a new gerabox fault diagnosis method based on lucy ... · les résul-tats des études...

A NEW GEARBOX FAULT DIAGNOSIS METHOD BASED ON LUCY–RICHARDSONDECONVOLUTION

Xinghui Zhang, Jianshe Kang, Hongzhi Teng and Jianmin ZhaoMechanical Engineering College, Shijiazhuang, China

E-mail: [email protected]; [email protected]; [email protected]; [email protected]

ICETI-2014, R1042_SCINo. 15-CSME-36, E.I.C. Accession 3811

ABSTRACTGear and bearing faults are the main causes of gearbox failure. Till now, incipient fault diagnosis of these twocomponents has been a problem and needs further research. In this context, it is found that Lucy–Richardsondeconvolution (LRD) proved to be an excellent tool to enhance fault diagnosis in rolling element bearingsand gears. LRD’s good identification capabilities of fault frequencies are presented which outperform en-velope analysis. This is very critical for early fault diagnosis. The case studies were carried out to evaluatethe effectiveness of the proposed method. The results of simulated and experimental studies show that LRDis efficient in alleviating the negative effect of noise and transmission path. The results of simulation andexperimental tests demonstrated outperformance of LRD compared to classical envelope analysis for faultdiagnosis in rolling element bearings and gears, especially when it is applied to the processing of signalswith strong background noise.

Keywords: gearbox; fault diagnosis; Lucy–Richardson deconvolution; bearing.

UNE NOUVELLE MÉTHODE DE DIAGNOSTIC DE DÉFAILLANCE DE LA BOÎTED’ENGRENGAGE BASÉE SUR LE PROCÉDÉ DE DÉCONVOLUTION LUCY–RICHARDSON

RÉSUMÉL’engrenage et le roulement sont les principales causes de la défaillance de la boîte d’engrenage. Jusqu’àmaintenant, le diagnostic dès le début de la défaillance de ces deux composantes est toujours un problèmeet demande des recherches plus poussées. Dans ce contexte, il a été établi que la déconvolution Lucy–Richardson (DLR) s’avère un excellent moyen d’améliorer le diagnostic de défaillance dans les éléments deroulement et d’engrenage. Les étonnantes capacités d’identification de la fréquence de défaillance DLR sontprésentées. Les études de cas ont été effectuées pour évaluer l’efficacité de la méthode proposée. Les résul-tats des études expérimentales et de simulation ont démontré l’efficacité de la méthode dans l’atténuationdes effets du bruit et de la trajectoire de la transmission. Ces résultats démontrent la performance exception-nelle de DLR en comparaison de l’analyse approximative de diagnostic de défaillance dans les éléments deroulement et d’engrenage, spécialement pour l’application du traitement des signaux en présence de bruitde fond élevé.

Mots-clés : boîte d’engrenage; diagnostic de défaillance; déconvolution Lucy–Richardson; roulement.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 593

1. INTRODUCTION

Gearboxes are one of key components for power transmission systems. They are widely used in windturbines, helicopters and many vehicles. If unplanned failures happen, they will lead to great productionloss and high maintenance cost. In the case of wind turbine for example, in order to replace the gearbox,crane cost alone will be $60,000 for an 800 kW wind turbine [1]. The crane cost will be even higher for theoffshore wind turbine. Therefore, many researchers pay great attention on condition monitoring of the windturbine gearbox.

There are two research directions to diagnose gearbox fault. One is to distinguish the different faultmodes using existing machine learning methods, the other is to enhance the fault diagnosis ability usingsome existing or new signal processing methods (regardless of the fault types). Yang et al. [2] proposed anew method to distinguish bearing normal state, outer race fault and inner race fault. In this paper, fault fea-tures were extracted based on improved intrinsic time-scale decomposition and Wrapper mode. Then, thesefeatures were used as input vectors to the variable predictive model based class discriminate for diagnosis.Lei and Zuo [3] put forward a two stage feature selection and weighting technique via Euclidean distanceevaluation technique. This method possesses the ability to effectively select fault features and it achievesa good classification performance. Shao et al. [4] used principle component analysis and kernel principalcomponent analysis to diagnose the different data extracted from different gear fault types based on waveletpacket transform. Data were acquired in four different speeds, such as 300, 900, 1200 and 1500 rpm. How-ever, these classification methods achieve good effect during experimental application, unlike the unrealisticappearance of fault modes in engineering. What is more, gear or bearing faults can emerge simultaneously,and usually gearboxes have multi-faults during regular operation. What is more, there are not so manyavailable fault case studies for the key engineering machines. In this context, application engineers preferdiagnosis of the gear and bearing faults using frequency analysis methods.

