Sagnac Interference-Based Contact-Type Fiber-Optic Vibration Sensor

Abstract

The observation and evaluation of vibration signals is crucial for enhancing engineering quality and ensuring the safe operation of equipment. This paper proposes a fiber-optic vibration sensor based on the Sagnac interference principle. The polarization-maintaining fiber (PMF) is spliced between two single mode fibers (SMFs) to form the SMF-PMF-SMF (SPS) fiber structure. The Sagnac interferometer consists of an SPS fiber structure connected to a 3 dB coupler. Due to the principle of the elastic-optical effect, the interferometric spectrum of the PMF-based Sagnac interferometric structure changes when the PMF is subjected to stress, enabling vibration to be measured. The experimental results show that the relative measurement error of the fiber-optic vibration sensor for healthy and faulty bearings is less than 1.8%, which verifies the effectiveness and accuracy of the sensor. The sensor offers benefits of excellent anti-vibration fatigue characteristics, simple production, small size, light weight, and has a wide range of applications in mechanical engineering, fault detection, safety and security, and other fields.

1. Introduction

Vibration is a form of motion that is prevalent in nature. Vibration monitoring is extremely important in engineering structures, civil infrastructure, mechanical engineering systems [1,2,3,4], etc. The current classification of vibration sensors includes three main categories: mechanical, electronic, and optical. Mechanical vibration sensors are characterized by defects such as low reading accuracy and signal transmission lag. Despite the wider usage of electronic vibration sensors, it is vulnerable to electromagnetic interference, a short transmission distance, poor stability, and other shortcomings [5]. Comparatively speaking, the optical fiber vibration sensor has received more and more attention because of its small size, anti-electromagnetic remote monitoring, and resistance to harsh environments and other advantages [6,7]. Various fiber sensors based on Fabry–Perot interferometric (FPI) [8,9], Mach–Zehnder interferometer (MZI) [10], Fiber Bragg Grating (FBG) [11,12,13], Sagnac interferometer (SI) [14,15], and Michelson interferometric (MI) [16] have been proposed and play respective advantages in different fields. Dong et al. [17] present an adiabatic optical microfiber coupler (OMC)-based SI. The experimental results show that the sensor can perform strain measurement with a sensitivity of −9.11 pm/µε in the range of 0–4500 µε and vibration measurement in the range of 0.5 Hz–5 kHz. Wang et al. [18] designed a microbubble FPI vibration sensor. The corresponding intrinsic frequency is 140 Hz and the amplitude sensitivity is 0.043. The signal-to-noise ratio is 56.21 dB at the vibration signal of 140 Hz. Liu et al. [19] used single mode fiber (SMF), two-mode step index fiber (TMSIF), and dispersion-compensated fiber (DCF) to construct a fiber-optic vibration sensor based on MZI. The sensors are designed for detecting vibration signals with frequencies from 1 to 23,000 Hz. Gao et al. [20] suggested a new type of dual-parameter optical fiber sensor based on few-mode fiber (FMF) and FBG. The strain sensitivities of the sensor are −2 pm/με and 0.67 pm/με in the range of 0 to 450 με.

Table 1. Different sensor key performance indicators.

Reference	Methods	Strain Sensitivities	Detection Range	Practical Application
[17]	SI	−9.11 pm/µε	0–4500 με	No
[18]	FPI	1.164 nm/N	-	No
[19]	MZI	-	1–23,000 Hz	No
[20]	FMF and FBG	−2 pm/με and 0.67 pm/με	0–450 με	No

summarizes and compares the key performance indicators of the sensors discussed. Several vibration sensors have high sensitivity and wide detection range, but the complex structure and high production cost make them difficult to apply in practical production. Among the existing fiber-optic vibration sensor types, the fiber-optic Sagnac interferometric structure, in which two beams of light are transmitted in the same fiber with zero optical range difference, does not have the noise caused by the difference between the reference arm and the sensing arm of the vibration sensors based on MZI and MI. In terms of detection effect, SI-based vibration sensors and FPI- and FBG-based vibration sensors have better vibration measurement effect. But in terms of vibration fatigue resistance, the vibration chamber of FPI-based vibration sensors is easily damaged in application environments, and the vibration fatigue resistance of FBG-based vibration sensors is poor. The fiber-optic Sagnac interferometric structure has a greater advantage than FBG-type interferometric structures in terms of vibration fatigue resistance.

