Analysis of dynamic deformation processes with adaptive KALMAN-filtering

Abstract

In this paper the approach of a full system analysis is shown quantifying a dynamic structural ("white-box''-) model for the calculation of thermal deformations of bar-shaped machine elements. The task was motivated 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 simulation 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 thermal load steps are applied to an aluminum column. Independent control measurements show that the identified model can be used to predict the columns bend with a mean deviation (r.m.s.) smaller than 10 mgon. These results show that the deformation model is a precise predictor and suitable for realistic simulations of thermal deformations. Experiments with modified heat sources will be necessary to verify the model in further frequency spectra of dynamic thermal loads.