Teng 2019

Renewable Energy 136 (2019) 393e402

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Compound faults diagnosis and analysis for a wind turbine gearbox via a novel vibration model and empirical wavelet transform Wei Teng a, Xian Ding b, Hao Cheng a, Chen Han a, Yibing Liu a, *, Haihua Mu c, ** a

Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Beijing 102206, China b Luneng New Energy (Group) Co., Ltd., Beijing 100020, China c Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 February 2018 Received in revised form 29 July 2018 Accepted 26 December 2018 Available online 4 January 2019

Fault diagnosis of a wind turbine gearbox can schedule maintenance strategy on a wind turbine and save operational cost for wind farms. Owing to low rotational speed and weak vibration energy, fault diagnosis for planetary stage is arduous in a wind turbine gearbox involving multi-stage transmissions. A novel modulation model is presented to support the fault diagnosis of the planetary stage of a wind turbine gearbox, which is described as the mesh frequency of intermediate stage, high speed stage, or mechanical natural frequency of the gearbox is a carrier wave modulated by the mesh frequency of planetary stage with distributed faults. Even possessing this presented vibration model, the fault feature of planetary stage with lower rotational speed is easily concealed by the meshing vibration energy of ordinary stages with higher speed, especially when faults simultaneously arise in the ordinary stages. Aiming at the diagnosis of the above compound faults in an industrial wind turbine gearbox, empirical wavelet transform is utilized to adaptively find weak fault frequency in planetary stage as well as evident fault characteristics in other ordinary stages. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Wind turbine gearbox Compound faults Modulation model Empirical wavelet transform

1. Introduction An increasing number of wind turbines have been put into operation worldwide because of the low generating cost and zeroemission of wind energy. Bearing stochastic wind speed and load, wind turbines operate under complex environment, leading the gearbox to be one of the most frequent failed subassemblies in wind turbines. Condition monitoring [1,2] is necessary for wind turbines to detect incipient fault and prevent them from catastrophic results induced by failed subassemblies. Vibration analysis is a powerful tool enabling the early detection of impending failure of bearings and gears [3]. Other monitoring techniques have been developed as well, e. g., electrical analysis for wind turbine synchronous generator [4], acoustic emission method to locate planet gear fault [5], oil debris monitoring for a wind turbine gearbox [6], thermophysics analysis for wind turbine drive trains [7] etc. As pointed out in

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Liu), [email protected] (H. Mu). https://doi.org/10.1016/j.renene.2018.12.094 0960-1481/© 2019 Elsevier Ltd. All rights reserved.

Ref. [8], among the referred monitoring approaches, vibration analysis is prevalent in fault detection of wind turbine gearboxes, because it has a high sensitivity to incipient defects and superior ability in fault location. As ISO 13373-1 [9], acceleration is recommended as the vibration measurement quantity for condition monitoring of rolling bearings and gears instead of displacement and velocity, because most of the faults of gears and bearings are exhibited at high frequency range. Vibration model is a theoretical description for the generating and transferring process of vibration energy in a gearbox, which enables providing fault characteristic frequency for further fault diagnosis. Due to the revolution of the planet carrier, the vibration mechanism of planetary gear is complicated and attracts increasing attentions. Feng and Zuo [10] deduced a vibration model for the fault diagnosis of planetary gearboxes on the basis of amplitude and frequency modulation effects and calculated the characteristic frequencies of faulty planet gear, sun gear and ring gear. Inalpolat and Kahraman [11] presented a mathematical model to express the vibration mechanism resulting in modulation sidebands of plane~ a [12] proposed phenomenological and tary gear. Parra and Vicun lumped-parameter models to study the frequency contents of planetary gearbox vibrations under non-fault and different fault

