Optical-fiber-based dynamic measurement system for 3D tip clearance of rotating blades

Xiaodong Zhang; Xiaodong Zhang; Xiaodong Zhang; Yiwei Xiong; Yiwei Xiong; Siying Xie; Hongcheng Liu

doi:10.1364/OE.27.032075

1. Introduction

The health status of a turbine is strongly dependent on the operating condition of the blades, which are subject to complex loads such as centrifugal load, aerodynamic load, and thermal load during the turbine operation. Hence, it is important to monitor the real-time characteristics of each blade. In general, to ensure safe and efficient operation, the blades should be designed with a twist shape [1,2], which makes the blade outline asymmetric in three-dimensional space. Thus far, researchers have investigated techniques for monitoring the health of turbine blades to determine the dynamic strain characteristics of the blades by measuring one-dimensional characteristic parameters such as blade tip timing signal and radial tip clearance.

Techniques for measuring the blade tip timing (BTT) have witnessed rapid development in recent years. Because the arrival time of each blade depends on the vibration of the turbine, the vibration characteristics can be determined by investigating the timing signal sequence of the blades. Lawson developed a tip timing measurement system using a dual capacitive tip clearance sensor, which can measure both the vibration amplitude and the blade tip timing [3]. However, its accuracy might be affected by the dielectric constant according to the principle of the capacitive sensor. Another practicable option is an optical sensor, which is being increasingly used in blade tip timing measurement systems owing to its good anti-interference performance and high thermo-stability [4–7].

Tip clearance measurement techniques mainly focus on the control strategy for turbomachines such as aero-engines, as the efficiency of the turbine depends on the tip clearance [8]; a large tip clearance may lead to large leakage flows and result in performance degradation of the turbine, while a small tip clearance may cause accidents. The tip clearance in previous studies usually refers to the radial displacement from the casing to the tip of the blade. An optical fiber probe is the most commonly used sensor in radial tip clearance measurement systems. Duan [9] proposed a method for measuring the radial tip clearance of an aero-engine using a two-circle coaxial optical fiber bundle. Subsequently, Iker [10,11] improved upon this method by proposing a more precise measurement system and verified its performance in ground tests of an aero-engine. Jia [12] developed a measurement system based on a two-circle coaxial optical fiber bundle as a part of an active control system for radial tip clearance measurement in aero-engines.

The blade has a twist shape in three-dimensional space so that the actual strain on the blade under various loads has three-dimensional features. Once the deformation of the blade occurs, its tip surface undergoes movement in three-dimensional space. Hence, the deformation information contained in the blade tip timing signal or radial tip clearance is limited; neither of them can describe the strain characteristics precisely. Therefore, the concept of three-dimensional (3D) tip clearance was introduced [13,14], which can indicate the deformation of the tip along the radial direction from the casing to the tip, the axial direction of the rotor, and the circumferential direction of the blisk, thereby reflecting the deformation of the blade. A probe with three two-circle coaxial optical fiber bundles as its sensing units was proposed to determine the variation in the 3D tip clearance characteristics using a non-contact measurement method [15,16], and a demodulation technique was studied to calculate the 3D tip clearance from the output signals of the bundles [17]. The performances of the optical 3D tip clearance probe and demodulation method were verified on a three-dimensional calibration table [16,17].

In this study, a dynamic measurement system based on a 3D tip clearance probe is designed and established for the dynamic measurement of the 3D tip clearance of the rotating blades of a turbine. A dynamic filtering method, blade tip location method, and dynamic demodulation method are studied, and the dynamic measurement performance of the system is tested on a simulated rotor bench.

2. Optical-fiber-based dynamic measurement model for 3D tip clearance

2.1 Space model of 3D tip clearance

3D tip clearance refers to the 3D displacement of the blade tip with regard to the inner surface of the casing. The space model of 3D tip clearance is expressed as (z₀, α, β), where z₀ denotes the radial vector length between the midpoint of the probe and its projective point on the tip, α denotes the axial deviation angle of the surface of the tip along the axial direction of the rotor, and β denotes the circumferential deviation angle along the rotating direction of the blisk, as shown in Fig. 1 [13].

Fig. 1. Space model of 3D tip clearance.

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The strain characteristic can be determined using a certain algorithm after measuring the real-time 3D tip clearance of the blade.

2.2 Sensing principle for 3D tip clearance using two-circle coaxial optical fiber bundle

Assuming that the surface of tip has a large stiffness, its deformation can be regarded as the 3D movements of several local flat surfaces. To determine the value of the 3D tip clearance, which is the 3D displacement of the local flat surface measured by the probe, three two-circle coaxial optical fiber bundles are employed as sensing units to form an isosceles-right-triangle sensing structure of the probe. Owing to the output characteristics, the light intensity on each bundle is coupled with (z₀, α, β). This sensing structure can yield three output signals modulated by (z₀, α, β), as shown in Fig. 2. The three units are optical fiber bundles with identical structures, manufactured parameters, and light resources. Hence, the intensity received by a particular point of the receiving fiber can be calculated through the equivalent calculation of the intensity on its symmetry point P on the virtual plane according to the specular imaging theory [15,16].

Fig. 2. Diagram of optical probe for 3D tip clearance. (a) Measurement principle of 3D tip clearance probe; (b) Cross section of the probe.

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The advantage of the two-circle coaxial optical fiber bundle is that it can eliminate some common-mode interference that exists in all the receiving fibers by division operation of the light intensity on the outer and inner circles of the receiving fiber [12,15,16]. According to the output characteristics of the bundle, the light intensity received by each fiber and the output ratio M of the bundle will be modulated by z₀, α, and β at the same time, which can be expressed as [17]

(1)$$M = f({z_0},\alpha ,\beta ) = \frac{{{I_{out}}({z_0},\alpha ,\beta )}}{{{I_{in}}({z_0},\alpha ,\beta )}}$$

where I_out (z₀, α, β) is the modulation function of the light intensity on the outer circle and I_in (z₀, α, β) is the modulation function of the light intensity on the inner circle.

