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Abstract
A high-precision wear measurement method with temperature stability achieved by measuring the length variation of a fiber Bragg grating (FBG) is proposed. The adoption of the optical frequency-domain reflectometry (OFDR) technology makes the spatial resolution of this measurement method reach 15.13 µm, and the offline and online measurement accuracies are 30 µm and 100 µm, respectively. The systematic error of the FBG length measuring system is within 30 µm. Because the length measurement is done with a short FBG instead of a much longer fiber, the measurement error induced by the time-varying temperature or strain is significantly reduced in the proposed method. The spatial resolution and accuracy of this method is suitable for wear measurements of various parts in the mechanical field, such as bearings, gears, and pistons.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Wear occurs universally in the daily operation of mechanical parts such as bearings, resulting in the expansion of bearing clearance, and might eventually lead to machinery failure [1,2]. According to the ISO standard ISO 12129-1, the mean relative clearance of metallic plain bearings in general engineering is 0.56‰ to 3.15‰. To monitor the change of the bearing clearance and prevent damage caused by wear, a measurement method with sufficiently small resolution is required. Mass or volume change analysis is commonly adopted for wear monitoring, which can be realized by technology such as ultrasonic–inductive pulse sensor, on-line particle counter, and radionuclide-technique [3–5]. However, because these technologies are accomplished by analyzing the wear debris generated by the machine parts during operation, it is almost impossible to achieve high resolution. Thin-film based wear sensors can monitor the loss of materials due to surface reducing wear [6,7] by measuring the electric current passing through the sensor. But the measurement is easily affected by the open and short circuits, as well as electromagnetic interference. Using charge-coupled device (CCD) based imaging system together with image analysis, highly accurate wear detection can be facilitated [8–10]. Nonetheless, the method is only suitable for exposed objects. Ultrasonic thickness measurement can also be used for high-resolution wear measurement [11,12], but the measurement accuracy of this method is sensitive to the temperature variation and environmental noise.
Compared with the above-mentioned methods, optical fiber sensors are immune to electromagnetic interference. In addition, they are small in size, simple in structure, and more flexible [13]. A sacrificial chirped fiber Bragg grating (CFBG) has been adopted to detect the surface reducing wear, by determining the length of the CFBG based on the intensity and the wavelength of the reflected light [14]. Ordinary FBGs with fixed pitches, as well as arrays formed by such FBGs, are also applied for wear measurement [15–17]. However, all these methods are based on light intensity measurement, resulting in limited accuracy, which is only about 200 µm.
In this paper, we monitor the thickness loss of the object under test (OUT) due to wear, with a sacrificial FBG at the end of a fiber under test (FUT). The OFDR technique is adopted to accurately detect the change in the length of the FBG [18,19]. With the wavelength of a tunable laser source (TLS) swept from 1500 nm to 1600 nm, spatial resolution of 15.13 µm is achieved. Offline and online wear measurements are performed using two ∼5-mm FBGs, exhibiting accuracies of 30 µm and 100 µm, respectively. Due to the use of a short FBG, instead of a much longer fiber, the length measurement error induced by temperature fluctuation is significantly reduced. By repeatedly measuring an FBG with a length of about 7.75-mm under the same experimental conditions, the systematic error of the measuring system is found to be less than 30 µm. By measuring the length of the FBG, instead of the much longer FUT, the wear measurement is much less sensitive to disturbances such as temperature and strain variation. The temperature insensitivity of the proposed method is confirmed by repeated length measurements of an ∼8.00-mm FBG, with the environmental temperature varied from 25°C to 85°C. The experimental results show a fluctuation of 27.64 µm, which is almost the same as the system error considering no temperature fluctuation. Likewise, the propose method would be less sensitive to the variation of strain along the fiber. Using a simple pin on disk experimental device, the system can perform online wear measurement under 150 r/min disk rotation. With the high spatial resolution and high precision, the proposed method is not only applicable to pin-like parts, but also to complex structural parts like gears.
2. Principle
FBG is essentially a length of fiber with periodic change in the core refraction index, thus presenting stronger reflectivity at the Bragg wavelength as compared to pure fibers. With proper installation, a sacrificial FBG in the FUT experiences the same degree of wear as the OUT. With such an arrangement, measurement of the physical length of the FBG can be applied to detect the wear-induced thickness loss of the OUT.