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conditions. Lei et al. [13] considered the time-varying vibration transfer paths to construct phenomenological model for epicyclic gearboxes. With the computed fault characteristic frequency from theoretical models, many approaches, like adaptive stochastic resonance [14], autocorrelation-based time synchronous averaging [15], discrete spectrum correction technique [16] and iterative generalized synchrosqueezing transform [17] etc., have been proposed to diagnose the defects in pure planetary gearboxes. The above models focused on the vibration analysis for pure planetary gear sets where the mesh frequency of the planetary stage is treated as a carrier wave that is probably modulated by the fault characteristic frequency of sun gear, planet gear and ring gear. Actually, an industrial wind turbine gearbox contains both planetary stage and ordinary stages, making the fault characteristics in planetary stage hard to emerge due to its lower rotational speed than the ordinary stages, particularly when faults simultaneously arise in the ordinary stages, causing more intensive vibration energy. Except the detection of tooth crack of ring gear [18], successful diagnosis cases for detecting faults of planetary stage in a real wind turbine gearbox are few, which demonstrates the vibration models of pure planetary gearboxes are unfeasible for industrial wind turbine gearboxes. In a wind turbine gearbox, except for the simplex fault in planetary stage, compound faults happen frequently because once one part (gear or bearing) fails, it could cause asymmetric forces and unexpected vibrations or shocks, thus leading to the failure of the other parts. For the diagnosis of compound faults emerged in planetary stage and ordinary stages, there exist three ticklish tasks: 1) The fault features in planetary stage are generally weak, and is readily hidden by the intensive vibration energy caused by faults in ordinary stages; 2) The frequency bands implicating faults are hard to be located due to the multi-stage transmission in a wind turbine gearbox, for this, conventional demodulation analysis is low accuracy and inefficiency; 3) It is difficult for analyzing the failure sequence of different parts, obstructing the judgment of primary failure incentive. Empirical wavelet transform presented by Gilles [19] in 2013, enable decomposing the vibration signal into a series of empirical modes on the basis of its energy distribution in frequency domain. Each decomposed empirical mode could automatically match the multiple fault features in different frequency bands in wind turbine gearboxes. Empirical wavelet transform not only has explicit physical meaning but good adaptivity like the classic empirical mode decomposition [20], thereby providing a way to deal with the above challenges in the detection of compound faults. As a novel signal processing method with excellent decomposition performances, empirical wavelet transform has been applied in the time-frequency analysis of noisy nonlinear and non-stationary signals [21], the short-term wind speed prediction [22], and the fault diagnosis of a wind turbine generator [23]. In this paper, a novel vibration model is proposed to support the fault diagnosis of planetary stage in a wind turbine gearbox, which is described as the mesh frequency of intermediate stage, the mesh frequency of high speed stage, or certain casing natural frequency is a carrier wave modulated by the mesh frequency of the planetary stage with distributed faults. Meanwhile, to manifest the fault frequencies in both planetary stage and ordinary stages without human interferences, empirical wavelet transform is applied to adaptively locate fault frequency bands and demodulate potential fault features caused by defective gears. In Section 2, the drive train including a gearbox of a wind turbine is illustrated and the novel modulation model is described in detail. The principle of empirical wavelet transform is referred in Section 3. In the study case of Section 4, multiple faults of a real wind turbine gearbox are detected using empirical wavelet transform, which verify the proposed modulation model. The failure mechanism of the multiple

gears is analyzed. Section 5 concludes this paper. 2. Wind turbine gearbox 2.1. Structure of the wind turbine gearbox The drive train of the wind turbine is shown in Fig. 1, which involves the blades, rotor hub, main bearing, gearbox, and generator. The blades assimilate stochastic winds, and promote the rotor hub to rotate at a low rotational speed. Then the low speed is accelerated by the gearbox, further drive the rotor of the generator to generate electric power. Suffering from harsh operational conditions, the critical parts (gears or bearings) transferring variational loads are vulnerable, thus seven piezoelectric accelerometers are installed on the surface of the drive train to monitor the health states of the critical parts. As shown in Fig. 2, a wind turbine gearbox falls into three parts: planetary stage (PS), intermediate stage (IS) and high speed stage (HSS). Among which, 1 is the planet carrier, 2 is the sun shaft, 3 is the intermediate shaft, and 4 is the high speed shaft. The PS consists of planetary gear Zp, sun gear Zs and ring gear Zc, the IS is formed by the big gear Zmi on the sun shaft and the pinion Zmo on the intermediate shaft, and the HSS is composed by the big gear Zhi on the intermediate shaft and the pinion Zho on the high speed shaft. For the drive train in Fig. 2, the rotational frequency fr of the planet carrier in the gearbox equals to the one of the rotor hub. The sun gear and the big gear in IS are both installed on the sun shaft with the same rotational frequency fs. The pinion in IS and the big gear in HSS are both on the intermediate shaft with the same rotational frequency fi. The pinion in HSS is on the high speed shaft with a rotational frequency fh. 2.2. A novel modulation model of the wind turbine gearbox In the wind turbine gearbox, the mesh frequency of PS is expressed as

fPS ¼ fr  Zc ¼ ðfs  fr Þ  Zs

(1)

The IS and HSS are ordinary stages in the wind turbine gearbox, whose mesh frequencies are computed as

fIS ¼ fs  Zmi ¼ fi  Zmo

(2)

fHSS ¼ fi  Zhi ¼ fh  Zho

(3)

For conventional fault diagnosis of a gearbox, a common theory is that the rotational frequency of shaft with a faulty gear will modulate the mesh frequency of the gear pair or other mechanical natural frequencies. No exception in a pure planetary gearbox, any local defects on sun gear, planet gear and ring gear will modulate the mesh frequency of planetary stage. Feng [10] proposed three characteristic frequencies representing potential faults on sun gear,

Fig. 1. Drive train of the wind turbine.

