Oscillator Model of Machine Tools for the Simulation of Self Excited Vibrations in Machining Processes

Biermann, D.^{1, a}; Surmann, T.^{1, b}; Kehl, G.^{2, c}

1)

Institut für Spanende Fertigung, Technische Universität Dortmund, Baroper Str. 301, 44227 Dortmund

2)

Gebr. Heller Maschinenfabrik GmbH, Gebrüder-Heller-Str. 15, 72622 Nürtingen

a) biermann@isf.de; b) surmann@isf.de; c) kehl@heller.de

Kurzfassung

For the simulation of chatter vibrations for cutting processes it is necessary to model the interaction between the machine tool and the workpiece. This requires an efficient model of the vibratory manufacturing system consisting of workpiece, tool, tool holder, spindle and machine. Manufacturing systems can be characterized by their frequency response function (FRF) which can be modelled efficiently by superposition of a set of decoupled damped harmonic oscillators. The FRF of these superposed oscillators is capable of approximating measured FRF of actual machines with a high accuracy, when using enough single oscillators. Since each single oscillator has three variables (mass, natural frequency and damping) a set of m oscillators has 3 times m variables which can be tuned in to the correct values by an evolutionary algorithm. Thus it is possible to model the vibration behaviour of a manufacturing system with a very high accuracy. Additionally, the presented model can be evaluated in order to predict the response to arbitrary acting forces.

Schlüsselwörter

Process Machine Interaction, Machine Model, Machine Vibration

Veröffentlichung

In: The 1st International Conference on Process Machine Interactions (PMI 2008), 3.9.-4.9. 2008, Hannover, Germany, Denkena, B. (Hrsg.), ISBN 978-3-939026-95-2, S. 23-29