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M. Rößler:
"Thermodynamical Coupling of a Machine Tool with its Environment";
Vortrag: MATHMOD 2012 - 7th Vienna Conference on Mathematical Modelling, Wien; 14.02.2012 - 17.02.2012; in: "Preprints Mathmod 2012 Vienna - Full Paper Volume", F. Breitenecker, I. Troch (Hrg.); Argesim / Asim, 38 (2012), S. 419 - 420.

Introduction Energy optimization is a very hot topic at the moment. For this reason, the research project INFO1,
which is supported by the FFG, the Austrian Research Promotion Agency, tries to make a comprehensive simulation
of a production plant, including all aspects, like machines, processes, the building envelope and so on, to be
able to make qualified predictions about the impact of certain energy-saving measures. In this context, the issue of
coupling different model-parts is very interesting. This work shall present a way to couple a simple machine tool
with the environment surrounding it. A linear guiding device is chosen to represent the machine tool and for the
environment, the surrounding room is discretised into compartments. The chosen modelling ansatz for both partial
models is physical modelling, a block-based, acausal and object-oriented approach to model physical systems.
Machine tool The linear guiding device is a very simple part of the machine tool. It consists of a permanent
magnet DC motor that is connected to a thread bar via a gear belt. The thread bar moves a cart, where the sliding
mass is attached. A model of this setup using components of the modelica standard library is depicted in the figure
below. The dissipative elements of the system, that are considered in the model are the electric motor, the bearing
friction and the friction between the thread bar and the cart. The heat emmission of these components is calculated
in the respective blocks and can then be used as a heating source for the environment model.
Environment For the model of the environment the room is discretised into compartments. Each compartment
has its own thermal mass, which depends on its volume, and for the heat transfer into adjacent compartments only
thermal conductance is considered. The thermal properties of the air, namely the density, specific heat capacity
and thermal conductivity, are assumed to be constant, because the rise of temperature in the compartments is
expected to be small and therefore an impact of temperature-dependent parameters on the simulation results can
be neglected. Additionally the walls of the room are assumed to be perfectly isolated, so there is no heat exchange
between the compartments and the adjacent walls and therefor no energy is lost in the system. The figure below
depicts the room model and one of its compartments, the parameters for the compartment are the dimensions into
the three axes, the rest of the parameters, like volume or thermal capacity are calculated in the parameterblock seen
in the top left corner. The components are again taken from the modelica standard library. One advantage of this
modelling approach, using compartments, is, that the model can easily be refined, if a higher resolution should be
necessary.