外文Fault diagnosis of wind turbine planetary gearbox

Fault diagnosis of wind turbine planetary gearbox under nonstationary conditions via adaptive optimal kernel time e frequency analysisZhipeng Feng a,Ming Liang b,*a School of Mechanical Engineering,University of Science and Technology Beijing,Beijing100083,Chinab Department of Mechanical Engineering,University of Ottawa,Ottawa ON K1N6N5,Canadaa r t i c l e i n f oArticle history:Received11July2013Accepted31December2013 Available online24January2014Keywords:Fault diagnosisPlanetary gearboxWind turbineNonstationaryTime e frequency analysis Adaptive optimal kernel a b s t r a c tPlanetary gearboxes play an important role in wind turbine(WT)drivetrains.WTs usually work under time-varying running conditions due to the volatile wind conditions.The planetary gearbox vibration signals in such an environment are hence highly nonstationary.Conventional spectral analysis and demodulation analysis methods are unable to identify the characteristic frequency of gear fault from such nonstationary signals.As such,this paper presents a time e frequency analysis methods to reveal the constituent frequency components of nonstationary signals and their time-varying features for WT planetary gearbox monitoring.More specifically,we exploit the adaptive optimal kernel(AOK)method for this challenging application because of itsfine time e frequency resolution and cross-term free nature, as demonstrated by our simulation analysis.In this study,the AOK method has been applied to identify the time-varying characteristic frequencies of gear fault or to extract different levels of impulses induced by gear faults from lab WT experimental signals and in-situ WT signals under time-varying running conditions.We have demonstrated that the AOK is effective diagnosis of:(a)both the local damage(a single chipped tooth)and distributed faults(wear of all teeth),(b)both sun gear and planet gear faults, and(c)faults with very weak signature(e.g.,the sun gear fault at the low speed stage of a WT planetary gearbox).Ó2014Elsevier Ltd.All rights reserved.1.IntroductionPlanetary gearboxes are widely used in the drivetrains of wind turbines(WTs)for its large power transmission capacity in a compact structure.Due to the highly volatile rough working con-ditions in wind farms due to,e.g.,wind gust,dust,corrosion and heavy yet unpredictable load,WT planetary gearboxes are partic-ularly prone to damage.Such damage can lead to a catastrophic failure of the entire WT,and consequently heavy investment and productivity losses.Therefore,planetary gearbox fault diagnosis is an important topic for WTs.Researchers have proposed various statistical indices to detect planetary gearbox fault[1].Lei et al.[2]presented two new in-dicators,i.e.root mean square of thefiltered signal and normalized summation of the difference spectrum.To diagnose faults via spectral analysis,it is important to have a thorough understanding of the vibration spectral properties of planetary gearboxes.For this purpose,McFadden[3],McNames[4],and Mosher[5]investigated the spectral characteristics of planetary gearbox vibration signals, and found that they are typically asymmetric due to the planet carrier rotation.Inalpolat and Kahraman[6,7]studied the side-bands of planetary gearbox vibration signals,considering the modulation effects caused by planet carrier rotation and manufacturing errors of gears.Mark and Hines[8,9]investigated the sideband characteristics caused by non-uniform planet loading and planet carrier torque modulation.Patrick et al[10]studied the effect of unequal planet spacing on vibration signal spectra,for identifying the cracks of planet carrier plate.Researchers have also applied other methods to fault diagnosis of planetary gearbox.For example,McFadden[11,12],Samuel and Pines[13]suggested vi-bration separation methods to discern the fault signatures from planet and sun gears by time domain averaging.Samuel and Pines [14]further proposed a constrained adaptive lifting wavelet transform to analyze individual tooth mesh waveforms,thereby detecting the damage in helicopter planetary transmissions.Bar-telmus and Zimroz[15]recently used the cyclostationary analysis method to study the modulation characteristics of planetary gearbox vibration signals for condition monitoring.Barszcz and*Corresponding author.Tel.:þ16135625800x6269;fax:þ16135625177.E-mail address:liang@eng.uottawa.ca(M.Liang).Contents lists available at ScienceDirect Renewable Energyjournal ho me page:www.elsevier.co m/locate/renene0960-1481/$e see front matterÓ2014Elsevier Ltd.All rights reserved./10.1016/j.renene.2013.12.047Renewable Energy66(2014)468e477Randall[16]applied the spectral kurtosis method for the detection of tooth crack in the planetary gearbox of a wind turbine.Lei et al.