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Abstract
Rotor-stator axial clearance is a crucial design parameter affecting rotating machines’ efficiency and safety. To accurately measure the dynamic axial clearance in high-speed machinery, a precise method based on time division multiplexing with frequency domain interferometry has been proposed. This method has proven robust and accurate through simulations and experiments. The inclusion of an optical switch enables the utilization of dispersive interferometry(DPI) and time division multiplexing for multiple channels of the light source. It achieves a static accuracy of 1.5 µm for a 15 mm range and a dynamic accuracy of 9 µm at 3000 rpm.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The axial clearance between the rotor and stator is a critical state parameter directly impacting major rotating machineries equipment such as aircraft engines, gas turbines, and wind tunnel compressors. Its variation is directly related to the dynamic behavior of the rotor and plays a crucial role in determining the operational efficiency and safety of the equipment. High-accuracy online axial gap measurement is essential to achieve active clearance control (ACC) of rotating machines and allow the rotor to operate at the optimal gap [1–3]. The measurement and active control of the axial clearance help prevent collision risks and improve the power-to-weight ratio of rotating machinery. Furthermore, it provides valuable data support for studying the dynamic behavior of rotor systems, making it of great significance [4,5].
However, measuring the axial clearance has always been challenging due to the complex internal structure, intense vibrations, high temperatures, and the non-cooperative moving target. The axial clearance is essentially an absolute distance measurement problem. The axial clearance value is generally composed of a gradually changing absolute distance component (axial movement) combined with end face runout [6]. Among them, axial movement is the dominant component with a large absolute value and low frequency. On the other hand, End Face Runout, resulting from unavoidable installation errors and the high rotational speed of the rotor, exhibits significant speed despite its relatively small magnitude [7].
In 2021, Guangyue Niu from Tianjin University utilized a microwave heterodyne structure to achieve measurements of a rotor at a distance of 18.5 mm in a laboratory environment [8]. However, the stator and rotor remained stationary for a single measure during the experiment. The accuracy achieved was also relatively low. Between 2020 and 2023, the team led by Weimin Chen made improvements based on frequency-swept interferometry (FSI). It achieved dynamic axial clearance measurement of rotating machinery [9,10], obtaining higher accuracy in their experiments. In 2023, our team also proposed an FSI-based method for measuring low-speed rotating machinery [11]. Interferometric methods generally offer high accuracy for absolute distance measurements and are less sensitive to the intensity of the returning light, making them suitable for measuring non-cooperative targets [12].Moreover, high-temperature-resistant fibers are already available in the market, and optical signals exhibit higher robustness to electromagnetic and thermal field variations, making them well-suited for axial clearance measurements. However, FSI, which derives absolute distances from a single data frame, has few advantages when measuring high-speed objects. It suffers from slow speed, and the target's movement during the frequency sweep can introduce hundreds of times more significant errors, thus significantly reducing measurement accuracy [13]. Additionally, the intensity of the returning light in rotating machinery constantly changes, and resolving the phase within a single frame becomes challenging when the linear velocity of the target is high.
Indeed, there are some methods available for measuring high-speed displacements. For instance, the phase-based distance measurement method based on microwave photonic mixing [14] has shown promising results and has been investigated for its potential application in axial clearance measurements [15]. However, in practical measures, the pigtail undergoes a long path with a potentially complex temperature distribution, along with vibrations caused by the rotating machinery [16]. The microwave photonic mixing method cannot separate the reflected light from the probe end face and the reflected light from the measurement target. As a result, it cannot utilize a common optical path design, and temperature-induced drift in the fiber directly affects the measurement results, leading to inaccurate or impossible to measure.
