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Shock and Vibration
Volume 2014 (2014), Article ID 787518, 10 pages
Research Article

On the Free Vibration Modeling of Spindle Systems: A Calibrated Dynamic Stiffness Matrix

Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3

Received 17 October 2013; Accepted 17 March 2014; Published 12 May 2014

Academic Editor: Valder Steffen Jr.

Copyright © 2014 Omar Gaber and Seyed M. Hashemi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The effect of bearings on the vibrational behavior of machine tool spindles is investigated. This is done through the development of a calibrated dynamic stiffness matrix (CDSM) method, where the bearings flexibility is represented by massless linear spring elements with tuneable stiffness. A dedicated MATLAB code is written to develop and to assemble the element stiffness matrices for the system’s multiple components and to apply the boundary conditions. The developed method is applied to an illustrative example of spindle system. When the spindle bearings are modeled as simply supported boundary conditions, the DSM model results in a fundamental frequency much higher than the system’s nominal value. The simply supported boundary conditions are then replaced by linear spring elements, and the spring constants are adjusted such that the resulting calibrated CDSM model leads to the nominal fundamental frequency of the spindle system. The spindle frequency results are also validated against the experimental data. The proposed method can be effectively applied to predict the vibration characteristics of spindle systems supported by bearings.