Modal Analysis of Machine Tool Structures Based on Experimental Data

Abstract

The basic problem in modal analysis of machine tool structures is the extraction of modal parameters from the measured transfer function data. Conventionally this task is performed in two steps. The transfer function is determined using a Digital Fourier Analyzer followed by a suitable curve fitting procedure. In order to avoid the inherent problems associated with these procedures a new approach for modal analysis is proposed in this paper. Anticipating the stochastic nature of the systems excitation and response Modified Autoregressive Moving Average Vector models (MARMAV) are proposed. The modeling procedure yields a parametric representation of the structural behavior allowing the extraction of the modal information in one step, directly, rather than in two as in the conventional approaches. The mathematical foundation for the approach is given along with its application to a simulated three-degree-of-freedom system and a knee type milling machine. The newly proposed procedure is commensurate to the existing ones in light of the computational efforts involved; however, it eliminates the subjective judgment of the analyst since the modeling procedure is based on rigorous statistical adequacy checks. Finally, the proposed approach is amenable for implementation in a computer-based machine tool structural dynamics analyzer.