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Abstract
In this paper, a high-accuracy measurement method for rotor-stator axial clearance in narrow spaces is proposed. The optical path structure based on all-fiber microwave photonic mixing is established. To improve the accuracy and expand the measurement range, the total coupling efficiency over the entire measurement range at different working distances of fiber probe was evaluated by Zemax analysis tool and theoretical model. The performance of the system was verified by experiments. The experimental results show that the measurement accuracy of axial clearance is better than 10.5 um within the range of 0.5–20.5 mm. The measurement accuracy has been effectively improved compared to previous methods. Additionally, the probe size is reduced to a mere diameter of 2.78 mm, which is more suitable for axial clearance measurement in narrow spaces inside rotating machines.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Rotor-stator axial clearance is a crucial design parameter that affects the safety and efficiency of rotating machines, such as aero-engines, gas turbines, steam turbines, and wind tunnel compressors [1–5]. When the clearance decreases, the efficiency improves [1]. However, if the clearance becomes too small, it can increase the probability of collision and friction between the rotor and stator, which poses significant safety hazards. Online measurement of rotor-stator clearance is an effective method to monitor the variation of clearance parameters under variable working conditions. This approach provides a foundation for investigating the rotor's dynamic behavior in major equipment and implementing active clearance control (ACC) [6].
Achieving high-accuracy non-contact online measurement of the rotor-stator axial clearance is challenging due to the complex internal structure, narrow measurement space, and extreme measurement environment of rotating machines. In particular, the narrow measurement space inside rotating machines presents significant measurement difficulties, necessitating the use of the smallest possible sensor probe [7]. Furthermore, when the size of the sensor probe is limited, the signal coupling efficiency between the sensor probe and the axial diffuse surface of the rotor is low [8–11]. This results in challenges in ensuring an effective, sufficiently large measurement range and high measurement accuracy simultaneously. Consequently, few effective measurement methods have been reported until recent years.
Currently, measurement methods can be categorized into two main groups: non-optical measurement methods and optical measurement methods. The non-optical measurement methods primarily comprise the eddy current method, the capacitance method, the discharge probe method, and the microwave method. Yang et al. introduced an eddy current method for axial clearance measurement in a scroll compressor in 2008 [12]. However, the eddy current method is not suitable for high-temperature measurement environments, as it fails above the Curie temperature. Lavagnoli et al. proposed a capacitance method for tip clearance in 2012 [13], and Addabbo et al. applied the capacitance method to both static and dynamic clearance measurements in 2018 [14]. However, the capacitance method requires a probe diameter of more than 10 mm when the measurement range is over 3 mm, making it unsuitable for narrow measurement spaces inside machines. Yu et al. introduced a discharge probe method for tip clearance measurement based on AC discharge in 2020 [15]. Nevertheless, according to current reports, the maximum measurement range of the discharge probe method is only 6 mm, which is insufficient to meet the required axial clearance measurement range. Aslinezhad et al. proposed a microwave method for tip clearance determination in 2020 [16]. The microwave frequency used was 22 to 27 GHz, enabling a measurement range of 1 to 5 mm. The probe size employed was 10.2 mm, and the relative measurement accuracy was reported to be greater than 1.8%. Moreover, Niu et al. proposed a microwave method for axial clearance measurement in 2021 [7]. The microwave measurement system used a 9 mm probe and had an axial clearance measurement range of 18.5 mm. However, due to the nonlinear effects of microwave components, the accuracy of the method was not sufficiently high, with a relative accuracy of 1% and an absolute accuracy value above 120um over the entire measurement range. Additionally, during the actual measurement process inside the machine, the microwave measurement system transmits signals through microwave cables that are not flexible enough.
