Identi cation of the Dynamic Models of Machine Tool Supporting Systems. Part I: An Algorithm of the Method

Abstract

In this paper we present an original algorithm for the identification of dynamic models of machine tool supporting systems on the basis of limited information about an object contained in the experimentally determined frequency response characteristics obtained for a given excitation. We have described the way of creating models that are later to be identified. The models have been built in the convention of the rigid finite element method, which is complemented by the added option that allows us to model slideway joints. Any stiffness and damping coefficients of any spring–damping elements of a given model can be estimated by means of the elaborated method. In order to select decision variables, we have used a sensitivity analysis of the frequency response characteristics on changes in the values of a model's parameters. The Fisher's model of uncertainty has been adopted for the algorithm. The minimization of the identification criterion has been carried out using gradient methods. In order to assess the uniqueness of the obtained solutions the Cramer– Rao information inequality has been used. On the basis of the presented algorithm a computer program IDENT has been elaborated. It enables an effective estimation of parameters of machine tool supporting systems. The numerical tests have confirmed both the reliability of the algorithm and the high effectiveness of the IDENT program. In this paper we present both the results and the commentary of one such test.