Zhu et al. [5] proposed a new method for bearing fault diagnosis. In the paper, the null space pursuit canextract the fault signal from the very noise background and finally S transform can be used to display thetime frequency character of fault signal. This method can be used to diagnose the incipient bearing fault ingearbox. Incipient fault is a qualitative concept. It always refers to the starting of physical damage. Insteadof the spectral analysis, Hong and Dhupia [6] developed a time domain method to diagnose the gear fault.This method overcomes the deficiency of spectral methods which is caused by limited frequency resolution.Xiao et al. [7] proposed an improved simplex-based adaptive evolutionary digital filter for bearing faultdiagnosis. This method overcomes the shortcomings of the original evolutionary digital filter. In order todiagnose the gear fault under non-stationary conditions, energy and Shannon entropy distribution measuredin time-frequency plane are used in [8]. Saidi et al. [9] proposed a new bearing fault diagnosis methodnamed bi-spectrum based-empirical mode decomposition (EMD). Original vibration signals collected fromsensors are decomposed by EMD and a set of IMFs is produced. Finally, the IMF signals are analyzed viabi-spectrum to detect the bearing faults. Feng and Liang [10] proposed using iterative atomic decompositionthresholding to detect the wind turbine planetary gearbox faults. This method can extract true constituentcomponents of complicated signals and suppress background noise interferences.

Besides previously mentioned methods, if the periodic impulse signals produced by faults could be en-hanced, the faults usually could be diagnosed easier. Minimum entropy deconvolution (MED) method isbased on this theory to enhance the gear and bearing fault diagnosis. Sawalhi et al. [11] combined MEDwith the spectral Kurtosis to enhance the bearing fault detection ability. Then, Gu et al. [12] combinedMED and EMD to extract trend degradation features from bearing life cycle data. Recently, Raj and Mu-rali [13] used a new deconvolution method named Lucy–Richardson deconvolution (LRD) to enhance thebearing fault detection. Similar to MED method, this new deconvolution method also can enhance theimpulsive signal produced by bearing or gear faults. For bearing fault diagnosis, envelope analysis is the

594 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015

classical method used several decades. The essence of this method is to find the optimum frequency bandwhich will be used to do the band pass filtering. Theoretically speaking, this frequency band contains thestrongest impulsive signal produced by bearing fault. The most popular method for determining this opti-mal frequency band is the spectral Kurtosis method [14, 15]. In addition to this, many other revised spectralKurtosis methods have been developed [16–20]. LRD method can alleviate the effect of noise and enablethe deconvolution result close to the original signal without transmission loss. In other words, the resonancefrequency surrounded by the fault frequencies can be found through this deconvolution method under strongnoise background. For the gear fault diagnosis, LRD method provides clear gear mesh frequencies and theirharmonics. The main contributions and innovations of this paper are previously explained findings. Theeffectiveness and performance of the proposed method application are verified throughout simulation andexperimental study. The results generated by the proposed method are compared with those of the originalFourier and envelope spectrum to demonstrate its superiority and practicability.

2. BRIEF REVIEW OF THE LUCY–RICHARDSON DECONVOLUTION

When we take a photo using camera, the image may be vague due to the relative motion between camera andscene during exposure. Then, the Lucy–Richardson deconvolution (LRD) is used to restore the deblurredimage to a clear one. Take the following equation as an example:

I(x) =∫ T

0δ I(x, t)d ≈

N

∑i=1

∆I(x, ti), (1)

where I(x) denotes the image recorded after exposure, ∆I(x, ti) are the images acquired within an instanta-neous time interval dt, region [0,T ] denotes the exposure time, and x is a vector. Additionally, the ∆I(x, ti)can be further expressed by