In comparison, fiber optic methods for axial clearance measurement have numerous advantages. The smaller size of the fiber probe, high accuracy, and better fiber flexibility make it more suitable for measuring axial clearance in rotating machines with complex structures and narrow spaces. In the past two years, researchers have conducted research on axial clearance measurement methods based on frequency-swept interferometry [17–20]. However, this approach has two limitations. Firstly, the power of the swept laser is limited, which restricts the range of axial clearance measurement and requires higher reflectivity of the axial end face. Secondly, the scanning speed of the swept laser is limited, which reduces its potential for high-speed measurement. Furthermore, if high-performance swept lasers were to be customized, it would significantly increase the cost of the system. Some other optical methods, such as the pulsed time-of-flight LIDAR, and the amplitude-modulated continuous wave (AMCW) LIADR, are also employed for determining the absolute distance of objects [21–24]. The range accuracy of pulsed LIDAR depends on the time counting error (currently 0.2 ns is considered state-of-the-art) [21], which does not meet the requirement for axial clearance measurement. AMCW LIDAR offers the advantages of simplicity and stability. However, conventional AMCW LIDAR utilizes an electrical down-conversion process, which imposes limitations on measurement accuracy due to the nonlinear properties of microwave components. This limitation becomes more pronounced when measuring in narrow spaces where the reflected signals are weak. Therefore, further advancements are required to enhance the accuracy of axial clearance measurement in narrow spaces.
In this work, we present a high-accuracy non-contact online measurement system for rotor-stator axial clearance based on all-fiber microwave photonic mixing. The system utilizes an axial clearance measurement optical path structure established on all-fiber microwave photonic mixing, which features small probe size and excellent fiber flexibility. In contrast to the microwave method, the down-conversion process is executed in the optical domain, minimizing the influence of electromagnetic interference and eliminating the use of microwave components with nonlinear properties [25–28], thus enhancing the accuracy of axial clearance measurement. Additionally, Zemax analysis tool and a theoretical model were employed to analyze the total coupling efficiency of the optical fiber probe across the required measurement range, enabling the selection of an appropriate probe working distance. This approach expands the measurement range and improves accuracy across the required measurement range, while maintaining a very small optical fiber probe size. Finally, experiments were conducted to verify the performance of the measurement system.
2. Method and working principle
2.1 Structure of the system
The rotor-stator axial clearance measurement system is organized as shown in Fig. 1(a), which comprises three main modules: the optical module, microwave signal synthesis module, and signal acquiring and processing module. The optical module includes a polarization-maintaining fiber-coupled laser (PFL), the first Mach-Zehnder electro-optic intensity modulator (EOM #1), a 10:90 optical fiber coupler, the second Mach-Zehnder electro-optic intensity modulator (EOM #2), the first photodetector (PD #1), the first erbium-doped fiber amplifier (EDFA #1), an optical fiber circulator, an optical fiber sensor probe, the second erbium-doped fiber amplifier (EDFA #2), the third Mach-Zehnder electro-optic intensity modulator (EOM #3), and the second photodetector (PD #2). The microwave signal synthesis module comprises a clock reference, the first phase-locked loop frequency synthesizer with integrated VCO (PLL #1), the first microwave power amplifier (PA #1), the second phase-locked loop frequency synthesizer with integrated VCO (PLL #2), a microwave power divider (MPD), the second microwave power amplifier (PA #2), and the third microwave power amplifier (PA #1). The signal acquiring and processing module includes a dual-channel data acquisition card (DAQ) and a personal computer (PC). In Fig. 1(a), the red lines indicate optical fibers, and the black lines represent electrical signals.
Fig. 1. (a) Diagram of the rotor-stator axial clearance measurement system structure. PFL: polarization-maintaining fiber-coupled laser, EOM: Mach-Zehnder electro-optic intensity modulator, EDFA: erbium-doped fiber amplifier, PD: photodetector, PLL: phase-locked loop frequency synthesizer with integrated VCO, PA: microwave power amplifier, MPD: microwave power divider, DAQ: data acquisition card, PC: personal computer, RF: microwave signal, DC: DC bias voltage. (b) The principle of phase difference method. (c) Diagram of microwave photonic mixing down-conversion. BPF: bandpass filter, IF: intermediate frequency signal.
The microwave signal synthesis module is responsible for generating the microwave signals RF1, RF2, and RF3, which are then applied to EOM #1, EOM #2, and EOM #3, respectively. It should be noted that the frequency of RF2 and RF3 is identical, while the frequency of RF1 differs, with an intermediate frequency difference.