The real-time dispersive Fourier transform ultrafast ranging method is a novel and effective approach for measuring high-speed moving objects. It is based on the transmission characteristics of femtosecond pulses in optical fibers [17] and utilizes the time-domain interference signals obtained from the dispersion suppression fiber to acquire distance information. This method significantly reduces the Doppler effect of high-speed moving objects to the femtosecond level [18]. It can also achieve high measurement accuracy by recording the time-domain and frequency-domain interference fringes separately using an oscilloscope and a spectrometer [19,20]. It holds great promise for application in axial clearance measurements, although no related articles have been reported yet. However, this method has several challenges that need to be addressed. It can only perform single-pulse measurements at a time, and the low intensity of the non-cooperative backscattered light poses a signal-to-noise ratio issue that needs to be resolved. Additionally, this method's measurement range depends on the frequency sampling rate. To achieve a large measurement range, the sampling speed of the data acquisition card and the data processing speed need to be increased, which significantly raises the measurement cost. Typically, the vibration frequency is several times the rotational frequency, and the vibration amplitude tends to decrease as the frequency increases. Usually, analyses are limited to frequencies not exceeding 10 times the base frequency because higher-order harmonics with very small amplitudes hold little significance for practical purposes [21,22]. Taking the highest rotational speed of 30,000 rpm as an example, a few tens of kHz sampling rate is sufficient. The redundant sampling of the MHz range has little significance but increases the cost.
Dispersive interferometry (DPI) uses white light as the measurement source and a spectrometer as the dispersive device to obtain absolute distance information by analyzing the light phase at different frequencies [23–25]. However, this method has limitations when measuring high-speed moving objects due to the integration time constraint of CCD. It often lacks interference fringes and is heavily affected by Doppler errors. Moreover, spectrometers often adopt scanning structures to achieve higher frequency resolution, resulting in slow measurement speeds [26,27].
In order to achieve accurate measurements of high-speed rotating machinery in motion, this paper proposes a high precision dynamic measurement method for axial clearance based on time-division multiplexing with DPI. Based on the motion characteristics of the high-speed object and considering the influence of pulse backscattered energy and noise factors from the fiber amplifier, the impacts of integrating multiple pulses on the CCD sensor were analyzed at different measurement speeds. The optimal number of pulses for different object velocities was determined through optimization. Further improvements were made to the traditional DPI method by implementing time-division multiplexing using a high-speed optical switch. This advancement allows for simultaneous measurements of multiple channels using a single light source. When measuring extremely high-speed objects, similar to real-time dispersive Fourier transform, it is also possible to achieve accurate measurements using a single optical pulse, effectively suppressing the Doppler effect to the fs level. Using the reflected light from the end face as a reference signal significantly reduced the impact of the measurement environment. Additionally, the effects of non-cooperative target backscattered light variations were suppressed by employing a saturated fiber amplifier. Experimental verification confirmed the stability of the measurement results even under vibration conditions.
In summary, this method overcomes most of the adverse effects by incorporating an optical switch. It not only enables DPI measurements of moving objects but also achieves more robust measurements of axial clearance at a lower cost under laboratory conditions. This provides a new method for axial clearance measurements.
2. Principle
2.1 DPI basic principle
Herein, the measurement principle is described, as shown in Fig. 1.
Fig. 1. Schematic diagram of DPI system (MO switch: micro-optical-electro-mechanical switch; FPGA&DAQ: data acquisition board; SMF: single model fiber;EDFA:Erbium-doped fiber amplifier; α: tilt angle of the rotor; P: light irradiation point; L(t): the axial dynamic clearance; L0:axial movement; ΔL(t): end face runout)
The pulsed laser beam enters the micro-optical-electro-mechanical switch(MO switch) and is split into multiple paths of non-continuous light with time delays. This description only depicts one of the measurement channels for simplicity. When the light signal enters channel n, it goes through the circulator and enters the SMF. The pigtail of the probe follows a lengthy and intricate path. In this study, the reflected light from the probe's end face is utilized as a reference signal to compensate for potential length drift of the SMF that affect the measurement. This approach enables convenient compensation of the measurement results.
The beam is transmitted through a long path and partially reflected back to the fiber probe from the end face of the rotating shaft under test, while the other part is reflected by the lens at the probe's end. The interference light then passes through the circulator and the erbium-doped fiber amplifier (EDFA) and enters the spectrometer. The implementation of the saturated EDFA effectively reduces the impact of backscattered light variations caused by high-speed rotating objects [28,29]. The spectrometer separates the light into different positions on the CCD sensor according to the frequency achieved by the raster. The CCD sensor converts the optical signals into analog electrical signals. These analog signals are then converted into digital signals by the FPGA&DAQ system for further processing on the computer.
