Gears are the most essential parts in rotating machinery. Crack fault is one of damage modes most frequently occurring in gears. So, this paper deals with the problem of different crack levels classification. The proposed method is mainly based on empirical mode decomposition (EMD) and Euclidean distance technique (EDT). First, vibration signal acquired by accelerometer is processed by EMD and intrinsic mode functions (IMFs) are obtained. Then, a correlation coefficient based method is proposed to select the sensitive IMFs which contain main gear fault information. And energy of these IMFs is chosen as the fault feature by comparing with kurtosis and skewness. Finally, Euclidean distances between test sample and four classes trained samples are calculated, and on this basis, fault level classification of the test sample can be made. The proposed approach is tested and validated through a gearbox experiment, in which four crack levels and three kinds of loads are utilized. The results show that the proposed method has high accuracy rates in classifying different crack levels and may be adaptive to different conditions.
Gearboxes are one of the fundamental and important components of rotating machinery. Its function is to transfer torque and power from one shaft to another. Representative applications involve motorcars, helicopters, and steel mills. Their failures will lead to great power loss and high maintenance fee. Therefore, condition monitoring and fault diagnosis of gearboxes are important topics in maintenance field.
Jardine et al. [
For gearbox fault diagnosis, fault level classification is more difficult than fault detection. However, limited papers reported research topic about different fault levels identification. Typical faults of gears include pitting, chipping, and crack [
The remaining sections of this paper are organized as follows. In Section
Hilbert Huang transform (HHT) is a new signal processing method developed by Huang et al. [
EMD is developed based on the assumption that any signal consists of many different IMFs. The procedures of decomposing a given signal
Ideally, after the sifting operation of (
The sifting process will be repeated
Then, make
And generate the residue signal
The IMFs
After getting all the IMFs of a signal, sensitive IMFs which contain main fault information should be selected to promote the velocity of calculation. This paper proposed a correlation coefficient based method to select sensitive IMFs, as follows. Assume one test sample of fault state Similarly, compute the correlation coefficients Calculate the fault factors Analyze the fault factors and select the
Then, the selected sensitive IMFs can be inputted into EDT. The algorithm is implemented by computing the Euclidean distances between the test sample and the trained sample as
Therefore, a feature parameter set
Euclidean distances between the test sample and trained samples can be calculated. If the distances between this test sample and each trained sample satisfy
Following the procedure described above, the crack level classification of gears can be performed. The classification process can be summarized as follows. Acquire vibration signal. Obtain IMFs by signal processing and EMD. Select the sensitive IMFs which contain main fault information. Extract feature parameters of sensitive IMFs and build the feature vector matrix. Obtain the diagnosis result using EDT.
The flowchart of the new proposed method is described in Figure
Flowchart of the classification process using EMD and EDT.
A mechanical test bed in the RCM laboratory of Mechanical Engineering College is used in this research to validate the effectiveness of the proposed method in this paper. The gearbox is driven by a 4 KW three-phase asynchronous drive motor. In addition, the speed and torque sensors are used to acquire the speed and torque information; a magnetic powder brake is utilized to provide load. These components are connected by couplings, as shown in Figure
The gearbox test rig.
The crack fault is implemented on one teeth of gear #2. Three crack levels are introduced and the length of each level is 1 mm, 2 mm, and 5 mm, respectively. Figure
(a) The structure of the gearbox. (b) The fault gear used in this study.
The sampling frequency of this experimental system is 20 kHz and sampling time is 6 s. Each fault mode has 60 samples. The input rotary speed of motor is 800 rpm and the loads generated by brake are 10 N·m, 15 N·m, and 20 N·m.
Following the procedure described in Section
The decomposition result by EMD.
In order to select the sensitive IMFs, the correlation coefficients and fault factors are calculated, which are shown in Table
The correlation coefficients and fault factor of IMFs.
