1850 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 5, OCTOBER 2006 Spindle Health Diagnosis Based on Analytic Wavelet Enveloping Li Zhang, Robert X. Gao, Senior Member, IEEE, and Kang B. Lee, Fellow, IEEE Abstract—A new diagnostic technique for identifying structural defects in spindles was developed based on the analytic wavelet transform. The new technique extracts defect-induced impulses from the spindle vibration signal and constructs their envelopes in a single step, eliminating the need for intermediate operations as traditionally required. Theoretical background of the analytic wavelet transform was first introduced, and numerical simulation was then conducted on a synthetic signal. The result was subse- quently compared with vibration signals measured on a spindle test bed. It was confirmed that the developed technique is effective in detecting defect-induced impulses buried in the spindle vibra- tion signals that otherwise were undetectable using the traditional spectral techniques. Index Terms—Analytic wavelet, enveloping, spindle health diagnosis. I. I NTRODUCTION I N THE machine tool industry, unexpected failure of spindles can lead to severe part damage and costly machine down- time, affecting the overall production logistics and productivity. Vibration signals measured on a spindle contain rich physical information about the operating conditions; thus, vibration signal analysis has long been regarded as a physics-based tech- nique for spindle defect detection and health diagnosis [1]. In a rotating spindle, the main causes contributing to its vibration in- clude manufacturing imperfection, assembly- and installation- related problems, and tool–work interactions [2]. Rolling element bearings are the most critical and vulnerable component in a machine tool spindle. As the bearings wear out, localized defects may develop on the raceways (inner or outer) or within the rolling elements (balls and rollers) themselves. Interactions between the rolling elements and the defects ex- press themselves as impulsive inputs to the bearing and spindle structure, which excites high-frequency structural resonance in the form of vibration impulses. Due to the rotating nature of the spindle, these impulses are repetitive and periodic in nature, and their strength depends on both the defect geometry and the spindle operating condition (e.g., applied load and shaft rotational speed). Furthermore, the specific location of a defect is reflected in its characteristic frequency [3], [4], e.g., ball spin frequency (BSF), ball pass frequency for inner raceway (BPFI), Manuscript received June 6, 2005; revised May 25, 2006. This work was supported by the Smart Machine Tools Program at the National Institute of Standards and Technology (NIST). L. Zhang and R. X. Gao are with the Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003 USA (e-mail: lizhang@ecs.umass.edu; gao@ecs.umass.edu). K. B. Lee is with the Manufacturing Metrology Division, National Insti- tute of Standards and Technology, Gaithersburg, MD 20899 USA (e-mail: kang.lee@nist.gov). Digital Object Identifier 10.1109/TIM.2006.880261 Fig. 1. Envelope and pattern of defect-induced vibration in rolling element bearings. and ball pass frequency for outer raceway (BPFO), as illustrated in Fig. 1. Therefore, spectral techniques can be employed to analyze spindle vibration signals for defect detection and identification. Spectral analysis of the envelope of a vibration signal (enve- lope spectrum) has shown to be a more effective approach to the detection and identification of structural defects than spectral analysis of the raw vibration signal itself [5], [6]. However, given that defect-induced vibration impulse is generally weak in amplitude and short in duration at the incipient stage [7], the effectiveness of enveloping generally suffers from a low signal- to-noise ratio (SNR). In recent years, wavelet transform has received considerable attention from the research community due to its ability in extracting time-dependent transient features from vibration signals with strong background noise by means of a combined time–frequency analysis [8]. Combining the advantages of enveloping and wavelet transform, this paper presents a new method for machine health diagnosis based on a specific class of wavelets called the “analytic wavelet,” which served as the base wavelet for spindle vibration signal decomposition and analysis. The rationale for investigating this class of wavelets is that they extract defect features and con- struct the signal’s envelope in a single step, thus eliminating the need for additional operations such as the Hilbert transform [9] or low-pass filtering to extract signal envelope. In addition, the analytic wavelet is inherently flexible in the selection of relative bandwidth, thus, it can be adaptively applied to the signal under investigation. 0018-9456/$20.00 © 2006 IEEE