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Shock and Vibration
Volume 2017 (2017), Article ID 2736545, 13 pages
Research Article

Dynamic Optimization of Constrained Layer Damping Structure for the Headstock of Machine Tools with Modal Strain Energy Method

1Key Laboratory of Mechanism Theory and Equipment Design, Ministry of Education, Tianjin University, Tianjin 300072, China
2School of Electrical Engineering and Automation, East China Jiaotong University, Nanchang 330013, China
3School of Engineering, University of Warwick, Coventry CV4 7AL, UK
4Shenji Group Kunming Machine Tool Company Limited, Kunming 650203, China

Correspondence should be addressed to Weiguo Gao

Received 3 November 2016; Accepted 31 January 2017; Published 22 February 2017

Academic Editor: Sergio De Rosa

Copyright © 2017 Yakai Xu et al. 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.


Dynamic stiffness and damping of the headstock, which is a critical component of precision horizontal machining center, are two main factors that influence machining accuracy and surface finish quality. Constrained Layer Damping (CLD) structure is proved to be effective in raising damping capacity for the thin plate and shell structures. In this paper, one kind of high damping material is utilized on the headstock to improve damping capacity. The dynamic characteristic of the hybrid headstock is investigated analytically and experimentally. The results demonstrate that the resonant response amplitudes of the headstock with damping material can decrease significantly compared to original cast structure. To obtain the optimal configuration of damping material, a topology optimization method based on the Evolutionary Structural Optimization (ESO) is implemented. Modal Strain Energy (MSE) method is employed to analyze the damping and to derive the sensitivity of the modal loss factor. The optimization results indicate that the added weight of damping material decreases by 50%; meanwhile the first two orders of modal loss factor decrease by less than 23.5% compared to the original structure.