∆I(x, ti) = ∆I(Π

ij=1h jx, t0

)=

1N

I0(Hix),Hi = Πij=1 h j. (2)

Finally, the projective motion blur model can be acquired as

B(y) =N

∑i=1

∆I(x, ti) =1N

N

∑i=1

I0(Hi,x). (3)

B(y) is the motion blurred image and I0(x) is the clear image we want to estimate. The purpose of the LRDis to acquire the clear image. The detailed algorithm can be found in [21]. Compared to image processing,vibration signal analysis is a one-dimensional problem. Original vibration signal containing the importantfault information will be blurred by noise and transmission path. So, the vibration signals we acquiredthrough sensors are not the ideal signal we need. They are blurred by the noise and transmission path.Theoretically, this is same to the image blur problem. So, we can also use LRD method to resolve thisproblem.

3. SIMULATION AND EXPERIMENTAL STUDY

3.1. Simulated Bearing Outer Race Fault StudyThe simulated bearing fault signal with single resonant frequency similar in [19] is given as follows:

y(t) = y0e−ξ×2π fn×τ sin(2π fn ×√

1−ξ 2 × t − τ), (4)

where ξ is equal to 0.1, fn is the resonant frequency equal to 2,100 Hz, and τ is used to simulate therandomness caused by slippage which is subject to a discrete uniform distribution. y0 (equal to one) is


Fig. 1. (a) Simulated signal with one resonant frequency under noise level 0.5; (b) Envelope spectrum of (a).

Fig. 2. Frequency spectrum of simulated signal under noise level 0.5 after LRD processing.

the amplitude of the simulated bearing impulse signal. Suppose the sampling frequency is 12,000 Hz.Then, the bearing fault signal is simulated according to the fault frequency (equal to 100 Hz). A total of24,000 samplings were used for each simulated signal. Finally, a random signal with a mean of zero andthe standard deviation of 0.5 were added to Eq. (4). Figures 1a and 1b show the simulated signal and itsenvelope spectrum, respectively.

Simulated signal contains only noise and fault frequency related signals. Therefore, it is very easy tofind the fault frequency and its harmonics in envelope spectrum. The entire frequency band is used for thisenvelope analysis. Frequency spectrum of the signal that is processed using LRD is shown in Fig. 2. It isobvious that LRD finds the position of fault frequency and its harmonics; the resonant frequency is evenmore enlarged, which is 2,100 Hz for simulated signal. This is the primary step of envelope analysis.

In the engineering case, vibration signals usually contain strong noise. In order to validate the merits ofLRD, signal with high noise level is used. Figure 3a shows simulation signal with increased noise level up to1. Figure 3b represents its envelope spectrum. It shows that no fault frequency (100 Hz) and harmonics canbe found because of the high noise level. Then, we used LRD to process simulated signal with high noiselevel and its frequency spectrum is shown in Fig. 4a. Although the fault frequency and its harmonics cannotbe found in this figure, the resonant frequency (2,100 Hz) is obvious. Base on this, we concluded the LRD ismore efficient in the determination of the frequency band for band pass filtering, which in this case is [1,8002,400] Hz and acquires its envelope spectrum as shown in Fig. 4b. It clearly presents fault frequency andsecond and third harmonic. This leads to conclusions that LRD not only has the similar function as envelopeanalysis, but could also be used to find resonance frequency which is useful to the envelope analysis.


Fig. 3. (a) Simulated signal with one resonant frequency under noise level 1; (b) envelope spectrum of (a).

Fig. 4. (a) Frequency spectrum of simulated signal under noise level 1 after LRD processing; (b) envelope spectrumof frequency band [1,800 2,400] Hz determined by LRD.

Fig. 5. (a) Frequency spectrum of bearing outer race fault data of CWRU; (b) frequency spectrum after LRD process-ing.

