced dimension set of ordinary differential equations is generated, i.e. the initially large number of DoF is condensed, while aiming to keep the dynamics of the original model as intact as possible. In the commercially available FE software tools, the static and the component mode syntheses (CMS) are the only available integrated condensation methods. The latter represents the state of the art generating well-correlated reduced order models (ROMs), which can be further utilized for FE or multi-body systems simulations. Taking into consideration the information loss of the CMS, which is introduced by its part-static nature, the improved CMS (ICMS) method is proposed. Here the algorithmic scheme of the standard CMS is adopted, which is qualitatively improved by adequately considering the advantageous characteristics of another MOR approach, the so-called improved reduction system method. The ICMS results in better correlated reduced order models in comparison to all the aforementioned methods, while preserving the required structural properties of the original FE model.

Standard input data for FEM–MBS coupling: importing alternative model reduction methods into SIMPACK

Various research areas in the field of vehicle modelling, structural mechanics, engine dynamics, microelectromechanical systems (MEMS), etc. require the utilization of both multibody system formalism (MBS) and finite element method (FEM) in order to sufficiently capture the models dynamics. The FEM–MBS coupling is accomplished by reducing the dimension of the FE-modelled part and then importing it into an MBS-code for further simulation. When using commercial FEM (Nastran, ANSYS, etc.) as well as MBS (SIMPACK) software packages the necessary standard input data (SID) file is needed for the coupling procedure (FEMBS interface). A problem arises by the restriction that both commercial FEM and MBS codes support only two condensation methods (Guyan reduction and component mode synthesis (CMS)), thus disabling the direct application of any other reduction approach (e.g. from the field of control theory) that actually could be better. In this article, the theoretical background of an implemented FEM–MBS interface (MORPACK) is presented allowing the application of any kind of reduction method for FE-modelled structures and furthermore their import (Ritz approximation) into SIMPACK via the SID file generation. A benchmark problem (UIC60-rail) is used in order to capture in SIMPACK the discrepancy between the standardized CMS and the Krylov subspace method (KSM), as one of the alternatives offered by the interface.

Computation of Thermo-Elastic Deformations on Machine Tools - A study of Numerical Methods

Modern machine tools are highly optimized with respect to their design and the production processes they are capable to. Now for further advances, especially a detailed knowledge about the thermo-elastic behavior is needed, because the nowadays still existing deficits are mainly related to this. That is why, endeavors in improvement, like the optimization of the design, the evaluation of new materials and the regulation of the production process, particularly rely on accurate computed thermal deformations. One possible approach to increase their quality is to also include the relevant structural variabilities of the machine tools as well as the resulting interactions between the coupled parts within the calculations. In this article, three different numerical methods are presented, which include structural motions in thermo-elastic analyses. Thereby, several conflicting criteria, like real-time capability, memory saving issues and accuracy are fulfilled each time in a different manner. Those methods are afterwards compared with respect to their runtime and accuracy. Finally, the paper concludes with a classification of the usability of the methods in real-time control and optimization tasks.

Innovative Simulation Technology for Real-Time Calculation of the Thermo-Elastic Behaviour of Machine Tools in Motion

Heat resulting from motors, moved contacts as well as cutting processes, causes time-dependent deformation of machine structures that reduces the precision of machine tools. For design optimization and especially for correction of thermal induced displacements, it is necessary to have compact models, which allow fast simulation of the thermo-elastic behaviour of the entire moving machine tool during the process. This paper presents an innovative simulation technology that permits, starting from CAD geometry through FE modelling, to come to a time-saving thermo-elastic calculation model of entire moved machine tools. Thereby, calculated temperature and deformation fields are of high geometrical resolution. Results and potentials of the new approach are demonstrated on example of a Hexapod machine tool.

Mathematical modeling of the dynamic yarn path depending on spindle speed in a ring spinning process

This paper presents a mathematical model to predict the distribution of yarn tension and the balloon shape as a function of spindle speed in the ring spinning process. The dynamic yarn path from the delivery rollers to the winding point on the cop has been described with a non-linear differential equation system. These equations have been integrated with a Runge–Kutta method using MATLAB software. Since the numerical solution of the equations strongly depends on initial values, an algorithm of sensitivity analysis has been developed to predict the right choice of initial values in order to find a stable solution. For model validation purposes, the yarn tension has been measured between delivery rollers and yarn guide. Furthermore, a high-speed camera has been used to capture the balloon shape at different spindle angular velocities in order to compare the theoretically determined balloon shape with the one that actually occurs on the machine.