In an OFDR system, the spatial resolution is defined as the smallest distance that can be resolved [20], which depends on the frequency (wavelength) sweeping range of the TLS [21]. Nowadays, the commercial TLS can readily achieve a wavelength tuning range of ∼100 nm in the 1550-nm wavelength band, facilitating spatial resolution of ∼15 µm. In this work, the wavelength tuning speed of the TLS is 100 nm/s, and the tuning range is from 1500 nm to 1600 nm. Figure 1 illustrates the principle of the proposed wear measurement method, which is enabled by FBG length measurement based on OFDR. The blue trace in Fig. 1 corresponds to the original reflection profile of the FBG. After the occurrence of wear, the length of the FBG is shortened, resulting in the red trace. While the position of the starting point S remains unchanged, the ending point moves leftward from E1 to E2, as wear progresses. Therefore, the length loss of FBG, |E1E2|, represents the thickness loss of the OUT along the axial direction of the FBG.
Fig. 1. The length of a sacrificial FBG in frequency spectrum before and after wear test. The length difference represented by the blue trance and the red trance can indicate the wear depth along the direction of the FUT.
As we know, Fresnel reflection is generated at fiber ends, which can also be measured by the OFDR. Consequently, the position change of the Fresnel reflection from E1 to E2 can also be used to measure the degree of wear. In other words, the measurement of |E1E2| can also be achieved by measuring the length change of the optical fiber. However, such a measurement method would be much more sensitive to environmental disturbances and the reason is explained in the following. With OFDR, we are measuring the optical length, in which the refractive index plays an important role. When the environmental temperature or strain changes, the measured optical length changes due to the influence on the refractive index, resulting in large measurement errors. In addition, because the magnitude of these measurement errors strongly depends on the length of the FUT, it would eventually be even higher than that of the traditional methods and render the advantage in spatial resolution brought by the OFDR meaningless, especially when long installation fibers are required. Although the refractive index of the FBG will also be affected by environmental changes, the length measurement error caused by temperature or stress is less than the spatial resolution of the measurement system because it is much shorter than FUT. Therefore, the wear measurement method we propose, which combines the use of FBG with the OFDR technology, is more accurate and stable than the method measuring the length of the optical fiber.
Figure 2(a) shows the device that is used to verify the feasibility of the wear measuring system, in which the OUT is a plastic rod. The FUT is attached to the OUT along the axial direction, as shown in Figs. 2(a) and 2(b). By pinning the OUT on the wear disk with proper pressure, abrasion is introduced to both the OUT and the sacrificial FBG as the wear disk rotates. As shown in Fig. 2(a), the length loss of the FBG, which is marked red, is equal to the thickness loss of the OUT, which is marked yellow. Therefore, the latter can be obtained by measuring the former. The upper measurement limit of the system is determined by the length of the sacrificial FBG. For reference, a dial indicator with 1-µm precision is used to measure the length of the OUT. By comparing to the results obtained from the proposed measuring system and those from the dial indicator, the accuracy of the sacrificial-FBG-based wear measurement can be characterized.
Fig. 2. (a) Schematic of the sensor package and experimental device. The yellow part of OUT will gradually disappear due to wear, and at the same time FBG will continue to become shorter. The length variation of FBG can represent the thickness loss of the OUT due to wear. (b) The end of FUT is pasted on the side of OUT, and the part marked with red is FBG.
3. Experimental results
3.1 Offline wear measurement
In order to verify the feasibility and accuracy of the proposed method, a 5.24-mm FBG is adopted for the wear measurement experiment. The rotation speed of the disk is set to 52 r/min, and FBG length measurement is carried out every 10 minutes while the test equipment is temporarily stopped. Twenty sets of data are collected in each measurement, in order to quantify the systematic error of the measuring system. It can be clearly seen from Fig. 3(a) that the reflection profile of FBG and Fresnel reflection at the end of FUT at different times, and it is noteworthy that the length of FBG shortens during the wear test. The starting point of FBG is determined by setting a threshold, which is 1/3 of the maximum value of the FBG reflection profile. Since Fresnel reflection introduces a high-reflectivity surface at the end of the FUT, as shown in Fig. 3(a), the corresponding peak is taken as the ending point of the FBG for convenience. If the Fresnel reflection peak is too weak or vanishes because of the angle deviation, the trace of FBG will be similar to the trace in Fig. 1. In this case, the method used for locating the starting point of the FBG is also applicable to the determination of the ending point. More specifically, the point at which the amplitude of the trace drops below the threshold can be regarded as the ending point of the FBG. At the same time, the full width at half maximum bandwidth of the Fresnel reflection peak is 15.13 µm, as shown in the inset in Fig. 3(a), which reflects the spatial resolution of the measurement method. Figure 3(b) shows the average length of the sacrificial FBG after each time of the 10-minute wear test, with the standard deviation, calculated from the 20 data sets, indicated by the red error bar. And the standard deviation of all measured lengths is 8.31µm.