However, the angles α and β of all the units are identical. Hence, the differences in the received light intensities will be related only to the different radial tip clearances. As shown in Fig. 2(a), z₀, z₁, and z₂ denote the radial displacements of the three bundles (Unit 0, Unit 1, Unit 2), respectively, where z₁ and z₂ can be expressed as a function of (z₀, α, β) as [16,17]

(2)$$\left\{ {\begin{array}{{c}} {{z_1} = {z_0} - dp \cdot \tan \alpha }\\ {{z_2} = {z_0} - dp \cdot \tan \beta } \end{array}} \right.$$

where dp denotes the interval between Unit 0 and Unit 1 and Unit 0 and Unit 2.

2.3 Demodulation principle for 3D tip clearance using signals from three units

It is obvious that the difference in the light intensities among three units contains the change information of (z₀, α, β), which makes it possible to extract (z₀, α, β) from the difference of the output signals of the three units. Owing to the characteristics of the two-circle coaxial optical fiber bundle, the output signals of each unit will be affected by all the three tip clearances at the same time, and demodulation using the coefficients matrix by calibration of a single sensing unit is infeasible [18]. Thus, a demodulation method using the ratios of the difference signal between any two bundles is proposed to calculate the value of the 3D tip clearance in a convergent subinterval briefly determined by the ratios of the three units themselves, based on the Taylor expansion principle [17]. According to a simulation study on the turbine blades [14,19], the variation scope of the 3D tip clearance is as follows: z₀, 1.5–2.5 mm; α, −0.2°–2.2°; β, −0.2°–2.2°. The variation scope can be regarded as consisting of several small subintervals depending on the convergence property of z₀, α, and β of the output function, as shown in Fig. 3.

Fig. 3. Diagram of subinterval in variation scope of 3D tip clearance.

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In a previous study [17], on the basis of the convergence property with respect to the output function, the variation scope could be divided into intervals of 0.05 mm for z₀ and intervals of 0.6° for both α and β. To simplify the demodulation, we hypothesize that the coordinates of the inclination angles α and β at the equivalent expansion points of all the subintervals are combinations of 0.2°, 0.8°, 1.4°, and 2.0°.

Before the demodulation starts, we should first clarify the convergent region to which the (z₀, α, β) being measured belongs, i.e., find the equivalent expansion point (C_z, C_α, C_β) of the predetermined subinterval. A determination method has been proposed [17] by investigating the calibration curves of the output ratio of the two-circle coaxial optical fiber bundle, assuming that the variation scope of the inclination angle of the tip is within 2.5°. This angle is too small to result in an obvious change in the ratio of the bundle at a stationary z₀. The ratios of the three units are denoted by M₀ (Unit 0), M₁ (Unit 1), and M₂ (Unit 2), respectively. Hence, the probable value of C_z can be determined using a fitting function for the calibration curve of M₀ as z₀ increases from 1.5 mm to 2.5 mm under the parallel reflector condition, which is expressed as

(3)$${M_0} = {f_{cal}}({z_0})$$

By assuming its inverse function as f*_cal(M₀), C_z can be obtained as

(4)$${C_z} = f_{_{cal}}^\ast ({M_0})$$

As for the determination of C_α and C_β, it should be noted that α and β are identical for the three units. Hence, the existence of α or β will lead to a difference in z₁ and z₂ compared to z₀. Thus, the determination of C_α and C_β mainly depends on z₁ and z₂. Because we assumed that the three bundles constituting the probe are identical in terms of their structures, materials, and light resources, the bundles should have similar calibration curves. According to the definition and structure of the probe, the difference of M₁ and M₀ will increase with the angle α and vice versa. Owing to the circumferential symmetric characteristics of the bundle, the output characteristics of the bundle at a certain z₀ follow the same trend as α and β. Consider C_α as an example to describe the determination algorithm. Record the output ratios M₀ and M₁ at α = 0.8°, 1.4°, and 2°, and denote their differences by DI_M_0.8, DI_M_1.4, and DI_M_2.0. Suppose that the difference between M₀ and M₁ of the real-time output signal is D_IM₀₁. Hence, we have

(5)$$\left\{ {\begin{array}{{c}} {{D_{IM01}} < D{I_{M0.8}}/2}\\ {D{I_{M0.8}}/2 \le {D_{IM01}} < D{I_{M1.4}} - (D{I_{M1.4}} - D{I_{M0.8}})/2}\\ {D{I_{M1.4}} - (D{I_{M1.4}} - D{I_{M0.8}})/2 \le {D_{IM01}} < D{I_{M2.0}} - (D{I_{M2.0}} - D{I_{M1.4}})/2}\\ {{D_{_{IM01}}} \ge D{I_{M2.0}} - (D{I_{M2.0}} - D{I_{M1.4}})/2} \end{array}\textrm{ }\begin{array}{{c}} {{C_\alpha } = 0.2^\circ }\\ {{C_\alpha } = 0.8^\circ }\\ {{C_\alpha } = 1.4^\circ }\\ {{C_\alpha } = 2.0^\circ } \end{array}} \right.$$

Once the (C_z, C_α, C_β) of the subinterval is determined, the demodulation can be performed. Assume that the output signals of the inner circle of Unit 0, Unit 1, and Unit 2 are V_0in, V_1in, V_2in, respectively, and the signals of the outer circle are V_0out, V_1out, and V_2out, respectively. Thus, the ratios of the differences between Unit 1 and Unit 0, Unit 2 and Unit 0, and Unit 1 and Unit 2 are DM₀₁, DM₀₂, and DM₂₁, respectively, which can be written as

(6)$$\left\{ {\begin{array}{{c}} {D{M_{01}} = \frac{{{V_{0out}} - {V_{1out}}}}{{{V_{0in}} - {V_{1in}}}}}\\ {D{M_{02}} = \frac{{{V_{0out}} - {V_{2out}}}}{{{V_{0in}} - {V_{2in}}}}}\\ {D{M_{21}} = \frac{{{V_{2out}} - {V_{1out}}}}{{{V_{2in}} - {V_{1in}}}}} \end{array}} \right.$$

Based on the hypothesis that the bundles of the three units are identical, the output function of the light intensity in the inner circles of the three bundles is I_in (z₀, α, β) and the output function of the light intensity in the outer circles is I_out (z₀, α, β). Therefore, in the convergent subinterval that includes the (z₀, α, β) to be measured, the relationship between DM₀₁, DM₀₂, DM₂₁, and (z₀, α, β) is expressed as [17]