In this work, a fiber-optic vibration sensor utilizing SI has been designed and implemented for fault detection in bearing speed measurement. The sensor has a more compact structure compared to existing sensors, a simpler configuration with high sensitivity, and an encapsulation design structure to protect the optical fiber structure, which shows a broader application prospect in the field of vibration monitoring.

2. Principle

2.1. Sensor Sensing Principle

Figure 1a shows the optical path diagram of SI. A length of PMF is fused between two sections of SMF to form an SPS structure and connected to a 3db coupler. After being coupled into a circulator, the output light passing through the SMF is split into two beams of equal size and opposite direction by a 3db coupler. When these two beams pass through the PMF, they acquire a phase difference because of the birefringence of the PMF and converge after traveling in opposite directions for one week inside the loop, producing an interference spectrum. The phase difference is given by [21]

$$\phi =2\mathsf{\pi }BL/\lambda ,$$

(1)

where λ, L, and B are the wavelength of the input light, the length of the PMF, and the birefringence of the PMF, respectively. The output interference spectrum T is a periodic spectrum with the expression

$$T=(1-\cos \phi )/2,$$

(2)

when the PMF is altered due to the receipt of external factors, its birefringence changes, leading to a variation in the phase difference, which in turn shifts the output interference spectrum, such as Figure 1b.

2.2. Sensor Fabrication and the Sensing System

A schematic configuration of the fiber-optic vibration sensor based on elastic-optical effect is shown in Figure 2a. Together, the shell base, shell cover, SPS structure, and the mass block pressed against the PMF form the sensor. As shown in Figure 2b, the sensor is mounted on the bearing vibration test platform. When the experiment starts, the bearing vibration test bench begins to rotate, and the sensor fixed in the test bench is subjected to vibration of the same frequency vibration. Then, the movement of the mass block changes the birefringence characteristics of the PMF, the output of the interference spectrum will be shifted, and thus the vibration measurements can be achieved. Compared to existing vibration sensors-based SI, the design in this paper better protects the PMF, ensures that the PMF is not affected by external forces other than vibration, and improves the durability of the sensor. The use of stainless steel material for sensor encapsulation improves the corrosion resistance of the sensor and better adapts to extreme environments such as high temperature and electromagnetism. Figure 2c,d shows the bearing test points and the sensor’s physical diagram, respectively.

Then, Figure 3 shows the experimental setup system constructed in this work. The experimental system consists of a pump source, a model 980/1550 nm wavelength division multiplexer (WDM), an erbium-doped fiber (EDF, Nurfen, EDFC-980-HP), an isolator (ISO), a dense wavelength division multiplexer (DWDM, 100 GHz), a 10:90 coupler, a photodetector (PD), a polarization controller (PC) and a data acquisition card (DA). In the experiment, a 980 nm-pump semiconductor laser is used as the pump source, and the power is set to 250 nw. The WDM effectively couples the pump light into the EDF, and a 3 m-long EDF is chosen as the gain fiber to ensure the unidirectional transmission of the light through the ISO. The DWDM is used as a filter to select the output wavelength of the laser, and 1550 nm is selected as the output wavelength for the experiment, and 90% of the output wavelengths in the 10:90 coupler are selected. In the 10:90 coupler, 90% of the output ports return most of the energy back to the ring cavity to form feedback, and 10% of the output ports are connected to the Sagnac interferometric structure, which ensures the effective recycling of the energy in the ring cavity, and at the same time provides the required light source input for the SI. A PC is connected to the SI for phase adjustment of the transmission spectrum, and a PD is connected to the other end of the SI to convert the received optical signals into electrical signals, and the converted electrical signals will be received by the DA, through which a connection is established with the computer system for storage and subsequent processing and analysis.

3. Experimental and Results

3.1. Parameter Selection of the Sensor

The length of the PMF is a crucial element in the development stage of the sensor. Free spectral range (FSR) refers to the wavelength interval between two adjacent peaks or troughs. The FSR expression for the interferometric spectrum of the Sagnac interferometric structure is [22,23]

$$FSR={\lambda }^2/BL$$

(3)

The SI interference spectra are experimentally measured under the same conditions and simulated by varying the length of the PMF for different lengths. Considering the experimental process, the loss of optical fibers during fusion splicing is unavoidable. The experimental and simulation comparison is shown in Figure 4a–c. Figure 4d shows the relationship between PMF length and FSR, with FSR decreasing as PMF length increases.

