Accurate Fault Location Method of the Mechanical Transmission System of Shearer Ranging Arm

In the process of coal mine production, the fault of the mechanical transmission system of the shearer ranging arm directly affects safety production. Therefore, it is very important to achieve the accurate fault location of the shearer ranging arm. The combination method of optimized continuous complex Morlet wavelet envelope demodulation spectrum analysis and spectrum analysis is proposed. Firstly, the spectrum contrast analysis of vibration signals between the normal state and fault state is performed, which can obtain the fault characteristics frequency and preliminary fault location. Then, the optimized continuous complex Morlet wavelet envelope demodulation algorithm is proposed to extract the side-bands characteristics of vibration signals, which can obtain the rotation frequency of fault location by the contrast analysis of side-bands characteristics in normal and fault state. In the algorithm, the center frequency and bandwidth of Morlet wavelet are optimized by wavelet Shannon entropy, and the optimal scale factor can be accurately determined by spectrum contrast analysis of vibration signals in normal and fault state. Finally, the accurate gear fault location is achieved by comprehensive analysis results of optimized continuous complex Morlet wavelet envelope demodulation spectrum and spectrum contrast. The simulation signals and practical vibration signals are applied to verify the proposed accurate gear fault location method. The experiment results indicate that the center frequency and bandwidth determined by wavelet Shannon entropy make the wavelet waveform best match the fault impact signal, and the optimal scale factor can be accurately determined by spectrum contrast analysis of vibration signals in normal and fault state, and the proposed method can achieve the precise fault location of the mechanical transmission system of shearer ranging arm. It provides the method for the on-site rapid accurate fault location of the mechanical transmission system. It is of great significance to the safe and efficient production of the coal mine.


