Bivariate uncertainty analysis for impact testing

Abstract

This paper evaluates uncertainty contributors for frequency response function (FRF) measurements obtained through impact testing. The FRF is an important estimator for the structural dynamics of tool-holder–spindle-machine assemblies and is used as an input to analyses of milling dynamics. Therefore, it is of interest to determine the confidence in the measurement results. In this work, we present a bivariate uncertainty analysis that considers statistical variations, imperfect calibration coefficients for the hammer and transducer, misalignment between the intended and actual force direction during impact and mass loading (when using an accelerometer). The complex-valued FRF can be expressed by its real and imaginary parts, which are potentially correlated. This correlation is included in the bivariate analysis. An ellipsoid-shaped confidence region (at each frequency) is defined in the complex plane; the size and orientation of this region is determined from the individual input uncertainties. The scalar, total uncertainty is then determined using an eigen analysis of the FRF covariance matrix. Experimental results are provided.

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