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The gearbox wears state monitoring and evaluation based on on-line wear debris features
Wear 426–427 (2019) 1719–1728
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The gearbox wears state monitoring and evaluation based on on-line wear debris features
T
Wei Caoa,c, , Han Zhanga, Ning Wanga, Hai Wen Wangb, Zhong Xiao Pengc ⁎
a
School of Mechanical and Electronic Engineering, Xi’an Technological University, Xuefu Road 2, 710032 Xi'an, Shaanxi, PR China Mechanical Design Institute of Shaanxi Province, Xianyang, Shaanxi 712000, PR China c School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia b
ARTICLE INFO
ABSTRACT
Keywords: Wears state On-line monitoring Wear debris Wear testing
The teeth of planetary gear trains are prone to wear and can be damaged. In traditional wear monitoring, the equipment needs to be disassembled, and the efficiency is low. The wear debris in lubricating oil can provide information about machine wear. On-line oil monitoring technology can easily recognize the change of wear debris concentration in the gearbox oil pan without the need for disassembling equipment. However, existing online monitoring systems are often based on wear debris concentration, providing limited information on particle shape and type, which are important for root cause analysis. In this study, some new features of wear debris were extracted for on-line wear monitoring in order to improve wear state evaluation and prediction using on-line approach.
1. Introduction The gearbox is an important transmission component of mechanical equipment, and its internal structure is complex and extremely prone to wear. The failure rate of a transmission gearbox in wind farms ranges from 40% to 50% [1–3]. In the aerospace industry, the teeth of helicopter planetary gear trains are prone to wear and breakage. Approximately 68% of helicopter accidents are attributed to the transmission system, which accounts for 58% of the total maintenance cost. The wear-related failure of gearbox includes (Ⅰ) abrasion wear. (Ⅱ) adhesive wear. (Ⅲ) abrasive wear. (Ⅳ) tooth surface fatigue and pitting [4,5]. The wear-related failure of the transmission system has caused huge economic losses and casualties. Thus, developing a wear state monitoring-based diagnosis and health management system for the gearbox is important. The vibration, acoustic emission, and wear debris are commonly monitored in gearbox health state diagnosis and management. The monitoring of vibration and acoustic emission highly depends on the sensor and signal amplifier operation [6,7]. However, in wear debris analysis, a signal generator is not required. Wear debris analysis can evaluate machine condition based on the change of tiny wear debris concentration in the oil system. Therefore, applying wear debris monitoring technology to the fault diagnosis and health management of gearbox transmission systems has great practical value. Wear debris monitoring technology includes on-line and off-line
⁎
analysis. Off-line analysis provides extensive and accurate information [8]. Among the off-line wear debris monitoring methods, ferrography is an effective technique to detect the wear state of machines [9], with which the wear position and wear mechanism of machines can be determined [10]. However, this technique is time consuming. On-line wear debris analysis is the current trend for increasing the monitoring efficiency and reducing the dependence on the manual operator. Peng [11] developed a compact and highly visible intelligence system, which consists of a three-dimensional (3D) particles image-generating system, particle screening system, and data conversion system. This 3D imaging system could view specific particles. In 2007, researchers in Xi’an Jiaotong University [12] developed an image-based on-line visual ferrograph (OLVF) to analyze wear particles in oil. In 2017, Zhu et al. [13] analyzed a variety of on-line sensors based on capacitance, induction, acoustics, and optical sensing to measure lubricant performance. These methods can provide the theoretical support for machine condition monitoring. With the development of computer image processing technology, many scholars focused on wear debris image analysis. Cao et al. [12,14–17] used the OLVF to monitor the wear state of equipment and found that it can obtain more comprehensive wear information than other methods. Wear debris image pre-processing and wear particle segmentation [18,19] are crucial to obtain accurate recognition results. However, the different shapes of wear debris and the noise in wear debris image bring challenges to wear debris image analysis and thus affect the wear state
Corresponding author.
https://doi.org/10.1016/j.wear.2018.12.068 Received 3 September 2018; Received in revised form 12 December 2018; Accepted 21 December 2018 0043-1648/ © 2019 Elsevier B.V. All rights reserved.
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Nomenclature IPCA wf hf Cfi BIPCA NP WP HP H{f}(t) fAS(t) uk
ωk
L
L- augmented Lagrangian Lagrangian multipliers α Quadratic penalty term PDF Probability density function Pi Probability distribution evaluated at the ith wear monitoring data KDR The kernel density representation to the random variable KDF The kernel density functions ME Maximum entropy MSRF Multi-scale relational factor KDME Kernel density maximum entropy GL The total gray level of the wear image GA The gray mean value Pw The probability of categories 2 (n ) The inter-class variance of the classes 2DVMD Two-dimensional variational mode decomposition
The Index of Particle-Covered Area The width of the wear image The height of the wear image The object pixel number of wear debris in the segmented wear image Cover area of wear debris after reconstruction Number of wear debris chains Width of wear debris chains Length of wear debris chains The Hilbert transform of a signal f(t) The complex-valued analytic signal Shorthand notations for the set of sub-modes (kth subsignals) The center frequencies of kth sub-mode
evaluation result. Classical wear debris image analysis algorithms only separate wear particles from the background. They cannot denoise the wear debris image and extract useful wear-related features. However, the actual working conditions of a gearbox are poor, and the gears always stir the oil pan, which will generate many bubbles. Thus, the on-line wear debris image may contain background noise, making it difficult to analyze the wear debris image. In 2014, Dragomiretskiy [21] developed variational mode decomposition (VMD) to realize signal decomposition. This method has been successfully used in fault diagnosis and feature extraction in equipment. The two-dimensional VMD (2DVMD) is a 2D extension of the VMD algorithm, which can achieve image noise reduction. more features about wear debris chains are worth of consideration in the wear debris image analysis, so that the capability of wear state evaluation and prediction using on-line approach can be improved. Existing on-line wear debris monitoring systems are often based on the wear debris concentration, providing limited information on particle shape and type. For the identification of wear particles, the shape, size, and surface features of wear debris are all important for root cause analysis [21]. In addition, conventional wear debris identification studies are usually performed on a single wear particle. However, in actual on-line wear debris monitoring systems, the wear particles are often deposited in the form of chains under the action of magnetic force. Therefore, directly analyzing the wear debris image using previous wear particle analysis algorithms does not provide perfect results. Thus the features of wear debris chains need to be considered to improve the capability of wear state evaluation and prediction using on-line approach. The health state division is another important factor in the evaluation of gearbox wear state. Henneberg [22] replaced the conventional experience value by multiple linear regression of the mean value and identified the gearbox wear state using the oil monitoring method. Sheng [23] performed an oil monitoring experiment on a high-power gearbox and studied the oil characteristics at running-in period and health state. By comparing the cumulative number of wear particles with the warning threshold and alarm threshold, the gearbox wear state was predicted. To divide the health state, many scholars applied the classical threeline method based on the assumption that the distribution of oil monitoring data obeys Gaussian distribution. However, this assumption is not accurate. The accurate distribution of data needs to be estimated. Huo [24] developed an improved probability density function (PDF) estimation method using maximum entropy. However, its parameters still need to be considered by the operator. Therefore, it is necessary to consider the correlation among various evaluation indicators and develop an improved PDF estimation method to estimate the accurate