[17]extracted the weak fault symptoms of a planetary gearbox using an improved adaptive stochastic resonance method.Sun et al.[18]proposed a method to construct customized multiwavelets based on the redundant symmetric lifting scheme,and applied it to detect damage-induced impulses for fault diagnosis of a planetary gearbox.Though the above studies have made important contri-butions to thisfield,they nevertheless focus on the detection problems under constant running conditions,and most of them rely on the assumption of signal stationarity.As mentioned earlier,WTs often work under time-varying running conditions due to the variations in wind velocity and di-rections,thus resulting in nonstationary vibration signals. Extracting fault information of planetary gearbox from such nonstationary signals is the key to the success in WT monitoring. However,to our best knowledge,the research on this topic has been very limited in the literature.A few publications include the recent work by Bartelmus and Zimroz[19,20].They presented an indicator for monitoring planetary gearboxes under time-varying running conditions.This indicator reflects the linear dependence between the meshing frequency amplitude and the operating condition.The proposed method is helpful to monitor the health status of planetary gearboxes,but the fault diagnosis issue under time-varying running conditions still needs further investigation.Recently,we have conducted a series of studies on fault diag-nosis of planetary gearboxes[21e23].We considered both the amplitude modulation and frequency modulation effects of a gear fault,as well as the amplitude modulation effects caused by the time-varying vibration transfer path or planet passing,in modeling planetary gearbox vibration signals,and summarized the spectral symptoms of both local and distributed faults of sun,planet and ring gears.We also derived the explicit equations for calculating the characteristic frequency of all the three types of gears with either local or distributed fault[21].To mitigate the complexity problem with the traditional spectral analysis caused by the complicated sideband structure,we proposed a joint amplitude and frequency demodulation analysis based on ensemble empirical mode decomposition and energy separation methods[22].To further reduce the amplitude modulation effects due to time-varying vi-bration transfer path or planet passing,a planetary gearbox fault diagnosis method was also proposed via torsional vibration signal analysis[23].These works have laid a foundation for further investigation of planetary gearbox fault diagnosis under nonsta-tionary running conditions.Planetary gearbox fault diagnosis essentially relies on detecting the presence of gear fault characteristic frequency,monitoring its magnitude change or,in other words,analyzing the periodicity of gear fault induced impulses.The gear fault characteristic frequency is dependent on the rotating speed of planetary gearbox.The time variations in speed and/or load will result in time-varying rotating frequency of planetary gearbox and thereby a time-varying gear fault characteristic frequency,i.e.,an irregular impulse train. Therefore,the key issue in fault diagnosis of planetary gearbox under nonstationary running conditions is to identify the time-varying gear fault characteristic frequency,track its magnitude change,or extract the gear fault induced impulses.Time e frequency analysis can effectively reveal the constituent frequency components of nonstationary signals and their time variation features,as well as transient events such as impulses.To date,various time e frequency analysis methods have been pro-posed[24].However,the inherent drawbacks of these time e fre-quency analysis methods limit their effectiveness in analyzing planetary gearbox vibration signals.For instance,linear transforms such as the short time Fourier transform(STFT)and wavelet transform are subject to Heisenberg uncertainty principle,i.e.the best time localization and highest frequency resolution cannot be achieved simultaneously.One of them can only be enhanced at the expense of the other and hence the time e frequency resolutions of linear transforms are limited[25].In addition,the basis in either the Fourier or wavelet transform isfixed.Therefore they lack adaptability in simultaneously matching the complicated compo-nents inherent in planetary gear vibration signals,such as the gear meshing frequency and their harmonics,gear fault induced