The FPGA plays a role in controlling the timing. It uses the synchronization signal from the pulsed laser as the reference to control the MO switch, ensuring that the optical signal's period matches the measurement period on the CCD sensor. The FPGA also controls the timing delay on the CCD sensor, ensuring that the CCD sensor is in the integration time window when the light from each channel reaches it. This enables the time-division multiplexing of the light source.
When the laser outputs from the laser source with $E(\omega )$ in the electric field, the reflectivity of the probe is $\gamma$, the reflectivity of the end face is $\rho$. The angular frequency of the light is $\omega$. From this, the light entering the spectrometer can be represented as:
After obtaining the interference signal on the CCD sensor, we can determine the measurement distance using the following equation.
In the equation, where L is the distance to be measured, n represents the group index, and in an air medium, it is close to the refractive index. c denotes light's speed. Furthermore, due to the limitations of the spectrometer's capabilities, the resolution of light frequency detection is restricted, resulting in a maximum value constraint for L. The ambiguous range ${L_{\max }}$ is given as follows:
Here, $\lambda$ represents the center wavelength of the laser, and $d\omega$ and $d\lambda$ denote the minimum angular frequency and minimum wavelength of light that can be detected by the spectrometer, respectively.
2.1 Optimal integration time in high-speed object measurements
The simplified representation of Eq. (1) is denoted as $p + q\cos \varphi$. In measurements of high-speed moving objects, both p and q vary with time. Introducing the time dimension, we have:
After undergoing spectral dispersion through the grating, the voltage obtained on the CCD sensor can be expressed as:
Simplify the above equation as follows:
(As the voltage derivation of a specific pixel is not helpful for analysis, the optical frequency was not digitized here.)
Among them, $\kappa$ is Conversion efficiency, $\bar{p}$ is the average value of p, and $\bar{q}$ is the average value of q. $T{{\kern 1pt} _0}$ is the starting time of integration, $\Delta T$ is the duration of integration, and v is the velocity of the object's motion. Simplify to obtain:
From the above equation, it can be seen that when measuring high-speed moving objects, if the integration time is too long, the above interference term will approach 0, which means that the interference fringes cannot be seen. From the above equation, it can be inferred that the contrast of the measurement signal is:
This function is a sinc function, and the maximum value should be obtained at $\Delta T = 0$. This can be achieved by using a single pulse of a pulsed laser for an ultra-short integration time. However, in practical applications, the end face reflectivity of non-cooperative targets is very low, and it is challenging to generate electrical signals with the energy of a single optical pulse. In addition, the surface of non-cooperative targets is not flat, and the reflected light from the end face changes rapidly during rotation. It is also necessary to use saturated EDFA to reduce the impact of input light changes.
Using an optical amplifier is necessary. However, when introducing an optical amplifier, unwanted optical noise is also introduced due to the spontaneous emission of the amplifier. The noise is quite complex and needs to be derived through rate and propagation equations [30–32]. Moreover, the noise factor is influenced by several factors, such as input optical power, doping concentration of the fiber, fiber length, and pumping method. To assess the signal-to-noise ratio of the output signal, the industry often employs the noise figure as a parameter. The noise figure is commonly used in circuit evaluation and is often used to assess the performance of optical amplifiers since they behave similarly to electronic amplifiers. It is represented by the ratio of the signal-to-noise ratio of the input signal to that of the output signal. In the case of this system, it refers to the ratio of the signal-to-noise ratio of the signal entering the EDFA to that received on the CCD. From this, we can obtain the formula:
The NF represents the noise figure, $SN{R_{EDFA}}$ signifies the signal-to-noise ratio entering the EDFA. As derived,
Here, $P_a^ +$ is the forward propagating ASE power, G is the gain of an erbium-doped fiber. $\Delta v$ is the bandwidth of the optical bandpass filter and $hv$ is the photon energy. As it can be seen, EDFA noise figure depends directly on forward ASE power and gain. Noise figure increases with increasing ASE power, on the other hand, decreases with increasing gain. We consider the contrast as the signal-to-noise ratio, and utilize the noise figure to obtain the optical signal-to-noise ratio at the input of CCD, which can be expressed as:
Based on the research findings [32], it has been observed that as the input optical power increases, the ASE power decreases. Consequently, there exists an optimal integration time that preserves the signal-to-noise ratio unaffected by the Doppler effect while minimizing the impact of ASE. It is important to note that the analysis provided focuses on the theoretical analysis of the contrast in the interference signal. In practical applications, the signal-to-noise ratio can be improved by biasing and amplifying the signal from the spectrometer using a circuit. Once the optimal integration time is determined, it becomes easier to calculate the maximum number of expandable channels:
Taking the experiment in this paper as an example, with a measurement speed of 35kHz, it is possible to perform 10 channels simultaneously using a single light source. This method enables white light interferometry for measuring moving objects and significantly reduces measurement costs.