(7)$$\begin{aligned} {z_0} = &(4{k_{2i}}{D_{out}} - 4{k_{2o}}{D_{in}})[(4{k_{2i}} - 2{k_{3i}})(D{M_{21}} - D{M_{02}})(4{k_{2o}} - 4{k_{2i}}D{M_{01}})\\ & - 2{k_{4i}}(D{M_{21}} - D{M_{01}})\\ &(4{k_{2o}} - 4{k_{2i}}D{M_{02}}) - (4{k_{2o}} - 4{k_{2i}}D{M_{02}})(4{k_{2o}} - 4{k_{2i}}D{M_{21}})]/\{ 4{k_{2i}}[(4{k_{2o}} - 4{k_{2i}}D{M_{01}})\\ &(D{M_{21}} - D{M_{02}})(4{k_{2o}} \cdot 2{k_{3i}} - 2{k_{3o}} \cdot 4{k_{2i}}) + (4{k_{2o}} - 4{k_{2i}}D{M_{01}})(4{k_{2o}} - 4{k_{2i}}D{M_{02}})\\ &(4{k_{2o}} - 4{k_{2i}}D{M_{21}}) + (4{k_{2o}} - 4{k_{2i}}D{M_{02}})(D{M_{21}} - D{M_{01}})(4{k_{2o}} \cdot 2{k_{4i}} - 2{k_{4o}} \cdot 4{k_{2i}})]\} \\ &- {D_{in}}/4{k_{2i}} \end{aligned}$$

(8)$$\begin{aligned} \alpha = &(4{k_{2i}}{D_{out}} - 4{k_{2o}}{D_{in}})(D{M_{21}} - D{M_{02}})(4{k_{2o}} - 4{k_{2i}}D{M_{01}})/[(4{k_{2o}} - 4{k_{2i}}D{M_{01}})\\ &(D{M_{21}} - D{M_{02}})(4{k_{2o}} \cdot 2{k_{3i}} - 2{k_{3o}} \cdot 4{k_{2i}}) + (4{k_{2o}} - 4{k_{2i}}D{M_{01}})(4{k_{2o}} - 4{k_{2i}}D{M_{02}})\\ &(4{k_{2o}} - 4{k_{2i}}D{M_{21}}) + (4{k_{2o}} - 4{k_{2i}}D{M_{02}})(D{M_{21}} - D{M_{01}})(4{k_{2o}} \cdot 2{k_{4i}} - 2{k_{4o}} \cdot 4{k_{2i}})] \end{aligned}$$

(9)$$\begin{aligned} \beta = &(4{k_{2i}}{D_{out}} - 4{k_{2o}}{D_{in}})(D{M_{21}} - D{M_{01}})(4{k_{2o}} - 4{k_{2i}}D{M_{02}})/[(4{k_{2o}} - 4{k_{2i}}D{M_{01}})\\ &(D{M_{21}} - D{M_{02}})(4{k_{2o}} \cdot 2{k_{3i}} - 2{k_{3o}} \cdot 4{k_{2i}}) + (4{k_{2o}} - 4{k_{2i}}D{M_{01}})(4{k_{2o}} - 4{k_{2i}}D{M_{02}})\\ &(4{k_{2o}} - 4{k_{2i}}D{M_{21}}) + (4{k_{2o}} - 4{k_{2i}}D{M_{02}})(D{M_{21}} - D{M_{01}})(4{k_{2o}} \cdot 2{k_{4i}} - 2{k_{4o}} \cdot 4{k_{2i}})] \end{aligned}$$

where k_1o, k_2o, k_3o, and k_4o denote the second-order Taylor expansion coefficients of I_0out (z₀, α, β) corresponding to z₀, z₀², z₀α, and z₀β, respectively. Further, k_1i, k_2i, k_3i, and k_4i denote the second-order Taylor expansion coefficients of I_0in (z₀, α, β) corresponding to z₀, z₀², z₀α, and z₀β, respectively. The constant terms D_out and D_in in Eqs. (7)–(9) are given by [17]

(10)$$\left\{ {\begin{array}{{c}} {{D_{in}} = 2{k_{1i}} - 4{k_{2i}}{C_z} - 2{k_{3i}}{C_\alpha } - 2{k_{4i}}{C_\beta }}\\ {{D_{out}} = 2{k_{1o}} - 4{k_{2o}}{C_z} - 2{k_{3o}}{C_\alpha } - 2{k_{4o}}{C_\beta }} \end{array}} \right.$$

The demodulation equation sets in the convergent subinterval are determined solely by the Taylor expansion of the output function at (C_z, C_α, C_β). Moreover, the arithmetic in the equation is rather simple to fulfill the requirements of the fast demodulation process.

2.4 Establishment of dynamic measurement system for 3D tip clearance

In summary, the fundamental measurement model of 3D tip clearance using the optical probe consisting of three bundles and the demodulation method using the ratios of the difference signals of the three units can be described as shown in Fig. 4. The three units of the probe yield three routes of light intensity signals modulated by (z₀, α, β). The light signals are transmitted to the processing circuits and then processed in the central processor. In the software inside the processor, the output ratios of the three units determine the convergent subinterval of (z₀, α, β) and its (C_z, C_α, C_β). Then, the difference ratios DM₀₁, DM₀₂, and DM₂₁ are substituted as input signals into the equation sets determined by (C_z, C_α, C_β). Thus, the actual value of (z₀, α, β) can be obtained.

Fig. 4. Measurement model of 3D tip clearance.

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3. Design of dynamic optical fiber measurement system for 3D tip clearance

In line with the measurement model presented in Fig. 4, the measurement system should be designed using an appropriate approach to fulfill the requirements of the dynamic rotating blades. Suppose that the verification condition of the rotating speed can reach 10000 r/min. The main challenge in the designation is the dynamic acquisition of the sensing signals of the three units, as the blade tip will pass through the sensing area of the probe at an extremely high speed. In addition, because there are many blades on the blisk, the identification of each blade is critical to the status monitoring of the rotating blades. Accordingly, the framework of the measurement system is shown in Fig. 5. To locate the position of the blade tip, a phase-frequency detector is required to produce periodic signals of the rotor.