im-pulses,and other transient vibration.The well-known Hilbert-Huang transform hasfine time e frequency resolution and is free of cross-term interferences,but it essentially relies on the empirical mode decomposition(EMD)using spline interpolation.It is sus-ceptible to singularities in signals,and may produce pseudo intrinsic mode functions(IMF),thus masking or interfering the time e frequency structure of true signal components[26].The recently proposed local mean decomposition(LMD)has the same merits but also suffers from the same shortcomings as EMD[27].As a typical representative of bilinear time e frequency representa-tions,Wigner-Ville distribution has the best time e frequency res-olution,but it has the inevitable cross-term interferences for multiple component signals.Such cross-term interferences complicate the interpretation of signal features in the time e fre-quency domain and make it unsuitable to analyzing the complex planetary gearbox vibration signals.Various modified bilinear time e frequency distributions including Cohen and affine class distributions may suppress the negative effect of cross-terms,but will compromise time e frequency resolution and auto-term integ-rity[28,29].In comparison with the Cohen and affine class distributions of fixed kernel functions,the adaptive optimal kernel(AOK)method can suppress the cross-terms more effectively with better time e frequency resolution[30,31].Sun et al.[32]applied the optimal Gaussian kernel method to identifying theflow pattern of gas e liquidfluids.Their research demonstrated that the optimal Gaussian kernel method had clearly extracted the characteristics for explaining the law offlow.Although this method provides new insights into the nature of nonstationary signals,it has not been widely used in signal analysis for machinery fault diagnosis.In this paper,we will adopt the AOK approach to revealing the compli-cated time e frequency features of planetary gearbox vibration sig-nals under time-varying running conditions and thus diagnosing the gear fault.Hereafter,the paper is organized as follows.Section2provides a brief overview on the principle of the AOK method.Section3il-lustrates the method by numerical simulated signal analysis.Sec-tions4and5show that the AOK method can be successfully applied to diagnose planetary gearbox faults as demonstrated using both the lab experimental signals of a WT planetary gearbox test rig and the in-situ measured signals of a real-world WT respectively.Sec-tion6draws conclusions.2.Adaptive optimal kernel methodThe Cohen and affine class bilinear distributions are the commonly used time e frequency analysis methods.Each of these distributions has a certain kernel function.The kernel function is fixed and it determines the ability to suppress cross-terms.One kind of kernel function is only effective for limited classes of signals. The corresponding distribution exhibits either interference com-ponents,amplitude distortion,or resolution reduction.Thus both the Cohen and affine class distributions with afixed kernel function lack adaptability to changes in signals.In order to overcome the limitations of the Cohen and affine class distributions,Baraniuk and Jones[30]proposed a method toZ.Feng,M.Liang/Renewable Energy469design signal-dependent kernel functions.It is motivated by the separation property of auto-terms and cross-terms in the ambi-guity domain,i.e.the auto-terms concentrate at the origin whereas the cross-terms lie away from the origin.Thus we may use a kernel as a 2-D lowpass filter to pass the auto-terms and suppress the cross-terms in the ambiguity domain,and obtain the time e fre-quency distribution of a signal x (t )TFD ðt ;f Þ¼ZþN ÀNZ þN ÀNA ðs ;y Þf ðs ;y Þexp ½Àj 2p ðy t þf s Þ d y d s ;(1)where A ðs ;y Þis the ambiguity function de fined asA ðs ;y Þ¼1pZ þN ÀNx t þs x * t Àsexp ðÀj 2py t Þd t :(2)The kernel function is de fined as a 2-D radially Gaussian func-tion so as to work as a lowpass filter in the ambiguity domainf ðs ;y Þ¼expÀs 2þy 22s q ¼exp Àr 22s q ¼f ðr ;q Þ;(3)where s ðq Þis the variance of the Gaussian function along the radial angle q ¼arctan ðs =y Þ.In polar coordinates,the optimal kernel function can be ob-tained by solving the following optimization problemmaxqZ2p 0Z þN 0j A ðr ;q Þf ðr ;q Þj 2r d r d q ;(4)subject to12pZ2p 0Z þN 0j f ðr ;q Þj 2r d r d q c ;c !0;(5)where A ðr ;q Þis the ambiguity function expressed in polar co-ordinates,r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis 2þy 2p ,and 1 c 5is the volume of the Gaussian kernel function.The performance measure,Eq.