3. Simulation
To validate the feasibility of adjusting the integration time for DPI to achieve axial gap measurements, this study conducted simulations on the contrast variation under different pulse numbers and reflectivity conditions.
In the simulations, the initial distance of the object was set to 5 mm. To simulate the extreme conditions of a non-cooperative surface, the reflectivity randomly fluctuated between 1% and 10% of the reference light. In this scenario, the reflected light from the non-cooperative surface is approximately ten-thousandth of the emitted light. Due to the short pulse duration of the pulsed laser, using the number of pulses as a counting tool allows for minor control of the minimum integration time. The relationship between the number of pulses N and the integration time can be transformed using the following equation:
where ${T_p}$ is the pulse duration, typically in the picosecond range, and ${T_{intvl}}$ is the pulse interval. To match the measurement instrument used in the experiment, a pulsed laser with a repetition rate of 22 MHz was used in the simulations, and ${T_{intvl}}$ is approximately 45 ns. After integrating multiple frequency components on each CCD pixel, the overall signal's contrast was analyzed, as shown in Fig. 2(a). This simulation did not involve EDFA amplification, thus the overall shape closely resembled a sinc function.Fig. 2. The relationship between contrast and the number of integrated pulses varies with the object's speed. We will consider two scenarios: (a) without EDFA and (b) considering the ASE of EDFA.
With the addition of EDFA, the relationship between contrast and the number of integration pulses is shown in Fig. 2(b). Due to the complex nature of EDFA noise composition and its dependence on factors such as input optical power, erbium-doped fiber concentration, fiber length, and pumping method, the noise coefficient used in our analysis is directly obtained from the EDFA used in our experiment. The relationship between the interference signal power divided by the total output power and the input power follows a similar trend to the 0 mm/s line in Fig. 2(b). Taking into account the amplification characteristics of EDFA, we can deduce the following essential information:
- 1. faster the motion speed of the object being measured, the shorter the optimal integration time, and the two are inversely proportional.
- 2. to the presence of EDFA background noise, the signal-to-noise ratio decreases on the spectrometer.
- 3. the simulated range, the larger the input optical power, the smaller the impact of EDFA background noise.
Due to the positive correlation between EDFA's background noise and pump current, we can derive the following beneficial conclusions for the experiment:
- 1. On the condition that the presence of saturated pixels in the spectrometer, it is advisable to minimize the pump current of EDFA to improve the signal-to-noise ratio.
- 2. Due to the constant presence of EDFA's background noise, a portion of the DC light intensity can be directly filtered out in the subsequent circuitry of the spectrometer.
- 3. From Fig. 2(b), it can be observed that the peak of the curve is not sharply defined. In this application scenario, precise integration time adjustment at the nanosecond level is not significant, and a slower optical switch can be used.
- 4. Under the same number of integration pulses, the contrast for high-speed object measurements is slightly lower than for low-speed objects. Therefore, the choice of the number of integration pulses can be based on the maximum velocity of the object being measured.
In order to directly correlate contrast, signal-to-noise ratio, and measurement error, this paper simulates signal-to-noise ratios ranging from -20 dB to 20 dB and contrast values ranging from 0.01 to 1. The relationship between the standard deviation (std) and the signal-to-noise ratio and contrast was analyzed, and the results are shown in Fig. 3. The std value was performed logarithmic operation for clarity.