W. Teng et al. / Renewable Energy 136 (2019) 393e402

395

Fig. 2. Structure of the wind turbine gearbox: 1 - planet carrier; 2 - sun shaft; 3 - intermediate shaft; 4 - high speed shaft.

planet gear and ring gear, which are all derived by considering the rotational frequency of related shafts and transfer paths. However, in a real wind turbine gearbox consisting of three stages in Fig. 2, the fault characteristics of the sun gear, ring gear or planet gears of the PS are difficult to be evidenced because the rotational speed of the PS is much lower than the ones of IS and HSS. In fact, local faults (crack on a tooth, or missing a tooth) seldom emerge in planetary stage due to its symmetric structure and strong load ability. By contrast, the distributed faults in planetary stage are usually inevitable after a long-term abrasive wear by meshing sun gear with planet gear, and planet gear with ring gear. Once distributed faults emerge in the planetary stage, the backlash between the meshed gears will increase, causing more intensive mesh shock than that in healthy state. The frequency of the enhanced mesh shock equals to the mesh frequency of the planetary stage. Due to staying in the same gearbox, the vibration energy from different mesh stages (PS, IS and HSS) can transfer with each other. Therefore, as shown at the top in Fig. 2, the enhanced mesh shock of PS will modulate the mesh process of IS and HSS, even excite the natural frequency of the casing of the wind turbine gearbox. The modulation process caused by the mesh frequency of PS is expressed as

yðtÞ ¼ ½1 þ A cosð2pfPS tÞcos½2pfc t þ B cosð2pfPS t þ 4Þ þ q

planetary stage in conventional models [10e13]. The carrier wave in Eq. (4) could be individual mesh vibration of IS, HSS, certain natural frequency of the casing, or their combination as well. Anyway, if the mesh frequency of the planetary stage is demodulated from the vibration signal, distributed faults could be deduced to arise in the planetary stage of the wind turbine gearbox. In vibration test, the accelerometer is mounted on the surface of the gearbox, equaling to on the outside of the stationary ring gear in the planetary stage (as the accelerometer 3 shown in Fig. 1). When one planet gear moves under the accelerometer, the vibration is maximum. After half circular revolution of the planet carrier, this planet gear moves at the farthest position from the accelerometer, the vibration is minimum. With the three planet gears driven by the planet carrier passing through the accelerometer one by one, three times of maximum and minimum arise during one revolution of the planet carrier. Thus the vibration signal caused by this pass effect [24] of the three planet gears is

hðtÞ ¼ ½1  cosð2p  3fr tÞ

(5)

The total vibration signal of the wind turbine gearbox with distributed faults in PS is shown as

xðtÞ ¼ yðtÞ  hðtÞ

(6)

(4)

where fc is the carrier wave frequency, A and B are the amplitudes of the amplitude-modulation and frequency-modulation waves, 4 is the initial phase of the frequency-modulation wave, and q is the initial phase of the vibration signal. Comparing with the vibration models of pure planetary gear sets in Refs. [10e13], the modulation frequency in Eq. (4) is not the concrete characteristic frequency of the ring gear, sun gear or planet gears, but the mesh frequency of the planetary stage with distributed faults. While the carrier wave frequency fc may be the mesh frequency of IS and HSS, or certain natural frequency of the casing instead of the mesh frequency of the

3. Empirical wavelet transform Empirical mode decomposition (EMD) is an effective tool to adaptively decompose a signal into different intrinsic mode functions (IMFs) through seeking the local maxima of the signal [20]. Due to its adaptability, EMD has been applied in the fault diagnosis of various rotating machinery [25e27]. However, the lack of theory is the most fatal drawback of EMD, making many decomposed IMFs difficult to be explained. In view of this, Gilles [19] proposed an

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empirical wavelet transform (EWT) considering both adaptability and interpretability. Similar to the traditional wavelet transform, in empirical b 1 ðuÞ and several wavelet wavelet transform a scaling function f b ðuÞ (n ¼ 1: N) are constructed in frequency domain to functions j n

form a series of filters [19].

of the critical parts, e.g., gears or bearings. Because of the lower rotational speed of the hub rotor than the other shafts in the gearbox, the sampling frequency for the first three accelerometers is 5120 Hz. Due to the higher rotational speed of the high speed shaft, the sampling frequency for the last four accelerometers is 25600 Hz. The rotational speed of the hub rotor was 14 rpm during

8 > > > > <

1; if juj  u1  t1  

p 1 b 1 ðuÞ ¼ cos b f ðjuj  u1 þ t1 Þ ; if u1  t1  juj  u1 þ t1 > 2t1 2 > > > : 0; otherwise

b ðuÞ ¼ j n

8 > > > > > > > > > < > > > > > > > > > :