Fig. 5. Framework of measurement system for 3D tip clearance.

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3.1 Design of the optical probe for 3D tip clearance

Based on the light intensity coupling analysis of the three units shown in Fig. 2, the embryonic form of the 3D tip clearance probe can be established. Figure 6(a) shows the diagram of the probe, where R denotes the radius of each bundle, φ denotes the diameter of the probe, the illuminating light is supplied by an external optical resource through the input fiber, and the modulated light intensity received by the inner and outer receiving fibers of each bundle will be transmitted to the pre-conditioning circuits for further photoelectric conversion. The surface of the entity is shown in Fig. 6(b), and the manufacturing parameters of the probe are selected by simulation of the coupling effect of the light intensity among the three units as follows: core radius of illuminating and receiving fiber, a₀ = 0.1 mm; interval between two adjacent fibers, d = 0.23 mm; aperture angle of illuminating and receiving fibers, θ_c = arcsin(0.22); and dp = 2 mm. Moreover, the diameter of the three illuminating light spots of the three units on the reflector is calculated as 3.9884 mm using the LD light resource with a wavelength of 820 nm [16,17]; it can cover the blade tip with a width of greater than 5 mm.

Fig. 6. Optical probe for 3D tip clearance. (a) Design diagram of 3D tip clearance probe; (b) Surface of the entity.

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3.2 Design of the hardware processing circuits of the measurement system

The principle of pre-conditioning mainly focuses on how to realize uniformity among photoelectric signals from the three units. Hence, the light resource is adopted as a constant current source circuit, which can offer three routes of stable illuminating light. Most parts of the circuits have been described in [16,17,20]. The photoelectric conversion chip employed is OPT101. It has a responsivity of 0.6 A/W (0.6 V/µW) at a wavelength 820 nm of the LD light resource. Note that the photoelectric conversion part is affected by the rotating speed. In consideration of the rising and falling edges of actual signals, the efficient range of the signal is limited, as shown in Fig. 7(a). Here, T_p is the time interval of two adjacent blades, T_b is the passing time of the blade tip, and t_r and t_p are the durations of the rising and falling edges of the photoelectric conversion signal, respectively. Therefore, the smaller the proportion of t_r in the T_b, the higher is the availability of the sensing signal.

Fig. 7. Photoelectric conversion and amplifier module. (a) Diagram of photoelectric conversion signal; (b) Structure of photoelectric conversion circuit.

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According to the highest speed of the rotating blade, i.e., 10000 r/min, and assuming that the number of blades on the blisk is 40 (turbine in aero-engine), T_b will be 75 µs. The chip OPT101 itself has a dynamic response time of t_r = 24.2 µs, which cannot meet the requirement of dynamic measurement on the signals. However, it can be reduced to 7 µs to fulfill the requirement of an aero-engine turbine blade with a rotating speed 10000 r/min by using suitable external amplifier circuits as shown in Fig. 7(b).

The data acquisition device used in the system is the NI-6210 data acquisition card. It has 16 channels for analog input signals with a sampling rate of 250 k/s. It can acquire 6 routes of signals and the phase-frequency will occupy a total of 7 channels; thus, the sampling rate of each channel is 35 k/s. In addition, the input voltage range is −10 V to + 10 V, and the sampling accuracy can reach 0.3 mV. In summary, the NI-6210 data acquisition card is appropriate for the dynamic data acquisition of the system. The hardware circuits are shown in Fig. 8 [17].

Fig. 8. Hardware circuits of the measurement system.

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3.3 Design of the measurement software in the processor

The measurement software is established on the basis of LabVIEW to provide a visual interface for the user to debug the system. The sketch map of the software is shown in Fig. 9.

Fig. 9. Sketch map of the measurement software.

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After the analog signals have been converted into digital signals, the rest of the processing is performed by the software in the processor. The software consists of five modules for collecting the output signals from the three units of the probe in time and performing rapid demodulation of the signals: data acquisition module, calibration module, dynamic signal processing module, demodulation module, and display module. The specific design methods of each module are as follows:

1) Data acquisition module

Owing to the high rotating speed of the blade, a high sampling speed and a large number of sampling points are required to obtain the effective sensing signals of the blade tip, while the demodulation may lead to a delay because of the pre-determination and calculation process. Hence, the acquisition module should have sufficient storage space to retain all the sampling data. Accordingly, the acquisition module has been designed with DAQmx in LabVIEW, based on the producer/consumer design pattern.

2) Calibration module

As the basis for demodulation, the coefficients of the demodulation equations in each subinterval should be obtained before the measurement. The method for obtaining equivalent Taylor expansion coefficients at the specific (C_z, C_α, C_β) using calibration data has been described in [17]. Integrated with the requirement of the pre-determination part described above, the structural array with modality is built as

\{ {z_0},\;\alpha ,\;\beta ,\;{V_{0out}},\;{V_{1out}},\;{V_{2out}},\;{V_{0in}},\;{V_{1in}},\;{V_{2in}},\;{M_0},\;{M_1},\;{M_2},\;D{I_{M01}},\;D{I_{M02}}\}

The calibration should record the signals V_0out, V_1out, V_2out, V_0in, V_1in, V_2in, M₀, M₁, M₂, DI_M₀₁, and DI_M₀₂ at each 3D point in the measurement scope. Then, they are stored in an array in the calibration data storage. The calibration can be realized using a calibration table with three degrees of freedom, described in [16,17]. Furthermore, according to the previous study [17], the calculation of equivalent Taylor expansion coefficients at (C_z, C_α, C_β) requires three sets of data at (C_z, C_α, C_β), (C_z, C_α-0.1°, C_β), and (C_z, C_α, C_β-0.1°), respectively. Thus, the software will select the three points through a search statement with regard to target (C_z, C_α, C_β) and every (z₀, α, β) of the structure in the calibration structural array. The following signals are extracted for further calculation. This procedure is performed in LabVIEW. The results should be stored in the coefficients structural array as

\{ {z_0},\;\alpha ,\;\beta ,\;{k_{1o}},\;{k_{2o}},\;{k_{3o}},\;{k_{4o}},\;{k_{1i}},\;{k_{2i}},\;{k_{3i}},\;{k_{4i}}\}

In addition, the fitting function of M₀ with regard to z₀ under the parallel reflector is obtained in this module using the calibration data of the parallel reflector with increasing z₀, and the threshold of DI_M_0.8, DI_M_1.4, and DI_M_2.0 to determine C_α and C_β is calibrated as well. All the calculations are performed in LabVIEW.

