In the article methods of vibroacoustic diagnostics of high-power toothed gears are described. It is shown below, that properly registered and processed acoustic signal or vibration signal may serve as an explicitly interpreted source of diagnostic symptoms. The presented analysis were based on vibration signals registered during the work of the gear of a rolling stand working in Katowice Steel Plant (presently one of the branches of Mittal Steel Poland JSC).U članku se opisuju metode vibroakustične dijagnostike zupčanika visoke snage. Dalje je pokazano, da ispravno registrirani i obrađeni akustični signal ili vibracijski signal može poslužiti kao eksplicitno interpretirani izvor dijagnostičkih simptoma. Predstavljene analize temeljile su se na vibracijskim signalima registriranima tijekom rada zupčanika valjačkog stana u pogonu u čeličani Katowice (trenutno jedan od ogranaka tvrtke Mittal Steel Poland JSC)

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521METALURGIJA 51 (2012) 4, 521-524P. CZECHDIAGNOSIS OF INDUSTRIAL GEARBOXES CONDITION BY VIBRATION AND TIME-FREQUENCY, SCALE-FREQUENCY, FREQUENCY-FREQUENCY ANALYSISReceived – Prispjelo: 2011-08-20Accepted – Prihvaćeno: 2012-02-20Preliminary Note – Prethodno priopćenje ISSN 0543-5846METABK 51(4) 521-524 (2012)UDC – UDK 621:621-833:534.6=111In the article methods of vibroacoustic diagnostics of high-power toothed gears are described. It is shown below, that properly registered and processed acoustic signal or vibration signal may serve as an explicitly interpreted source of diagnostic symptoms. The presented analysis were based on vibration signals registered during the work of the gear of a rolling stand working in Katowice Steel Plant (presently one of the branches of Mittal Steel Poland JSC).Key words: mechanical engineering, gear, acoustic signal, diagnosisDijagnoza stanja industrijskih zupčanika pomoću vibracijske, vermensko frekvencijske, skalno frekvencij-ske, frekvencijsko frekvencijske analize. U članku se opisuju metode vibroakustične dijagnostike zupčanika vi-soke snage. Dalje je pokazano, da ispravno registrirani i obrađeni akustični signal ili vibracijski signal može poslužiti kao eksplicitno interpretirani izvor dijagnostičkih simptoma. Predstavljene analize temeljile su se na vibracijskim signalima registriranima tijekom rada zupčanika valjačkog stana u pogonu u čeličani Katowice (trenutno jedan od ogranaka tvrtke Mittal Steel Poland JSC)Ključne riječi: strojarstvo, zupčanik, akustički signal, dijagnozeINTRODUCTIONResidual phenomena are inseparable phenomena during the work of a technical object, and among them there are vibrations and noise [1,2]. The evaluation of the technical condition on the basis of research is known under the name of vibroacoustic diagnostics. The basis for the research on the use of vibroacous-tic signals in the diagnostics of the object technical con-dition is the creation of symptoms measures, which will enable to defi ne the condition precisely. Vibroacoustic diagnostics uses, as source of infor-mation about the condition of the tested object the dy-namic parameters, describing the appearance and the propagations of the vibroacoustic disturbance both in a tested object and in the outer environment [3]. The vibroacoustic signal includes both information required about the processes in progress in a technical object and the unnecessary information from the point of view of diagnostic aim, the, so called, information noise. A very important issue here is the right recon-struction of the information model of a given object condition, being the basis to treat it as the information carrier.In the vibroacoustic diagnosis of the technical ob-jects lots of various signal analysis methods are used [4]. P. Czech, Silesian University of Technology, Faculty of Transport, Department of Automotive Vehicle Construction, Katowice, PolandRESEARCH OBJECTTests were conducted on 10 single-stage and double stage gears with additional meshing of the roll cage. In the power transmission system of the cages the asyn-chronous engines with the power of 200 kW were ap-plied. The rotational speeds of the input shafts are con-stant for each gear and are included in the range from 380 to 800 rotation/minute. In the course of research the measurements of vibration accelerations in three direc-tions were conducted and the impulse signals were reg-istered, consistent with the rotations of the input shaft which served for synchronic averaging. The measure-ments of the gearbox vibrations were conducted during idle running and with a load during rolling. Registration and processing of the vibration signals was conducted with the use of an analysis-measurement system which is presented in Figure 1.Diagnostic signals were processed in the Matlab-Simulink environment. The applied measurement