Although the engine's experimental environment may be harsh in practical measurements, the vibration-related components are all involved in optical signals. The signal processing, including photoelectric conversion, is carried out in the laboratory, where the electrical signal-to-noise ratio is relatively high and can be guaranteed to be above -10 dB. At this level, if the contrast can reach around 0.2, achieving measurements with micron-level accuracy is possible. The precision is sufficient to meet the requirements for axial gap measurements.
Fig. 3. The relationship between the std and the signal-to-noise ratio and contrast. (Due to the large differences between the test results, we have taken the logarithm of the obtained error standard deviation (lg(std/um)). The red lines represent contour lines for different magnitudes of std. Due to the randomness of noise, the shape of the curves is not regular, but it reveals the magnitude and variation trend of the standard deviation.)
4. Experiment
Further, we conducted an experimental setup to validate the feasibility of our system for measuring axial gaps. The experiment consisted of three main parts:
In the first part, we achieved displacement measurements of a high-speed moving object using a linkage mechanism. This part aimed to confirm the accuracy of the mathematical analysis mentioned earlier.
The second part involved using a polarization controller and an eccentric rotor motor with a cantilever beam structure. By adjusting the polarization state of the probe's end fibers and the motor's vibration frequency, we verified our measurement method's robustness in environments with interference.
The third part encompassed a comprehensive validation of the system's performance. We performed calibration using a triangular laser sensor to achieve dynamic measurement with small probes(φ3). Subsequently, we conducted calibration tests on the experimental setup using a laser displacement sensor to evaluate the nonlinearity and measurement repeatability across the entire range.
Through the experiments, we confirmed the feasibility of our method, achieving a dynamic measurement standard deviation of 9µm. Within a measurement range of 15 mm, the average standard deviation was 1.5µm, with a deviation within 3µm. These indicators are sufficient to meet the requirements for axial gap measurements. The overall diagram of the experiment is shown in Fig. 4.
The pulse laser used in the experiment had a repetition rate of 22 MHz and a single pulse energy of 1.5 nJ. The optical path and MO switch were enclosed in a fiber device box to save space. A frosted surface disk was installed at the motor's front end to simulate the rotor surface. The measurement light was emitted from the probe, reflected by the disk through diffuse reflection, and then entered the optical spectrum analyzer after passing through the EDFA (erbium-doped fiber amplifier). The rangefinder utilized a triangulation displacement sensor principle. Although it has a limited measurement range, it is suitable for measuring non-smooth surfaces and was employed for dynamic calibration during the rotation of the disk. To determine the instrument's measurement range, we replaced the rangefinder with the reflective mirror of a laser interferometer.
The measurement range required for the axial clearance is around 10 mm, comparable to the ambiguous range. When the measured value is close to the ambiguous range, the error tends to be significant. If the measurement range exceeds the ambiguous range, an additional Fabry-Perot etalon (FPE) is required, increasing the cost. Therefore, we directly conducted measurements within the ambiguous range. Considering the need for compact frequency sampling and adjustability, we built our spectrometer. Through testing, the spectral range of the spectrometer was found to be approximately 1552-1565 nm, with a spectral resolution of about 0.1 nm. The CCD sensor consists of 1024 pixels and the highest sampling frequency is 40kHz, which can be adjusted depending on the integration time. The optical signal is converted to an electrical signal by the CCD sensor, which is then digitized by a DAQ card and transferred to a computer for data processing. The entire experiment was conducted under laboratory conditions.
4.1 Contrast experiment using a linkage with different speeds
As shown in Fig. 5(a), this study conducted a contrast experiment under different integration time conditions using a linkage mechanism. The linkage mechanism was chosen as the moving target for the following reasons:
- 1. The motion curve of the linkage in the rotational motion process of the motor approximates a sine wave (as shown in the measurement result in Fig. 5(b)), similar to the motion trajectory of the non-verticality disk.