I. INTRODUCTION
The shearer is the key equipment of modern fully mechanized mining face, which is used in harsh environment. It easily subjects to large impact load from hard coals and rocks, and corrosion from water vapor and coal dust during operation. Also, it is improperly managed, operated, and maintained by workers. For these reasons, the failures frequently caused in The associate editor coordinating the review of this manuscript and approving it for publication was Vicente Alarcon-Aquino . the mechanical transmission system of the shearer ranging arm. The failures will lead to equipment damage and production interruption, great economic losses, and even casualties. Due to the complicated working conditions, long transmission chain and complicated structure, the fault diagnosis of mechanical transmission system of shearer ranging arm is still difficult. Both the gear and bearing fault of the shearer ranging arm will appear. However, the main fault is the gear fault,which is presented in Figure 1. Therefore, the gear fault diagnosis is deeply studied in this article. Because of the mechanical transmission system fault, abnormal changes such as lubricating oil quality, temperature, and mechanical vibration can happen. Therefore, its fault diagnosis is mainly carried out using ferrography analysis, temperature detection, and vibration detection [1], [2]. The ferrography analysis method relies on the experience of human beings, which may cause serious misjudgment because of the irregular spectrum process. The temperature detection method is difficult to achieve early fault diagnosis and accurate fault location of the mechanical transmission system. The vibration detection method can be used to monitor the operating state of equipment without stopping the machine, and to achieve early diagnosis and accurate fault location, which is widely used in the field of fault diagnosis and prediction of mechanical transmission system [3]. In recent decades, the research on fault diagnosis of the mechanical transmission system at home and abroad mainly focuses on evaluating the fault based on vibration intensity and vibration standard, and denoising of vibration signals, and multi-class fault intelligent recognition based on artificial neural network, fuzzy theory or support vector machine [4]- [7]. While, for a complex mechanical transmission system with multiple coincident fault characteristic frequencies, few researchers study on fault location of specific components, especially in the aspect of shearer ranging arm. In engineering practice, accurate fault location of the mechanical transmission system for shearer is very important to reduce unscheduled downtime and greatly improve maintenance efficiency.
The fault diagnosis methods of the mechanical transmission system were explored by some researchers. The fault diagnosis of rotating machinery was carried out using the waveform in the time domain, kurtosis index, and cepstrum [8]. A novel adaptive singular value decomposition (SVD) method is proposed for fault feature detection based on the correlation coefficient [9]. A fast algorithm was proposed for computing the kurtogram, which improves computational efficiency and makes kurtosis applicable to on-line industrial applications [10]. However, the above methods mainly are used to identify the faults, which are difficult to achieve fault location. It is found that there are harmonics of vibration characteristic frequencies and lots of side-bands around the vibration characteristic frequencies. According to the side-bands around the vibration characteristic frequencies, rolling element bearing and gear faults can be identified and located [11]- [13]. Several demodulation methods have been used to extract the side-bands characteristics of vibration signals, such as the Hilbert envelope spectrum analysis method and continuous complex Morlet wavelet envelope demodulation analysis method. The Hilbert envelope spectrum analysis method is used to extract the fault characteristic frequencies of the planetary gearbox, in order to realize the fault identification [14]. The bearing fault is identified by improved Hilbert time-time transform demodulation analysis method [15]. The short-time Fourier transform (STFT) also has its shortcomings. such as STFT only using a single resolution to analyze the target signal [16]. Compared with the method of Hilbert transform demodulation analysis method and short-time Fourier transform method, the continuous complex Morlet wavelet envelope demodulation analysis method can perform envelope analysis in the whole frequency range and eliminate the impact of artificially setting the center frequency, and adjust the time and frequency resolution by changing the center frequency and bandwidth. Compared with the other wavelet transform methods, there is 90 • phase difference between the real part and imaginary part in the continuous complex Morlet wavelet envelope demodulation. Moreover, the left and right sides of the Morlet wavelet exhibit exponential attenuation, which is the similar to the characteristic of the shock attenuation waveform of the mechanical fault vibration signal. So, the Morlet wavelet can be used to better match the fault signal [17]. Therefore, according to the principle of envelope demodulation and Morlet wavelet characteristic, the continuous complex Morlet wavelet envelope demodulation method can achieve envelope detection and extract the side-bands characteristics of vibration signals [18]. However, the parameters of continuous complex Morlet wavelet such as center frequency, bandwidth, and scale factor have a large impact on sidebands characteristics extraction [19]. The optimal parameters of continuous complex Morlet wavelet are very difficult to be obtained. Therefore, it needs to deeply study how to obtain the optimal center frequency, bandwidth, and scale factor of Morelet wavelet.
In this study, our main contribution is to propose a combination method of optimized continuous complex Morlet wavelet envelope demodulation spectrum analysis and spectrum analysis to apply to the accurate gear fault location of the mechanical transmission system of shearer ranging arm. In the algorithm, the fault characteristics frequency is obtained by spectrum contrast analysis of vibration signals, and the fault rotation frequency is obtained by the contrast analysis of optimized continuous complex Morlet wavelet envelope demodulation spectrum in normal and fault state. According to the meshing frequency and rotation frequency of gear fault, the fault accurate location of the mechanical transmission system of shearer ranging arm can be obtained. In the algorithm, the optimal center frequency and bandwidth of Morlet wavelet can be obtained by wavelet Shannon entropy, which can get the best time-frequency resolution of vibration signals, and the optimal scale factor is obtained by proposed VOLUME 8, 2020 spectrum contrast analysis of vibration signals in normal and fault state. Therefore, the optimal Morlet wavelet basis can be selected by the original vibration signals. The proposed method can achieve fault accurate location of the mechanical transmission system of shearer ranging arm. It is of great significance to the safe and efficient production of the coal mine.