3) Dynamic signal processing module

The most difficult software step is to select effective sensing signals of the three units at the position when the blade tip is just passing the sensing area of the probe. First, the signals should be filtered. The normal high-pass and low-pass filtering method is no longer practical owing to the wide range of speed change. However, the sensing signals when the blade is tip passing through the probe have similar patterns, i.e., no significant output can be detected while there is no blade below the probe. Hence, the time synchronous averaging method has been introduced to solve the filtering issue [21]. Assuming that the sampling sequence of sensing signals is x(n), n = 0, 1, 2,…, N₁ with time interval Δt and the variation period of the signals is T, the principle of the time synchronous averaging method can be expressed as

(11)$$y(n) = \frac{1}{N}\sum\limits_{k = 0}^{N - 1} {x(n - {m_k})\;,\;n = {N_1} - M + 1,{N_1} - M + 2, \ldots ,} {N_1}$$

where y(n) is the new sequence produced by the time synchronous averaging method with length M, M is obtained through rounding of T/Δt, m_k is the result of rounding kT/Δt, and N is the number of sequence segments to be averaged. The period sequence of x(n) is intercepted by the output of the phase discriminator sensor installed above the rotor.

This procedure will start as the 6 routes of sensing signals enter. To locate the position of the tip in the light of the output signals from the three units, the first-order difference method is adopted immediately after the filtering part. In other words, the filtering signal sequence undergoes a further first-order difference operation. The principle of the first-order difference method is shown in Fig. 10.

Fig. 10. Diagram of the first-order difference method.

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The objective of the first-order difference method is to obtain the moment of the rising and falling edges of a pulse when a single blade passes through. Thus, the position of the blade tip can be confirmed by calculating the middle moment between the rising and falling edges, as indicated by the red point in Fig. 10, and the sensing signal at this particular point is the effective signal needed for further demodulation. Note that the filtered signals may require further morphological filtering to avoid the error produced by the sharp point in the sensing signals in the first-order difference operation.

The function of the phase-frequency signal is to set a starting position of a period, through which the sequence of the blades can be deduced by counting the pulses behind the phase-frequency pulse.

4) Demodulation module

Based on the demodulation model in Fig. 4, the sensing signals output from the dynamic signal processing module will first be applied to the input signals with a specific form in the structure as

\{ {M_0},\;D{I_{M01}},\;D{I_{M02}},\;D{M_{01}},\;D{M_{02}},\;D{M_{21}}\}

As described above, M₀ and DI_M₀₁, DI_M₀₂ will be the input signals of the pre-determination part to determine the equivalent expansion point (C_z, C_α, C_β) in the subinterval to which (z₀, α, β) belongs. Once the (C_z, C_α, C_β) is determined, the equivalent Taylor expansion coefficients k_1o, k_2o, k_3o, k_4o, k_1i, k_2i, k_3i, and k_4i can be selected using a search statement in the coefficients structural array. Hence, the coefficients of the demodulation equations (refer to Eqs. (7)–(9)) in the subinterval are all known.

With the definite demodulation equations, the ratio signals DM₀₁, DM₀₂, and DM₂₁ of the difference in the light intensity between any two units will be obtained as the input signals for accurate demodulation in the pre-determined subinterval of the sensing signals. The flowchart of the demodulation module is shown in Fig. 11.

Fig. 11. Flowchart of the demodulation module.

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5) Display module

The interface of the 3D tip clearance measurement software is designed using LabVIEW, where the calibration data and the demodulation results can be displayed, and the users can assign the specific parameters required for the dynamic sampling.

3.4 Entity of measurement system for 3D tip clearance

According to the design of the optical probe, hardware circuits, and measurement software, the dynamic measurement system for 3D tip clearance is established as shown in Fig. 12.

Fig. 12. Dynamic measurement system for 3D tip clearance.

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As shown in Fig. 12, the dynamic measurement system for 3D tip clearance consists of an optical fiber probe, a pre-conditioning circuit box, a data acquisition card, and measurement software. The illuminating and receiving fiber cables extending from the probe are encapsulated in metal armored tubes, and the cables can be made to order at any length. The probe can be installed independently with subsequent circuits to eliminate noise. All the photoelectric processing circuits are integrated and packaged in the pre-conditioning circuit box to isolate them from interference due to light and electromagnetic waves from the environment. The box has two additional photoelectric conversion ports to allow connection with a phase-frequency detector (using an optical fiber sensor). The analog signals from the pre-conditioning circuits will be transmitted the data acquisition card and then output to the processor through the USB interface in the form of digital signals. Then, the measurement will be accomplished in the software.

The measurement software designed in this study can realize the functions of data acquisition, calibration, signal debugging, and signal demodulation. The interface of data acquisition and calibration is shown in Fig. 13. The real-time signals of V_0out, V_1out, V_2out, V_0in, V_1in, V_2in, M₀, M₁, and M₂ can be seen from the interface with regard to (z₀, α, β). The left side of the panel shows the variation curves of M₀ depending on z₀, α, and β, respectively. In the calibration, when we set the current value of (z₀, α, β) and press the button “Record”, the data obtained by the probe will be displayed on the right side of the panel. The calibration data file can be saved in the “.csv” or “.xls” format for further calculation of the demodulation coefficients.

Fig. 13. Panel of data acquisition and calibration.

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The interface of dynamic signal processing is designed as shown in Fig. 14. Using the left side of the interface, the user can set the sampling rate and sampling number required in the dynamic data acquisition. The right side of the panel displays the signals of V_out, V_in, and M of each unit (represented by different colors). In addition, the information of the blade location can be obtained. Further, the interpolation parameters and peak/trough amplitude threshold can be adjusted to conduct the time synchronous averaging operation and to reduce misjudgment of the location of the blade based on the differential signals of the probe. The results of location of the blades will be displayed.