The laser emitted by the PFL is coupled into the fiber of the optical path and is then modulated through EOM #1 by microwave signal RF1. The resulting microwave-modulated laser is split into two parts by the coupler, with 10% serving as the reference laser and the remaining 90% as the measurement laser. The reference laser is further modulated through EOM #2 by microwave signal RF2 and the modulated reference laser is detected by PD #1. The measurement laser is amplified by EDFA #1, and then guided by the circulator to reach the optical fiber sensor probe which is installed in the aero-engine. The measurement laser is emitted from the end of the optical fiber and focused by the probe's lens. The focused laser passes through the axial clearance and is irradiated onto the axial end face. The laser is diffusely reflected by the axial end face and received by the fiber probe. The return laser passes through the circulator and is amplified by EDFA #2. The amplified return measurement laser is modulated through EOM #3 by microwave signal RF3 and the resulting microwave-modulated measurement laser is detected by PD #2. The measurement and reference signals are received and photoelectrically converted by PD #1 and PD #2, respectively, and the measurement signal data and reference signal data are acquired by the dual-channel DAQ. The measurement and reference signal data are then transferred to a PC for processing. By comparing and processing the phase of the measurement signal and reference signal, the value of axial clearance can be determined.
As described above, the measurement and reference lasers are both modulated twice by microwave signals in order to achieve microwave photonic mixing within the all-fiber optical path. This allows us to down-convert the measurement and reference microwave signals to intermediate frequency signals in the optical path, while preserving the phase information. As a result, we only need to receive, photoelectric-convert, acquire, and process the intermediate frequency signals in the system. This approach eliminates the need for microwave components to convert the amplitude into the phase and mix the microwave signals, which can introduce inaccuracies due to nonlinearity properties.
2.2 Principle of axial clearance measurement based on microwave photonic mixing
As shown in Fig. 1(b), axial clearance measurement based on microwave photonic mixing is realized by measuring the phase difference between microwave-modulated measurement signal and reference signal, which determines the time-of-flight value with axial clearance information. The relation between phase difference $\Delta \varphi $ and time of flight (TOF) value ${\tau _{TOF}}$ can be expressed as below
where ${f_M}$ is the intensity modulation frequency.The initial phase of the measurement signal and reference signal after being intensity modulated by EOM #1 is the same, denoted as ${\varphi _0}$. Next, the measurement signal and reference signal are divided by a coupler, and they will undergo different laser propagation processes. The phase difference introduced by the propagation in optical fibers and other optical devices of the measurement signal and reference signal are denoted as ${\varphi _{m1}}$ and ${\varphi _{r1}}$, respectively. Additionally, the phase difference introduced by the propagation in the axial clearance space between the probe and rotor end face of the measurement laser is denoted as ${\varphi _d}$, and the relation between ${\varphi _d}$ and the axial clearance value d can be expressed as below
where ${n_{air}}$ is the refractive index of air, c is the speed of light in vacuum.Therefore, the phase difference $\Delta \varphi $ between measurement signal and reference signal can be expressed as
The phase difference ${\varphi _d}$ with axial clearance information can be expressed as
Therefore, axial clearance value d can be expressed as
where $\Delta {\varphi _0}$, c, ${n_{air}}$ and ${f_M}$ are constants, and can be obtained by calibration experiments.Before solving for the phase difference $\Delta \varphi $, the measurement signal and reference signal are down-converted by microwave photonic mixing. In the proposed system, the frequency of microwave signal RF1 is ${f_M}$, and the frequency of microwave signal RF2 and RF3 is ${f_M} - {f_{IM}}$. There is an intermediate frequency difference ${f_{IM}}$ between RF1 and RF2/RF3. The microwave signals RF1 and RF2/RF3 can be expressed as
According to the characteristics of MZM electro-optic intensity modulator, the intensity ${I_0}$ of the laser beam after being modulated by the modulator EOM #1 can be expressed as
Through Jacobi–Anger expansion, ${I_0}$ can be expressed as
The fundamental frequency component, denoted as ${f_M}$, is used for measurement. By adjusting the DC bias voltage DC1 and the amplitude ${A_{M1}}$ of microwave signal RF1, the coefficient of the fundamental frequency component ${f_M}$, namely ${J_1}({\pi {A_{M1}}/{V_{\pi 1}}} )$, can be maximum.