meth-od enabled the synchronic averaging of the vibration sig-nals with the rotations of the input shafts. The changes of the diagnosed gearboxes condition have signifi cant infl u-ence on the structure of the vibroacoustic signal. TIME-FREQUENCY ANALYSISIn vibroacoustic diagnostics such methods of signal analysis are used, which enable to analyse simultane-ously in time domain and frequency domain. They are 522  METALURGIJA 51 (2012) 4, 521-524P. CZECH et al.: DIAGNOSIS OF INDUSTRIAL GEARBOXES CONDITION BY VIBRATION AND TIME-FREQUENCY...used for time variable signals in the sense of amplitude and frequency; that is for the non-stationary signals [3]. In the group of such methods one fi nds the Short Time Fourier Transform STFT, defi ned as:dtetxbtwfbSTFT ftj∫+∞∞−−⋅⋅−= 2)()(),(where:w(t – b) – window function shifted in time domain,b – given shift of window function.Time signal is divided into smaller parts, and then for each of them the Fast Fourier Transform FFT is cal-culated. The side-by-side confi guration of the marked spectra creates the time-frequency map. STFT can be treated as a comb of simultaneously working fi lters [3].Figure 2 presents the marked STFT of the difference signal of toothed gears vibrations in rolling stands drives.In this method, the use of the wide window increases the resolution in frequency domain, and decreases in time domain. For a narrow window the effect is re-verse.The transform which lacks this disadvantage is the Wigner–Ville distribution and its pseudo transform with the applied Choi–Wiliams window:ττττ τπ detxtxwftWVD fj∫+∞∞−−⋅ −⋅ +⋅= 2*22)(),(where:x*(t) – complex time signal, compressed with x(t),w(τ) – symmetric weight function, similar to win-dow function in STFT.The comparison of STFT method with the WVD method taking into account their advantages and disad-vantages was presented in [3]. Wigner–Ville Distribution for the difference signal of the toothed gear vibrations in rolling stands drives during rolling is presented in Figure 3.WAVELET ANALYSISWavelet analysis consists of signal decomposition and presenting it in the form of linear combination of ba-sic functions, called wavelets [2]. The feature which dis-tinguishes this method of signal analysis from other methods is the multi-stage signal decomposition, variable resolution in time and frequency domain and possibility to use basic functions other than harmonic functions. Continuous wavelet transform is defi ned as follows: ( )dttxabtabaCWT ∫+∞∞−⋅ −=1),(where:ya,b(t) – the analyzing wavelet,a – the scale parameter, a∈R+, a≠0,b – the time parameter, b∈R.Wavelet frequency is regulated by the parameter of scale a, whereas using parameter b one can test the local properties of the time runs.This method, due to the possibility of adjustment of the window width to the analysed frequency range ena-bles testing the non-stationary signals. For the long-Figure 1  Diagram of the measurement system of toothed gears of the rolling stands drives, where: 1 – engine, 2 – clutch, 3 – tested gear, 4 – rotational speed sensor, 5 – measurement points, 6 – preamplifi er BK2626, 7 – measurement recorder BK7003, 8 – signal analyser SigLab50-21, 9 – computerFigure 2  STFT distributions of the vibration diff erence signals of toothed gears in rolling stands drives during rolling – gear classifi ed for repair, fa, fm – shaft rotation, meshing frequencyFigure 3  Pseudo Wigner Ville distribution of the diff erence signals in toothed gears vibrations of the rolling stands gears during rolling – gear classifi ed for repair, fa, fm – shaft rotation, meshing frequency523METALURGIJA 51 (2012) 4, 521-524P. CZECH et al.: DIAGNOSIS OF INDUSTRIAL GEARBOXES CONDITION BY VIBRATION AND TIME-FREQUENCY...term variation runs the window expands in time domain, whereas with high frequencies it narrows preserving a constant surface area. The proper choice of the basic wavelet and the array of the scale value determine the correctness of the diagnosis process of the object tech-nical condition with the use of wavelet analysis.The CWT distribution of toothed gears vibration signals in rolling stands drives, in time of idle running is presented in Figure 4.BISPECTRUM ANALYSISLow-energy changes of a modulating character ac-companying the early stages of elements malfunction in power transmission systems are possible to be traced with the use of bispectrum analysis [1].In the notion of the bispectral analysis, a third-order cumulant is used, described with the dependence: [ ])()()(),( 21213 ττττ ++= txtxtxECwhere:E – expected value.Higher-order cumulants, known also as semi-invari-ants are the measures of the size of signal changes around its mean value. They also possess the ability to expose the existence of non-linearity in a signal.Bispectrum is a function of two frequencies defi ned as