As can be seen from Figure 4, the SI interference spectra of the PMF lengths of 6 cm, 10 cm, and 14 cm contain one, two, and three cycles, respectively, in the wavelength interval of 1530 nm–1600 nm. Under the same range, the spectral changes are more obvious with more cycles. When the external environment changes, the sensor force produces a slight change, and the mass of the block causes vibration in the PMF due to inertia. Due to the elastic optical effect of the internal environment, birefringence will occur corresponding to the change, which leads to a change in the output of the interference spectrum of the corresponding shift, and the degree of interference spectral shift affects the accuracy of vibration monitoring. The long PMF length will also increase 1e response time of the sensor and reduce the dynamic performance of the sensor. The shorter the length, the larger the free spectral range, and the slower the variation in the spectrum affect the measurement effect of the sensor. The interference spectra of three lengths of PMF and the effect of length on the sensor are considered comprehensive, and a PMF with a length of 10 cm is chosen to measure the vibration. The sensor is fixed on the vibration platform, the rotation speed of the vibration detection platform is set to 1000 r/min, and the change in the interference spectrum is randomly recorded; the result is shown in Figure 5a. With the change in the external environment, the interference spectrum changed, indicating that the sensor responded to the vibration. The output wavelength of the laser is 1550 nm; it is found that the change in the output spectrum is more obvious near the wave valley. The phase of output spectrum can be modified using a PC to satisfy the design requirements of the sensor. The spectrum of the adjusted output is shown in Figure 5b.

3.2. Parameter of Rolling Bearing

A rolling bearing is a precision mechanical element that significantly reduces friction losses by changing the sliding friction between the operating shaft and the shaft housing into rolling friction. This design makes rolling bearings an important part of all kinds of rotating machinery and a key component in ensuring its proper functioning [24,25]. In this work, the bearing type is SKF6200 rolling bearing, which is shown in

Table 2. The bearing specifications.

Diameter of Inner Ring (mm)	Rolling Element Diameter (mm)	Diameter of Outer Ring (mm)	Number of Balls	Contact Angle	Pitch Diameter (mm)
10.0	4.8	30.0	8	0°	20.0

for its parameters.

The rotational frequency of a rolling bearing, which is related to its speed, denotes the number of times periodic changes are fulfilled per unit time. The rotation frequency is described as

$$f_r=n/60,$$

(4)

where n is the rotational speed of the rolling bearing, $f_r$ is the rotation frequency of the rolling bearing. The main failures of rolling bearings include fatigue spalling, wear or abrasion, rust and galvanic corrosion, fracture, roller rupture, etc., which occur on the raceway surfaces, rolling body surfaces, inner and outer ring surfaces, and contact surfaces of rolling bodies and raceways [26]. If the surface of the rolling bearing is defective or damaged, the remaining part collides with the defective part and generates low-frequency shock vibrations. The frequency of this impact vibration is called the characteristic frequency of bearing failure [27]. During the experimental process, a typical outer race fault (ORF) in rolling bearings is chosen. To simulate a fault on the outer ring of the SKF6200 bearing, a long groove measuring 0.5 mm deep and 1 mm wide was machined on the outer ring using wire cutting. The formula for the eigenfrequency of the ORF is [28,29]

$$f={\displaystyle \frac{N}{2}}{f}_r\left(1-{\displaystyle \frac{d}{D}}COS\phi \right)$$

(5)

where f, N, D, d, φ are the characteristic frequency of the bearing ORF, the number of rolling elements, the pitch diameter, the ball diameter, and the contact angle, respectively.

3.3. Experiments and Analysis

The healthy bearing is fixed in the vibration platform to detect its rotational speed. The sampling frequency of the acquisition card is set to 6.4 kHz in the experiment. The vibration signals collected are discrete signals and need to be processed by the Fast Fourier Transform (FFT). Figure 6 shows the vibration signals of rolling bearings at four different rotational speeds, along with the spectra obtained after FFT processing.