II. SIDE-BANDS AROUND THE MESHING FREQUENCY OF GEARS
The vibration signals usually contain multiple harmonics and change with the rotation speed, load, and fault. The changes are presented by the amplitude or phase of vibration signals, which is the modulation phenomenon of vibration signals. When there is a fault in gears, the side-bands usually appear around the meshing frequency of gears and their harmonics. The side-bands imply the fault information, and it is helpful to the fault location. The side-bands are produced because of the modulation. In the modulation, the meshing frequency and its harmonics are carrier frequencies, and the rotation frequency and its multiple frequencies are the modulation frequencies. The vibration signals with modulation are presented in equations (1)∼(3).
where, f z is the meshing frequency of gears, and ϕ m is the phase, and A m is the amplitude, and M is the number of maximum harmonics, and a m (t) is the function of amplitude modulation, and b m (t) is the function of phase modulation, and α m and β m are the respective initial phase of the nth modulation component.

III. ACCURATE FAULT LOCATION SCHEME AND METHOD OF THE SHEARER RANGING ARM A. ACCURATE FAULT LOCATION SCHEME OF THE SHEARER RANGING ARM
The combination method of optimized continuous complex Morlet wavelet envelope demodulation spectrum analysis and spectrum analysis is applied to the accurate fault location of the mechanical transmission system of shearer ranging arm. The accurate fault location scheme of shearer ranging arm is presented in Figure 2.
The main processes of accurate fault location are as follows: (1) The vibration signals in normal and fault states are collected.
(2) The noise reduction of vibration signals is performed by the wavelet transform algorithm. (3) The spectrum contrast analysis of vibration signals between the normal state and fault state is performed, which can obtain the fault characteristics frequency and preliminary fault location. Due to the same meshing frequency of multiple pairs of gears, it is difficult to precisely locate the faulty gear.
(4) The optimal center frequency and bandwidth are obtained by wavelet Shannon entropy.
(5) The optimal scale factor is obtained by spectrum contrast analysis of vibration signals in normal and fault state. (6) The envelope demodulation spectrum is obtained by an optimized continuous complex Morlet wavelet envelope demodulation algorithm. The rotation frequency of fault location is got by the contrast analysis of the envelope demodulation spectrum in normal and fault state.
(7) Because different gears have different rotation frequencies, the comprehensive analysis results of optimized continuous complex Morlet wavelet envelope demodulation spectrum and spectrum can uniquely determine the fault location of gears.

B. ACCURATE FAULT LOCATION METHOD OF THE SHEARER RANGING ARM 1) THE ENVELOPE DEMODULATION THEORY OF CONTINUOUS COMPLEX MORLET WAVELET
The envelope demodulation theory of continuous complex Morlet wavelet is presented as follows [20]- [22]: The wavelet basis is obtained from the ''mother wavelet'' ψ (t) by translation and dilation, which is presented in where, a is the scale factor, and b is the time localization parameter.
According to the principle of the wavelet transform, the wavelet transform of a finite energy signals x (t) can be operated by a convolution between x (t) and the wavelet basis ψ a,b (t),which is presented in Equation (5).
The continuous complex Morlet wavelet function in time domain is presented in Equation (6).
where, f c and f b determine the center frequency and bandwidth of the wavelet window.
According to the Equation (6), the continuous complex Morlet wavelet function in frequency domain is presented in Equation (7).
According to the Equation (6), the real part ψ r (t) and the imaginary part ψ i (t) of the continuous complex Morlet wavelet are presented in Equations (8) and (9), respectively.
According to the principle of wavelet transform, Morlet wavelet envelope demodulation signals W (a, b) with different scale factors can be obtained by convolution of reality signals x (t) and continuous complex Morlet wavelet with Shrinking transformation, which is presented in Equation (10).
Based on the real part and imaginary part of the continuous complex Morlet wavelet in Equations (8) and (9), the real part and imaginary part of W (a, b) are presented in Equations (11) and (12), respectively.
According to Equations (11) and (12), the Morlet wavelet envelope signals u(a, t) with different scale factors is presented in Equations (13).
By performing Fourier transform on the Morlet wavelet envelope signals u(a, t) with different scale factors, the continuous complex Morlet wavelet envelope demodulation spectrum with different scale factors can be obtained.

