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Mathematical Problems in Engineering
Volume 2014, Article ID 454156, 11 pages
Research Article

Analytical and Finite Element Modeling of the Dynamic Characteristics of a Linear Feeding Stage with Different Arrangements of Rolling Guides

1Department of Automation Engineering, Nan Kai University of Technology, No. 568 Zhongzheng Road, Caotun Township, Nantou County 54243, Taiwan
2Graduate Institute of Precision Manufacturing, National Chin-Yi University of Technology, No. 57, Section 2, Zhongshan Road, Taiping District, Taichung 41170, Taiwan

Received 22 February 2014; Accepted 6 April 2014; Published 1 July 2014

Academic Editor: Her-Terng Yau

Copyright © 2014 Jyh-Cheng Chang and Jui-Pin Hung. 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.


This study was aimed at investigating the dynamic behaviors of the linear driven feeding stage by means of the analytical and finite element modeling approaches. To assess the dynamic characteristics of the stages with different linear guide arrangements, the finite element model of the stages was created, in which the linear components with rolling interface were accurately modeled based on the Hertzian theory. On the other hand, the analytically mathematical model was derived to determine how the linear guide arrangement affects the dynamic characteristics of the stage. Results of the modal analysis show that the vibration behaviors of the positioning stage are dominated by the rigidity of the linear components and the platform. In addition, comparisons of the results from the two approaches further indicate that the platform rigidity is an important factor determining the accuracy of the prediction of the vibration frequencies by the analytically mathematical model. As a conclusion of the study, the analytically mathematical model can approximate well to the finite element model when the linear stage is designed with appropriate structure rigidity.