- 2. The linkage mechanism exhibits a large amplitude of motion, and the speed can reach thousands of rpm. Due to the small installation errors in the engine, the end face runout is generally in the sub-millimeter range. The linkage mechanism's motion can simulate an engine's movement speed with tens of thousands of rpm.
- 3. The back-and-forth motion of the linkage mechanism helps mitigate the variation in reflectance caused by the tilt angle between the disk and the probe, thus providing additional supporting evidence for the aforementioned analysis.
To further reduce the influence of varying reflectance at different distances, this study utilized contrast data from multiple complete cycles and calculated their average as the measurement result. Figure 6 illustrates the plotted results.
Since the minimum integration time of the CCD allows for the integration of over 460 optical pulses, the maximum pulse count was set to 400. We have normalised the simulation data based on its maximum values to visually compare the simulation results with the actual measurement results. From the graph, we can deduce the following points:
- 1. The measured results agree with the theoretical and simulated results. The contrast increases and then decreases with the increase in pulse duration, showing an optimal integration time inversely proportional to the speed.
- 2. 209 mm/s, the peak contrast appears at approximately 40 pulse counts, about 1.8 µs. Under 262 mm/s, the peak contrast appears at about 50 pulse counts, about 2.3 μs.
- 3. change of integration time significantly improved contrast.
4.2 Measurement experiments with interfering environments
The internal measurement space of the target axial clearance is limited, and the measurement environment is harsh with complex routing. In addition, the surrounding high temperature and vibrations pose significant challenges to traditional measurement methods. Vibrations and high temperatures primarily affect the measurement results through changes in the fiber tail and alterations in the polarization state of light. This method utilizes the reflection of light from the probe end-face, which fundamentally solves the issue of inaccurate measurement results caused by fiber length changes due to temperature. However, to verify the robustness of this method in vibrating environments and its feasibility for measurements in harsh conditions, the following experiments were conducted:
Firstly, a polarization controller was used to traverse and change the polarization state of the fiber. The polarization controller used in this experiment was a squeezed type, which applies mechanical stress to the fiber to induce stress birefringence, making it equivalent to a rotating variable waveplate. This polarization controller can replace traditional free-space polarization controllers consisting of two quarter-wave plates and one half-wave plate. It can convert the input polarization state to the desired output polarization state [33].
By traversing all polarization states, as shown in Fig. 7, we can observe that although different polarization states may change the spectral envelope on the optical spectrum analyzer through the propagation phase in two orthogonal directions, they do not affect the original signal that needs to be solved for the frequency. After removing the external envelope using the algorithm, the impact on the measurement results is minimal.
Furthermore, as shown in Fig. 8(a), we simulated the measurement environment of the fiber under vibration conditions. One end of the experimental motor was fixed on a vertical mechanical wall, while the motor body was suspended mid-air as a cantilever beam. An unbalanced rotor was attached to the motor, causing vibrations at a frequency corresponding to the motor's rotation. After the pigtail of the probe was wound around the motor, it entered the polarization controller. The test end face and the probe were placed on another optical platform to minimize the influence of vibrations from the optical platform on the measurement results (not shown in the figure).
Fig. 8. (a) Environmental robustness experimental testing device diagram (b) Vibration measurement experiment result diagram
The measurement results are shown in Fig. 8(b). It can be observed that there are differences in the standard deviation (std) obtained at different distances. However, there is a slight variation in the std value between the static condition and after changing the vibration frequency. This experiment demonstrates the robustness of the common-path interference against vibrations.
4.3 Axial clearance measurement experiment
The experimental schematic diagram is shown in Fig. 4. Based on the confirmation from the experiment in Section 4.1, considering the maximum rotation speed of our motor at 3000 rpm and a top speed of not exceeding 200 mm/s, we selected an integration time of 60 pulses, which is approximately 2.7 µs. In the dynamic testing, a laser triangulation displacement sensor (Keneyce LK-H025) capable of measuring non-cooperative surfaces was used as the reference source. The sensor has a repeatability accuracy of approximately 0.02 µm and a maximum sampling speed of 392 kHz. However, it has a small measurement range of only 6 mm.