Fig. 3. (a) The variation of the FBG length and the Fresnel reflection peak in the inset to determine the spatial resolution. (b) The length of FBG under different wear time.
It should be noted that the starting points of the FBG measured at different times are not at exactly the same distance to begin with. In Fig. 3(a), the starting points are aligned before the traces are plotted. The misalignment indicates that the position of the FBG is different in each measurement, and accordingly, the measured FUT length is also different. As discussed previously, this measurement error originates from the time-varying reflective index of the FUT, which is induced by the temperature or strain fluctuation in the environment and affect the length measurement. However, since we measure the length of the FBG, even if the position of the FBG is different in each measurement, it does not affect the wear measurement result because the influence of the environmental disturbances is much smaller than that affecting the entire FUT.
Since the standard deviation of the measured FBG length appears to be small, we randomly select one of the 20 results at each moment to calculate the thickness loss of the OUT over time, as shown by the red curve in Fig. 4(a). The results are also compared with those measured by the dial indicator, which is represented by the black curve. The deviation between the two set of results is shown by the blue diamonds, which is no more than 16 µm. Figure 4(b) shows the maximum deviation occurred in the measurement by repeating the experiment in Fig. 4(a) for 100 times. The maximum deviation seen in the 100 measurements is only 31.37 µm and the rest are less than 30 µm, indicating that the proposed method presents excellent repeatability. Meanwhile, 30 µm is considered as the system accuracy.
Fig. 4. (a) The thickness loss of OUT we detect by a sacrificial FBG and the dial indicator, and the deviation of two method. (b) The maximum deviation of the two measurement methods.
The positioning of the FBG and the measurement of its length are the key steps to the wear measurement using the sacrificial FBG. The FBG length needs to be measured at least twice before and after abrasion, in order to calculate the length loss of the FBG. To characterize the systematic error, the FBG length measurement is repeated 200 times to calculate the fluctuation range of the FBG length. Figure 5 shows the FBG length obtained from the 200 measurements. With a ∼7.75-mm sacrificial FBG, the maximum fluctuation range and the standard deviation are 24.97 µm and 6.01 µm, respectively. In addition, the results in Fig. 5 are distributed around four length values. The origin of the discrete measurement values is explained in the following. To perform FBG length measurement using OFDR, the length value is calculated by multiplying the number of points representing the FBG in the frequency domain by the length between two points. Meanwhile, the length between two points in the frequency domain is different in each measurement because of the varied frequency sweep speed. Consequently, even when the number of points from one measurement is the same as that from another measurement, the calculated FBG length fluctuates around a certain value, as observed in Fig. 5.
3.2 Online wear measurement
In practical applications, it is preferred if the wear monitoring can be carried out in an online manner. To verify the feasibility of the proposed method for online measurement, we carry out the following experiment while the wear disk is rotating. Figure 6 shows the experimental results when the disk speeds are 26 r/min and 52 r/min respectively. In addition, 8 repeated experiments have proven that the deviation does not exceed 100 µm, which is considered as the accuracy of the online measurement. From the experimental results of online wear measurement, we noticed the trend of decreasing accuracy as the rotation speed increases. However, the trend is not monotonical. In general, the difference in the accuracies is not much at low rotation speeds.
Fig. 6. The thickness loss of OUT by a sacrificial FBG and the dial indicator, and the deviation of two method at two rotational speeds.
The accuracy of the online measurements is obviously degraded as compared to that of the offline measurements. The performance degradation is attributed to the increased noise in the data collected during the online measurement. The OFDR trace from an online measurement is shown in Fig. 7(a). In this case, it is more difficult to distinguish the exact position of the FBG along the FUT, because the start and end points of the FBG are less obvious due to the additional noise introduced by the rotating disk. It is inferred that the additional noise originates from the vibration of the FBG caused by the rotating disk, which leads to time-varying reflectivity along the sacrificial FBG. To overcome this issue, a denoising stage based on smoothing is introduced before positioning the start and end points of the FBG. The denoised trace and that measured under the static condition (stopping the experimental device immediately after the dynamic data is collected) are shown in Fig. 7(b), by the red and the blue traces, respectively. Comparing the two, it is confirmed that denoising does help to determine the start and end points of the FBG with enhanced accuracy, as the difference between the online and offline measurements is only 10.71 µm.