distribution of the monitoring indicators. Therefore, in this study, an on-line wear debris monitoring system was used to monitor the wear state of the gearbox. Several wear debris image analysis algorithms, including wear debris segment, image denoising, 2DVMD image reconstruction, and image projection algorithms, were developed to reprocess the on-line wear debris monitoring data. New features of wear debris for on-line wear monitoring were extracted. The concentration, size, shape, and edge information of wear particles were utilized to analyze the wear state. In addition, an improved PDF estimation method was used to acquire the actual PDF of feature curves. A multiscale relational factor (MSRF) was developed to describe and evaluate the wear-related health conditions. Finally, tests on a self-made planetary gearbox were conducted to verify the performance of the newly developed indicators and algorithms. The ultimate goal of this study is to develop effective and reliable on-line wear debris analysis techniques for wear state evaluation and remaining useful life prediction for the gearbox. 2. Wear debris image denoising and feature extraction 2.1. Denoising processing for wear debris images When monitoring and acquiring the on-line wear debris images, they are often influenced by the noise. Some bubbles and shadows can be seen in the wear monitoring image, which affect image quality and information extraction. Therefore, denoising is very important for image processing. The denoising processing for wear debris images is shown in Fig. 1. As shown in Fig. 1, to achieve the objective, first the wear particle image is divided, and the transform of histogram for each wear debris sub-image is acquired. Then, the gray scale of each wear debris subimage is adjusted. Thus, the contrast between each wear debris subimage and its background is enhanced. Second, Otsu's method is used to calculate the threshold of each wear debris sub-image. This threshold can be used to convert an intensity image to a binary image. In this study, the Otsu algorithm [25] is adopted to segment wear
Fig. 1. Denoising processing for wear debris images. 1720
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particles. At first, each gray value in the image is thought as a possible threshold. Then, the gray level of the whole picture is divided into two categories, and the between class variance of each classification is calculated successively. The gray level with the maximum between class variance is selected as the optimal threshold. This between class variance method is very sensitive to noise and target size and is faster to calculate. For any gray value n,1≤ n ≤ GL, the gray scale of image is divided into two categories: C0 and C1, where C0 = {1, 2, 3, …, n} and C1 = {n + 1, n + 2, …, GL}. GL is the total gray level of the image. GA is the categories mean. Pw0 is the probability of C0 categories and Pw1 is the probability of C1 categories. PGi is the probability of pixels with the gray level equals”i”. GAj is the average grayscale value of C0 categories. For C0, GA0 denotes the gray mean value, Then:
GA0 =
GAj PW 0
To acquire clearer picture of wear debris image, 2DVMD method was used as a faster approach to Reconstruction of the wear debris images. 2.2. Reconstruction of the wear debris images based on 2DVMD The 2DVMD method [20] was used to adaptively decompose the wear debris images into different modes by separating spectral bands. The method is defined as follows: Let f(t) be a purely real signal. The complex analytic signal is defined as
The goal of VMD is to decompose an input signal into a discrete number of sub-signals (modes). To assess the bandwidth of a mode, the resulting constrained variational problem is
n
GAn =
iPGi
(1)
i=1
For C1, the gray mean value GA1 can be calculated:
GA1 =
GA
GAn
min
{uk },{ k }
(2)
PW 1
s. t .
Then, the inter-class variance of the classes C0 and C1 is: 2 (n )
= PW 0 (GA
GA 0 )2 + PW 1 (GA
GA1)2
(4)
fAS (t ) = f (t ) + jH {f }(t )
k
[uAS, k (x ) e
j
k, x
2 2
]
k
x:
uk (x ) = f (x ) k
{uk } = {u1,
(3)
, uk }, {
k}
= { 1,
,
k}
(5)
The reconstruction constraint can be addressed by using the augmented Lagrangian L as follows:
Change the value of j from 1 to GL, so that the threshold j with the maximum inter-class variance 2 (j) is the best threshold.
Fig. 2. Decomposition result of wear debris image. 1721
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Fig. 3. Image of wear debris. 2
L({uk }, {
k }, )
[uAS,k e
k
j
k,x
]
k
+
(x ), f (x )
2 2
+ f (x )
uk (x ) k
2
Fig. 4. Process of feature extraction.
uk (x )
(6)
k
Initialize and update ukn + 1 ,
ukn +1 = argmin
[uAS, k (x ) e
k
uk
, and
n+1 k
j
k, x
]
2 2
Based on above work, some features will be extracted to obtain the shape and size characteristics of the wear debris chains.
n+1 . k
+ f (x )
u i (x ) + i
(x ) 2
2
2.3. Wear debris feature extraction
2
(7)
Previous studies only focused on the wear debris concentration, but the wear state and wear mechanism of the equipment can be characterized by the size distribution, color, and morphology of wear debris in the lube oil. In addition, previous on-line wear debris monitoring results show that many wear particle chains can be found in the wear debris image. Thus, in this study, the wear particle chains are analyzed, and new features are extracted to obtain the shape and size characteristics of each wear particle picture. Based on the result of image denoising, new indicators, including the covered area (BIPCA), chain number (NP), and length (LP) and width (WP) of wear debris chains, are quantitatively characterized to reflect the wear debris concentration and their shapes and sizes.
The center frequencies ωk do not appear in the reconstruction fidelity term, but only in the bandwidth prior, the optimization can take place in Fourier domain, and we end up optimizing: The relevant problem thus writes: The center frequencies ωk do not appear in the reconstruction fidelity term, but only in the bandwidth prior. The optimization can take place in the Fourier domain. Then relevant problem is thus written as 2
n+1 k
=
uk ( ) d 2
uk ( ) d
(8)
Algorithm for 2D-VMD: 0
0
1) Initialize uk ,
k
,
0
, n
2) Repeat n ← n + 1, update uk and 3) Update n+1
( )=
n
( )+
n+1
f ( )
uk k
2.3.1. Wear debris covered area after reconstruction (BIPCA) The traditional on-line wear debris monitoring parameter is IPCA (Index of Particle-Covered Area), is derived based on the area covered by the debris deposited in the OLVF flow channel through magnetomotive force. Which has been used in many monitoring experiments [14–17], to identify the variation in wear debris in the lube oil and characterize wear degrees. For a wear debris image (Fig. 3), the IPCA can be calculated according to Eq. (10).
0. k.
( )
(9)
Until: k
n +1 u^k n 2 u^k 2
n u^k
IPCA =
2 2
< Ke
Cfi wf hf
× 100%
(10)
Where ∑Cfi denotes the object pixel number of wear debris in the segmented image, as shown in Fig. 3. Based on the result of image denoising, each decomposition mold of the wear debris image can be analyzed. In this study, the IPCA for each mold is calculated and used in feature extraction. Based on the compare result of IPCA, the noisy image is excluded (with larger IPCA value), and then, after the wear image denosing, the wear debris image is reconstructed. Finally, the new parameter, cover area of wear debris after reconstruction, can be calculated, that is called new BIPCA index. The process of feature extraction is shown in Fig. 4.
Fig. 2(a) is the original wear debris monitoring image acquired by using the wear debris analysis system. While the Fig. 2(b) is the gray scale image of Fig. 2(a), because the original image should be changed into a gray scale image for further data processing. Fig. 2(a) and (b) serves as an example to expound the denoising algorithm. Through2DVMD, the noise image can be decomposed into a series of sub-modes with different center frequencies (see Fig. 2(c)–(e)). Normally, some sub-modes include the original information of the wear debris image (see Fig. 2(c) and (d)), while others include the background noise (see Fig. 2(e) and (f)). After removing the sub-modes with the background noise, the wear debris monitoring image is reconstructed. Fig. 2(g) shows the reconstruction result of wear debris monitoring image, and Fig. 2(h) shows the binary image after denosing. Fig. 2(i) is the transform of histogram for wear debris image, which can be used to adjust the gray scale of wear debris image.
2.3.2. Size and morphology analysis of wear debris chains Step 1: Extract the skeleton of wear debris chain. Based on the result of image denoising for each sub-image, the 1722
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Fig. 5. Wear debris image denosing and processing.
Fig. 6. Wear debris image denosing and processing result.