Considering the fundamental frequency component, the laser intensity after being modulated by EOM #1 can be expressed as
Then the laser will be divided into measurement laser and reference laser by the coupler, which propagate along different optical paths and introduce different phase difference. When arriving at EOM #2 and EOM #3, the intensity of reference laser and measurement laser can be expressed as below
After being modulated by EOM #2 and EOM #3, the microwave signal RF2 and RF3 are mixed with the modulated signals from EOM #1, resulting in the appearance of the intermediate frequency component. Thus, the intensity of the reference laser and measurement laser can be expressed as follows
The phase difference $\Delta \varphi $ between the measurement signal and reference signal can be expressed as
Therefore, the down-conversion process by microwave photonic mixing will not alter the phase difference between the measurement signal and the reference signal. The down-conversion process is illustrated in Fig. 1(c). After down-conversion, the laser signal can be received and converted into electrical signal by a photodetector. Subsequently, the phase difference between the measurement signal and the reference signal can be determined using Hilbert transformation [29]. The axial clearance can be computed by Eq. (5).
2.3 Theoretical analysis for fiber sensor probe
In the application of online measurement of axial clearance, as shown in Fig. 2(a), the optical fiber sensor probe must be installed inside the aero-engine, where the installation space for the probe is typically very limited. Therefore, it is necessary to design a fiber probe with a small diameter. However, a small diameter can lead to low coupling efficiency of the return light, resulting in a low signal-to-noise ratio (SNR). In addition to the probe diameter, the working distance of the probe is also a crucial factor affecting the coupling efficiency. The working distance of the probe is a controllable parameter in the probe design stage. To maximize the coupling efficiency over the entire measurement range under the condition of a limited probe diameter, it is essential to design the working distance of the probe to an appropriate value. We first present a theoretical model for the coupling efficiency of optical fiber probes based on the ray tracing method.
Fig. 2. (a) Installation diagram of optical fiber probe inside rotating machines. (b) Diagram of optical fiber probe structure. $d$: axial clearance, $l$: the distance from the end face of the optical fiber to the left end face of the lens, $h$: the thickness of lens, $W.D.\; $: the working distance of probe. (c) Theoretical model of optical fiber probe. $2{w_a}$: the diameter of the circular optical fiber end face, ${z_a}$: the distance between the end face of the optical fiber and the point light source in the z-axis direction, $\delta B$: subdivided face area, $f({x,y,z} )$: the equation of the end face of rotor. (d) The first-stage fiber beam subdivision method. ${r_i}$: the radial distance from the center of fiber end face, ${\theta _j}$: the angle to the x-axis. (e) The second-stage diffuse beam subdivision method. ${\varphi _p}$: the meridian angle of the second-stage ray, ${\psi _q}$: the sagittal angle of the second-stage ray, $\delta \varphi $: subdivision angle interval in the meridian direction, $\delta \psi $: subdivision angle interval in the sagittal direction.
The installation structure of the optical fiber probe is depicted in Fig. 2(a), and an enlarged view of the optical fiber sensor probe is presented in Fig. 2(b). The probe consists of a fiber, a lens, and external tooling. As illustrated in Fig. 2(b), the working distance (W.D.) represents the distance between the beam convergence point and the right end face of the lens. The coupling efficiency within the measuring range is mainly determined by the working distance when the lens is selected. The working distance of the probe is defined as the distance from the end face of the optical fiber to the left end face of the lens, which can be expressed as
where $W.D.$ refers to the working distance of the fiber probe, l is the distance from the end face of the optical fiber to the left end face of the lens, $f(x )$ represents the relationship between l and $W.D.$, which is determined by the lens system.The axial end face can be approximated as a diffuse surface. Based on previous studies [09,11], the following assumptions can be made: 1) The light emitted from the fiber probe can be approximated to Gauss point light source. 2) The maximum illumination angle of the light source is equal to the numerical aperture (NA) of the optical fiber.
The analytical model is based on a two-stage ray tracing method, which is illustrated in the flowchart in Fig. 3. The steps for establishing the model are as follows.