Fig. 14. Panel of dynamic signal processing.

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As for the demodulation interface, because the pre-determination of (C_z, C_α, C_β) and extraction of coefficients in the demodulation equations will be performed by MATLAB script in LabVIEW, the panel displays only the demodulation results from the signals processed previously, as shown in Fig. 15.

Fig. 15. Panel of demodulation for 3D tip clearance.

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4. Dynamic measurement for 3D tip clearance of simulated rotating blade

In the previous article, the static performance of the 3D tip clearance probe (with core radius a₀ = 0.1 mm) was studied on the basis of a 3D static calibration table [17]. The demodulation accuracy using the ratio of difference signals between two units is strongly dependent on the convergence property of the pre-determined subinterval, while the equivalent Taylor expansion coefficients are calculated on the basis of calibration data from Unit 0, Unit 1, and Unit 2 at three points separated by a short distance. Thus, the degree of inclination of the reflector affects the demodulation accuracy, as a larger inclination causes a larger difference among z₀, z₁, and z₂. For these reasons, the study focuses on the demodulation results of the reflector with three different degrees of inclination to indicate the static performance of the measurement system. The largest demodulation error of z₀ using the 3D tip clearance probe with a₀ = 0.1 mm is around 0.2 mm owing to the manufacturing error among the three bundles in the probe, and the largest demodulation error of α and β is 0.13° (caused by manufacturing error of the center alignment). In other cases, the demodulation error of α and β may be less than 0.05°. Owing to the limited adjustment accuracy of the calibration table, the minimum variation angle of α or β is 0.1°, and it can be deduced that the actual resolution ratio of the probe is less than 0.1° [17].

To observe the dynamic performance of the proposed measurement system for 3D tip clearance, a simulated rotor test bench is set up, as shown in Fig. 16.

Fig. 16. Framework of simulated rotor test bench.

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The simulated blisk is mounted on the rotor through the center of the casing as shown in Fig. 16, while the probe is installed at the top of the casing and it faces the rotor along the radial direction of the blisk. The 90SY56-G DC speed regulating motor is employed to supply the variation range of the rotating speed from 0 r/min to 10000 r/min. All the components of the motor and rotor are connected by flexible coupling. To facilitate the dynamic experiment, the simulated blades on the blisk are manufactured with a reduced shape, as shown in Fig. 17.

Fig. 17. Diagram of simulated blisk and blades.

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The blades are mounted on the surface of the blisk at angle of 45° with a length of 50 mm along their radial direction. The thickness of a single blade is 5 mm, the diameter of the blisk (including the blades) is 140 mm, and the internal diameter of the casing is 146 mm. Thus, the initial radial tip clearance is 3 mm. We establish the dynamic measurement system based on the simulated rotor test bench as shown in Fig. 18.

Fig. 18. Dynamic measurement system for 3D tip clearance.

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In the test run process of the rotor, abnormal noise appears when the speed increases over 7000 r/min. Hence, for safety, the highest rotating speed is 6000 r/min. The signals of the three units are observed at speeds of 1000 r/min, 2000 r/min, 3000 r/min, 4000 r/min, 5000 r/min, and 6000 r/min, and the sampling rates are set to 5000, 10000, 15000, 20000, 25000, and 30000, respectively. The sampling points are set to 5000. Figure 19 shows the voltage signals received by the outer and inner circles of the receiving fibers with regard to Unit 0, Unit 1, and Unit 2. In a rotating period, each signal sequence is filtered.

Fig. 19. Dynamic sensing signals from three units.

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As shown in Fig. 19, a pulse is generated when each blade passes through the probe. But because of the small measuring range of optical sensor, the receiving light intensity is almost zero when the blade tip isn’t under the probe, resulting the voltage is zero. On the other hand, the measurement results will be affected by several factors. Intensity-modulated fiber optic sensor is used in this study, so the fluctuation in light resource intensity is a major factor which will affect measurement results of 3D tip clearance directly, hence, constant current source circuit is design to reduce the fluctuation [16,17,20]. In addition, random noises in the dynamic measurement system also have effect on the measurement results, hence, the time synchronous averaging method is introduced to suppress the random noises.

We picked a segment of the signals when the blade passes through the probe at 1000 r/min, as shown in Fig. 20, and the effective moment on the blade tip is marked by a black dotted line. The blade tip location is confirmed using the differential signals of the output from Unit 0.

Fig. 20. Sensing signals from three units within a blade. (a) V_in; (b) V_out.

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Using the signals shown above to demodulate (z₀, α, β), the results are depicted in Figs. 21(a)–(c), corresponding to the measurement results of z₀, α, and β as a function of the speed from 1000 r/min to 6000 r/min.

Figure 21(a) indicates that the variation trends of z₀ show a decreasing trend except blade 1 and blade 3. On one hand, we can see from Figs. 17 and 18 that the rotor axis is much longer than the length of blade; in such cases, the vibration amplitude of the axis increases with the rotating speed; hence, the radial tip clearance z₀ of each blade decreases. On the other hand, with the increasing of the rotating speed, the centrifugal load on the blade also increases, resulting in the radial elongation of the blade. Therefore, the radial tip clearance z₀ of the blade decreases with the increasing of the rotating speed. The measurement result can be regarded as consistent with reality. The discrepancy in the case of blade 1 and blade 3 is probably due to the manufacturing error of the two blades when welding them onto the blisk. Thus, an offset from the relative position between the probe and the blade tip might appear, which may lead to a deviation of the relative position from the center of Unit 0, and a demodulation error will be produced during the calculation with DM₀₁, DM₀₂, and DM₂₁ based on the right-triangle structure.

Fig. 21. Dynamic measurement results of 3D tip clearance of simulated blades.

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The variation curves of α at different rotating speeds shown in Fig. 21(b) are much smoother and steadier, except for blade 1 and blade 2. The blades are only subjected to centrifugal load caused by rotating speed, and no aerodynamic load is applied to the blades. Besides, the solid blades are manufactured with high rigidity, thus, the axial deformation of the blade will be extremely small with the increasing of the rotating speed. The simulated rotor is manufactured by welding the blades on the blisk manually, thus, the installation angle of each blade is slightly different, resulting in the difference of axial deflection angle α among different blades. The manufacturing error will also lead to different vibration amplitude for each blade under various rotating speed. This effect is much more obvious on blade 1 and blade 2, which cause the axial deviation angle α of the two blades various with rotating speed.