Canny computational theory of edge detection [25] is adopted to detect the edge of the wear debris chain and extract the skeleton for each subimage, as shown in Fig. 5. After the final combination of sub-images, the entire wear debris chain skeleton of the whole image can be obtained (see Fig. 6(a)).
image can be extracted. The mathematical method of projection transformation can be found in Eq. (11). According to Eq. (11), firstly, the skeleton value f (x i , yj ) should be recalculated first. Only the pixles inside the skeleton of wear debris chains is set as “1”, and others will be set as “0”. Then, the projected value Py can be culculated. Thus, the two-dimensional curve f (x i , yj ) (the skeleton of the wear debris chains in Fig. 6(a)) is projected on the y axis, and the one-dimensional projection curve will be acquired (See Fig. 6(b)).
Step 2: Projection and new indicators extraction. Attracted by the magnetomotive force, the wear debris are often deposited or overlapped in a chain shape. Therefore, the skeletons of the wear debris in Fig. 6(a) are also in a chain shape. The projection transformation is performed on the y-axis of Fig. 6(a) to reduce the dimension of the image, and then, the two-dimensional image is converted into one-dimensional curve. Based on this projection curve, several important new features of the on-line wear debris monitoring
f (xi , yj ) = Py (yj ) = 1723
1, if(x i , yj )
skeleton of the wear debris chains
0, others
200 i=1
f (x i , yj ), yj = 1, 2 …, N
(11)
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is Gaussian. However, this assumption is not always accurate. Therefore, in this study, an improved PDF estimation method using maximum entropy [24] and kernel density representation (KDR) [26] is first adopted to estimate the accurate distribution of the above indicators. Let X be a random variable with support Ω and fX(x) be it's unknown PDF. Algorithm to seek fX(x) and health state division:
Table 1 New indicators for wear debris images. Indicator
Relationship
BIPCA NP WP HP
Cover area of wear debris after reconstruction Number of wear debris chains Width of wear debris chains Length of wear debris chains
1. Choose a support bounded domain Ωx ⊆ Ω, Ωx ≡[xmin; xmax]. 2. Develop the coordinate transformation z = (x − xmin)/(xmax − xmin), by introducing the random variable Z. defined in Ωz ≡ [0, 1] where μ1, μ2, …, μM are the first M generalized moments of Z. pi is the probability distribution of Z. The constraints imposed by the available information of X are E(gk).
E(gk)
µk =
n i=1
gk (z i ) pi
(13)
3. Apply the KDR to the random variable Z. N
lim f XK (x ; x i , h) = (x
h
Fig. 7. Health state division of the gearbox.
4.
The peaks of the one-dimensional projected curve in Fig. 6(b) correspond to the horizontal wear debris chains skeleton in Fig. 6(a). Therefore, the features of the on-line wear debris chains image, such as the number, width and length of the wear debris chains, can be reflected in the one-dimensional projected curve. Based on the projection curve in Fig. 6(b), new features, Four new indicators can be extracted, see Table 1. BIPCA denotes the cover area of wear debris in wear debris images after reconstruction and denoising. NP is the number of peaks in the projection curve, which is related to the number of wear debris chains. WP is the equivalent width of peaks in the projection curve, which is related to the width of wear debris chains. HP is the equivalent height of peaks in the projection curve, which is related to the length of wear debris chains.
5. 6. 7.
0
x i ) fX (x )
fKD (x; p, ) =
pi (x i=1
xi )
(14)
ϑ is another N‐vector collecting the parameters of the N KD functions (KDFs). A discrete random variable Z1 is defined in Ωz, whose probability distribution is determined from the maximum entropy (ME) solution [24]. Choose the KDF that best fits the target PDF fz(z) to determine the KDME PDF fKDME (z ) fZ (z ) . Obtain the KDME approximation of fX(x) by the inverse coordinate transformation from z to x. Suppose the PDF of some wear debris monitoring features f(x) has been acquired using the above novel PDF estimation method. Then, the probability in interval [0, y] is y
p (y ) =
f (x ) dx 0
Step 3: MSRF. MSRF is developed to describe and evaluate the wear-related health conditions.
MSRF =
NP i=1
(WPi )
NP i=1
(HPi )
NP 2
/ BIPCA
(15) 4. Verification of the method
(12)
4.1. Experimental setup
3. Health state recognition of the gearbox
To evaluate the above methods and indicators, wear tests were conducted on a self-made planetary gear box (Fig. 8). The test rig includes NGW11 planetary gear reducer, motor, inverter, magnetic powder brake, and tension controller. Based on the theory that the wear debris concentration and shape in the oil sample indicate the lubricant's contaminated rate and wear degree, an on-line wear debris monitoring system was used to record the real-time wear debris images every 10 min. By analyzing the wear debris deposited in the monitoring system, the health state of the planetary gearbox can be evaluated. The parameters of the wear debris analysis system are listed in Table 2. The planetary gearbox wear test time was set as 900 min(15 h), and the tests were conducted under stable working conditions with heavy load (60 N) and fast speed (1200 r/min) to accelerate the wear process of the gearbox.
3.1. Defining the health state of the gearbox In this study, the health state of the machine is divided into health state (S1), sub-health state (S2), alarm status (S3), and danger/failure (S4) status. The division method is shown in Fig. 7. Once the critical thresholds for different states are determined, the wear-related health status of the machine can be determined based on the trend of feature curve extracted from the wear debris image. 3.2. Threshold determination When determining the critical thresholds for different states, the threeline method is used. This traditional method, such as three-line method, is based on the assumption that the distribution of the wear monitoring data 1724
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The reason is that the IPCA indicator was calculated using original wear debris images with noise. Thus, some shadows and bubbles were recognized as wear debris. Fig. 10(b) shows that, after the reconstruction and denoising of wear debris images, the BIPCA curves can reflect the trend of wear process. In segment A of Fig. 10(b), the gearbox was working at the run-in stage. Thus, the wear debris concentration suddenly increased. With the increase of test time, the debris concentration gradually decreased into a stable state (see segment B of Fig. 10(b)). According to the estimated PDF of the BIPCA curves, the thresholds for four stages (S1–S4 in Fig. 10 (b)) were determined quickly. Thus, the BIPCA curves were first clustered into two stages. However, as shown from the monitoring result in Fig. 9, at the last 150 min (2.5 h) of the experiment, the size and shape of wear debris chains changed. This finding indicates that the wear of the gearbox was severe. Fig. 10(c) shows the MSRF curve. The MSRF was calculated by using shape- and size-related indicators. As shown in Fig. 10(c), the MSRF curve exhibited an increasing trend in segment A and then gradually decreased into a stable state in segment B. However, in segment C of Fig. 10(c), the MSRF curve increased again, indicating that segment C belongs to the severe wear state. According to the estimated PDF of the MSRF curve, the thresholds were also determined and are shown in Fig. 10(c). In segment C, several MSRF values are larger than the threshold of S2. Thus, the wear-related health conditions of the gearbox are clustered into four stages. As shown in Fig. 10, when using the IPCA parameters only, it is difficult to accurately present the concentration variation. Combined with the BIPCA parameters, the overall concentration variation trend can be obtained. However, this parameter is not sensitive to subtle changes in size and shape of wear debris chains. When the wear state changes, the size and shape of the wear debris chains would also change. Using MSRF values, the change in number, size, and shape of the wear debris chains can be reflected. Therefore, the new indicator, MSRF, can be used to evaluate the health state of the planetary gearbox more thoroughly and can reflect the wear process more
Fig. 8. The planetary gear box test rig.