Number |
|
|
|
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IMF1 | 0.471 | 0.001 | 0.470 |
IMF2 | 0.494 | −0.007 | 0.501 |
IMF3 | 0.556 | 0.012 | 0.543 |
IMF4 | 0.384 | −0.012 | 0.396 |
IMF5 | 0.285 | 0.001 | 0.284 |
IMF6 | 0.154 | 0.000 | 0.154 |
IMF7 | 0.028 | −0.004 | 0.032 |
IMF8 | 0.005 | 0.000 | 0.005 |
IMF9 | 0.006 | 0.002 | 0.004 |
IMF10 | 0.017 | 0.005 | 0.013 |
IMF11 | 0.011 | −0.005 | 0.016 |
IMF12 | 0.000 | 0.000 | 0.000 |
IMF13 | 0.001 | 0.000 | 0.000 |
IMF14 | 0.000 | 0.000 | −0.001 |
IMF15 | −0.001 | 0.000 | −0.001 |
It can be seen from Table
The vibration signal of a gearbox is a mixture of many components, such as shafts and bearings, not limited to gear meshing vibration only. To validate the selected IMFs containing gear fault information, this paper analyzed the frequency spectrum of original signal and each IMF, respectively. The signal is acquired from 1 mm crack state with 800 rpm speed and 20 Nm load condition.
Usually, shaft and bearing rotating frequencies are all in low frequency area. And gear meshing frequency will be a little high relatively. Figure
Envelope analysis of original signal.
Figure
Envelope analysis of IMF1.
Envelope analysis of IMF2.
Then, the feature parameter vectors can be calculated. This paper selects energy of IMF as feature parameter. In addition, the gear has 4 crack levels and 30 test samples are chosen for each crack level. So, the energy set,
The distance values when normal test samples are inputted and the load is 10 N·m.
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To show the distance values more directly and save space, the results are all shown by figures. When the load is 10 N·m, the results can be depicted as in Figures
The classification result when normal test samples are inputted.
The classification result when 1 mm crack test samples are inputted.
The classification result when 2 mm crack test samples are inputted.
The classification result when 5 mm crack test samples areinputted.
To validate the effectiveness of EMD, the energy of original signal that is not processed by EMD is extracted and the classification results are shown as in Figures
The classification result of original signal when normal test samples are inputted.
The classification result of original signal when 1 mm crack test samples are inputted.
The classification result of original signal when 2 mm crack test samples are inputted.
The classification result of original signal when 5 mm crack test samples are inputted.
In order to validate the proposed method for which sensitive IMFs are selected, energy of first to third IMFs is extracted and the final classification results are shown as in Figures
The classification result using first to third IMFs when normal test samples are inputted.
The classification result using first to third IMFs when 1 mm crack test samples are inputted.
The classification result using first to third IMFs when 2 mm crack test samples are inputted.
The classification result using first to third IMFs when 5 mm crack test samples are inputted.
All the samples above are under the load of 10 N·m; for the purpose of checking the adaptability to different conditions of the method, the load of 15 N·m and 20 N·m is also considered and the classification results are shown as in Figures
The classification result of 15 N·m load when normal test samples are inputted.
The classification result of 15 N·m load when 1 mm crack test samples are inputted.
The classification result of 15 N·m load when 2 mm crack test samples are inputted.
The classification result of 15 N·m load when 2 mm crack test samples are inputted.
The classification result of 20 N·m load when normal test samples are inputted.
The classification result of 20 N·m load when 1 mm crack test samples are inputted.
The classification result of 20 N·m load when 2 mm crack test samples are inputted.
The classification result of 20 N·m load when 5 mm crack test samples are inputted.
It can be obtained from above analysis that the gear crack level classification method is effective to identify different crack levels no matter whether the fault is in early stage (1 mm) or sever stage (5 mm). In addition, EMD and the method of selecting sensitive IMFs are crucial during process of the original signal.
In this paper, a new gear crack level classification method based on empirical mode decomposition (EMD) and Euclidean distance technique (EDT) is proposed. The approach was tested and validated successfully using a test rig implanted crack fault experiment case. The results show the proposed method obtains high accuracy rate in classifying different crack levels and adapts to different conditions. Additionly, it is found through comparison that EMD and the method of selecting sensitive IMFs are crucial during process of the original signal.
The authors declare that there is no conflict of interests regarding the publication of this paper.