1; if un þ tn  juj  unþ1  tnþ1  

p 1 cos b ðjuj  unþ1 þ tnþ1 Þ ; if unþ1  tnþ1  juj  unþ1 þ tnþ1 2tnþ1 2  

p 1 sin b ðjuj  un þ tn Þ ; if un  tn  juj  un þ tn 2tn 2 0;

bðmÞ ¼

> :

0 if m  0   m4 35  84m þ 70m2  20m3 ; 1;

if m2½0; 1

(9)

if m  1

The aim of EWT is to decompose the vibration signal x(t) into several empirical modes (EMs) using the filter bank Eq. (7) and Eq. (8). The filters number Nþ1 depends on the number of local maxima in frequency domain of the signal, thus EWT is adaptive. As we know, the convolution between the vibration signal and the temporal expression of a filter is equivalent to the product of the referred two terms in frequency domain. On the basis of this, the EMs in empirical wavelet transform are obtained as

   b 1 ðuÞ EM1 ¼ F 1 F nxðtÞg  f  b ðuÞ EMn ¼ F 1 F xðtÞg  j

(8)

otherwise

where un is the center frequency of the drop edge of the nth filter and the ascendant edge of the (nþ1)th filter, tn is a half frequency b 1 ðuÞ width of the above edges, and the superscript ‘^’ denotes that f b ðuÞ are from their time form f ðtÞ and j ðtÞ by Fourier and j 1 n n transform. The designed filter bank include Nþ1 filters. b(m) is an arbitrary function defined in range [0 1], which is used to construct Meyer's wavelet. Referring to Ref. [28], b(m) is

8 > <

(7)

(10)

n

where F denotes the Fourier transform of the original signal, F ¡1 denotes the inverse Fourier transform, and x(t) is the original vibration signal.

4. Case study 4.1. Faulty wind turbine gearbox The rated power of the tested wind turbine is 2.0 MW. Its drive train and the structure of the gearbox are shown in Figs. 1 and 2 with one planetary stage and two ordinary stages. The transmission ratio of the gearbox is 100.5, with the numbers of teeth of the multiple gears listed in Table 1. Seven accelerometers are installed on the surface of the drive train to monitor the health state

this vibration test, and the rotational frequency of the other shafts and the mesh frequency of different stages are listed in Table 2 according to Eq. (1) through (3). 4.2. Vibration analysis for the faulty wind turbine gearbox The aim of this paper is to monitor the health state of the wind turbine gearbox and find the potential faults in it. Fig. 3 shows the vibration signals from the four accelerometers mounted on the surface of the gearbox. The vibration amplitudes of accelerometers 2, 3 and 4 are in a range ±10 m/s2, and the accelerometer 5 approaches ±20 m/s2 owing to the higher speed of the rotational shafts there. Regardless of the obvious and regular shocks in Fig. 3b, the stochastic vibration components almost occupy the vibration signals of accelerometers 2, 4 and 5, and it is difficult to detect the hidden faults only through observing these temporal signals. Accelerometer 3 is installed on the top of the planetary stage, thus it can directly reflect the health state of the sun gear, planet gear and ring gear. Fig. 4a is the vibration signal of accelerometer 3 within 22.4 s, where the evident impulses represent some potential gear fault. The signal is stretched as in Fig. 4b within 1 s. Here the interval of the impulses is 0.168 s corresponding to the rotational frequency fi in Table 2, which means one of the two gears on the intermediate shaft fails. Except for this, no other fault information can be found in Fig. 4. The vibration signal in Fig. 4a is transformed into power

Table 1 The numbers of teeth of multiple gears in the wind turbine gearbox. Zp

Zs

Zc

Zmi

Zmo

Zhi

Zho

35

17

87

101

24

82

21

Table 2 Shaft rotational frequencies and gear meshing frequencies. fr

fs

fi

fh

fPS

fIS

fHSS

0.234

1.43

6.04

23.6

20.4

144.9

495.3

397

a

20 0 -20

0

5

10

b

20

15

20

15

20

t [s]

0 -20

0

5

10 t [s]

c

20

2

A [m/s ]

2

A [m/s ]

2

A [m/s ]

W. Teng et al. / Renewable Energy 136 (2019) 393e402

0 -20

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

3

3.5

4

4.5

2

A [m/s ]

t [s]

d

20 0 -20 0

0.5

1

1.5

2

2.5 t [s]

Fig. 3. Vibration signals: a) accelerometer 2; b) accelerometer 3; c) accelerometer 4; d) accelerometer 5.

a

20

2

A [m/s ]

10 0 -10 -20

0

5

10

15

20

t [s]

b

20

2

A [m/s ]