To verify the on-line analysis results, 20 ml oil samples were taken every 20 min, and the collected wear particles were examined using offline techniques. 4.2. Experimental result and discussion 4.2.1. On-line wear debris monitoring Fig. 9 shows the on-line wear debris monitoring images at different time points during the test. As shown in Fig. 9(a) and (b), at the beginning of the test, many wear debris were observed in the image, and approximately 120 min (2 h) later, they began to decrease and maintained a stable state. After 840 min (14 h), the number of wear debris increased again, which indicates that the wear of gears was becoming worse. The monitoring data processing methods described above were used to process the images and extract the features. The indicator curves, including original IPCA, BIPCA and MSRF curves are shown in Fig. 10. For BIPCA and MSRF curves, the improved maximum entropy PDF estimation method was used to acquire the actual PDF of feature curves and divide the wear debris images and health state of machine according to the PDF. The threshold line from S1 to S4 is drawn in Fig. 10(b) and (c). As shown in Fig. 10(a), the trend of IPCA curve cannot be observed. Table 2 Parameters of the wear debris monitoring system. Magneto_ Motive force (Ampere turn)
Flushing volume (s)
Flow rate (ml/min)
Deposit time (s)
Sampling volume (ml)
1200
30
1.5
60
5
Fig. 9. On-line wear debris monitoring result. 1725
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Fig. 11. The working process of off- line oil analysis.
glass slide that is placed on a magnetic cylinder of ferrogram slide maker to attract the wear debris. Step4: Let oil flow across a new glass slide (0.4 ml/min), which is placed on a magnetic cylinder of ferrogram slide maker to attract the wear debris. Step5: Remove excess oil, heating the slide and waiting for 10 min, then the slide can be analyzed under a microscope. Fig. 12 (a)-(d) show the off-line analysis result at different test stage. By referring to the knowledge of analytical ferrograph and wear particle analysis [10,27]. The wear particle was analyzed, and wear severity levels was recognized. At the beginning of the test, the values of the number, width, and length of the wear debris chains were the largest. With the increase of experiment time, the number, width, and length of the wear debris chains gradually decreased. After 13 h, they gradually increased again. Further analyzing the off-line slides under the microscope, the details of the wear debris can be acquired. As shown in Fig. 12 (e), after 900 min (15 h), some fatigue wear debris are observed. The method to recognize the fatigue wear debris can be found in Ref. [27]. Thus, the wear mode can be researched. According to the test result and the MSRF curve (Fig. 10c), the segment C belongs to the severe wear state or alarm health stage(S3). Fig. 12(f) are the images of the gear teeth surfaces after the test of 900 min, pitting can be found on the surface of the gear teeth surfaces. Pitting is a fatigue failure of the surface of a material commonly seen in rolling bearings and gears [5–7]. That verify the fatigue of the gear teeth surfaces, thus the on-line analysis result is consistent with the offline analysis result and is consistent with the damage extend of the gear. 5. Conclusion In this study, a set of wear debris image analysis methods and wear state recognition algorithms were developed for on-line wear monitoring. They were based on the on-line wear debris monitoring data and can also be applied to other on-line wear monitoring systems. The wear debris image processing algorithms were developed to enhance the contrast between wear debris images and their background, so that their inherited issues are reduced or eliminated. After reconstructing and denoising the monitoring images, the wear debris images were denoised, and more accurate monitoring information was acquired. The shape and concentration were analyzed. Several indicators of wear debris chains were quantitatively characterized. An improved PDF estimation method was developed to estimate the accurate distribution of the indicators. Then, the MSRF was extracted to describe and evaluate the wear debris images more thoroughly. According to the estimated PDF of MSRF, the thresholds of wear state evaluation were determined quickly, and the wear-related health conditions were clustered into four stages to further realize the prediction. Gearbox wear test was conducted, and on-line wear debris analysis
Fig. 10. Feature curve and health state division result.
comprehensively. By using the new indicators, further wear prediction can be realized accordingly. 4.2.2. Off-line wear debris analysis To verify the on-line analysis results, the off-line analysis was also used to research the wear mechanism [10]. 20 ml oil samples were taken every 20 min, and wear particles were collected. Fig. 11 shows the off- line oil analysis process. Step1: A sample of the gearbox's lubricating oil is taken. Step2: Diluting the oil (3 ml). Step3: Turn on the ferrogram slide maker and let oil across a new 1726
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Fig. 12. Off-line analysis and experiment result.
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was used to evaluate the performance of the methods. By combining the on-line wear debris monitoring result with other off-line analysis results, the wear mode of the gearbox can be recognized, and the accuracy of equipment health condition monitoring can be improved. The results demonstrate that the wear debris image analysis methods and wear state recognition algorithms were accurate and fast in recognizing the change of health conditions of the planetary gearbox, and the health state recognition was consistent with the gearbox inspections. the techniques developed in this study can be utilized for real-time wear state evaluation and prediction for the planetary gearbox using on-line wear debris image analysis.
[9] V. Macián, R. Payri, B. Tormos, Applying analytical ferrography as a technique to detect failures in Diesel engine fuel injection systems, Wear 260 (4–5) (2006) 562–566. [10] B.J. Roylance, Ferrography – then and now, Tribol. Int. 38 (10) (2005) 857–862. [11] Z. Peng, An integrated intelligence system for wear debris analysis, Wear 252 (9) (2002) 730–743. [12] W. Cao, G. Dong, Y.B. Xie, Prediction of wear trend of engines via on-line wear debris monitoring, Tribol. Int. 120 (2018) 510–519. [13] X. Zhu, C. Zhong, J. Zhe, Lubricating oil conditioning sensors for online machine health monitoring – a review, Tribol. Int. 109 (2017) 473–484. [14] W. Cao, W. Chen, G.N. Dong, Wear condition monitoring and working pattern recognition of piston rings and cylinder liners using on-line visual ferrograph, Tribol. Trans. 57 (2014) 690–699. [15] J. Wu, J. Mao, W. Cao, Characterization of wear-debris group in on-line visual ferrographic images, Proc. Inst. Mech. Eng. Part J -J. Eng. Tribol. 228 (11) (2014) 1298–1307. [16] W. Cao, W. Chen, G.N. Dong, Multi-sensor information integration for on-line wear condition monitoring of diesel engines, Tribol. Int. 82 (Part A) (2015) 68–77. [17] W. Cao, G.N. Dong, W. Chen, Correction strategies of debris concentration for engine wear monitoring via online visual ferrograph, Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 229 (11) (2015). [18] X. Dai, Y. Wang, S. Yu, Ferrographic analysis of pivot jewel bearing in oil-bath lubrication, Wear 376–377 (2017) 843–850. [19] B. Xu, G. Wen, Z. Zhang, Wear particle classification using genetic programming evolved features, lubrication, Science 11 (2018) 1–18. [20] Konstantin Dragomiretskiy, Dominique Zosso, Two-dimensional variational mode decomposition, International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, Springer, Cham, 2015, pp. 197–208. [21] M. Kumar, P.S. Mukherjee, N.M. Misra, Advancement and current status of wear debris analysis for machine condition monitoring: a review, Ind. Lubr. Lubr. Tribol. 65 (1) (2013) 3–11. [22] M. Henneberg, B. Jorgensen, R.L. Eriksen, Oil condition monitoring of gears onboard ships using a regression approach for multivariate T2, control charts, J. Process Control 46 (2016) 1–10. [23] S. Sheng, Monitoring of wind turbine gearbox condition through oil and wear debris analysis: a full-scale testing perspective, Tribol. Trans. 59 (1) (2016) 149–162. [24] H. Huo, Z. Li, Y. Xia, Application of maximum entropy probability density estimation approach to constituting oil monitoring diagnostic criterions, Tribol. Int. 39 (6) (2006) 528–532. [25] B. Liu, X. Zhang, H. Hong.Threshold-adaptive canny operator based on cross-zero points, MIPPR 2017: Pattern Recognition and Computer Vision, 10609, 2018. [26] U. Alibrandi, M. Khalid, Mosalam, Kernel density maximum entropy method with generalized moments for evaluating probability distributions, including tails, from a small sample of data, Int. J. Numer. Methods Eng. 113 (13) (2018) 1904–1928. [27] D.P. Anderson. Wear Partical Atlas[M], Report NAEC-92-163. 〈http://www. protechanalytical.com/Picguide.htm〉.