As for the variation characteristics of β at different rotating speeds shown in Fig. 21(c), the oscillation characteristics are more prominent than those of z₀ and α. As we mentioned before, the rotor blades are welded on the blisk manually, so it’s inevitable for the rotor to be imbalanced. With the increasing of rotating speed, the vibration of rotor becomes more obvious especially in circumferential direction. The bearing house and coupling of test bench limit the axial displacement of the rotor, so the axial vibration is relatively small compared with circumferential vibration. Thus, the oscillation of circumferential deviation angle β is much obvious than that of axial deviation angle α with increasing rotating speed.

From the variation characteristics of (z₀, α, β) in Fig. 21, we can deduce that the vibration of the simulated rotor and blisk will lead to movements in the radial and circumferential directions of the blade, as indicated, which means that the measurement results of the 3D tip clearance of the simulated blade are feasible.

The dynamic calibration table for 3D tip clearance is not available owing to its space model characteristics. In addition, the true value of 3D tip clearance is unknown when the rotor is running, so the standard deviation is used to evaluate the repeatability of dynamic measurement instead of errors. Therefore, repeated experiments are performed to describe the dynamic reliability of the measurement system [22]. The evaluation index of the repeated experiments commonly used is the standard deviation, deduced by the mean shift method. Suppose that the experiments are repeated N times under similar conditions. The sample data measured are

{Y_{(x)}} = \{ {y_{1(x)}},{y_{2(x)}}, \ldots ,{y_{N(x)}}\}

Create a translation over y(x) related to the average of samples ${\bar{y}_i}$; then, from a new set of sample data Y_i(x), the standard deviation σ can be expressed as

(12)$$\sigma = \sqrt {\frac{1}{{N\textrm{ - }1}}\sum\nolimits_{i = 1}^N {{{[{{\bar{Y}}_{i(x)}} - {Y_{i(x)}}]}^{_2}}} }$$

In addition, to investigate the dispersion of the measurement results of (z₀, α, β), the index type A uncertainty u is introduced to indicate the half width of confidence interval based on the measurement results, and it can be written as:

(13)$$u = \frac{\sigma }{{\sqrt N }} = \frac{{\sqrt {\frac{1}{{N\textrm{ - }1}}\sum\nolimits_{i = 1}^N {{{[{{\bar{Y}}_{i(x)}} - {Y_{i(x)}}]}^{_2}}} } }}{{\sqrt N }}$$

The experiments were repeated 10 times under rotating speeds of 2000 r/min, 4000 r/min, and 6000 r/min. The corresponding values of $\overline {{z_0}} $, σ, and u related to (z₀, α, β) are summarized in Tables 1–3.

Table 1. Evaluation index of repeated experiments with regard to z₀

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Table 2. Evaluation index of repeated experiments with regard to α

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Table 3. Evaluation index of repeated experiments with regard to β

View Table | View all tables in this article

From the results presented above, we find that the maximum σ of z₀ is 0.0471 mm for blade 1, at 6000 r/min, and its uncertainty u reaches 0.011 mm. The maximum σ of α with a value of 0.2094° appears in the case of blade 3, at 6000 r/min, and its uncertainty u reaches 0.0662°. Finally, the maximum σ of β with a value of 0.3657° appears in the case of blade 3, at 6000 r/min, and its uncertainty u reaches 0.1156°. The remaining results are basically correlated with the dynamic measurement requirements.

From our previous research [17], the largest demodulation error of the 3D tip clearance is 0.005mm, 0.02°, and 0.02°, respectively, based on simulation results. The demodulation errors of the 3D tip clearance based on experimental results are higher than those obtained from simulations results, because different noises exit in the dynamic measurement system. In most cases, the demodulation errors of 3D tip clearance meet the basic requirement of dynamic measurement. But in a few cases, the largest demodulation error of β reaches 0.136° [17], which is unacceptable to dynamic measurement. Therefore, an optical fiber probe with higher manufacturing precision and a processing circuit with better stability are needed in future research.

In order to check the correctness of dynamic measurement results of 3D tip clearance, a comparison with other measurement methods should have been presented. However, it’s really difficult to measure the 3D tip clearance with other sensors, such as eddy current sensor and capacitive sensor, because at least three sensors are required but the area of blade tip in our test bench is too small for three probes arranged in isosceles right triangle. On the other hand, from the current published literature, other scholars and research teams mainly focus on the measurement of traditional radial tip clearance. Therefore, the comparison with other measurement methods may be further studied in the future.

Overall, the dynamic measurement performance on the simulated blades was not desirable with regard to blade 1 and blade 3. The measurement error mainly arose from the manufacturing deviation of the blades on the blisk. However, for the other blades, the dynamic measurement results showed better values. Therefore, the proposed dynamic measurement system for 3D tip clearance can be considered to fulfill the measurement requirements, and the established measurement model for 3D tip clearance is feasible according to the experimental results. However, to achieve high demodulation accuracy of z₀, α, and β in dynamic measurement applications under a variety of environmental conditions, the processing circuits and the blade location algorithm should be optimized and adjusted to meet special requirements. Further, the manufacturing accuracy of the three bundles in the probe should be improved to reduce the demodulation errors.

5. Conclusion

This paper proposed a dynamic measurement model for 3D tip clearance using an optical fiber probe based on a sensing structure of three identical two-circle coaxial optical fiber bundles in a isosceles-right-triangle layout, along with a demodulation method using the ratios of the difference signals between any two bundles based on the Taylor expansion principle. The measurement system comprising the optical probe, pre-conditioning circuits, and measurement software was designed and established, and it could realize data acquisition and demodulation at the right moment when the blade tip passes through the sensing area of the probe in a wide speed range of 0–10000 r/min. To evaluate the performance of the system, a simulated rotor test bench was set up and repeated dynamic experiments were performed on simulated blades.