Taking the point light source as the origin and the optical axis as the z axis, the coordinate system can be established as shown in Fig. 2(c). The first-stage beam subdivision method is illustrated in Fig. 2(d). The diameter of the circular optical fiber end face is $2{w_a}$. Divide the end face of circular optical fiber into m rings at equal intervals ${r_0} = 2{w_a}/m$ in the radial direction, and subdivide the end face by equal interval ${\theta _0} = 2\pi /n$ in the circumferential direction. Using this subdivision method, the end face of the optical fiber can be divided into $m \times n$ micro-ring sectors $\delta A$, and each micro-ring sector represents a ray. The vertex of each micro-ring, denoted as $({{x_{{a_{ij}}}},{y_{{a_{ij}}}},{z_{{a_{ij}}}}} )$, can be considered as the intersection point of each ray and the fiber end face, which can be expressed as
In this step, matrix optics will be used to solve the ray propagation path. Take one ray as the example, the direction vector of which is $({{x_{{a_{ij}}}},{y_{{a_{ij}}}},{z_{{a_{ij}}}}} )$. Use $({{\varepsilon_{{a_{ij}}}},{\tau_{{a_{ij}}}}} )$ to represent the direction cosine between the ray and the x-axis, y-axis. Therefore, the initial parameters of a ray can be expressed as ${\left[ {\begin{array}{{cccc}} {{x_{{a_{ij}}}}}&{{y_{{a_{ij}}}}}&{{\varepsilon_{{a_{ij}}}}}&{{\tau_{{a_{ij}}}}} \end{array}} \right]^T}$. The transformation matrix of the first stage can be expressed as
The parameters when the ray reaches the diffuse reflection surface of the rotor can be expressed as
According to the intensity distribution law of Gaussian beam [30,31], the power of each first-stage ray can be expressed as
Each micro-ring area $\delta {A_{ij}}$ will be projected onto the diffuse surface through the propagation of light and become $\delta {B_{ij}}$. The light intensity reflected by $\delta {B_{ij}}$ follows Lambert's cosine law, which can be expressed as
The second-stage beam subdivision method in the first stage is shown in Fig. 2(e). Subdivide the diffuse hemisphere at equal angle intervals $\delta \varphi = \pi /({2k} )$ in the meridian direction and at equal angle intervals $\delta \psi \textrm{ = }2\pi /l$ in the sagittal direction. In this way, the diffuse hemisphere can be subdivided into $k \times l$ micro-pyramids. And each micro-pyramid represents a second-stage ray. The meridian and sagittal angles of the second-stage ray in $({p,q} )$ micro-pyramid can be represented using $({{\varphi_p},{\psi_q}} )$. And the parameters of second-stage $({p,q} )$ ray can be expressed as
The calculation method of the ray propagation path is the same as explained in step (2). The transformation matrix of the second-stage can be represented by ${M_2}$. Therefore, the parameters when the ray reaches the plane of the fiber end face can be expressed as
The angle between rays and optical axis can be expressed as
There are two conditions for rays to be received by optical fiber: 1) The intersection points of rays and end face of lens and fiber must fall within the aperture of lens and fiber. 2) The angle between the rays and the optical axis is less than numerical aperture angle of the fiber. The effective rays are the ones that meet the above two conditions.
Assuming
Whether a ray is considered effective depends on whether its propagation path satisfies the two conditions mentioned earlier.
At a certain axial clearance value and working distance, the total power received by the optical fiber can be expressed as
Therefore, the formula for coupling efficiency can be expressed as
In order to maintain a good signal-to-noise ratio throughout the entire measurement range, it is important to achieve good coupling efficiency across the range. This can be achieved by optimizing the working distance of the probe when the lens size is limited. Assuming that the required measurement range of the axial clearance is H, between ${d_{\min }}$ and ${d_{\max }}$. Therefore, the following conditions need to be met at a certain working distance.
By finding the maximum point of the curve $Q({W.D.} )$, we can obtain the appropriate working distance.
3. Simulations and results
Using the Zemax analysis tool for ray tracing simulation, the coupling efficiency curves at different working distances can be obtained. Based on these curves, the appropriate working distance of the optical fiber probe can be calculated using Eq. (25) and Eq. (26).
The optical fiber probe is mainly composed of a fiber and a lens. The parameters of the fiber probe and the probe components are listed in Table 1.
Table 1. Parameters of the probe components
To investigate the coupling efficiency of the optical fiber sensing probe at different working distances, we varied the working distance from 6 to 20 mm in 1 mm intervals, and generated coupling efficiency curves by simulations of Zemax analysis tool. The ray tracing simulation results for different working distances are shown in Fig. 4. The X-axis represents the axial distance from 0 to 30 mm, while the Y-axis represents the normalized coupling efficiency. The normalization process involves dividing the coupling efficiency by 0.0018, as the maximum coupling efficiency occurs at a working distance of 6 mm, where it reaches approximately 0.0018. As shown in Fig. 4(a)-(o), the peak normalized coupling efficiency decreases as the working distance increases. In addition, we defined the effective range as the measurement range where the coupling efficiency is greater than a certain threshold value ($1 \times {10^{\textrm{ - }5}}$). Based on Fig. 4(a)-(o), the effective range increases as the working distance increases. Figure 4(p) shows that when the working distance is infinite, i.e., when the beam is collimated and emitted, the normalized coupling efficiency is very low, indicating that the collimating probe is not suitable for measuring axial clearance.