2) OBTAINING THE OPTIMAL CENTER FREQUENCY AND BANDWIDTH BY WAVELET SHANNON ENTROPY
We hope the Morlet wavelet basis function has the greatest similarity with vibration signals. The wavelet Shannon entropy is a good evaluation criterion for signals similarity, which reflects the uniformity of the probability distribution. Therefore, the optimal center frequency f c and bandwidth parameter f b of Morlet wavelet are obtained by Wavelet Shannon entropy. The most uncertain probability distribution has the largest entropy value. The smaller the entropy value, the better the corresponding Morlet wavelet basis function matches the vibration signals. The wavelet Shannon entropy is presented in Equation (14) [23]. where, , P i is the uncertain probability distribution, which is presented in Equation (15).
where, W (a i , t) is the wavelet transform coefficients of a i scale.

3) OBTAINING THE OPTIMAL SCALE FACTOR OF MORLET WAVELET BY SPECTRUM CONTRAST ANALYSIS
The relationship between scale and characteristic frequency of vibration signals is presented in Equation (16). According to the comparative analysis of the spectrum in normal and fault state, the characteristic frequency of the fault can be determined. In order to accurately perform the morlet wavelet transform, the corresponding transform scale is found by the determined characteristic frequency. The scale corresponding to the fault characteristic frequency of vibration signals is the optimal scale.
where, f i is the gear meshing frequency, f s is the sampling frequency, a i is the scale, and f c is the center frequency. VOLUME 8, 2020

IV. THE INFLUENCE ANALYSIS OF CENTER FREQUENCY AND BANDWIDTH BY SIMULATE SIGNALS A. THE TIME AND FREQUENCY RESOLUTION OF MORLET WAVELET
Time and frequency resolution of mother wavelet is presented in Equation (17) and Equation (18). t ai is the time resolution of mother wavelet when the scale is a i . f ai is the frequency resolution of mother wavelet when the scale is a i . The larger t ai is, the worse time resolution is. The larger f ai is, the worse frequency resolution is.
where, f i is the gear meshing frequency, f s is the sampling frequency, a i is the scale, f b is the bandwidth parameter, and f c is the center frequency.

B. THE TIME-FREQUENCY RESOLUTION CONTRAST ANALYSIS WITH DIFFERENT f c AND f b
In order to verify the effect of parameters f c and f b on time and frequency resolution, the simulation signals of fault shock is presented in Equation (19).
The simulation signals are composed by three components with the frequency of 1/10Hz, 1/10Hz, and 1/15Hz, and the phases of three components are different. The time domain waveform of simulation signal is presented in Figure 3. Based on the simulation signals of fault shock, the optimal center frequency f c and bandwidth parameter f b are obtained by wavelet Shannon entropy, which is presented as follows: The range of f c is set as [0.05, 0.7], and the step size is 0.05. The range of f b is set as [0. 5,50], and the step size is 0.5. The relationship between wavelet Shannon entropy and center frequency f c , bandwidth parameter f b can be obtained, which is presented in Figure 4 by three-dimensional plot. As can be observed in Figure 4, the minimum entropy value The time-frequency image contrast of simulation signals using continuous Morlet wavelet with f c = 0.5 and f b = 5/16.5/95 is presented in Figure 5. And, the time resolution and frequency resolution can be obtained by Equation (18), which are presented in Table 1. According to equation (19), the simulation signal is composed of three components with the frequency of 1/10Hz, 1/10Hz, and 1/15Hz, and the phases of three components are different. As can be observed in Figure 5(b), the time and frequency resolution are the most suitable with f c = 0.5 and f b = 16.5, because the three components of simulation signal are completely separated in time and frequency direction. As can be observed in Figure 5(a) and Table 1, the three components of simulation signal are separated in time direction, but two components with frequency 1/10Hz and 1/15Hz are not separated in frequency direction. Because the frequency resolution in Figure 5(a) is lower than in Figure 5(b). As can be observed in Figure 5(c) and Table 1, the three components of simulation signal separated in frequency direction, but two components of frequency 1/10Hz with different phase are not separated in time direction. Because the time resolution in Figure 5(c) is lower than in Figure 5(b).
The time-frequency image contrast of simulation signals using continuous Morlet wavelet with f c = 0.2/0.5/0.8 and f b = 16.5 is presented in Figure 6. And, the time resolution and frequency resolution can be obtained by Equation (18)   which are presented in Table 2. The simulation signal is composed of three components with the frequency of 1/10Hz, 1/10Hz, and 1/15Hz, and the phases of three components are different. As can be observed in Figure 6(b), the time and frequency resolution are the most suitable with f c = 0.5 and f b = 16.5, because the three components of simulation signal are completely separated in time and frequency direction. As can be observed in Figure 6(a) and Table 2, the three components of simulation signal are separated in time direction, but two components with frequency 1/10Hz and 1/15Hz are not separated in frequency direction. Because the frequency resolution in Figure 6(a) is lower than in Figure 6(b). As can be observed in Figure 6(c) and Table 2, the three components of simulation signal separated in frequency direction, but two components of frequency 1/10Hz with different phase are not separated in time direction. Because the time resolution in Figure 6(c) is lower than in Figure 6(b).
In summary, the time resolution and frequency resolution with the center frequency f c = 0.5 and the bandwidth f b = 16.5 obtained by wavelet Shannon entropy is the best. Therefore, the simulation results indicate that the best time and frequency resolution of Morlet can be obtained by wavelet Shannon entropy, which can make the wavelet waveform best match the fault impact signal.

