Evaluating tool point dynamics using output-only modal analysis with mass-change methods

Abstract

This paper discusses the evaluation of tool point dynamics using output-only modal analysis methods. As compared to the traditional experimental modal analysis procedures that rely on the input and the output, both being known, output-only methods discussed herein can evaluate modal parameters using only the measured response of the tool subjected to unknown impact-based excitations. Since the input is not known, the estimated shapes are unscaled. To correctly scale shapes, we use the mass-change method. We present analytical models to guide the optimal selection of the mass to be added as well as to guide its placement on the tool. Analytical models systematically characterize errors in scaling the eigenvector and errors due to uncertainties in the estimation of the natural frequencies. The model suggests placement of the mass to be added at the anti-node(s) for the mode(s) of interest. These models guide experiments on two tools – a slender boring bar, and an end mill. Tool point frequency response functions (FRFs) reconstructed with the natural frequencies, damping ratios, and scaled mode shapes evaluated with the output-only mass-change method are compared with and found to be in good agreement with FRFs obtained from the traditional experimental modal analysis procedures. Since output-only methods require one less transducer, and since these methods are robust to uncertainties and inconsistencies in the input, output-only methods promise advantages from the industrial point of view.