Acknowledgement The financial support for the present research was provided by National Science Foundation of China (Grant No. 51505360), Natural Science Basic Research Plan in Shaanxi Province of China (Grant Nos. 2016JM5083 and 2018JM5166) and Key Laboratory Research Program of Education Department of Shanxi Province (No. 18JS044). References [1] Z. Hameed, Y.S. Hong, Y.M. Cho, Condition monitoring and fault detection of wind turbines and related algorithms: a review, Renew. Sustain. Energy Rev. 13 (1) (2009) 1–39. [2] S. Sheng, Wind Turbine Gearbox Reliability Database, Condition Monitoring, and O &M Research Update, 2016. [3] Stephan Ebersbach, Z. Peng, Expert system development for vibration analysis in machine condition monitoring, Expert Syst. Appl. 34 (1) (2008) 291–299. [4] I. Akinci, D. Yilmaz, M. Çanakci, Failure of a rotary tiller spur gear, Eng. Fail. Anal. 12 (3) (2005) 400–404. [5] X. Liang, M.J. Zuo, Z. Feng, Dynamic modeling of gearbox faults: a review, Mech. Syst. Signal Process. 98 (2018) 852–876. [6] C.Q. Hu, W. Smith, R.B. Randall, Development of a gear vibration indicator and its application in gear wear monitoring, Mech. Syst. Signal Process. 01 (2016) 76–77. [7] Z. Peng, N.J. Kessissoglou, Cox MA study of the effect of contaminant particles in lubricants using wear debris and vibration condition monitoring techniques, Wear 258 (11–12) (2005) 1651–1662. [8] W.W. Seifert, V.C. Westcott, A method for the study of wear particles in lubricating oil, Wear 21 (1) (1972) 27–42.
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The gearbox wears state monitoring and evaluation based on on-line wear debris features
T
Wei Caoa,c, , Han Zhanga, Ning Wanga, Hai Wen Wangb, Zhong Xiao Pengc ⁎
a
School of Mechanical and Electronic Engineering, Xi’an Technological University, Xuefu Road 2, 710032 Xi'an, Shaanxi, PR China Mechanical Design Institute of Shaanxi Province, Xianyang, Shaanxi 712000, PR China c School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia b
ARTICLE INFO
ABSTRACT
Keywords: Wears state On-line monitoring Wear debris Wear testing
The teeth of planetary gear trains are prone to wear and can be damaged. In traditional wear monitoring, the equipment needs to be disassembled, and the efficiency is low. The wear debris in lubricating oil can provide information about machine wear. On-line oil monitoring technology can easily recognize the change of wear debris concentration in the gearbox oil pan without the need for disassembling equipment. However, existing online monitoring systems are often based on wear debris concentration, providing limited information on particle shape and type, which are important for root cause analysis. In this study, some new features of wear debris were extracted for on-line wear monitoring in order to improve wear state evaluation and prediction using on-line approach.
1. Introduction The gearbox is an important transmission component of mechanical equipment, and its internal structure is complex and extremely prone to wear. The failure rate of a transmission gearbox in wind farms ranges from 40% to 50% [1–3]. In the aerospace industry, the teeth of helicopter planetary gear trains are prone to wear and breakage. Approximately 68% of helicopter accidents are attributed to the transmission system, which accounts for 58% of the total maintenance cost. The wear-related failure of gearbox includes (Ⅰ) abrasion wear. (Ⅱ) adhesive wear. (Ⅲ) abrasive wear. (Ⅳ) tooth surface fatigue and pitting [4,5]. The wear-related failure of the transmission system has caused huge economic losses and casualties. Thus, developing a wear state monitoring-based diagnosis and health management system for the gearbox is important. The vibration, acoustic emission, and wear debris are commonly monitored in gearbox health state diagnosis and management. The monitoring of vibration and acoustic emission highly depends on the sensor and signal amplifier operation [6,7]. However, in wear debris analysis, a signal generator is not required. Wear debris analysis can evaluate machine condition based on the change of tiny wear debris concentration in the oil system. Therefore, applying wear debris monitoring technology to the fault diagnosis and health management of gearbox transmission systems has great practical value. Wear debris monitoring technology includes on-line and off-line
⁎
analysis. Off-line analysis provides extensive and accurate information [8]. Among the off-line wear debris monitoring methods, ferrography is an effective technique to detect the wear state of machines [9], with which the wear position and wear mechanism of machines can be determined [10]. However, this technique is time consuming. On-line wear debris analysis is the current trend for increasing the monitoring efficiency and reducing the dependence on the manual operator. Peng [11] developed a compact and highly visible intelligence system, which consists of a three-dimensional (3D) particles image-generating system, particle screening system, and data conversion system. This 3D imaging system could view specific particles. In 2007, researchers in Xi’an Jiaotong University [12] developed an image-based on-line visual ferrograph (OLVF) to analyze wear particles in oil. In 2017, Zhu et al. [13] analyzed a variety of on-line sensors based on capacitance, induction, acoustics, and optical sensing to measure lubricant performance. These methods can provide the theoretical support for machine condition monitoring. With the development of computer image processing technology, many scholars focused on wear debris image analysis. Cao et al. [12,14–17] used the OLVF to monitor the wear state of equipment and found that it can obtain more comprehensive wear information than other methods. Wear debris image pre-processing and wear particle segmentation [18,19] are crucial to obtain accurate recognition results. However, the different shapes of wear debris and the noise in wear debris image bring challenges to wear debris image analysis and thus affect the wear state
Corresponding author.
https://doi.org/10.1016/j.wear.2018.12.068 Received 3 September 2018; Received in revised form 12 December 2018; Accepted 21 December 2018 0043-1648/ © 2019 Elsevier B.V. All rights reserved.