V. EXPERIMENTAL RESULTS AND DISCUSSION
DH186E vibration acceleration sensors with the sensitivity 9.97mv/m · s −2 and DH5901 vibration tester were used to collect the vibration signals of MG1480 and MG1660 shearer VOLUME 8, 2020 ranging arm in normal and fault state. The vibration sensors were fixed on the ranging arm of shearer by a magnetic suction base. In order to verify the proposed accurate gear fault location method, the MG1480 and MG1660 shearer are used to experimental verification.

A. EXPERIMENTAL VERIFICATION OF MG1480 SHEARER FAULT LOCATION 1) COLLECTION OF VIBRATION SIGNALS IN NORMAL AND FAUIT STATE
The vibration sensors layout of the MG1480 shearer ranging arm was presented in Figure 7. As can be observed, the vibration sensors are arranged 4 axial positions and 4 radial positions, respectively. By comprehensive analysis of vibration detection signals at different positions, the axial vibration signals of the idler shaft obviously change in normal and fault state. So, the axial vibration signals of the idler shaft is used to fault location analysis.

2) THE CONTRAST ANALYSIS OF THE TIME DOMAIN SIGNALS BEFORE AND AFTER NOISE REDUCTION
In fault diagnosis of mechanical transmission system, Daubechies wavelet is usually applied [24]. By noise reduction experiment, the db17 wavelet basis and the decomposition layer for 5 are determined to noise reduction of the axial vibration signals of idler shaft. The time domain signals of MG1480 shearer normal ranging arm and fault ranging arm before and after noise reduction are presented in Figure 8. As can be observed in Figure 8, the wavelet transform method has good noise reduction effeteness. The maximum absolute value of vibration amplitude for normal ranging arm after noise reduction is 376.5m/s 2 . While, the maximum absolute value of vibration amplitude for fault ranging arm after noise reduction is 687.8m/s 2 , which is much larger than the vibration amplitude of normal ranging arm.