Simulation of Pose- and Process-Dependent Machine Tool Models

Within the CRC/TR 96, when calculating the thermal behaviour of machine tools, the consideration of the structural variability of machine tools is an approach to enhance the representational quality of the associated simulation models. A potential solution, which uses embedding moving model elements in sequential thermo-elastic analyses using discrete moving loads, is described in the following. The method is implemented in the proprietary FE software ANSYS. Based on selected theoretical fundamentals, embedding of motion is outlined in detail, focussing on an efficient use of the modelling tools made available by ANSYS. Various non-trivial special features that may hinder a successful simulation are highlighted. Measures to avoid these problems are described. Finally the influence of the method on the simulation results is described using the example of experiments carried out in an application.

An Arithmetic Correction for Avoiding Non-Uniform Heat Input Distribution Caused by Translational Motions Within Time-Discrete Thermal Analyses

Using a coarse time discretisation for saving calculation effort will induce non-uniform heat input within thermal-transient analyses which include translational rigid body motions by the technique of discrete displacement adjustment. We are going to show, why these non-uniformities are generally unavoidable and how a suitable choice of time step size pre-minimizes their consequences. Afterwards, the amount and location of the remaining load-bumps are analytical deduced for an arbitrary motion. With this information, we develop a correction method based on arithmetic calculations to avoid these numerical caused errors. For practical use, the correction is applied as an algorithm to the solution process of analyses with spatial discretized motion partners. We finish by demonstrating the performance of the correction.Copyright

MORPACK-Schnittstelle zum Import von FE-Strukturen nach SIMPACK

Zusammenfassung Ausgehend von der Finite-Elemente-Methode — dem am häufigsten verwendeten numerischen Verfahren in der Strukturmechanik — und der Methode der Mehrkörpersimulation — zur Modellierung von mechanischen Systemen mit großen Starrkörperbewegungen — beschreibt der Beitrag Grundlagen und Methodik zur Kopplung beider Verfahren. Die Kombination führt auf eine Beschreibung als elastisches Mehrkörpersystem und erfordert meist eine Modellordnungsreduktion. Für diesen Zweck sind diverse Techniken in der hauseigenen Software MORPACK implementiert, deren Funktionalität am Beispiel des kommerziellen Finite-Elemente-Programmes ANSYS und des kommerziellen Mehrkörpersimulationsprogrammes SIMPACK vorgestellt wird. Abstract Based on the Finite-Element-Method — the most frequently used numeric principle of structural mechanics — and the method of Multi-Body-Dynamics — which serves the modeling of mechanical systems with large deflections — this paper presents the background of the coupling process of both methods. The combination leads to elastic Multi-Body-Dynamics and utilizes usually a Model Order Reduction. For this purpose, diverse techniques are implemented in the in-house software MORPACK that is introduced at the example of the commercial Finite-Element-Program ANSYS and the commercial Multi-Body-Dynamics-Program SIMPACK.

A Robot Competition to Encourage First-Year Students in Mechatronic Sciences

In 2010, for the first time, a robot competition was organized at the Technische Universitaet Dresden for first-year students of mechatronics. The competition was supposed to give the students a push of motivation for their studies. Four different challenges were developed and combined to a relay competition. The robots were built with Lego Mindstorms NXT 2.0 and programmed with National Instruments LabVIEW. In this article the project’s organization and implementation as well as the gained experiences are described.

A method for correcting a moving heat source in analyses with coarse temporal discretization

The numerical simulation of a moving heat source from a fixed point observer is often done by discretely adjusting its position over the steps of a thermal transient analysis. The efficiency of these simulations is increased when using a coarse temporal discretization whilst maintaining the quality of results. One systematic error source is the rare update of a nonconstant moving heat source with regard to its magnitude and location. In this work, we present an analysis of the error and propose a correction approach based on conserving the specified heat from a continuous motion in analyses with large time-step sizes. Deficiencies associated with the correction in special motion situations are identified by means of performance studies and the approach is extended accordingly. The advantages of applying the proposed correction are demonstrated through examples.