Fig. 4. Simulation results of the relationship between normalized coupling efficiency and axial distance under different working distances by Zemax analysis tool.
Based on the data obtained from Zemax analysis tool and using Eq. (25) and Eq. (26), we generated curves for the effective range and the maximum total efficiency within 20 mm as a function of the working distance, as shown in Fig. 5. To ensure that the axial clearance measurement range is met, the effective range should be greater than 20 mm. Based on Fig. 5, working distances between 11 mm and 20 mm can meet this requirement. Moreover, Fig. 5 shows that the maximum total efficiency within 20 mm decreases as the working distance increases. Therefore, the working distance of the optical fiber sensor probe should be set to about 11 mm to achieve both a sufficient effective range and a high total efficiency.
Fig. 5. The curve between effective range and working distance and the curve between the maximum total efficiency within 20 mm and working distance.
4. Experiments, results, and discussion
4.1 Experimental setup
To verify the performance of the axial clearance measurement method based on the microwave photonic mixing, an experimental setup was constructed, as depicted in Fig. 6. The experimental system consisted of several components, including a microwave signal synthesis module, an optical module, a signal receiving and conditioning module, a dual-channel DAQ (data acquisition card), a PC, a simulated structure of rotor and stator, and a linear guide. Two microwave signal generators (N5172B and N5222A, Keysight Technologies) were utilized to generate microwave signals with frequencies of 6 GHz (${f_M}$) and 5.9975 GHz (${f_M} - {f_{IM}}$), respectively. The signal generators were operated under the same clock reference, and the measurement frequency is 6 GHz, corresponding to an ambiguity range of 25 mm, thereby covering the axial clearance measurement range. Alternatively, the two signal generators can be replaced with the microwave signal synthesis module, as shown in Fig. 1. In the optical module, a polarization-maintaining laser diode (PL-FP-1550-A-A81-PA, LD-PD INC) with a central wavelength of 1550 nm was used, driven by a hardware circuit. Three Mach-Zehnder electro-optic modulators (MXAN-LN-10, iXblue Photonics) were utilized for intensity modulating and microwave photonic mixing. Additionally, two erbium-doped fiber amplifiers (EYDFA-HP-C-BA-30-SM and EDFA-C-PA-35-SM-M, Max-ray photonics) were employed in the measurement path. The receiving and conditioning module included two photodetectors (UPD-15-IR2-FC, ALPHALAS GMBH) and a signal conditioning hardware circuit. The DAQ acquired the measurement and reference signals after they were conditioned. The sampling rate of the DAQ was set to 125 MHz/s. To simulate axial clearance changes, we installed a simulated rotor and stator structure on a motorized positioning system.
4.2 Measurement performance evaluation experiments of the system
A series of experiments were conducted on the proposed system to evaluate the performance of the rotor-stator axial clearance measurement method. These experiments aimed to assess the repeatability, resolution, static accuracy, and dynamic accuracy of the proposed method.