(4),determines the passband shape of the optimal radially Gaussian kernel,and aims to minimize auto-term distortion by passing auto-term energy as much as possible for a kernel of fixed volume.The constraint,Eq.(5),limits the volume of the kernel,so as to suppress cross-terms.However,the above signal-dependent kernel method calculates the ambiguity function of the entire signal,and designs only one kernel for the whole time span of the signal.Because each point in the ambiguity domain includes information from all times and frequencies in the signal,the method may lose the responsiveness to local signal characteristics.To avoid this drawback,Baraniuk and Jones [31]further pro-posed an adaptive optimal kernel (AOK)method.The AOK method adapts signal-dependent radially Gaussian kernel over time,thus better tracking local changes in a signal.In order to find the optimal kernel best matching the local structure of a signal,the short-time ambiguity function (STAF)at time t is de fined asA ðt ;s ;y Þ¼12pZ þN ÀN x u þs 2 w u Àt þs 2 x * u Às 2w * u Àt Às 2exp ðÀj 2py u Þd u ;(6)where w ($)is a symmetrical window function.Applying the radially Gaussian kernel optimization procedure to the STAF A ðt ;s ;y Þ,centered at time t ,yields a localized optimal kernel f opt ðt ;s ;y Þ.The STAF varies with time,so does the optimal signal-dependent kernel.Furthermore,a time e frequency distri-bution slice at time t can be obtained by applying 2-D Fourier transform to the product of STAF and localized optimal kernelAOK ðt ;f Þ¼ZþN ÀNZ þN ÀNA ðt ;s ;y Þf opt ðt ;s ;y Þexp ½Àj 2p ðy t þf s Þ d y d s :(7)Cascading all the time e frequency distribution slices over theentire time span,we obtain the AOK time e frequency distribution of the signal.The AOK time e frequency distribution inherits the good prop-erties,such as fine time e frequency resolution and suppressed cross-terms,from the signal-dependent kernel method.Mean-while,it also has good adaptability to signal variations by matching the optimal kernel to the local changes of a signal.3.Simulation evaluationIn this section,we examine the performance of the AOK in identifying the time-varying frequency components of gearbox vibration signals using a numerical synthetic signal as followsx ðt Þ¼X3n ¼1cos "n pf 1Àf03t 21t 3þf 0t !þðn À2Þp 2#þX 2i ¼1A exp ½Àz f r ðt Àt c i Þ cos ½2p f r ðt Àt c i Þ þn ðt Þ:(8)where t ¼0,0.0005,.,0.511s,i.e.the sampling frequency is 2000Hz,and f 1¼600Hz,f 0¼200Hz,t 1¼0.511s,A ¼5,z ¼0.3p ,f r ¼800Hz,t c1¼0.171s,and t c1¼0.341s.The synthetic signal consists of three quadratic frequency modulated components and two impulses as expressed by the first and second summation terms on the right-hand side of Eq.(8),respectively.The instantaneous frequency of the three quadratic frequency modulated components can be obtained by taking time derivative of the phase function,respectively,as followsIF 1ðt Þ¼12f 1Àf 0t 21t 2þf 0!;IF 2ðt Þ¼f 1Àf 0t 21t 2þf 0and IF 3ðt Þ¼32f 1Àf 0t 21t 2þf 0!:They are proportional to each other at any time.This featuremimics the frequency modulation characteristics of gearbox vi-bration signals during a speed varying process,since the meshing frequency and the fault characteristic frequency of each gear of planetary gearbox are all proportional to the input or output shaft rotating frequency.Fig.1shows the nonlinear trajectories of the three modulated frequency components along time.The two impulses mimic the impact vibration caused by a gear fault.To simulate the backgroundZ.Feng,M.Liang /Renewable Energy470noise interferences,we add a white Gaussian noise n (t )to the synthetic signal at a signal-to-noise ratio of 5dB.Fig.2shows the AOK time e frequency distribution of the syn-thetic signal.The signal waveform is on the top,the power spec-trum on the left,and a color bar showing the magnitude of the time e frequency distribution on the right.We cannot identify the time-varying features of each frequency components from either the waveform or the power spectrum.However,from the AOK time e frequency distribution (in the middle of the figure),we can see clearly the time variation of the three nonlinear time-varying frequency components.The revealed instantaneous frequencies match the theoretical curves in Fig.1very well.Moreover,the two impulses are extracted,as shown by the two lines perpendicular to the time axis and parallel to the frequency axis.Their time locations correspond exactly to those of the peaks in the waveform.This shows the effectiveness of the AOK method in identifying nonsta-tionary transient features of complex multiple component signals.For comparison,we also analyze the synthetic signal using the traditional short time Fourier transform.Fig.3shows