10 0 -10 -20

0.168 0

0.1

0.2

0.3

0.168 0.4

0.5

0.168 0.6

0.168 0.7

0.8

0.9

1

t [s] Fig. 4. Vibration signals of accelerometer 3: a) within 22.4s; b) within 1s.

spectrum density shown in Fig. 5a where three concentrated energy bands are evidenced. Then three 4th-order Butterworth bandpass filters are designed to filter the vibration signal. The cut-

off frequencies of the bandpass filters are [500 Hz, 700 Hz], [950 Hz, 1250 Hz], and [1250 Hz, 1600 Hz] respectively. Fig. 5b through Fig. 5d are the envelope spectra of the filtered signals from the

W. Teng et al. / Renewable Energy 136 (2019) 393e402

band 2

band 1

0.1

band 3

-20 500

1000

1500

2000

2500

b

-5 2

0.05 0 0

5

10

15

Psd [(m/s2 ) 2/Hz]

Psd [(m/s2 ) 2/Hz]

f [Hz]

5.94 0.5

11.7

0 0

5

0.2

10

5.94

15 f [Hz]

0 0

5

10

20

25

17.5 15

30

d 23.4

20

29.2 25

Psd [(m/s2 ) 2/Hz]

2

A [m/s ]

0 -5 0

10

15

20

Psd [(m/s2 ) 2/Hz]

c

2

A [m/s ]

20

5

0

0

5

10

15

20

e

10 2

Psd [(m/s2 ) 2/Hz]

-20

0 -10

0

5

10 15 t [s]

20

0.1

10

15

20

e

0

5

10

15

20

g

30

0

0

0.01 0

0.01

10

11.7

17.5 23.4

10

20

5.94

5

10

15

20

i

1

0

0

0.02

0

5

10 15 t [s]

20

0

10

20

0

5

10

10

0

10

20

20.7

15

30

f

17.5 23.4 29.2 0

10

20

30

f [Hz]

Fig. 6. Analysis results using EWT: a) EM1; b) envelope spectrum of EM1; c) EM2; d) envelope spectrum of EM2; e) EM3; f) envelope spectrum of EM3.

30

The envelope analysis enable the diagnosis for all the potential faults in the wind turbine gearbox, but the bandpass filters still need to be designed by experienced individuals, resulting in lacking the intelligence of fault diagnostic. For the condition monitoring of wind turbines, a great number of vibration signals need to be duly processed due to the high sampling frequency and massive turbines in a wind farm. Therefore, an intelligent and adaptive approach to diagnose faults in wind turbine gearboxes is urgent. Although the wind speed is time-variant, the huge inertia generated by the heavy blades and rotor makes the rotational speed of the drive train of a wind turbine vary slowly in a relative short

5.94 11.7

0.05

30

Fig. 7. Analysis results using EMD: a) IMF1; b) envelope spectrum of IMF1; c) IMF2; d) envelope spectrum of IMF2; e) IMF3; f) envelope spectrum of IMF3; g) IMF4; h) envelope spectrum of IMF4; i) IMF5; j) envelope spectrum of IMF5.

17.5 20

0.1

30

f [Hz]

d 11.7

f

j

5.94

0.01

15

h

0.005 0

30

d 5

5.94

0.02 0

20

5.94

0.5

0

5

10 0.78 1.4

2.8 0

1

0

-5

0

b

11.7

b

0.78 0.05 1.4 0

0

0

-1

three frequency bands. In Fig. 5b, there is a hump at 0.78 Hz representing the pass effect of three planet gears (the rotational frequency of the planet carrier is 0.234 Hz, 0.234*3 z 0.78 Hz). Another frequency component 1.4 Hz is distinct, which matches the rotational frequency fs of the sun shaft in Table 2. This phenomenon illustrates that one of the two gears on the sun shaft may be faulty. In Fig. 5c, the prominent rotational frequency 5.94 Hz (fi in Table 2) and its harmonics are in agreement with the temporal intervals in Fig. 4b. Combining the arisen frequencies fs and fi in the envelope spectra, we deduce that the two gears in IS are failure. In Fig. 5d, in addition to the rotational frequency 5.94 Hz and its harmonics, the mesh frequency 20.8 Hz of the PS emerges, matching the modulation process in Eq. (4), which reveals the possible distributed defects in PS.

a

0

20

0

Fig. 5. Power spectrum density: a) power spectrum density of the vibration signal; b) envelope spectrum from band 1; c) envelope spectrum from band 2; d) envelope spectrum from band 3.