transform FFT from third-order cumulant: ( ) ( )∫ ∫+∞∞−+∞∞−+−= 212213212211,),( ττττ ddeCffBS ffjBispectra take complex values including the infor-mation concerning the amplitude and the signal phase. The infl uence of the toothed gear condition in a roll-ing stand on the bispectrum distribution is presented in Figure 5.NON-DIMENSIONAL DISCRIMINANT VALUESChanges in the condition of the diagnosed transmis-sions toothed gear have a signifi cant infl uence on the vibroacoustic signal structure. The registered vibro-acoustic signals have to be converted by using appropri-ate signal measures so that they constitute symptoms showing wear intensity and advancement. In order to analyse signals registered during the test residual signal and difference signal have been used residual signal and difference signal. The residual signal r(t) is obtained by removing the bands which contain rotation components of shafts, their harmonics as well as mesh frequency components and their harmonics. The difference signal d(t) is obtained in a similar way but the removed bands in the area of mesh frequencies and their harmonics are much wider and cover the sidebands connected with gear rotation frequencies.In order to assess the dynamic condition of a rolling stand transmission toothed gear, non-dimensional dis-criminants [5,6] have been used, calculated on the basis of signals of vibrations synchronically averaging:∑== nkkPPAAFM10( )( )21214114−−=∑∑==NnnNnnddNddNFM ( )( )21214114−−=∑∑==NnnNnnrrNrrNNA( )( )31216116−−=∑∑==NnnNnnddNddNAM ( )( )41218118−−=∑∑==NnnNnnddNddNAMwhere:N – sampling point number,App – peak-to-peak value,Ak – amplitude of gear mesh harmonics,d(t) – average signal value d(t), r̄ (t) – average signal value r(t),In Table 1 values of selected non-dimensional dis-criminants have been compared. Values crest factor CF and kurtosis K have also been presented to show com-parison. M6A and M8A discriminants calculated on the basis of vibration signals of the transmission toothed gear qual-ifi ed for repair show a big increase in value (by approx. 100-200 %), irrespective of load. Simultaneously, static measures CF and K change only by approx. 9-36 %. Figure 4  CWT distribution of toothed gears vibration signals of rolling stands drives during idle running – gear classifi ed for repairFigure 5  Bispectrum distributions of the vibration diff erence signals of toothed gears in rolling stands drives during idle running – gear classifi ed for repair, fa, fm – shaft rotation, meshing frequency524  METALURGIJA 51 (2012) 4, 521-524P. CZECH et al.: DIAGNOSIS OF INDUSTRIAL GEARBOXES CONDITION BY VIBRATION AND TIME-FREQUENCY...CONCLUSIONFrom the number of vibroacoustic signals analysis methods applied in diagnostic practice only some are presented in this paper in reference to the analysis meth-ods of time-frequency, time-scale and frequency-fre-quency domain. Those analyses are the starting point in defi ning the diagnostic measures for particular diag-nosed cases [4]. The damage descriptors of particular elements of power transmission systems built on their basis are used in forming the complete diagnostics sys-tems. The most recently designed diagnosis systems work according to methods of artifi cial intelligence.REFERENCES[1] L. Bouillaut, M. Sidahmed, Cyclostationary approach and bilinear approach: comparison, applications to early dia-gnosis for helicopter gearbox and classifi cation method based on HCOS, Mechanical Systems and Signal Proces-sing 15(2001)5, 923-943.[2] Z.K. Peng, F.L. Chu, Application of the wavelet transform in machine condition monitoring and fault diagnostics, Mechanical Systems and Signal Processing 18 (2004), 199-221.[3] J. Korbicz, J. M. Kościelny, Z. Kowalczuk, W. Cholewa (Eds.), Fault Diagnosis: Models, Artifi cial Intelligence, Applications, Springer, Berlin, Germany (2004).[4] P. Czech, Toothed gear troubleshooting by means of artifi -cial intelligence, Doctoral thesis graduated with Prize from the Prime Minister of Poland (not published), Poland (2006).[5] C. James Li, J. D. Limmer, Model – based condition index for tracking gear wear and fatigue damage, Wear 241(1), 2000, 26-32.[6] Zakrajsek J. J., Townsend D.P., Transmission Diagnostic Research at NASA Lewis Research Center, NASA TM-106901, 1995.Note:  The responsible translator for English language is Dr Michel Bouquet, POLIGLOCI, Katowice, PolandTable 1 Discriminant valuesidle running under loadgood conditionbad conditiongood conditionbad conditionCF 4,0 4,5 3,9 2,9K 3,3 3,6 2,8 3,8FM0 14,2 11,4 2,1 4,5FM4 2,8 3,3 2,6 3,3NA4 2,8 3,2 2,6 3,5M6A 11,9 21,2 9,7 19,4M8A 63,3 215,1 45,0 150,7

Dijagnoza stanja industrijskih zupčanika pomoću vibracijske, vermensko frekvencijske, skalno frekvencij ske, frekvencijsko frekvencijske analize

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