The measurement signal and reference signal acquired by DAQ are shown in Fig. 7(a). To enhance the signal-to-noise ratio, initial processing was applied to the raw measurement and reference signals obtained through DAQ using a finite impulse response (FIR) digital bandpass filter. Both the raw measurement signal and the reference signal had an intermediate frequency of 2.5 MHz. The bandpass filter was configured with a passband of 2.49 MHz to 2.51 MHz and a bandwidth of 20KHz. The spectrums of the raw measurement signal and the filtered measurement signal are shown in Fig. 8. The spectral comparison reveals a significant improvement in the signal-to-noise ratio (SNR) of the filtered signal. As the frequencies of the measurement signal and the reference signal are fixed, identical, and single (2.5 MHz), the phase difference introduced by the filter to the two signals remains constant, thereby avoiding additional measurement errors. The phase difference introduced by the filter can be incorporated into the initial phase $\mathrm{\Delta }{\varphi _0}$ in Eq. (5). After passing through the digital bandpass filter, the signals are shown in Fig. 7(b). The phases of the two signals were determined using Hilbert transformation, with the wrapped phase results shown in Fig. 7(c). The real phases were then obtained by applying the unwrapping phase algorithm, as shown in Fig. 7(d). Finally, the phase difference between the measurement signal and reference signal could be solved. According to Eq. (5), the factor between the value of axial clearance and the phase difference is determined by constants $\Delta {\varphi _0}$, c, ${n_{air}}$ and ${f_M}$. In order to improve the accuracy, calibration experiments were carried out to solve the factor. The axial clearance reference values were obtained using the measured values of the laser interferometer (SJ6000, CHOTEST). The calibration experiments were conducted within the range of 0.5 mm to 20.5 mm. Initially, the motorized positioning system was set to the initial measurement point, and the interferometer was zeroed. Then, starting from 0.5 mm and moving up to 20.5 mm with an interval of 0.5 mm, the measurement value of the interferometer was taken as the reference while the motorized positioning system was adjusted accordingly. At each measurement point, data collected by the dual-channel DAQ and the laser interferometer were recorded. The measured phase value was calculated using the data collected by the DAQ, and the reference value was obtained by calculating the mean value of the recorded data from the laser interferometer. Finally, polynomial fitting was employed to achieve calibration. After calibration, the performance evaluation experiments were conducted.
Fig. 7. The results of the signal processing process: (a) The original acquired signal. (b) The filtered signal. (c) The wrapped phase results solved by Hilbert transformation. (d) The unwrapped phase results.
Fig. 8. Signal spectrum diagrams. (a) Spectrum of the acquired raw signal. (b) Spectrum of the filtered signal.
At first, the measurement repeatability evaluation experiments were completed. The motorized positioning system was moved 0.5 mm at a time over the range of 0.5 mm to 20.5 mm, resulting in a total of 41 measurement points. At each measurement point, measurements were taken every 20 ms for a total measurement time of 60s. The standard deviation was then calculated for each point, as shown in Fig. 9. The maximum standard deviation is found to be 6.4um at an axial clearance of 1.0 mm. Moreover, the standard deviation curve exhibits a trend of decreasing initially and then increasing, with the minimum occurring near the working distance of the optical fiber sensing probe.
Next, the measurement resolution evaluation experiments were completed. A measurement point was randomly selected within the measurement range of 0 mm to 20 mm, and the motorized positioning system was moved in steps of 5um to measure the change in output phase difference. The results of the experiment are shown in Fig. 10. As shown in the figure, the axial clearance measurement resolution is better than 5um.
In addition, the static measurement accuracy evaluation experiments were completed. Initially, the motorized positioning system was adjusted to the position where the laser interferometer measured a value of 0, and this position corresponds to the 0-point established during the calibration experiment. Subsequently, the motorized positioning system was incrementally moved at intervals of 0.5 mm within the range of 0.5 mm to 20.5 mm. The step size of 0.5 mm was based on the measurement value provided by the laser interferometer as a reference. At each measurement point, the measurement accuracy was obtained by comparing the axial clearance measurement value with the reference value obtained from the interferometer. Perform the accuracy evaluation experiments for three times. The measured axial clearance curve is shown in Fig. 11(a), where the X-axis represents the reference value of axial clearance obtained by laser interferometer, and the Y-axis represents the measured axial clearance obtained by the proposed system. The measurement error at each axial clearance measurement point is shown in Fig. 11(b), while Fig. 11(c) shows the distribution of the relative values of the measurement errors. The experimental results demonstrate that the measurement accuracy of the proposed system is better than 10.5um over the entire measurement range of 0.5 mm to 20.5 mm.
Fig. 11. The results of the static measurement accuracy evaluation experiments: (a) The measurement curve. (b) The distribution of the measurement error. (c) The relative value of the measurement error.
Furthermore, the dynamic measurement performance evaluation experiments were completed. We conducted the repeatability evaluation experiments and accuracy evaluation experiments to assess the dynamic performance. Make the axial end face rotate at a constant speed. The measurement steps were the same as the static measurement repeatability and accuracy evaluation experiments. The standard deviation of each measurement point was calculated, as shown in Fig. 12, with a maximum value of 17.8um. The measurement error and the relative measurement errors are presented in Fig. 13(a) and Fig. 13(b), respectively. The experimental results demonstrate that the proposed system's measurement accuracy is better than 28.3um across the entire measurement range of 0.5 mm to 20.5 mm.
