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Mathematical Problems in Engineering
Volume 2016, Article ID 2739208, 8 pages
Research Article

Analytical Modeling of a Ball Screw Feed Drive for Vibration Prediction of Feeding Carriage of a Spindle

1School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
2Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China
3School of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, China

Received 30 July 2016; Revised 21 October 2016; Accepted 14 November 2016

Academic Editor: Jaromir Horacek

Copyright © 2016 Lei Zhang 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.


An analytical modeling approach for ball screw feed drives is proposed to predict the dynamic behavior of the feeding carriage of a spindle. Mainly considering the rigidity of linear guide modules, a ball-screw-feeding spindle is modeled by a mass-spring system. The contact stiffness of rolling interfaces in linear guide modules is accurately calculated according to the Hertzian theory. Next, a mathematical model is derived using the Lagrange method. The presented model is verified by conducting modal experiments. It is found that the simulated results correspond closely with the experimental data. In order to show the applicability of the proposed mathematical model, parameter-dependent dynamics of the feeding carriage of the spindle is investigated. The work will contribute to the vibration prediction of spindles.