the spectro-gram obtained using STFT.Though the three time-varying fre-quency components can also be observed,the time e frequency resolution is much lower than that of the AOK method,and the revealed frequency trajectories are not as smooth as those shown inthe AOK result.In addition,the impulse features are quite ambig-uous,which could be misinterpreted as some transient harmonics around the impulse occurring times.The above analysis clearly demonstrates the effectiveness of the AOK method in identifying the instantaneous frequencies of time-varying signal components and the impulses.This shows its po-tential in extracting the time-varying fault characteristic fre-quencies of planetary gearbox from vibration signals under nonstationaryconditions.Fig. 1.Instantaneous frequencies of the three modulated time-varying signalcomponents.Fig.2.AOK time e frequencydistribution.Fig.3.Short time Fourier transformspectrogram.Fig.4.WT drivetrain test rig.Z.Feng,M.Liang /Renewable Energy 4714.Experimental evaluationsIn this section,we evaluate the AOK method by using it to extract fault features from the experimental signals of a planetary gearbox in a WT drivetrain test rig at the University of Ottawa lab.4.1.Experimental settingFig.4shows the WT test rig with a two-stage planetary gearbox.Table 1lists the gear parameters of the fixed-shaft gearbox and the planetary gearboxes.To mimic gear faults,we introduced two types of damage to the sun gear of the stage 1of the planetary gearbox.One has wear on every tooth,and the other has a chipped tooth (Fig.5).Using a normal sun gear and the two damaged sun gears,we carried out three experiments associated with the three gear conditions,i.e.,baseline,wear,and chipping.An accelerometer is mounted on top of the casing of stage 1of the planetary gearbox to measure the vibration.A load of 16.284N m is applied to the output shaft of stage 2of the planetary gearbox by the brake.To validate the AOK method in extracting fault symptom from nonstationary signals,we collect the vibration signals at a sampling frequency of 20kHz during speed down processes,in which the rotating speed of the drive motor reduces from 60Hz to approximately 50Hz (in the meantime,the drive motor speed is also recorded at a sampling frequency 20Hz).Correspondingly,the rotating speed of WT blades changes from 0.486Hz to 0.162Hz,covering the usual rotating speed of WTs.Given the time-varying speed of the drive motor f d (t )at any time and the con figuration of both the fixed shaft and planetary gear-boxes,we can calculate the characteristic frequencies of the two-stage planetary gearboxes using the equations of planetary gearbox characteristic frequencies [21e 23]as listed in Table 2.4.2.Baseline signal analysisFig.6shows the normal planetary gearbox vibration signal waveform and its Fourier spectrum,as well as the drive motor speed during a speed down process.From Fig.6(c),we see that the maximum speed of the drive motor is 60Hz.Accordingly,the maximum meshing frequencies of planetary gearbox are 222.222Hz and 48.6111Hz for stage 1and stage 2,respectively.Since the gear fault information is mainly contained in the sidebands around the gear meshing frequency and its harmonics,we focus on the fre-quency band of 0e 340Hz,which spans 3/2of the stage 1meshing frequency and nearly 7times the stage 2meshing frequency.The signal Fourier spectrum,shown in Fig.6(b),has a broadband feature with many peaks.It is however dif ficult to identify what they are,because of the time-varying rotating frequency.Fig.7shows the AOK time e frequency distribution of the normal signal.According to the drive motor speed and the equations for calculating the characteristic frequencies in Table 2,we can esti-mate the time variation feature of the planetary gearbox charac-teristic frequencies.As displayed in Fig.7,the dominant frequency is the difference between the meshing frequency and the sun gear fault characteristic frequency,i.e.,f m (t )Àf s (t ).There are also some transients in frequency band of 200e 300Hz and during the period of 0e 4s.However,the magnitudes of these transients are relatively low which could be artifacts of the gear manufacturing errors and minor damage.4.3.Detection of sun gear wearNow we examine the signal of the sun gear with worn teeth.Fig.8shows the vibration signal waveform of the stage 1worn sunTable 1Con figuration parameters of gearboxes.GearboxGearNumber of gear teeth Stage 1Stage 2Fixed shaft Drive 3240Driven 8072PlanetarySun 2028Planet 40(4)36(4)Ring100100Note:the number of planet gears is indicated in theparenthesis.Fig.5.Sun gear damage (left:wear on every tooth,right:chipping