Journal of Sound and < ibration (2002) 254(5), 1012}1024 doi:10.1006/jsvi.2001.4106, available online at http://www.idealibrary.com on COMPARISON OF DIFFERENT MODELLING TECHNIQUES TO SIMULATE THE VIBRATION OF A CRACKED ROTOR H.KEINER AND M.S.GADALA Department of Mechanical Engineering, ¹ he ;niversity of British Columbia, < ancouver, BC, Canada <6¹ 1Z4. E-mail: gadala@mech.ubc.ca (Received 30 January 2001, and in ,nal form 10 September 2001) 1. INTRODUCTION Large-scalerotatingmachinery,suchasturbines,generatorsordrums,oftendevelopfatigue cracks throughout their service life, which can severely damage machine components or even lead to catastrophic failure. In general, non-destructive testing is used in inspection intervals to prevent such failures, but recently vibration analysis has received much attention in trying to continuously monitor the machine's condition. The advantages of on-lineconditionmonitoringareearlywarningsofmachinefailureandreduceddowntime. The vibration of a cracked shaft has been investigated by many researchers. Extensive reviewsoftheliteratureonthistopichavebeencompiledbyWauer[1]andmorerecently byDimarogonas[2].Ingeneral,aslightdecreaseandsplittingofthe "rstnaturalfrequency, resonance at half the "rst natural frequency, a slight increase in the 1/rev. and 3/rev. harmonicresponsesandastrongincreaseinthe2/rev.harmonicresponsearereferredtoas key indicators for a transverse crack in a shaft [3}5]. These observations have been con"rmed in experimental studies [5}7]. The results have been implemented in crack detection systems in industry [4, 8]. There have been several incidents where vibration monitoring led to the detection of a crack preventing catastrophic failure [9}11]. Until today, the greatest di$culty in crack detection and identi"cation remains the quantitative evaluation of the crack parameters and the distinction between a developing crack from other faults such as imbalance, misalignment, shaft bow, bearing failure, etc. [8,11].Thekeyissuesindevelopinganaccuratemodellingtechniqueofacrackedrotorare the reduced sti!ness of the cracked cross-section, the variation of sti!ness over one revolutionduetotheopeningandclosingofthecrack(crackbreathing)andthecomplexity in geometry of the rotor, in particular in the region of the developing crack. Dimarogonas [2] developed an analytical expression for the additional local crack compliance for a six-degree-of-freedom cracked beam segment. Alternatively, the local compliance matrix can be determined through a 3-D static "nite element (FE) analysis [4, 12, 13]. The crack breathingmechanismhasbeenmodelledinavarietyofways,allresultinginatime-varying local compliance matrix, which is incorporated into the dynamic equations for the rotor [12,14].Theequationsofmotionhavebeensolvedanalytically[6],inalinearizedform[5], or numerically through time-integration from the initial conditions [4, 12, 15]. Inmostcases,thegeometryoftherotorhasbeenlimitedtoasimpleLavalrotormodel and a single transverse crack placed at various locations along the axis. Sekhar [16] and Tsai and Wang [17] analyzed the behaviour of a rotor containing more than one crack. Sekhar [15] also investigated the in#uence of a slanted crack in a shaft. Researchers using 0022-460X/02/$35.00  2002 Elsevier Science Ltd. All rights reserved.