Chapter28 Prediction of Dynamics of Modified Machine Tool by Experimental Substructuring Christian Brecher, Stephan Bäumler, and Matthias Daniels Abstract Until now the methods of experimental substructuring are rarely adopted in the machine tool sector, except for receptance coupling of tools and tool holders. In this paper, the methods are adopted to predict a general modification of a machine tool structure by coupling experimental and numerical models. This approach seems appropriate, since most design changes of machine tools affect only some part of the structure. Additionally, single components of a machine tool are easier to simulate than the complete machine tool, since they include less joints, which are usually difficult to parameterize. This contribution evaluates the proposed method, when it is applied to a single axis test bench. The slide is taken as the modified component—thus its dynamics are modeled analytically—and the remaining assembly is modeled experimentally. Particular emphasis is put on the modeling of the interfaces of the linear guides connecting the slide to the frame. Both a fixed connection between slide and frame and a linear spring-damper joint are adopted. Moreover, the dynamics of the assembly are predicted, for different positions of the slide. As a reference, the dynamics of the test bench are measured, when the slide is mounted. Keywords Vibration • Machine tool • Frequency based substructuring • Joints • Design modification 28.1 Introduction The dynamic behavior is an important criterion, when evaluating the performance of machine tools, [1]. The dynamic compliance at the Tool Center Point (TCP) describes the relative compliance between tool and work piece and is commonly measured or calculated as Frequency Response Functions (FRFs). These FRFs are used to compare different machine tools, but also represent the dynamic behavior of machine tools, when simulating the stability of cutting processes. In [2] the stability simulation is proposed as a decision criterion during the development of machine tools. As stressed there, the reliability of the stability prediction strongly depends on how well the dynamic behavior of the machine tool is modeled. Previous works (e.g. [2–4]) mostly update the parameters of a full machine model with respect to measurements of the corresponding physical machine. This approach is not satisfying with regard to the prediction of machine dynamics during the development since it presumes the existence of the physical machine. Moreover model updating of a complete machine tool is an elaborate task, considering that in most of the cases only rough initial estimates for the numerous joint characteristics (stiffness and damping properties) are possible, [1]. Especially the reliable choice of damping coefficient is currently a major research topic in the machine tool sector, [5]. Regarding that the majority of development tasks in the machine tool division are design variations or design adaptions [6], where only machine components, e.g. the machine table or a machine axis are modified, the combination of experimental and analytical models might allow to predict the dynamic machine tool behavior more efficiently. The unmodified part of the machine tool is then modeled experimentally while the modified part is modeled analytically. Following this approach the C. Brecher • S. Bäumler • M. Daniels ( ) Laboratory for Machine Tools and Production Engineering (WZL), RWTH Aachen University, Steinbachstraße 19, 52074 Aachen, Germany e-mail: m.daniels@wzl.rwth-aachen.de M. Allen et al. (eds.), Dynamics of Coupled Structures, Volume 1: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04501-6__28, © The Society for Experimental Mechanics, Inc. 2014 297
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