on one tooth).Table 2Characteristic frequencies of planetary gearbox FrequencySymbol and equation Stage 1Stage 2Meshingf m ðt Þ¼f c ðt ÞZ r 100f d ðt Þ175f d ðt ÞPlanet carrier rotating f c ðt Þ127f d ðt Þ7864f d ðt ÞSun gear rotating f ðr Þs ðt Þ2f dðt Þ1f d ðt ÞSun gear fault f s ðt Þ¼N p f mðt ÞZ s 20f d ðt Þ175f d ðt ÞPlanet gear faultf p1ðt Þ¼f m ðt Þp5f d ðt Þ1757776f d ðt Þf p2ðt Þ¼2f mðt Þp527f d ðt Þ1753888f d ðt ÞRing gear faultf r ðt Þ¼N p f mðt Þr427f d ðt Þ1755400f d ðt ÞNote:Z r ,Z p and Z s are the numbers of ring,planet and sun gear teeth,respectively,and N p is the number of planet gears.Z.Feng,M.Liang /Renewable Energy472gear of the planetary gearbox and its Fourier spectrum,as well as the drive motor speed during a speed down process.From Fig.8(c),we see that the maximum speed of the drive motor is still around 60Hz.Thus,we focus on the frequency band of 0e 340Hz again,in order to extract the gear fault information from the sidebands around the gear meshing frequency.Once again,many peaks appear in the Fourier spectrum (Fig.8(b))and we are facing the same dif ficulty to associate them with any characteristic frequencies because of the time-varying speed.As such,we plot the AOK time e frequency distribution of the faulty gear signal in Fig.9.The difference between the meshing frequency and the stage 1sun gear fault characteristic frequency,f m (t )Àf s (t )again appears as one of the dominant frequency.However,several other strong frequency components are also observed.These include the meshing frequency of stage 1,f m (t );the difference between the meshing frequency and the sixth harmonic of the sun gear rotating frequency of stage 1,f m (t )À6f s (r)(t );the sum of the meshing frequency and the seven fourth of the sun gear fault characteristic frequency of stage 1,f m (t )þ7/4f s (t );and the sum of the meshing frequency and third harmonic of the sun gear fault characteristic frequency of stage 1,f m (t )þ3f s (t ).All these compo-nents are associated with the sun gear fault characteristic fre-quency of stage 1and have a pronounced magnitude,indicating the existence of a fault on the sun gear of stage 1.This finding is consistent with the actual condition of the sun gear.4.4.Detection of sun gear chippingHere we demonstrate the effectiveness of the AOK in detecting sun gear chipping at stage 2of the planetary gearbox.The associ-ated vibration signal and its Fourier spectrum,as well as the drive motor speed during a speed down process are presented in Fig.10.As the maximum speed of the drive motor is again 60Hz (Fig.10(c))and the maximum meshing frequency of planetary gearbox stage 2is accordingly 48.6111Hz,we target at the frequency band of 0e 73Hz,which covers 3/2of the stage 2meshing frequency of the planetary gearbox.It should be noted that this frequency range is narrower than that on the previous subsections because the stage 2rotational speed is much lower than that of stage 1.The signal Fourier spectrum (Fig.10(b))does not provide suf fi-cient information about the chipping fault.Though several peaks exist in Fig.10(b),their locations shift with time and it is obviously challenging to make connection between such moving peaks and the chipping fault.To reveal the chipping fault,the AOK method is applied to the experimental data.The resulting AOK time e frequency distribution of the signal is displayed in Fig.11.The dominant frequency is the drive motor rotating frequency,f d (t ).However,a few other fre-quency components also clearly stand out in Fig.11.They include,e.g.,the sum of the meshing frequency and second harmonic of the sun gear (stage 2)fault characteristic frequency of the planetary gearbox,f m (t )þ2f s (t ),and the difference between the meshing frequency and third harmonic of the sum of the sun gear fault characteristic frequency and the sun gear rotating frequency ofstage 2,f m (t )À3[f s (t )þf s (r )(t )].These components are associated with the sun gear fault characteristic frequency of stage 2with prominent magnitudes,a clear sign of a faulty sun gear at stage 2.This finding is expected and shows that the AOK method can be used to detect both local (chipping)and distributed (wear)fault effectively.It should be noted that after the speed reduction via the fixed-shaft gearbox and stage 1of the planetary gearbox,the rotating speed at stage 2of the planetary gearbox stage 2is very low.Under a low speed,it is dif ficult for the sun gear fault to excite signi ficantFig.6.Vibration and speed signals of a normal planetarygearbox.Fig.7.AOK time e frequency distribution of normal vibration signal.Z.Feng,M.Liang /Renewable Energy 473。