Fig. 7. (a) The FBG is measured online while the disk speed is less than 150 r/min. (b) The red trance is the denoising result of the FBG measured online in (a), and the blue trance is the FBG measured under static condition. (c) There is a big noise in the FBG measured online while the disk speed is more than 150 r/min. (d) Denoising results of FBG measured online in (c) and the FBG measured under static condition.
However, as the rotating speed of the wear disk increases to over 150 r/min, the sensing system is strongly affected by the noise, resulting in the occasionally-appeared significantly-distorted OFDR trace shown in Fig. 7(c). In addition, there will be sidebands on both sides of the Fresnel reflection peak due to vibration [22]. In such a case, the start and end points cannot be determined correctly, even with the assistance of denoising. The occurrence of distorted traces becomes more frequent as the rotating speed of the wear disk increases. When the speed of the disk reaches 180 r/min, this situation appeared 7 times in 100 measurements. Therefore, the speed of 150 r/min is regarded as the upper limit speed of the measurement system used in the experiment. This speed can meet the wear measurement requirements of some bearings, especially sliding bearings.
3.3 Experiment result of temperature stability
Since the wear measurement is performed based on FBG length measurement, it is rational to question whether the results would be affected by the temperature variation, which leads to thermal expansion of the fiber. In fact, due to the low thermal expansion coefficient of 0.55×10−6 /°C, the length expansion of a 10-mm FBG caused by 100°C temperature variation is only 0.55 µm, which is much smaller than the accuracy and spatial resolution of the system. Another factor that affects temperature stability is the change in optical length caused by the refractive index. When the temperature increases from 25°C to 75°C, the refractive index of the single-mode fiber changes from 1.4681 to 1.4685. Considering the 8.5-mm FBG used in the experiment, a measurement error of 2.295 µm would be introduced. Since this error is much smaller than the spatial resolution of 15.13 µm, the proposed wear measurement method is considered temperature insensitive. If the measurement is done based on an 8.5-m FUT, the measurement error induced by the temperature increase from 25°C to 75°C would be 2295 µm. The error is much larger than the currently demonstrated spatial resolution, making high-spatial-resolution wear measurement impossible.
To verify the temperature insensitivity, the average length of an 8.00-mm FBG is measured repeatedly, while the temperature increasing from 25°C to 85°C, with a 10°C step. At each temperature, the measurement is performed 20 times. As shown in Fig. 8(a), the maximum difference in the FBG length is 27.64 µm, with maximum standard deviation of 7.35 µm, which is similar to the systematic error of the system at room temperature. Therefore, it can be considered that the measured length fluctuation of the FBG here is caused by systematic errors of the system. Thus, the temperature insensitivity of the proposed method is thus confirmed experimentally.
4. Conclusion
We propose a method for wear measurement based on length measurement of a sacrificial FBG using OFDR. The most important reason for using FBG is to increase the stability and accuracy of the measurement method, making the measurement much less sensitive to environmental disturbances such as temperature and strain fluctuations. In order to detect a tiny thickness loss due to wear, OFDR is used for the detection of the FBG length, and by increasing the wavelength tuning range of TLS to 100 nm, the spatial resolution of the measuring system is 15.13 µm. We choose to measure the length of a short sacrificial FBG, instead of the long FUT, because the optical length of the FUT is directly affected by the refractive index of the fiber, which is sensitive to the change of temperature or strain, and would lead to time-varying measurement errors. From the offline and online wear experiments, the feasibility and accuracy of this method are proved, and the measurement accuracy of the system in these two states is 30 µm and 100 µm respectively. When measuring online, we can find the FBG and observe the change of its length under the disk speed of 150 r/min. In addition, the systematic error of the system is within 30 µm, and experiments have also shown that the measuring system is not sensitive to temperature changes. This method relies on changes in the length of the FBG, so the upper measurement limit of the wear measurement method depends on the length of the FBG, which would be a few centimeters and sufficient for most applications. On the other hand, it should be noted that the wear measurement of OUT is performed by using only one FBG sensor in the experiment, which is performed under the condition that the wear degree is the same everywhere. For irregular contact surfaces and different degrees of wear, using more FBGs simultaneously can restores the overall wear. These advantages make the method well applicable to the wear detection of parts of machinery.
Funding
National Natural Science Foundation of China (61735013); Natural Science Foundation of Hubei Province (2018CFA056); Fundamental Research Funds for the Central Universities (WUT: 2019III055XZ, 205209017); National Science and Technology Planning Project (2017-V-0003-0052).
Disclosures
The authors declare no conflicts of interest.
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