Efficient Static and Dynamic Modelling of Machine Structures with Large Linear Motions
Natanael Lanz*,, Daniel Spescha**, Sascha Weikert**, and Konrad Wegener*
*Institute of Machine Tools and Manufacturing (IWF), ETH Zürich
Leonhardstrasse 21, 8092 Zürich, Switzerland
**inspire AG, Zürich, Switzerland
Mechatronic structures deform under static and dynamic loads. These deformations lead to deviations at the tool center point (TCP), affecting the reachable accuracy and/or productivity of the machines. The scope of this work is the comparison of calculations and measurements of different static and dynamic errors on a dynamic test bench. A reduced-order modelling approach is applied for the test bench modelling. It uses a combination of modal condensation and moment-matching methods with Krylov subspaces. The different modelling steps and requirements are presented. The same model is used for all static and dynamic evaluations presented within this paper. Static deformations, leading to roll and pitch deviations at the TCP of the test bench structure, are simulated using the described modelling methodology and validated by inclination measurements. The modal behavior of the system is investigated by calculation and compared to the measurements at a single axes position. The spatial change of the frequency response functions of the modelled system is investigated further, by calculation and measurement of the velocity open-loop FRFs of one axis for different machine configurations. In addition, a transient trajectory simulation is performed and compared to the Heidenhain KGM and encoder measurements. The large variety of comparisons shows the efficient applicability of the modelling environment MORe.
-  D. Spescha, “Framework for Efficient and Accurate Simulation of the Dynamics of Machine Tools,” Ph.D. thesis, Technische Universität Clausthal, 2018.
-  D. Spescha, “More Software,” 2017. https://www.more-simulations.ch/ [Accessed August 24, 2018]
-  J. Berkemer, “Gekoppelte Simulation von Maschinendynamik und Antriebsregelung unter Verwendung linearer Finite Elemente Modelle,” Ph.D. thesis, Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen, Universität Stuttgart, 2003.
-  S. B. Salimbahrami, “Structure preserving order reduction of large scale second order models,” Ph.D. thesis, Universität München, 2005.
-  D. Siedl, “Simulation des dynamischen Verhaltens von Werkzeugmaschinen während Verfahrbewegungen,” Ph.D. thesis, Institut für Werkzeugmaschinen und Fertigung, Technische Universität München, 2008.
-  N. Lanz, D. Spescha, N. Ceresa, A. Ryser, and S. Weikert, “Modelling and Validation of Position Dependant Structural Deformations of a Machine Tool Structure under Gravitational Loads,” euspen 17th Int. Conf. & Exhibition, 2017.
-  D. Spescha, S. Weikert, S. Retka, and K. Wegener, “Krylov and Modal Subspace based Model Order Reduction With A-Priori Error Estimation,” ETH Zürich Research Collection, doi: 10.3929/ethz-b-000284435, 2018.
-  B. Salimbahrami, R. Eid, and B. Lohmann, “Model reduction by second order Krylov subspaces: Extensions, stability and proportional damping,” Proc. of the 2006 IEEE Conf. on Computer Aided Control Systems Design, CACSD, pp. 2997-3002, 2007.
-  “Whyler Blue Level,” 2017. https://www.wylerag.com/ [Accessed August 24, 2018]
-  O. Zirn, “Machine tool analysis – modelling, simulation and control of machine tool manipulators,” A Habilitation Thesis, ETH Zürich, 2008.
-  D. Spescha, S. Weikert, O. Zirn, and K. Wegener, “Synchronisation of feed axes with differing bandwidths using set point delay,” Int. J. Automation Technol., Vol.11, No.2, pp. 155-164, 2017.
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