3) THE CONTRAST ANALYSIS OF SPECTRUM IN NORMAL AND FAULT STATE AFTER NOISE REDUCTION
The mechanical transmission system of MG1480 shearer ranging arm is presented in Figure 9. The synchronous rotation speed of the motor is 1500r/min. The gears vibration characteristic frequencies of MG1480 shearer ranging arm can be obtained and presented in Table 3. The key vibration characteristic frequencies of gears are meshing frequency and rotation frequency.
The contrast of spectrum between normal ranging arm and fault ranging arm for MG1480 shearer is presented in Figure 10. The contrast of amplitudes at the key frequencies between normal ranging arm and fault ranging arm 202266 VOLUME 8, 2020   can be obtained by Figure 10 and are presented in Table 4. As can be observed, the amplitudes at the 472.5Hz and its frequency multiplications are much larger in fault state than in the normal state. Especially at 472.5Hz, the amplitude in fault state is 44.32 times the normal state. While the amplitudes at the 700Hz and its 2 times frequency are smaller in fault state than in the normal state. So, the fault is located at the meshing frequency of 472.5Hz. Therefore, the fault may occur at one or more gears in Z18, Z19, Z20, and Z21, and the rotation frequency of fault gear may be 17.5Hz, 14.32Hz, or 11.81Hz. It can be seen that the spectrum analysis does not accurately locate the specific location of the fault.

4) THE CONTRAST ANALYSIS OF MORLET WAVELET ENVELOPE DEMODULATION SPECTRUM
Based on the vibration signals of MG1480 shearer, the optimal center frequency f c and bandwidth parameter f b are obtained by wavelet Shannon entropy, which are presented as follows: The range of f c is set as [0.1, 3.0] and the step size is 0.1. The range of f b is set as [0.1, 2.0], and the step size is 0.1. The relationship between wavelet Shannon entropy and center frequency f c , bandwidth parameter f b can be obtained, which is presented in Figure 11 by three-dimensional plot. As can be observed in Figure 11, the minimum entropy value forms a ''ridge-line'' at the bottom along with the changes of f c and f b , and the value of Shannon entropy is minimum with VOLUME 8, 2020   The sampling frequency is 51200Hz, and the center frequency f c = 1, and the fault frequency is 472.5Hz. Therefore, according to Equation (18), the optimal scale of the Morlet wavelet envelope demodulation is 108. According to the optimal center frequency, bandwidth and scale of Morlet wavelet, the envelope demodulation spectrum of normal ranging arm and fault ranging arm is presented in Figure 12 and Table 5. As can be observed, the amplitude of 17.5Hz and 2 times frequency in the fault state is 16.17 and 11.29 times the normal state, respectively. Therefore, the rotation frequency of faulty gear is 17.5Hz, and the is fault located at one or more gears in Z17 and Z18.

5) THE ACCURATE FAULT LOCATION
The gear fault can be accurately located by the meshing frequency and rotation frequency. The meshing frequency of gear fault can be obtained by the spectrum contrast analysis in the normal state and fault state, and the rotation frequency of gear fault can be obtained by the contrast analysis of the envelope demodulation spectrum in normal and fault state.
According to the spectrum contrast analysis in the normal state and fault state in Figure 10, the gear fault is located at the meshing frequency of 472.5Hz. According to the contrast analysis of the envelope demodulation spectrum in normal and fault state in Figure 12, the gear fault is located at the rotation frequency of 17.5Hz. By the comprehensive contrast of the spectrum and Morlet wavelet envelope demodulation spectrum, As can be observed in Table 3, the fault is located at Z18 gear. Because the meshing frequency and rotation frequency of Z18 gear is 472.5Hz and 17.5Hz, respectively. The reality is that there is an abrasion fault at Z18 gear, which is presented in Figure 13. The results of fault diagnosis indicate that the fault of the mechanical transmission system for the MG1480 shearer ranging arm has been accurately located by the combination method of optimized continuous complex Morlet wavelet envelope demodulation spectrum analysis and spectrum contrast analysis between the normal state and the fault state.

B. EXPERIMENTAL VERIFICATION OF MG1660 SHEARER FAULT LOCATION 1) COLLECTION OF VIBRATION SIGNALS IN NORMAL AND FAUIT STATE
The vibration sensors layout of MG1660 shearer ranging arm was presented in Figure 14. As can be observed, the vibration sensors are arranged 8 positions which are axial and radial of the motor shaft, idler shaft, transmission I shaft, and roller shaft. By comprehensive analysis of vibration detection signals at different positions, the axial vibration signals of the idler shaft obviously change in normal and fault state. So, the axial vibration signals of the idler shaft is used to fault location analysis.