5

15

0.05

5

-2

20.8

0.1

10

0

17.5

11.7

5

c

2

c

f [Hz]

A [m/s ]

A [m/s ]

Psd [(m/s2 ) 2/Hz]

0.78

0

0

1.4

5.94

0.5

5

f [Hz]

0.1

1

0

0.05 0

a

20

a

Psd [(m/s2 ) 2/Hz]

Psd [(m/s2 ) 2/Hz]

398

Fig. 8. The broken pinion on the intermediate shaft.

W. Teng et al. / Renewable Energy 136 (2019) 393e402

Fig. 9. The broken big gear on the sun shaft.

time. This property accords with the application characteristic of empirical wavelet transform [19]. Here, the vibration signal of accelerometer 3 is decomposed into three EMs using empirical wavelet transform, shown in Fig. 6. The number of EMs is selected as three because there are three energy bands in the power spectrum density of Fig. 5a. In Fig. 6, the left column shows the decomposed EMs, and the right one shows the corresponding envelope spectra. In Fig. 6b, the 0.78 Hz, three times of the rotational frequency of the planet carrier denotes the pass effect of three planet gears in Eq. (5). In Fig. 6b, d and f, the 1.4 Hz, 5.94 Hz and their harmonics are the rotational frequencies of the sun shaft and intermediate shaft, associating to the failure of the gear pair in IS. In Fig. 6f, the 20.7 Hz, the modulation frequency in Eq. (6), is also demodulated, corresponding to the distributed faults in PS. Except for the modulation components 3fr and fPS in Eq. (6), and the rotational frequency of the shafts in IS, any other characteristic frequencies concerning sun gear, ring gear and planet gears are not found in Fig. 6, demonstrating that the novel model in Eq. (6) performs superior in detecting the distributed faults of PS in a wind turbine gearbox than the vibration models of the pure planetary gear sets [10,11]. The diagnosis result about defective gears on the sun shaft, intermediate shaft and PS is further verified by EWT. Comparing with the conventional demodulation analysis in Fig. 5, although the same diagnosis result is drawn, EWT is more intelligent because it is unnecessary to artificially design bandpass filters. As a contrast, EMD is adopted to decompose the original vibration signal and the analysis results are shown in Fig. 7. 1.4 Hz representing the rotational frequency of the sun shaft emerges in Fig. 7d and 5.94 Hz and its harmonics representing the rotational frequency of the intermediate shaft are distinct in Fig. 7b, f, h and j. Unfortunately, the mesh frequency of PS, a modulation component in Fig. 6f, is absent in Fig. 7, which demonstrates that EMD is less

a

b

399

c

Fig. 10. The photography of the sun gear: a) the worn sun gear; b) one worn tooth of the sun gear; c) another worn tooth of the sun gear.

400

W. Teng et al. / Renewable Energy 136 (2019) 393e402

gear, planet gear and ring gear are less severe than the broken gears in IS, the mesh frequency 20.7 Hz of the PS is still distinctly demodulated by EWT in Fig. 6f, which proves that the emergence of the mesh frequency of the PS as a modulation information denotes the faults in PS.

4.3. Analysis of the failure mechanism

Fig. 11. The scratched planet gear.

favorable than EWT in detecting the compound faults of the wind turbine gearbox. The disassembled wind turbine gearbox is shown from Figs. 8e12. Fig. 8 is the broken pinion on the intermediate shaft, and Fig. 9 is the broken big gear on the sun shaft. They correspond to the rotational frequency 5.94 Hz and 1.4 Hz respectively. Fig. 10a is the photography of the sun gear where some wear signs happen. Fig. 10b and c are the nicks on the sun gear. Fig. 11 shows the scratched planet gear. Fig. 12a exhibits the part of the ring gear, and there is local pitting in Fig. 12b. Although the defects on the sun

In order to explore the failure reason of the tested wind turbine gearbox, the vibration signals two years and four years ago are collected and shown in Fig. 13. In Fig. 13a the vibration signal two years earlier, the vibration amplitude approached the range in Fig. 4a, while the degree of shocks was less intensive than the current test. Due to the property of the varying rotational speed, the rotational frequency of the hub rotor was 0.286 Hz at that time. The analysis result of Fig. 13a using EWT is shown in Fig. 14, from which, the three times of rotational frequency of hub rotor (0.86 Hz) denoting the pass effect of the planet gears is evident, and the rotational frequencies of the sun shaft (1.64 Hz and its harmonics) are dominant. The above phenomenon indicates that the gear fault or imbalance of the sun shaft has already emerged from then on. But the absence of the mesh frequency of the PS in Fig. 14 signifies that there was no fault in PS two years earlier. While observing the vibration signal four years earlier in Fig. 13b, the vibration amplitude is much lower than the one in Fig. 13a. In the analysis results of Fig. 15 using EWT, the vibration energies of the demodulated frequencies are faint, meaning the gearbox was in a good health condition four years earlier. The analysis results from EWT at different times show that the failure process was deteriorating progressively. Four years ago, the status of this wind turbine gearbox was superior. Two years ago, an abnormal modulation frequency (the rotational frequency of the sun shaft) arose, which exhibited incipient fault feature. After another two years, the gearbox breaks down, resulting in the destroyed gears as Figs. 8 and 9. The imbalance or eccentricity of the sun shaft two years earlier is deduced as the primary incentive for the successive catastrophic damage. It makes the mesh forces of the gear pair in IS asymmetric, further damaging the gear pair. At the same time, the imbalance of the sun shaft affects the planetary stage, leading to the distributed scratches in PS. The debris from the broken gears in IS fall into the clearance of the PS, and form the indentation in Fig. 12b.

