Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 510406, 15 pages
Research Article

Tool Wear Detection Based on Duffing-Holmes Oscillator

Wanqing Song,1 Shen Deng,2 Jianguo Yang,1 and Qiang Cheng2

1College of Mechanical Engineering, Donghua University, Shanghai 201620, China
2Shanghai University of Science, 333#, Longteng Road, Songjiang district, Shanghai 201620, China

Received 28 May 2008; Accepted 27 July 2008

Academic Editor: Carlo Cattani

Copyright © 2008 Wanqing Song 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.


The cutting sound in the audible range includes plenty of tool wear information. The sound is sampled by the acoustic emission (AE) sensor as a short-time sequence, then worn wear can be detected by the Duffing-Holmes oscillator. A novel engineering method is proposed for determining the chaotic threshold of the Duffing-Holmes oscillator. First, a rough threshold value is calculated by local Lyapunov exponents with a step size 0.1. Second, the exact threshold value is calculated by the Duffing-Holmes system in terms of the law of the golden section. The advantage of the method is low computation cost. The feasibility for tool condition detection is demonstrated by the 27 kinds of cutting conditions with sharp tool and worn tool in turning experiments. The 54 group data sampled as noisy are embedded into the Duffing-Holmes oscillator, respectively. Finally, one chaotic threshold is determined conveniently which can distinguish between worn tool or sharp tool.