Vibration in a Cracked Machine Tool Spindle with Magnetic Bearings

Huang-Kuang Kung, Bo-Wun Huang*
Department of Mechanical Engineering, Cheng Shiu University, Taiwan.

© 2008 Kung and Huang

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mechanical Engineering, Cheng Shiu University, Taiwan; E-mail:


Due to manufacturing flaws or cyclic loading, cracks frequently appear in a rotating spindle system. These cracks markedly affect the dynamic characteristics in higher modes of the rotating machinery. For faster rotational speeds, especially for super-high-speed cutting, a spindle with magnetic bearings is necessary. However, most investigations into spindle system dynamic characteristics have been confined to ball-bearing-type spindles. The dynamic response of rotating cracked spindle systems with magnetic bearings is examined in this article. A Euler-Bernoulli beam of circular cross section is used to approximate the spindle and the Hamilton principle is employed to derive the equation of motion for the spindle system. The effects of crack depth, rotation speed and bearing length on the dynamic response of a rotating magnetic bearing spindle system are studied.