As shown in Fig. 9, the measurement results exhibit a remarkable similarity between the 1000 rpm and 3000 rpm conditions. A relatively thin disk was utilized to mitigate the impact of resonance, resulting in changes in the end face during rotation. As depicted in the figure, the amplitude of vibration in the rotating end face diminishes with increasing rotational speed. While this behavior is not typically observed in axial gap measurements, it confirms the suitability of this method for accurately measuring axial gaps in high-speed moving objects.
Fig. 9. Comparison of the measurement results of this instrument with the laser triangulation rangefinder at different rotational speeds (a) 1krpm (b) 3krpm
The standard deviation between this instrument and the laser displacement sensor is approximately 9µm. Besides the inherent errors of the system itself, several factors contribute to the relatively large standard deviation in this experiment:
- 1. It was challenging to precisely adjust the positions of the two probes relative to the center during the measurement, resulting in potential differences in the measurement points of the two sensors and a scaling discrepancy.
- 2. During rotation, the different positions of the two probes introduce phase differences in the measurement results, and the phase alignment may not be precise.
- 3. To eliminate the influence of Doppler errors, the laser displacement sensor adopted a higher sampling rate. The two measurement methods have different sampling rates, and resampling may introduce errors.
Furthermore, to validate the measurement range of this method and confirm its measurement accuracy, a prism was employed as a substitute for the rangefinder. The system was calibrated using a laser interferometer (SJ6000, CHOTEST). The measurement results of three experiments are depicted in the Fig. 10.
The experimental results indicate that the average standard deviation within a measurement range of 15 mm is 1.5µm, and the measurement range is approximately 15 mm. Since a collimator is used for the probe, the reflected light is reflected from the end face of the fiber. Therefore, this experiment has an initial distance of approximately 5 mm. For safety, the initial working distance was set to 6 mm. By coating the surface of the collimator and reducing the reflection from the fiber, the reference surface can be changed, and the measurement range of the gap can be increased up to 20 mm.
5. Conclusion
This study proposes a low-cost, Doppler-free, time-division multiplexing-based DPI to measure high-speed rotating machinery in motion accurately. Due to multiple rotor stages in most engines, using only one channel for measurements is uncommon. By utilizing an MO switch, measurements can be performed on high-speed rotating machinery, and time-division multiplexing of white light sources can be achieved, thereby reducing the measurement cost while enabling high-speed measurements for multichannel.
The analysis is based on the motion characteristics of the high-speed object under test, combined with the EDFA's noise figure and pulse echo energy factors. The effects of integrating multiple pulses simultaneously on the CCD are analyzed, and the optimal number of pulses is determined for different measurement speeds. Using a saturated EDFA mitigates the impact of optical intensity variations, and the utilization of reflected light from the end face as a reference signal reduces the influence of the measurement environment on the measurement results. The robustness and accuracy of the proposed method are validated through experimental investigations.
A cost-effective alternative of using a continuous broadband light source instead of a pulsed laser is explored for applications with a smaller required measurement range, such as axial gap measurements. On the other hand, this method can also be used when adding an FPE for more extensive measurement ranges. Furthermore, for practical axial gap measurements, real-time estimation of dynamic speed can be achieved by synchronizing the rotational speed and adjusting the integration time to achieve an optimal signal-to-noise ratio.
In summary, this method overcomes many detrimental influences and realizes high-precision, large-range measurements of axial gaps under laboratory conditions at a relatively low cost. It exhibits simplicity, efficiency, and robustness, providing a new approach to axial clearance measurements.
Funding
National Natural Science Foundation of China (52205573, 61971307, 62231011, U2241265); National Key Research and Development Plan Project (2020YFB2010800); China Postdoctoral Science Foundation (2022M720106); Joint Fund of Ministry of Education for Equipment Pre-research (8091B022144); National Defense Science and Technology Key Laboratory Fund (6142212210304); Guangdong Province Key Research and Development Plan Project (2020B0404030001); Fok Ying Tung Education Foundation (171055); Young Elite Scientists Sponsorship Program by CAST (2021QNRC001); Scientific Research Foundation of Yunnan Education Bureau (2023J0794).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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