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A. Eichhorn:
"Analysis of dynamic deformation processes with adaptive Kalman-filtering";
Talk: 3rd IAG Symposium on Geodesy for Geotechnical and Structural Engineering & 12th FIG Symposium on Deformation Measurement, Baden; 2006-05-22 - 2006-05-24; in: "Proceedings of the 3rd IAG Symposium on Geodesy for Geotechnical and Structural Engineering & 12th FIG Symposium on Deformation Measurements", H. Kahmen, A. Chrzanowsky (ed.); (2006), ISBN: 3-9501492-3-6; 9 pages.

The analysis of dynamic deformation processes is an important task in civil and in
mechanical engineering. One main emphasis is set on the derivation of the objects transmission
function, represented by systems of ordinary or partial differential equations ("white
box"-models). The parametric identification of the initial and boundary conditions and
relevant material parameters is one of the new challenges in the application of least-square
algorithms. Embedding the investigation of the deformation process in a combination of a
theoretical and an experimental system analysis suitable methods are provided with adaptive
KALMAN-filtering as central identification tool. In this paper the approach of a full system
analysis is shown quantifying a dynamic "white-box"-model for the calculation of thermal
deformations of bar-shaped machine elements. The task was motivied from mechanical
engineering searching new methods for the precise prediction and computational compensation
of thermal influences in the heating and cooling phases of machine tools (i.e. robot
arms, etc.). The quantification of thermal deformations under variable dynamic loads requires
the modelling of the non-stationary spatial temperature distribution inside the object. Based
upon FOURIERS law of heat flow the high-grade non-linear temperature gradient is represented
by a system of partial differential equations within the framework of a dynamic Finite
Element topology. It is shown that adaptive KALMAN-filtering is suitable to quantify relevant
disturbance influences and to identify thermal parameters (i.e. thermal diffusivity) with a
deviation of only 0,2%. As result an identified (and verified) parametric model for the
realistic prediction respectively simu-lation of dynamic temperature processes is presented.
Classifying the thermal bend as the main deformation quantity of bar-shaped machine tools,
the temperature model is extended to a temperature deformation model. In lab tests with an
aluminium column control measurements show that the identified model can be used to predict
the columns bend with a mean deviation smaller than 10 mgon. Consequently the
deformation model is a precise predictor and suitable for realistic simulations of thermal
deformations under variable dynamic loads. In future our activities will be primarily focussed
on applications in industrial manufacturing.

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