3.2. Experimental Electric Motor Bearing Outer Race Fault StudyThe vibration data used for analysis were obtained from the bearing data set of Case Western ReserveUniversity (CWRU) [22]. The deep groove ball bearing with outer race fault (6205-2RS JEM SKF) onthe drive end of electric motor under speed 28.83 Hz and 3 Hp load constitute the test study. The outerrace fault location is at the six o’clock direction and the size is 0.007 inch. For this case, the bearing faultwas implanted artificially. The four fault frequencies of this bearing under rotating frequency 28.83 Hz are67.97 Hz (ball fault frequency), 11.48 Hz (cage fault frequency), 103.36 Hz (outer race fault frequency),and 156.13 Hz (inner race fault frequency). Fourier spectrum of its vibration data is given in Fig. 5a.


Fig. 6. Test-rig of gearbox.

Analyzing the vibration signal data from faulty bearing, it is not possible to find outer race fault frequencyand its harmonics from Fig. 5a. But we can see equal spaced frequency at [2,000 4,000] Hz. This frequencyband may contain the resonant frequency, but it is impossible to determine that this frequency band is justthe resonant frequency band. Further, this signal is processed by LRD and the frequency spectrum is givenin Fig. 5b. Similar to the bearing simulation study, we concluded the LRD not only is capable to find theouter race fault frequency and its harmonics, but it is also capable of finding the resonant frequency band.What is more, envelope analysis of whole frequency band could identify the outer race fault frequency.However, except the bearings operation in the electric motor, many bearings are in operation in the gearbox.In practice, the vibrations induced by bearing faults are usually overwhelmed by powerful deterministiccomponents like gear meshing and bearing faults diagnostics in this environment is even more challengingtask.

3.3. Experimental Gearbox Bearing Outer Race Fault StudyThe test-rig structure is depicted in Fig. 6. In this test-rig, two speed and torque sensors are used to record thespeed and torque information related to the input shaft and output shaft, respectively. For the speed sensor,60 impulses will be produced in one revolution. The locations of number 1-4 are the relative locations offour acceleration transducers. In this gearbox, there are two shafts supported by bearings. Input shaft issupported by 6206 and output shaft by 7207 bearings. Gear on input shaft has 30 teeth and meshes withgear on output shaft which has 50 teeth. Input shaft rotating frequency is 19.60 Hz, which gives 588 Hz themeshing frequency.

The artificial fault was 0.5 mm width, 1.5 mm depth on groove, which was cut on the outer race ofinput shaft bearing (6206) at position 1 using wire-electrode cutting. The sampling frequency and thesampling time were 12,800 Hz and 2.56 second, respectively. The four fault frequencies of this bearing under19.60 Hz input shaft rotating frequency are 45.29 Hz (ball fault frequency), 7.77 Hz (cage fault frequency),69.93 Hz (outer race fault frequency), and 106.46 Hz (inner race fault frequency). In order to suppressthe interference from gear vibration, time synchronous technology is used to extract the residual signalwhich mainly contains the vibration produced by bearing fault. Firstly, the vibration signal is resampledaccording to the rotational information which ensures the signal is sampled with equal shaft degree. Then,this resampled signal minus the equal length of time synchronous averaging signal will result in the residualsignal. The detailed process can be seen in [23]. Next, the post processing is based on the residual signal.

Figure 7 shows envelope spectrum of whole frequency band of residual signal. This figure shows thatenvelope analysis of whole frequency band can find the outer race fault frequency and its harmonics. Then,LRD is used to process the residual signal and the frequency spectrum is shown in Fig. 8. We could note


Fig. 7. (a) Envelope spectrum of whole frequency band of residual signal; (b) local amplify of (a).

Fig. 8. (a) Frequency spectrum of residual signal after LRD processing; (b) local amplify of (a).

Fig. 9. (a) Envelope spectrum of the band pass filtering signal; (b) local amplify of (a).

the LRD has similar function as envelope analysis because it can find fault frequency and its harmonics.Except this, it could be used to find the resonant frequency band, which is in this case in the range of [1,5005,000] Hz. Figure 9 represents envelope spectrum of band pass filtering signal. From it, we can see obviousfault frequency and harmonics.

Outer race fault of this experiment is implanted artificially similar to the case in Section 3.2. So, boththe envelope analysis of whole frequency spectrum and the band pass filtering signal determined by LRDmethod show good diagnosis capabilities.