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Nomenclature IPCA wf hf Cfi BIPCA NP WP HP H{f}(t) fAS(t) uk
ωk
L
L- augmented Lagrangian Lagrangian multipliers α Quadratic penalty term PDF Probability density function Pi Probability distribution evaluated at the ith wear monitoring data KDR The kernel density representation to the random variable KDF The kernel density functions ME Maximum entropy MSRF Multi-scale relational factor KDME Kernel density maximum entropy GL The total gray level of the wear image GA The gray mean value Pw The probability of categories 2 (n ) The inter-class variance of the classes 2DVMD Two-dimensional variational mode decomposition
The Index of Particle-Covered Area The width of the wear image The height of the wear image The object pixel number of wear debris in the segmented wear image Cover area of wear debris after reconstruction Number of wear debris chains Width of wear debris chains Length of wear debris chains The Hilbert transform of a signal f(t) The complex-valued analytic signal Shorthand notations for the set of sub-modes (kth subsignals) The center frequencies of kth sub-mode
evaluation result. Classical wear debris image analysis algorithms only separate wear particles from the background. They cannot denoise the wear debris image and extract useful wear-related features. However, the actual working conditions of a gearbox are poor, and the gears always stir the oil pan, which will generate many bubbles. Thus, the on-line wear debris image may contain background noise, making it difficult to analyze the wear debris image. In 2014, Dragomiretskiy [21] developed variational mode decomposition (VMD) to realize signal decomposition. This method has been successfully used in fault diagnosis and feature extraction in equipment. The two-dimensional VMD (2DVMD) is a 2D extension of the VMD algorithm, which can achieve image noise reduction. more features about wear debris chains are worth of consideration in the wear debris image analysis, so that the capability of wear state evaluation and prediction using on-line approach can be improved. Existing on-line wear debris monitoring systems are often based on the wear debris concentration, providing limited information on particle shape and type. For the identification of wear particles, the shape, size, and surface features of wear debris are all important for root cause analysis [21]. In addition, conventional wear debris identification studies are usually performed on a single wear particle. However, in actual on-line wear debris monitoring systems, the wear particles are often deposited in the form of chains under the action of magnetic force. Therefore, directly analyzing the wear debris image using previous wear particle analysis algorithms does not provide perfect results. Thus the features of wear debris chains need to be considered to improve the capability of wear state evaluation and prediction using on-line approach. The health state division is another important factor in the evaluation of gearbox wear state. Henneberg [22] replaced the conventional experience value by multiple linear regression of the mean value and identified the gearbox wear state using the oil monitoring method. Sheng [23] performed an oil monitoring experiment on a high-power gearbox and studied the oil characteristics at running-in period and health state. By comparing the cumulative number of wear particles with the warning threshold and alarm threshold, the gearbox wear state was predicted. To divide the health state, many scholars applied the classical threeline method based on the assumption that the distribution of oil monitoring data obeys Gaussian distribution. However, this assumption is not accurate. The accurate distribution of data needs to be estimated. Huo [24] developed an improved probability density function (PDF) estimation method using maximum entropy. However, its parameters still need to be considered by the operator. Therefore, it is necessary to consider the correlation among various evaluation indicators and develop an improved PDF estimation method to estimate the accurate
distribution of the monitoring indicators. Therefore, in this study, an on-line wear debris monitoring system was used to monitor the wear state of the gearbox. Several wear debris image analysis algorithms, including wear debris segment, image denoising, 2DVMD image reconstruction, and image projection algorithms, were developed to reprocess the on-line wear debris monitoring data. New features of wear debris for on-line wear monitoring were extracted. The concentration, size, shape, and edge information of wear particles were utilized to analyze the wear state. In addition, an improved PDF estimation method was used to acquire the actual PDF of feature curves. A multiscale relational factor (MSRF) was developed to describe and evaluate the wear-related health conditions. Finally, tests on a self-made planetary gearbox were conducted to verify the performance of the newly developed indicators and algorithms. The ultimate goal of this study is to develop effective and reliable on-line wear debris analysis techniques for wear state evaluation and remaining useful life prediction for the gearbox. 2. Wear debris image denoising and feature extraction 2.1. Denoising processing for wear debris images When monitoring and acquiring the on-line wear debris images, they are often influenced by the noise. Some bubbles and shadows can be seen in the wear monitoring image, which affect image quality and information extraction. Therefore, denoising is very important for image processing. The denoising processing for wear debris images is shown in Fig. 1. As shown in Fig. 1, to achieve the objective, first the wear particle image is divided, and the transform of histogram for each wear debris sub-image is acquired. Then, the gray scale of each wear debris subimage is adjusted. Thus, the contrast between each wear debris subimage and its background is enhanced. Second, Otsu's method is used to calculate the threshold of each wear debris sub-image. This threshold can be used to convert an intensity image to a binary image. In this study, the Otsu algorithm [25] is adopted to segment wear
Fig. 1. Denoising processing for wear debris images. 1720
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particles. At first, each gray value in the image is thought as a possible threshold. Then, the gray level of the whole picture is divided into two categories, and the between class variance of each classification is calculated successively. The gray level with the maximum between class variance is selected as the optimal threshold. This between class variance method is very sensitive to noise and target size and is faster to calculate. For any gray value n,1≤ n ≤ GL, the gray scale of image is divided into two categories: C0 and C1, where C0 = {1, 2, 3, …, n} and C1 = {n + 1, n + 2, …, GL}. GL is the total gray level of the image. GA is the categories mean. Pw0 is the probability of C0 categories and Pw1 is the probability of C1 categories. PGi is the probability of pixels with the gray level equals”i”. GAj is the average grayscale value of C0 categories. For C0, GA0 denotes the gray mean value, Then:
GA0 =
GAj PW 0
To acquire clearer picture of wear debris image, 2DVMD method was used as a faster approach to Reconstruction of the wear debris images. 2.2. Reconstruction of the wear debris images based on 2DVMD The 2DVMD method [20] was used to adaptively decompose the wear debris images into different modes by separating spectral bands. The method is defined as follows: Let f(t) be a purely real signal. The complex analytic signal is defined as
The goal of VMD is to decompose an input signal into a discrete number of sub-signals (modes). To assess the bandwidth of a mode, the resulting constrained variational problem is
n
GAn =
iPGi
(1)
i=1
For C1, the gray mean value GA1 can be calculated:
GA1 =
GA
GAn
min
{uk },{ k }
(2)
PW 1
s. t .
Then, the inter-class variance of the classes C0 and C1 is: 2 (n )
= PW 0 (GA
GA 0 )2 + PW 1 (GA
GA1)2
(4)
fAS (t ) = f (t ) + jH {f }(t )
k
[uAS, k (x ) e
j
k, x
2 2
]
k
x:
uk (x ) = f (x ) k
{uk } = {u1,
(3)
, uk }, {
k}
= { 1,
,
k}
(5)
The reconstruction constraint can be addressed by using the augmented Lagrangian L as follows:
Change the value of j from 1 to GL, so that the threshold j with the maximum inter-class variance 2 (j) is the best threshold.
Fig. 2. Decomposition result of wear debris image. 1721
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Fig. 3. Image of wear debris. 2
L({uk }, {
k }, )
[uAS,k e
k
j
k,x
]
k
+
(x ), f (x )
2 2
+ f (x )
uk (x ) k
2
Fig. 4. Process of feature extraction.
uk (x )
(6)
k
Initialize and update ukn + 1 ,
ukn +1 = argmin
[uAS, k (x ) e
k
uk
, and
n+1 k
j
k, x
]
2 2
Based on above work, some features will be extracted to obtain the shape and size characteristics of the wear debris chains.
n+1 . k
+ f (x )
u i (x ) + i
(x ) 2
2
2.3. Wear debris feature extraction
2
(7)
Previous studies only focused on the wear debris concentration, but the wear state and wear mechanism of the equipment can be characterized by the size distribution, color, and morphology of wear debris in the lube oil. In addition, previous on-line wear debris monitoring results show that many wear particle chains can be found in the wear debris image. Thus, in this study, the wear particle chains are analyzed, and new features are extracted to obtain the shape and size characteristics of each wear particle picture. Based on the result of image denoising, new indicators, including the covered area (BIPCA), chain number (NP), and length (LP) and width (WP) of wear debris chains, are quantitatively characterized to reflect the wear debris concentration and their shapes and sizes.
The center frequencies ωk do not appear in the reconstruction fidelity term, but only in the bandwidth prior, the optimization can take place in Fourier domain, and we end up optimizing: The relevant problem thus writes: The center frequencies ωk do not appear in the reconstruction fidelity term, but only in the bandwidth prior. The optimization can take place in the Fourier domain. Then relevant problem is thus written as 2
n+1 k
=
uk ( ) d 2
uk ( ) d
(8)
Algorithm for 2D-VMD: 0
0
1) Initialize uk ,
k
,
0
, n
2) Repeat n ← n + 1, update uk and 3) Update n+1
( )=
n
( )+
n+1
f ( )
uk k
2.3.1. Wear debris covered area after reconstruction (BIPCA) The traditional on-line wear debris monitoring parameter is IPCA (Index of Particle-Covered Area), is derived based on the area covered by the debris deposited in the OLVF flow channel through magnetomotive force. Which has been used in many monitoring experiments [14–17], to identify the variation in wear debris in the lube oil and characterize wear degrees. For a wear debris image (Fig. 3), the IPCA can be calculated according to Eq. (10).
0. k.
( )
(9)
Until: k
n +1 u^k n 2 u^k 2
n u^k
IPCA =
2 2
< Ke
Cfi wf hf
× 100%
(10)
Where ∑Cfi denotes the object pixel number of wear debris in the segmented image, as shown in Fig. 3. Based on the result of image denoising, each decomposition mold of the wear debris image can be analyzed. In this study, the IPCA for each mold is calculated and used in feature extraction. Based on the compare result of IPCA, the noisy image is excluded (with larger IPCA value), and then, after the wear image denosing, the wear debris image is reconstructed. Finally, the new parameter, cover area of wear debris after reconstruction, can be calculated, that is called new BIPCA index. The process of feature extraction is shown in Fig. 4.