2) THE CONTRAST ANALYSIS OF VIBRATION SIGNALS OF MG1660 SHEARER BEFORE AND AFTER NOISE REDUCTION
The mechanical transmission system of the MG1660 shearer ranging arm is presented in Figure 15. The synchronous rotation speed of the motor is 1500r/min. The gears vibration characteristic frequencies of MG1660 shearer ranging arm can be obtained and presented in Table 6. The key vibration characteristic frequencies of gears are meshing frequency and rotation frequency.  The contrast analysis of axial vibration signals for the idler shaft in the time domain between normal ranging arm and fault ranging arm is presented as follows: The wavelet transform with db17 wavelet basis and the decomposition layer for 5 is used to noise reduction of the axial vibration signals of the idler shaft. The time-domain signals of MG1660 shearer normal ranging arm and fault ranging arm before and after noise reduction are presented in Figure 16. As can be observed in Figure 16, the wavelet transform method has good noise reduction effeteness. The maximum absolute value of vibration amplitude for normal ranging arm after noise reduction is 359.9m/s 2 . While, the maximum absolute value of vibration amplitude for fault ranging arm after noise reduction is 933.3m/s 2 , which is much larger than the vibration amplitude of normal ranging arm.

3) THE CONTRAST ANALYSIS OF SPECTRUM IN NORMAL AND FAULT STATE AFTER NOISE REDUCTION
The contrast of amplitudes at the key frequencies between normal ranging arm and fault ranging arm can be obtained by Figure 17 and are presented in Table 7. As can be observed, the vibration of amplitudes at the approximate 525Hz and its frequency multiplications are much larger in fault state than in the normal state. Especially at the approximate 525Hz, the amplitude in fault state is 11.09 times the normal state. The fault is located at the meshing frequency of 525Hz. Therefore, the fault is located at one or more gears in Z1, Z2, and Z3, and the rotation frequency of fault gear may be 25Hz, 20.2Hz, or 18.1Hz. It can be seen that the spectrum analysis does not accurately locate the specific location of the fault. VOLUME 8, 2020

4) THE CONTRAST ANALYSIS OF MORLET WAVELET ENVELOPE DEMODULATION SPECTRUM
The range of f c is set as [0.1, 3.0] and the step size is 0.1. The range of f b is set as [0.1, 2.0], and the step size is 0.1. The relationship between wavelet Shannon entropy and center frequency f c , bandwidth parameter f b can be obtained, which is presented in Figure 18 by three-dimensional plot. As can be observed in Figure 18 For the MG1660 shearer, the sampling frequency is 51200Hz, and the center frequency f c = 1.3, and the fault frequency is 525Hz. Therefore, according to Equation (18), the optimal scale of Morlet wavelet envelope demodulation  is 127. According to the optimal center frequency, bandwidth and scale of Morlet wavelet, the envelope demodulation spectrum of normal ranging arm and fault ranging arm for MG1660 shearer is presented in Figure 19 and Table 8. As can be observed, the key frequencies are approximate 18.10Hz,20.19Hz,25Hz, and frequency multiplications of 18.1Hz and 20.19Hz. Especially at the approximate 18.10Hz, the amplitude in fault state is 10.64 times the normal state. While the amplitudes at the approximate 20.19Hz and 25Hz and their 2 times frequency are close in fault state and in normal state. So, the fault is located at the rotation frequency  of 18.10Hz. Therefore, the fault is located at one or more gears in Z3 and Z4.