a

20

2

A [m/s ]

10 0 -10 -20

0

5

10

15

20

15

20

t [s]

b

1

2

A [m/s ]

0.5 0 -0.5 -1 Fig. 12. The pitting on the surface of the ring gear: a) a part of the ring gear; b) a pitting on the tooth.

0

5

10 t [s]

Fig. 13. Vibration signals of accelerometer 3: a) two years earlier; b) four years earlier.

W. Teng et al. / Renewable Energy 136 (2019) 393e402

401

-3

Psd [(m/s2 ) 2/Hz]

0

2

-2 -4

0

10

15

20

c

10 2

A [m/s ]

5

Psd [(m/s2 ) 2/Hz]

A [m/s ]

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Fig. 14. Analysis results two years earlier using EWT: a) EM1; b) envelope spectrum of EM1; c) EM2; d) envelope spectrum of EM2; e) EM3; f) envelope spectrum of EM3.

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parts. A novel modulation model of a wind turbine gearbox is presented in this paper, which is described as the mesh frequency of intermediate stage, the mesh frequency of high speed stage, or certain casing natural frequency is a carrier wave modulated by the mesh frequency of the planetary stage with distributed faults. The emergence of the mesh frequency of the PS as a modulation information represents the distributed faults on the gears of planetary stage. For the diagnosis of the compound faults in an industry wind turbine gearbox, empirical wavelet transform enables decomposing the vibration signal adaptively and detecting multiple modulation components accurately, performing superior than classic empirical mode decomposition. The failure mechanism of the compound faults in the tested wind turbine gearbox can be summarized as the initial imbalance or eccentricity of the sun shaft. The proposed vibration model and the usage of EWT provide an effective tool for the diagnosis of compound faults in wind turbine gearboxes.

f [Hz]

Fig. 15. Analysis results four years earlier using EWT: a) EM1; b) envelope spectrum of EM1; c) EM2; d) envelope spectrum of EM2; e) EM3; f) envelope spectrum of EM3.

According to the damage degrees from Figs. 8e12, the broken gears in the IS must be changed, and the defect gears in the PS can be milled and put into operation again. 5. Conclusion In wind turbine gearboxes, the multi-stage transmission with various gears and bearings makes the vibration signal complicated, enhancing the difficulty of fault diagnosis. Moreover, the failure of one part causes a variation of stiffness, strength and mesh force of the gear pair, which is prone to lead to successive faults of other

Acknowledgments The research presented in this paper was supported by National Natural Science Foundation of China (No. 51775186, 51305135), the Fundamental Research Funds for the Central Universities of China (No. 2018MS013), Science and Technology Plan Projects of Hebei (15214307D), and the National High Technology Research and Development Program of China (863 Program) (No. 2015AA043702). References [1] Y. Amirat, M.E.H. Benbouzid, E. Al-Ahmar, B. Bensaker, S. Turri, A brief status on condition monitoring and fault diagnosis in wind energy conversion systems, Renew. Sustain. Energy Rev. 13 (9) (2009) 2629e2636. [2] Z. Tian, T. Jin, B. Wu, F. Ding, Condition based maintenance optimization for

402

[3]

[4]

[5] [6]

[7]

[8]

[9] [10] [11]

[12]

[13]

[14]

[15]