Fig. 2(a) is the original wear debris monitoring image acquired by using the wear debris analysis system. While the Fig. 2(b) is the gray scale image of Fig. 2(a), because the original image should be changed into a gray scale image for further data processing. Fig. 2(a) and (b) serves as an example to expound the denoising algorithm. Through2DVMD, the noise image can be decomposed into a series of sub-modes with different center frequencies (see Fig. 2(c)–(e)). Normally, some sub-modes include the original information of the wear debris image (see Fig. 2(c) and (d)), while others include the background noise (see Fig. 2(e) and (f)). After removing the sub-modes with the background noise, the wear debris monitoring image is reconstructed. Fig. 2(g) shows the reconstruction result of wear debris monitoring image, and Fig. 2(h) shows the binary image after denosing. Fig. 2(i) is the transform of histogram for wear debris image, which can be used to adjust the gray scale of wear debris image.
2.3.2. Size and morphology analysis of wear debris chains Step 1: Extract the skeleton of wear debris chain. Based on the result of image denoising for each sub-image, the 1722
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Fig. 5. Wear debris image denosing and processing.
Fig. 6. Wear debris image denosing and processing result.
Canny computational theory of edge detection [25] is adopted to detect the edge of the wear debris chain and extract the skeleton for each subimage, as shown in Fig. 5. After the final combination of sub-images, the entire wear debris chain skeleton of the whole image can be obtained (see Fig. 6(a)).
image can be extracted. The mathematical method of projection transformation can be found in Eq. (11). According to Eq. (11), firstly, the skeleton value f (x i , yj ) should be recalculated first. Only the pixles inside the skeleton of wear debris chains is set as “1”, and others will be set as “0”. Then, the projected value Py can be culculated. Thus, the two-dimensional curve f (x i , yj ) (the skeleton of the wear debris chains in Fig. 6(a)) is projected on the y axis, and the one-dimensional projection curve will be acquired (See Fig. 6(b)).
Step 2: Projection and new indicators extraction. Attracted by the magnetomotive force, the wear debris are often deposited or overlapped in a chain shape. Therefore, the skeletons of the wear debris in Fig. 6(a) are also in a chain shape. The projection transformation is performed on the y-axis of Fig. 6(a) to reduce the dimension of the image, and then, the two-dimensional image is converted into one-dimensional curve. Based on this projection curve, several important new features of the on-line wear debris monitoring
f (xi , yj ) = Py (yj ) = 1723
1, if(x i , yj )
skeleton of the wear debris chains
0, others
200 i=1
f (x i , yj ), yj = 1, 2 …, N
(11)
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is Gaussian. However, this assumption is not always accurate. Therefore, in this study, an improved PDF estimation method using maximum entropy [24] and kernel density representation (KDR) [26] is first adopted to estimate the accurate distribution of the above indicators. Let X be a random variable with support Ω and fX(x) be it's unknown PDF. Algorithm to seek fX(x) and health state division:
Table 1 New indicators for wear debris images. Indicator
Relationship
BIPCA NP WP HP
Cover area of wear debris after reconstruction Number of wear debris chains Width of wear debris chains Length of wear debris chains
1. Choose a support bounded domain Ωx ⊆ Ω, Ωx ≡[xmin; xmax]. 2. Develop the coordinate transformation z = (x − xmin)/(xmax − xmin), by introducing the random variable Z. defined in Ωz ≡ [0, 1] where μ1, μ2, …, μM are the first M generalized moments of Z. pi is the probability distribution of Z. The constraints imposed by the available information of X are E(gk).
E(gk)
µk =
n i=1
gk (z i ) pi
(13)
3. Apply the KDR to the random variable Z. N
lim f XK (x ; x i , h) = (x
h
Fig. 7. Health state division of the gearbox.
4.
The peaks of the one-dimensional projected curve in Fig. 6(b) correspond to the horizontal wear debris chains skeleton in Fig. 6(a). Therefore, the features of the on-line wear debris chains image, such as the number, width and length of the wear debris chains, can be reflected in the one-dimensional projected curve. Based on the projection curve in Fig. 6(b), new features, Four new indicators can be extracted, see Table 1. BIPCA denotes the cover area of wear debris in wear debris images after reconstruction and denoising. NP is the number of peaks in the projection curve, which is related to the number of wear debris chains. WP is the equivalent width of peaks in the projection curve, which is related to the width of wear debris chains. HP is the equivalent height of peaks in the projection curve, which is related to the length of wear debris chains.
5. 6. 7.
0
x i ) fX (x )
fKD (x; p, ) =
pi (x i=1
xi )
(14)
ϑ is another N‐vector collecting the parameters of the N KD functions (KDFs). A discrete random variable Z1 is defined in Ωz, whose probability distribution is determined from the maximum entropy (ME) solution [24]. Choose the KDF that best fits the target PDF fz(z) to determine the KDME PDF fKDME (z ) fZ (z ) . Obtain the KDME approximation of fX(x) by the inverse coordinate transformation from z to x. Suppose the PDF of some wear debris monitoring features f(x) has been acquired using the above novel PDF estimation method. Then, the probability in interval [0, y] is y
p (y ) =
f (x ) dx 0
Step 3: MSRF. MSRF is developed to describe and evaluate the wear-related health conditions.
MSRF =
NP i=1
(WPi )
NP i=1
(HPi )
NP 2
/ BIPCA
(15) 4. Verification of the method
(12)
4.1. Experimental setup
3. Health state recognition of the gearbox
To evaluate the above methods and indicators, wear tests were conducted on a self-made planetary gear box (Fig. 8). The test rig includes NGW11 planetary gear reducer, motor, inverter, magnetic powder brake, and tension controller. Based on the theory that the wear debris concentration and shape in the oil sample indicate the lubricant's contaminated rate and wear degree, an on-line wear debris monitoring system was used to record the real-time wear debris images every 10 min. By analyzing the wear debris deposited in the monitoring system, the health state of the planetary gearbox can be evaluated. The parameters of the wear debris analysis system are listed in Table 2. The planetary gearbox wear test time was set as 900 min(15 h), and the tests were conducted under stable working conditions with heavy load (60 N) and fast speed (1200 r/min) to accelerate the wear process of the gearbox.
3.1. Defining the health state of the gearbox In this study, the health state of the machine is divided into health state (S1), sub-health state (S2), alarm status (S3), and danger/failure (S4) status. The division method is shown in Fig. 7. Once the critical thresholds for different states are determined, the wear-related health status of the machine can be determined based on the trend of feature curve extracted from the wear debris image. 3.2. Threshold determination When determining the critical thresholds for different states, the threeline method is used. This traditional method, such as three-line method, is based on the assumption that the distribution of the wear monitoring data 1724
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The reason is that the IPCA indicator was calculated using original wear debris images with noise. Thus, some shadows and bubbles were recognized as wear debris. Fig. 10(b) shows that, after the reconstruction and denoising of wear debris images, the BIPCA curves can reflect the trend of wear process. In segment A of Fig. 10(b), the gearbox was working at the run-in stage. Thus, the wear debris concentration suddenly increased. With the increase of test time, the debris concentration gradually decreased into a stable state (see segment B of Fig. 10(b)). According to the estimated PDF of the BIPCA curves, the thresholds for four stages (S1–S4 in Fig. 10 (b)) were determined quickly. Thus, the BIPCA curves were first clustered into two stages. However, as shown from the monitoring result in Fig. 9, at the last 150 min (2.5 h) of the experiment, the size and shape of wear debris chains changed. This finding indicates that the wear of the gearbox was severe. Fig. 10(c) shows the MSRF curve. The MSRF was calculated by using shape- and size-related indicators. As shown in Fig. 10(c), the MSRF curve exhibited an increasing trend in segment A and then gradually decreased into a stable state in segment B. However, in segment C of Fig. 10(c), the MSRF curve increased again, indicating that segment C belongs to the severe wear state. According to the estimated PDF of the MSRF curve, the thresholds were also determined and are shown in Fig. 10(c). In segment C, several MSRF values are larger than the threshold of S2. Thus, the wear-related health conditions of the gearbox are clustered into four stages. As shown in Fig. 10, when using the IPCA parameters only, it is difficult to accurately present the concentration variation. Combined with the BIPCA parameters, the overall concentration variation trend can be obtained. However, this parameter is not sensitive to subtle changes in size and shape of wear debris chains. When the wear state changes, the size and shape of the wear debris chains would also change. Using MSRF values, the change in number, size, and shape of the wear debris chains can be reflected. Therefore, the new indicator, MSRF, can be used to evaluate the health state of the planetary gearbox more thoroughly and can reflect the wear process more
Fig. 8. The planetary gear box test rig.