5) THE ACCURATE FAULT LOCATION
The gear fault can be accurately located by the meshing frequency and rotation frequency. The meshing frequency of gear fault can be obtained by the spectrum contrast analysis in the normal state and fault state, and the rotation frequency of gear fault can be obtained by the contrast analysis of the envelope demodulation spectrum in normal and fault state.
According to the spectrum contrast analysis in the normal state and fault state in Figure 17, the gear fault is located at the meshing frequency of 525Hz. According to the contrast analysis of the envelope demodulation spectrum in normal and fault state in Figure 19, the gear fault is located at the rotation frequency of 18.10Hz. By the comprehensive contrast of the spectrum and Morlet wavelet envelope demodulation spectrum, As can be observed in Table 6, the fault is located  at Z3 gear. Because the meshing frequency and rotation frequency of Z3 gear is 525Hz and 18.10Hz, respectively.The real fault is that the tooth profile error of the Z3 gear is 23.2 µm and the tooth direction error is 32.2 µm. Because of the tooth profile error and tooth direction of the Z3 gear, the Z3 gear is caused to wear by the partial meshing of the Z2 and Z3 gears.The Z3 gear with partial meshing is presented in Figure 20. The results of fault diagnosis indicate that the fault of the mechanical transmission system for the MG1660 shearer ranging arm has been accurately located by the combination method of optimized continuous complex Morlet wavelet envelope demodulation spectrum analysis and spectrum analysis between the normal state and the fault state.

C. DISCUSSION
The vibration sensors layout of the MG1480 shearer ranging arm was presented in Figure 7. The contrast of amplitudes at the key frequencies between the axial vibration signals of the roller shaft and the axial vibration signals of the idler shaft are presented in Figure 21. As can be observed in Figure 21, the amplitudes of the axial vibration signals of idler shaft at the key frequency are much larger than the axial vibration signals of the roller shaft, and the meshing frequency 472.5Hz was severely submerged. Because the sensor of the axial vibration signals for the roller shaft is far away from the corresponding to meshing frequency of 472.5Hz, and the vibration signal amplitude reduction after a long transmission path. So, in order to detect the fault of the low-speed shaft and the high-speed shaft of the shearer ranging arm, it is necessary to at least arrange the sensors at the idler and roller shaft. The optimized complex Morlet wavelet envelope demodulation spectrum and the Hilbert envelope spectrum are presented in Figure 22(a) and 22(b), respectively. As can be observed, the characteristic frequency of 17.5Hz and the double frequency of 17.5Hz in Figure 22(a) are more obvious than those in Figure 22(b). And the double frequency characteristic of 17.5Hz in Figure 22(b) is submerged by the noise. The contrast results indicate that the proposed optimized continuous complex Morlet wavelet envelope demodulation method can effectively extract the fault characteristics than the Hilbert envelope demodulation method.

VI. CONCLUSION
Aiming at the problem of accurate fault location of the mechanical transmission system of shearer ranging arm, the gear faults are diagnosed by vibration detection method. The combination method of optimized continuous complex Morlet wavelet envelope demodulation spectrum analysis and spectrum analysis is proposed to apply to the accurate gear fault location of the mechanical transmission system of shearer ranging arm. In the algorithm, the optimal center frequency and bandwidth of the Morlet wavelet can be obtained by a wavelet Shannon entropy and the optimal scale factor can be accurately determined by spectrum contrast analysis of vibration signals in normal and fault state.
In order to verify the effect of center frequency and bandwidth on a time-frequency resolution, the simulation signals of fault shock are used. The results indicate that the bandwidth and center frequency optimized by wavelet Shannon entropy can obtain the best time and frequency resolution.
In order to verify the proposed accurate gear fault location method, the vibration signals of MG1480 and MG1660 shearer ranging arm are used to experimental verification. The experiment results indicate that the proposed method can achieve accurate gear fault location of shearer ranging arm. In order to detect the fault of the low-speed shaft and the high-speed shaft of the shearer ranging arm, it is necessary to at least arrange the sensors at the idler and roller shaft. By the contrast of the optimized complex Morlet wavelet envelope demodulation spectrum and the Hilbert envelope spectrum, the results indicate that the proposed optimized complex Morlet wavelet envelope demodulation method can better highlight the fault characteristics than the Hilber envelope demodulation method.
In the future, we will study the fault location method of the mechanical transmission system with variable speed and loads based on this research.