{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T03:07:05Z","timestamp":1778382425470,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,4,13]],"date-time":"2015-04-13T00:00:00Z","timestamp":1428883200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The root mean square (RMS) value of a vibration signal is an important indicator used to represent the amplitude of vibrations in evaluating the quality of high-speed spindles. However, RMS is unable to detect a number of common fault characteristics that occur prior to bearing failure. Extending the operational life and quality of spindles requires reliable fault diagnosis techniques for the analysis of vibration signals from three axes. This study used empirical mode decomposition to decompose signals into intrinsic mode functions containing a zero-crossing rate and energy to represent the characteristics of rotating elements. The MSE curve was then used to identify a number of characteristic defects. The purpose of this research was to obtain vibration signals along three axes with the aim of extending the operational life of devices included in the product line of an actual spindle manufacturing company.<\/jats:p>","DOI":"10.3390\/e17042170","type":"journal-article","created":{"date-parts":[[2015,4,14]],"date-time":"2015-04-14T03:11:46Z","timestamp":1428981106000},"page":"2170-2183","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["High-Speed Spindle Fault Diagnosis with the Empirical Mode Decomposition and Multiscale Entropy Method"],"prefix":"10.3390","volume":"17","author":[{"given":"Nan-Kai","family":"Hsieh","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, Taipei, 10617 Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei-Yen","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, Taipei, 10617 Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong-Tsu","family":"Young","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, Taipei, 10617 Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.ymssp.2012.06.015","article-title":"A new procedure for extracting fault feature of multi-frequency signal from rotating machinery","volume":"32","author":"Xiong","year":"2012","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1016\/j.measurement.2012.02.030","article-title":"An insight concept to select appropriate IMFs for envelope analysis of bearing fault diagnosis","volume":"45","author":"Tsao","year":"2012","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1007\/s00170-004-2449-0","article-title":"Condition monitoring studies on spindle bearing of a lathe","volume":"28","author":"Saravanan","year":"2006","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1016\/j.ymssp.2008.11.005","article-title":"Application of the EEMD method to rotor fault diagnosis of rotating machinery","volume":"23","author":"Lei","year":"2009","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ymssp.2012.09.015","article-title":"A review on empirical mode decomposition in fault diagnosis of rotating machinery","volume":"35","author":"Lei","year":"2013","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/S0924-0136(02)00051-1","article-title":"Effect of misalignment on the cutting force signature in drilling","volume":"124","year":"2002","journal-title":"J. Mater. Process. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.ymssp.2012.01.022","article-title":"Characterization of gear faults in variable rotating speed using Hilbert-Huang Transform and instantaneous dimensionless frequency normalization","volume":"30","author":"Wu","year":"2012","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454A","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1115\/1.1948399","article-title":"Empirical model decomposition based time-frequency analysis for the effective detection of tool breakage","volume":"128","author":"Peng","year":"2006","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.ymssp.2012.12.010","article-title":"An improved EEMD with multiwavelet packet for rotating machinery multi-fault diagnosis","volume":"36","author":"Jiang","year":"2013","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0888-3270(03)00099-2","article-title":"Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings","volume":"19","author":"Yu","year":"2005","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.ymssp.2004.11.002","article-title":"A fault diagnosis approach for roller bearings based on EMD method and AR model","volume":"20","author":"Cheng","year":"2006","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2607","DOI":"10.1016\/j.ymssp.2006.12.004","article-title":"Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert-Huang transform","volume":"21","author":"Rai","year":"2007","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1016\/j.ymssp.2004.01.006","article-title":"A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing","volume":"19","author":"Peng","year":"2005","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1177\/2041297510394062","article-title":"Condition-based shaft fault diagnosis with the empirical mode decomposition method","volume":"225","author":"Lin","year":"2010","journal-title":"Proc. IMechE Part B: J. Eng. Manuf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","article-title":"Approximate entropy as a measure of system complexity","volume":"88","author":"Pincus","year":"1991","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.ymssp.2006.02.009","article-title":"Approximate entropy as a diagnostic tool form machine health monitoring","volume":"21","author":"Yan","year":"2007","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1016\/j.eswa.2007.12.065","article-title":"Automatic detection of elileptic seizures in EEG using discrete wavelet transform and approximate entropy","volume":"36","author":"Ocak","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am J. Physiol. Heart. Circ. Physiol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"068102","DOI":"10.1103\/PhysRevLett.89.068102","article-title":"Multiscale entropy analysis of complex physiologic time series","volume":"89","author":"Costa","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6077","DOI":"10.1016\/j.eswa.2010.02.118","article-title":"Bearing fault diagnosis using multi-scale entropy and adaptive neuro-fuzzy inference","volume":"37","author":"Zhang","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7200","DOI":"10.1016\/j.eswa.2010.04.009","article-title":"Motor shaft misalignment detection using multiscale entropy with wavelet denoising","volume":"37","author":"Lin","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1016\/j.triboint.2007.01.025","article-title":"Effect of lubricant viscosity grade on mechanical vibration of roller bearings","volume":"40","author":"Serrato","year":"2007","journal-title":"Tribol. Int."},{"key":"ref_24","unstructured":"Wilosn, J.S. (2005). Sensor Technology Handbook, Newnes."},{"key":"ref_25","unstructured":"Hansen, T.F. (2007). Accelerometer mounting techniques. B&K Web Course."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.measurement.2013.08.036","article-title":"Application of Hilbert-Huang transform to acoustic emission signal for burn feature extraction in surface grinding process","volume":"47","author":"Yang","year":"2014","journal-title":"Measurement"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.jsv.2004.10.005","article-title":"An improved Hilbert-Huang transform and its application in vibration signal analysis","volume":"286","author":"Peng","year":"2005","journal-title":"J. Sound Vib"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1146\/annurev.fluid.31.1.417","article-title":"A new view of nonlinear water waves: The Hilbert Spectrum","volume":"31","author":"Huang","year":"1999","journal-title":"Annu. Rev. Fluid Mech"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"021906","DOI":"10.1103\/PhysRevE.71.021906","article-title":"Multiscale entropy analysis of biological signals","volume":"71","author":"Costa","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.precisioneng.2004.06.005","article-title":"A parametric study on oil\/air lubrication of a high-speed spindle","volume":"29","author":"Wu","year":"2005","journal-title":"Precis. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/S0890-6955(00)00081-X","article-title":"Vibration based preload estimation in machine tool spindles","volume":"41","author":"Spiewak","year":"2001","journal-title":"Int. J. Mach. Tools Manuf"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"8","DOI":"10.9790\/1684-0330820","article-title":"Detection of unbalance in rotating machines using shaft deflection measurement during its operation","volume":"3","author":"Saleem","year":"2012","journal-title":"J. Mech. Civil Eng"},{"key":"ref_33","unstructured":"(SKF-Catalogue 4950\/IE, 2000). SKF-Catalogue 4950\/IE."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1007\/s00170-011-3356-9","article-title":"A comparative study on the dynamics of high speed spindles with respect to different preload mechanisms","volume":"57","author":"Cao","year":"2011","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_35","unstructured":"Available online: www.budmgt.com\/machanic\/mcn-pdf\/vibration-guide.pdf."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/4\/2170\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:44:36Z","timestamp":1760215476000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/4\/2170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,13]]},"references-count":35,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,4]]}},"alternative-id":["e17042170"],"URL":"https:\/\/doi.org\/10.3390\/e17042170","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,13]]}}}