Fig. 13. The results of the dynamic measurement accuracy evaluation experiments: (a) The distribution of the measurement error. (b) The relative value of the measurement error.
4.3 Comparison of results and discussion
Based on the experimental results of the proposed method, it can be concluded that the static measurement accuracy of axial clearance is better than 10.5um across the entire measurement range of 0.5 mm to 20.5 mm, and the dynamic accuracy is better than 28.3um. In comparison, previous research [7] has indicated that the microwave measurement method has a measurement accuracy better than 30um at 0.5-3 mm and 1% at 3-18.5 mm, but the absolute measurement error over the entire measurement range of 0.5-18.5 mm can exceed 120um. As shown in Fig. 14, the comparison of the measurement results between the two methods clearly demonstrates that the proposed method achieves a significant improvement in measurement accuracy while also expanding the measurement range to 0.5mm-20.5 mm.
Fig. 14. The comparison of measurement results between the proposed method and the microwave method: (a) The comparison of measurement error. (b) The comparison of relative value of measurement error.
The improved accuracy of the proposed method is attributed to the use of microwave photonic mixing, which enables avoidance of microwave components with nonlinear effects that can reduce measurement accuracy. Additionally, the microwave sensing probe used in the microwave method emits energy in a divergent mode, which can lead to lower coupling efficiency as the axial clearance increases, thereby reducing measurement accuracy. In contrast, by designing the fiber optic probe with an appropriate working distance, the proposed method achieves a higher coupling efficiency over the entire measurement range, which improves the signal-to-noise ratio and contributes to the enhanced measurement accuracy.
It is important to note that the actual measurement environment inside a large rotating machine can have an impact on the accuracy of axial clearance measurement. For instance, when the blades of rotating machines start to rotate, high-speed and high-temperature airflows are induced through the inlet, leading to alterations in air temperature and pressure within the axial clearance area. According to Edlén formula, these changes can cause fluctuations in the refractive index of the air, potentially introducing errors in axial clearance measurements. In addition, the fiber optic winding path is complex and relatively long inside the rotating machines. Consequently, vibrations and temperature fluctuations inside the machine can cause variations in the optical path length, resulting in fluctuations in the optical path difference between the measurement laser and the reference laser. Therefore, further research should focus on understanding the effects of environmental changes on axial clearance measurement and developing methods to mitigate these effects.
5. Conclusions
It is a great challenge to maintain high accuracy and large measurement range while requiring a small sensor probe size for axial clearance measurement inside rotating machines with narrow spaces. In the present study, a high-accuracy non-contact online measurement method for rotor-stator axial clearance using all-fiber microwave photonic mixing is proposed. The proposed system is based on the principle of the laser microwave amplitude modulation phase difference method. The theoretical model of axial clearance measurement based on microwave photonic mixing was analyzed, and the axial clearance measurement optical path structure was established. By applying microwave photonic mixing for down-conversion, it avoids the use of microwave devices with nonlinear effects. In addition, the total coupling efficiency of the optical fiber probe over the entire measurement range was analyzed by Zemax analysis tool and theoretical model, which was used to select an appropriate working distance of probe. That can expand the measurement range and improve the accuracy while the size of the optical fiber probe remains very small. Finally, a series of experiments were conducted to verify the performance of the measurement system. Experimental results show that the system’s measurement range is 0.5-20.5 mm, the measurement resolution is better than 5um, the standard deviation in the measurement repeatability evaluation experiments is better than 6.4um, the static measurement accuracy is better than 10.5um, and the dynamic accuracy is better than 28.3um. Compared to the previous method, the measurement range, repeatability, and accuracy have all been improved, and the sensor probe used is smaller, with a diameter of only 2.78 mm, making it more suitable for axial clearance measurement in narrow spaces inside rotating machines. Future research should focus on understanding the impact of environmental factors on axial clearance measurement and developing methods to eliminate their effects.
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); the Fok Ying Tung Education Foundation (171055); Young Elite Scientists Sponsorship Program by CAST (2021QNRC001).
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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