W. Teng et al. / Renewable Energy 136 (2019) 393e402 wind power generation systems under continuous monitoring, Renew. Energy 36 (5) (2011) 1502e1509. R.U. Maheswari, R. Umamaheswari, Trends in non-stationary signal processing techniques applied to vibration analysis of wind turbine drive train - a contemporary survey, Mech. Syst. Signal Process. 85 (2017) 296e311. W. Yang, P.J. Tavner, M.R. Wilkinson, Condition monitoring and fault diagnosis of a wind turbine synchronous generator drive train, IET Renew. Power Gener. 3 (1) (2009) 1e11. Y. Zhang, W.X. Lu, F.L. Chu, Planet gear fault localization for wind turbine gearbox using acoustic emission signals, Renew. Energy 109 (2017) 449e460. R. Dupuis, Application of oil debris monitoring for wind turbine gearbox prognostics and health management, in: Proceedings of the Annual Conference of the Prognostics and Health Management Society, Portland, OR, USA, October 2010, pp. 10e16. Y. Qiu, Y. Feng, J. Sun, W. Zhang, D. Infield, Applying thermophysics for wind turbine drivetrain fault diagnosis using SCADA data, IET Renew. Power Gener. 10 (5) (2016) 661e668. B. Lu, Y.Y. Li, X. Wu, Z.Z. Yang, A review of recent advances in wind turbine condition monitoring and fault diagnosis, in: IEEE Conferences on Power Electronics and Machines in Wind Applications, 2009, pp. 1e7 (Lincoln, NE, USA). ISO 13373-1, Condition Monitoring and Diagnostics of Machines e Vibration Condition Monitoring, Part 1: General Procedures, July, 2002. Z.P. Feng, M.J. Zuo, Vibration signal models for fault diagnosis of planetary gearboxes, J. Sound Vib. 331 (22) (2012) 4919e4939. M. Inalpolat, A. Kahraman, A theoretical and experimental investigation of modulation sidebands of planetary gear sets, J. Sound Vib. 323 (3e5) (2009) 677e696. ~ a, Two methods for modeling vibrations of planetary J. Parra, C.M. Vicun gearboxes including faults: comparison and validation, Mech. Syst. Signal Process. 92 (2017) 213e225. Y.G. Lei, Z.Y. Liu, J. Lin, F.B. Lu, Phenomenological models of vibration signals for condition monitoring and fault diagnosis of epicyclic gearboxes, J. Sound Vib. 369 (2016) 266e281. Y.G. Lei, D. Han, J. Lin, Z.J. He, Planetary gearbox fault diagnosis using an adaptive stochastic resonance method, Mech. Syst. Signal Process. 38 (1) (2013) 113e124. J.M. Ha, B.D. Youn, H. Oh, B. Han, Y. Jung, J. Park, Autocorrelation-based time synchronous averaging for condition monitoring of planetary gearboxes in

wind turbines, Mech. Syst. Signal Process. 70e71 (2016) 161e175. [16] G.L. He, K. Ding, W.H. Li, X.T. Jiao, A novel order tracking method for wind turbine planetary gearbox vibration analysis based on discrete spectrum correction technique, Renew. Energy 87 (2016) 364e375. [17] Z.P. Feng, X.W. Chen, M. Liang, Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions, Mech. Syst. Signal Process. 52e53 (1) (2015) 360e375. [18] T. Barszcz, R.B. Randall, Application of spectral kurtosis for detection of a tooth crack in the planetary gear of a wind turbine, Mech. Syst. Signal Process. 23 (4) (2009) 1352e1365. [19] J. Gilles, Empirical wavelet transform, IEEE Trans. Signal Process. 61 (16) (2013) 3999e4010. [20] N.E. Huang, Z. Shen, S.R. Long, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. Ser. 454 (1998) 903e995. [21] J.P. Amezquita-Sanchez, H. Adeli, A new music-empirical wavelet transform methodology for time-frequency analysis of noisy nonlinear and nonstationary signals, Digit. Signal Process. 45 (C) (2015) 55e68. [22] J. Hu, J. Wang, Short-term wind speed prediction using empirical wavelet transform and Gaussian process regression, Energy 93 (2015) 1456e1466. [23] J.L. Chen, J. Pan, Z.P. Li, Y.Y. Zi, X.F. Chen, Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals, Renew. Energy 89 (2016) 80e92. [24] Z.P. Feng, M.J. Zuo, J. Qu, T. Tian, Z.L. Liu, Joint amplitude and frequency demodulation analysis based on local mean decomposition for fault diagnosis of planetary gearboxes, Mech. Syst. Signal Process. 40 (2013) 56e75. [25] S. Braun, M. Feldman, Decomposition of non-stationary signals into varying time scales: some aspects of the EMD and HVD methods, Mech. Syst. Signal Process. 25 (7) (2011) 2608e2630. [26] Y.G. Lei, J. Lin, Z.J. He, M.J. Zuo, A review on empirical mode decomposition in fault diagnosis of rotating machinery, Mech. Syst. Signal Process. 35 (1e2) (2013) 108e126. [27] W. Teng, F. Wang, K.L. Zhang, Y.B. Liu, X. Ding, Pitting fault detection of a wind turbine gearbox using empirical mode decomposition, Strojniski vestnik - J. Mech. Eng. 60 (1) (2014) 12e20. [28] I. Daubechies, Ten Lectures on Wavelets, Ser. CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, PA, USA, 1992.