3.4. Experimental Planetary Gearbox Roller Bearing Fault StudyThis bearing analyzed in this study is an intermediate shaft bearing of wind turbine gearbox [24]. The faultmode of this bearing is roller fault. The four fault frequencies of this bearing under rotating frequency


Fig. 10. (a) Envelope analysis of whole frequency band; (b) zoomed envelope spectrum.

Fig. 11. (a) Frequency spectrum of the bearing fault signal after LRD processing; (b) zoomed spectrum.

6.32 Hz are 24.30 Hz (roller fault frequency), 2.75 Hz (cage fault frequency), 51.89 Hz (outer race faultfrequency), and 67.84 Hz (inner race fault frequency). Figure 10 (a) illustrates the envelope spectrum ofwhole frequency band and (b) zoomed envelope spectrum. From Fig. 10b, we can identify the roller faultfrequency and its harmonics, but it still has some interference frequencies. Then, LRD is used to processthe vibration signals. The LRD frequency spectrum of processing signal is given in Fig. 11.

Figure 11a shows that there are three possible resonant frequency bands for the envelope analysis. Exceptthat, from zoomed spectrum it is possible to see the roller fault frequency. Furthermore, three possible reso-nant frequency bands are analyzed. The results are given in Fig. 12. From envelope spectrum of frequencyband [21,200 21,400] Hz, it is not possible to find any information about roller fault frequency. However, itis possible to see obvious roller fault frequency and its harmonics in envelope spectrum of frequency band[10,600 10,700] Hz. Especially in envelope spectrum of frequency band [4,400 4,700] Hz, the roller faultfrequency is obvious and other interference frequencies are small on amplitude. This demonstrates thatthe frequency bands determined by LRD method are very appropriate for envelope analysis. Based on thisdiscovery, this could represent another method to determine the optimal frequency band.

3.5. Experimental Gear Crack Fault StudyThe test rig used for gear fault study is the same as the bearing outer race fault experiment in Section 3.3.A crack defect fault was implanted artificially by cutting the gear tooth at the root of the driving gear ofthe input shaft [25]. The artificial defect was 20% of the tooth thickness in depth and the width of thegroove was 0.5 mm. Input shaft rotation frequency was 19.74 Hz, which gives gear meshing frequency of592.23 Hz. Fourier spectrum of tested rig gearbox with crack on gear is given in Fig. 13a. LRD basedFourier spectrum is given in Fig. 13b. Comparing these two spectrums, it is revealed that there are more


Fig. 12. (a) Envelope spectrum of frequency band [21,200 21,400] Hz; (b) envelope spectrum of frequency band[10,600 10,700] Hz; (c) envelope spectrum of frequency band [4,400 4,700] Hz.

Fig. 13. (a) Frequency spectrum of gear crack signal; (b) frequency spectrum of gear crack signal after LRD process-ing.

harmonics of gear mesh frequency in LRD based one, so LRD frequency spectrum can reveal more evidentgear mesh irregularities.

4. CONCLUSIONS

Traditionally, deconvolution methods are used to enhance the impulse signals related to the bearing andgearbox faults. A new function of LRD deconvolution method has been found in this paper. The processingresults demonstrated that the LRD is very efficient in optimal frequency band determination for band passfiltering. This method demonstrated good results, especially under the strong noise background. Comparingthe LRD processing results with those generated by methods based on Fourier and Envelope analysis, theeffectiveness and superiority of new method function are verified and supported. Beside this, LRD itselfhas a similar function as envelope analysis. It can find the fault frequency and its harmonics clearly likethe envelope analysis. For these two characters of LRD, one bearing fault simulation case study and threereal bearing fault case studies are used to validate its effectiveness. For gear fault, more harmonics ofmesh frequency means severe fault than those with less harmonics. While LRD just has this function, thefrequency spectrum of LRD processed signal has more mesh frequency harmonics than the original signal.Gear crack experiment demonstrates its effectiveness. However, there are some issues that deserve furtherresearch, for example, (1) theoretical reasons why LRD analysis has similar function as envelope analysisand the ability to find the resonant frequency band more efficiently; (2) theoretical reasons why LRD revealsmore harmonics of mesh frequency; and (3) how the LRD affects the degradation feature of life data. Thisis very important for the remaining useful life prediction and maintenance decision making.


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