The rotation frequencies measured at 1200 r/min, 1500 r/min, 2100 r/min, and 2400 r/min are 19.92 Hz, 25.00 Hz, 35.16 Hz, and 39.84 Hz, respectively, and the highest harmonics measured are 79.68 Hz, 150.30 Hz, 175.00 Hz, and 159.36.00 Hz, respectively. The octave frequencies corresponding to the rotational frequencies of the vibration signals at different speeds can also be seen in the spectrogram. The theoretical value of the rpm at the corresponding speed can be calculated by Equation (4). Comparison of the test results with the theoretical values of the calculated rpm at the corresponding speeds is shown in

Table 3. Comparison of experiment and theory.

Speed (r/min)	Theoretical (Hz)	Experiment (Hz)	Relative Error/%
1200	20.00	19.92	0.40
1500	25.00	25.05	0.20
2100	35.00	35.16	0.45
2400	40.00	39.84	0.40

.

According to Table 2, under the same conditions, the relative error of the results of the tests and theoretical calculations at the four rotational speeds is less than 0.5%.

The speed of the vibration platform is fixed at 1500 r/min and 2100 r/min for continuous rotation, and the vibration signals are collected after 2 h and 4 h of rotation. Figure 7 shows the original 2 h and 4 h after the two rotational speeds of the data. From the figure, it can be seen that the sensor can still accurately collect the vibration signal, which proves that the sensor has strong stability.

The bearing with outer ring failure is installed in the fiber-optic sensing vibration detection experimental platform for testing. The fault location was adjusted closer to the sensor mounting location to make the fault signature more visible. The sampling frequency used in the experiment is 6.4 kHz and the acquisition time is 10 s. The acquired signals are analyzed by selecting the outer ring fault signals at two different rotational speeds, as illustrated in Figure 7. Envelope detection is one of the more typical and effective bearing signal processing methods for early bearing failures [30,31]. The spectrum of the envelope in the figure shows the corresponding fault frequencies at different rotational speeds and the octave frequencies corresponding to the corresponding fault frequencies.

As shown in Figure 8, at rotational speeds of 1300 r/min and 2000 r/min, the characteristic frequencies of the outer ring fault are 64.84 Hz and 100 Hz, respectively. The sensor detects the highest harmonic components at 194.90 Hz and 300.00 Hz for these speeds. The highest harmonic component detected by the sensor can be up to 300.00 Hz. The theoretical values of the corresponding fault eigenfrequencies at the three rotational speeds are calculated using Equation (5), and the test values of the fault eigenfrequencies obtained from the experiment are compared with the theoretical values, and the comparison results are shown in

Table 4. The comparison results of ORF.

Speed (r/min)	Theoretical (Hz)	Experiment (Hz)	Relative Error/%
1300	66.03	64.84	1.80
2000	101.58	100.00	1.56

.

The relative errors between the test value and the theoretical value at the two rotational speeds were compared, resulting in 1.8% and 1.56%, respectively. The measurement accuracy of the sensor is interfered by various factors, such as the test environment, the fixed position of the sensor, the algorithm operation and other factors. Consequently, the accurate detection of bearing faults can be achieved using the fiber-optic vibration sensor designed in this work.

This paper successfully applies a sensor, designed and manufactured based on SI, to bearing fault detection.

Table 5. Comparison with existing sensors.

Methods	Relative Error	In Bearing Fault Detection	Packing	References
MMF-TCF-MMF	2.20%	No	No	[32]
FBG	-	Yes	No	[33]
FBG	1.0%	Yes	Yes	[34]
FBG	-	Yes	Yes	[35]
FP	0.9%	No	Yes	[8]
Sagnac	1.8%	Yes	Yes	This work

displays a comparative analysis of the sensors being designed based on SI with other sensors in the literature in terms of relative error, application in bearing fault detection, and other aspects.

4. Conclusions

In this paper, a fiber-optic vibration sensor has been applied in bearing fault detection. A new structure of vibration sensor is designed using fiber-optic Sagnac interferometry and the whole sensor is armored with fiber-optic connection and encapsulated in stainless steel. After experimental and theoretical studies, the relative error of the fiber-optic vibration sensor for the analysis of healthy bearing speed measurement results is less than 0.5%, and for the analysis of faulty bearing results is less than 1.8%, which verifies the effectiveness and accuracy of the sensor. The sensor has a good resistance to vibration fatigue, which has a certain practical value.