To verify the on-line analysis results, 20 ml oil samples were taken every 20 min, and the collected wear particles were examined using offline techniques. 4.2. Experimental result and discussion 4.2.1. On-line wear debris monitoring Fig. 9 shows the on-line wear debris monitoring images at different time points during the test. As shown in Fig. 9(a) and (b), at the beginning of the test, many wear debris were observed in the image, and approximately 120 min (2 h) later, they began to decrease and maintained a stable state. After 840 min (14 h), the number of wear debris increased again, which indicates that the wear of gears was becoming worse. The monitoring data processing methods described above were used to process the images and extract the features. The indicator curves, including original IPCA, BIPCA and MSRF curves are shown in Fig. 10. For BIPCA and MSRF curves, the improved maximum entropy PDF estimation method was used to acquire the actual PDF of feature curves and divide the wear debris images and health state of machine according to the PDF. The threshold line from S1 to S4 is drawn in Fig. 10(b) and (c). As shown in Fig. 10(a), the trend of IPCA curve cannot be observed. Table 2 Parameters of the wear debris monitoring system. Magneto_ Motive force (Ampere turn)
Flushing volume (s)
Flow rate (ml/min)
Deposit time (s)
Sampling volume (ml)
1200
30
1.5
60
5
Fig. 9. On-line wear debris monitoring result. 1725
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Fig. 11. The working process of off- line oil analysis.
glass slide that is placed on a magnetic cylinder of ferrogram slide maker to attract the wear debris. Step4: Let oil flow across a new glass slide (0.4 ml/min), which is placed on a magnetic cylinder of ferrogram slide maker to attract the wear debris. Step5: Remove excess oil, heating the slide and waiting for 10 min, then the slide can be analyzed under a microscope. Fig. 12 (a)-(d) show the off-line analysis result at different test stage. By referring to the knowledge of analytical ferrograph and wear particle analysis [10,27]. The wear particle was analyzed, and wear severity levels was recognized. At the beginning of the test, the values of the number, width, and length of the wear debris chains were the largest. With the increase of experiment time, the number, width, and length of the wear debris chains gradually decreased. After 13 h, they gradually increased again. Further analyzing the off-line slides under the microscope, the details of the wear debris can be acquired. As shown in Fig. 12 (e), after 900 min (15 h), some fatigue wear debris are observed. The method to recognize the fatigue wear debris can be found in Ref. [27]. Thus, the wear mode can be researched. According to the test result and the MSRF curve (Fig. 10c), the segment C belongs to the severe wear state or alarm health stage(S3). Fig. 12(f) are the images of the gear teeth surfaces after the test of 900 min, pitting can be found on the surface of the gear teeth surfaces. Pitting is a fatigue failure of the surface of a material commonly seen in rolling bearings and gears [5–7]. That verify the fatigue of the gear teeth surfaces, thus the on-line analysis result is consistent with the offline analysis result and is consistent with the damage extend of the gear. 5. Conclusion In this study, a set of wear debris image analysis methods and wear state recognition algorithms were developed for on-line wear monitoring. They were based on the on-line wear debris monitoring data and can also be applied to other on-line wear monitoring systems. The wear debris image processing algorithms were developed to enhance the contrast between wear debris images and their background, so that their inherited issues are reduced or eliminated. After reconstructing and denoising the monitoring images, the wear debris images were denoised, and more accurate monitoring information was acquired. The shape and concentration were analyzed. Several indicators of wear debris chains were quantitatively characterized. An improved PDF estimation method was developed to estimate the accurate distribution of the indicators. Then, the MSRF was extracted to describe and evaluate the wear debris images more thoroughly. According to the estimated PDF of MSRF, the thresholds of wear state evaluation were determined quickly, and the wear-related health conditions were clustered into four stages to further realize the prediction. Gearbox wear test was conducted, and on-line wear debris analysis
Fig. 10. Feature curve and health state division result.
comprehensively. By using the new indicators, further wear prediction can be realized accordingly. 4.2.2. Off-line wear debris analysis To verify the on-line analysis results, the off-line analysis was also used to research the wear mechanism [10]. 20 ml oil samples were taken every 20 min, and wear particles were collected. Fig. 11 shows the off- line oil analysis process. Step1: A sample of the gearbox's lubricating oil is taken. Step2: Diluting the oil (3 ml). Step3: Turn on the ferrogram slide maker and let oil across a new 1726
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Fig. 12. Off-line analysis and experiment result.
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was used to evaluate the performance of the methods. By combining the on-line wear debris monitoring result with other off-line analysis results, the wear mode of the gearbox can be recognized, and the accuracy of equipment health condition monitoring can be improved. The results demonstrate that the wear debris image analysis methods and wear state recognition algorithms were accurate and fast in recognizing the change of health conditions of the planetary gearbox, and the health state recognition was consistent with the gearbox inspections. the techniques developed in this study can be utilized for real-time wear state evaluation and prediction for the planetary gearbox using on-line wear debris image analysis.
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Acknowledgement The financial support for the present research was provided by National Science Foundation of China (Grant No. 51505360), Natural Science Basic Research Plan in Shaanxi Province of China (Grant Nos. 2016JM5083 and 2018JM5166) and Key Laboratory Research Program of Education Department of Shanxi Province (No. 18JS044). References [1] Z. Hameed, Y.S. Hong, Y.M. Cho, Condition monitoring and fault detection of wind turbines and related algorithms: a review, Renew. Sustain. Energy Rev. 13 (1) (2009) 1–39. [2] S. Sheng, Wind Turbine Gearbox Reliability Database, Condition Monitoring, and O &M Research Update, 2016. [3] Stephan Ebersbach, Z. Peng, Expert system development for vibration analysis in machine condition monitoring, Expert Syst. Appl. 34 (1) (2008) 291–299. [4] I. Akinci, D. Yilmaz, M. Çanakci, Failure of a rotary tiller spur gear, Eng. Fail. Anal. 12 (3) (2005) 400–404. [5] X. Liang, M.J. Zuo, Z. Feng, Dynamic modeling of gearbox faults: a review, Mech. Syst. Signal Process. 98 (2018) 852–876. [6] C.Q. Hu, W. Smith, R.B. Randall, Development of a gear vibration indicator and its application in gear wear monitoring, Mech. Syst. Signal Process. 01 (2016) 76–77. [7] Z. Peng, N.J. Kessissoglou, Cox MA study of the effect of contaminant particles in lubricants using wear debris and vibration condition monitoring techniques, Wear 258 (11–12) (2005) 1651–1662. [8] W.W. Seifert, V.C. Westcott, A method for the study of wear particles in lubricating oil, Wear 21 (1) (1972) 27–42.
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