The experimental results showed that the dynamic measurement system performs well in most cases, except when the simulated blades have manufacturing deviations. The results also confirmed the feasibility of the proposed dynamic measurement model for 3D tip clearance. Nevertheless, in the future, the measurement can be further improved through intensive study of the pre-conditioning circuits and measurement software.

Funding

National Natural Science Foundation of China (51575436).

Acknowledgments

We wish to thank Mr. Bing Wu for his contribution to the system design.

References

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16. S. Y. Xie, X. D. Zhang, B. Wu, and Y. W. Xiong, “Output characteristics of two-circle coaxial optical fiber bundle with regard to three-dimensional tip clearance,” Opt. Express 26(19), 25244–25256 (2018). [CrossRef]

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Speed (r/min)	Index	Blade 1	Blade 2	Blade 3	Blade 4	Blade 5	Blade 6
	$\bar{z_{0}}$ (mm)	2.0704	2.2273	2.3517	2.3856	2.2022	2.1408
2000	σ_z (mm)	0.0347	0.0041	0.0119	0.0078	0.0023	0.0096
	u_z (mm)	0.0110	0.0013	0.0038	0.0025	0.0007	0.0030
	$\bar{z_{0}}$ (mm)	2.0959	2.1861	2.2792	2.2467	2.1456	2.1177
4000	σ_z (mm)	0.0415	0.0092	0.0272	0.0057	0.0045	0.0125
	u_z (mm)	0.0131	0.0029	0.0086	0.0018	0.0014	0.0040
	$\bar{z_{0}}$ (mm)	2.0581	2.1592	2.2053	2.1937	2.0889	2.0132
6000	σ_z (mm)	0.0471	0.0107	0.0156	0.0069	0.0116	0.0132
	u_z (mm)	0.0149	0.0034	0.0049	0.0022	0.0037	0.0042

Speed (r/min)	Index	Blade 1	Blade 2	Blade 3	Blade 4	Blade 5	Blade 6
	$\bar{α}$ (°)	0.1035	1.4783	3.3722	−2.8563	−2.7910	−0.8655
2000	σ_α (°)	0.0233	0.0262	0.1189	0.0989	0.0115	0.0278
	u_α (°)	0.0074	0.0083	0.0376	0.0313	0.0036	0.0088
	$\bar{α}$ (°)	−1.0253	−1.2322	3.1941	−3.0711	−2.7056	−1.1310
4000	σ_α (°)	0.0357	0.0171	0.1209	0.1498	0.0072	0.0315
	u_α (°)	0.0113	0.0054	0.0382	0.0474	0.0023	0.0100
	$\bar{α}$ (°)	−1.7562	−1.5241	2.9831	−3.1052	−2.5136	−0.8322
6000	σ_α (°)	0.0587	0.0267	0.2094	0.1534	0.0149	0.0318
	u_α (°)	0.0186	0.0084	0.0662	0.0485	0.0047	0.0101

Speed (r/min)	Index	Blade 1	Blade 2	Blade 3	Blade 4	Blade 5	Blade 6
	$\bar{β}$ (°)	−1.5324	−1.2449	−0.8789	−1.7795	−2.0351	−0.9973
2000	σ_β (°)	0.2489	0.09932	0.1792	0.0742	0.0512	0.0358
	u_β (°)	0.0787	0.0314	0.0567	0.0235	0.0162	0.0113
	$\bar{β}$ (°)	−2.7941	−1.6762	−1.5329	−1.9319	−2.1729	−0.5689
4000	σ_β (°)	0.3324	0.1022	0.0981	0.1053	0.0927	0.0577
	u_β (°)	0.1051	0.0323	0.0310	0.0333	0.0293	0.0182
	$\bar{β}$ (°)	−2.0785	−1.3746	−1.2732	−1.5229	−2.2352	−0.6707
6000	σ_β (°)	0.3657	0.08713	0.2805	0.1165	0.0632	0.1816
	u_β (°)	0.1156	0.0276	0.0887	0.0368	0.0200	0.0574

Speed (r/min)	Index	Blade 1	Blade 2	Blade 3	Blade 4	Blade 5	Blade 6
	$\bar{z_{0}}$ (mm)	2.0704	2.2273	2.3517	2.3856	2.2022	2.1408
2000	σ_z (mm)	0.0347	0.0041	0.0119	0.0078	0.0023	0.0096
	u_z (mm)	0.0110	0.0013	0.0038	0.0025	0.0007	0.0030
	$\bar{z_{0}}$ (mm)	2.0959	2.1861	2.2792	2.2467	2.1456	2.1177
4000	σ_z (mm)	0.0415	0.0092	0.0272	0.0057	0.0045	0.0125
	u_z (mm)	0.0131	0.0029	0.0086	0.0018	0.0014	0.0040
	$\bar{z_{0}}$ (mm)	2.0581	2.1592	2.2053	2.1937	2.0889	2.0132
6000	σ_z (mm)	0.0471	0.0107	0.0156	0.0069	0.0116	0.0132
	u_z (mm)	0.0149	0.0034	0.0049	0.0022	0.0037	0.0042

Speed (r/min)	Index	Blade 1	Blade 2	Blade 3	Blade 4	Blade 5	Blade 6
	$\bar{α}$ (°)	0.1035	1.4783	3.3722	−2.8563	−2.7910	−0.8655
2000	σ_α (°)	0.0233	0.0262	0.1189	0.0989	0.0115	0.0278
	u_α (°)	0.0074	0.0083	0.0376	0.0313	0.0036	0.0088
	$\bar{α}$ (°)	−1.0253	−1.2322	3.1941	−3.0711	−2.7056	−1.1310
4000	σ_α (°)	0.0357	0.0171	0.1209	0.1498	0.0072	0.0315
	u_α (°)	0.0113	0.0054	0.0382	0.0474	0.0023	0.0100
	$\bar{α}$ (°)	−1.7562	−1.5241	2.9831	−3.1052	−2.5136	−0.8322
6000	σ_α (°)	0.0587	0.0267	0.2094	0.1534	0.0149	0.0318
	u_α (°)	0.0186	0.0084	0.0662	0.0485	0.0047	0.0101

Optical-fiber-based dynamic measurement system for 3D tip clearance of rotating blades

Abstract

1. Introduction

2. Optical-fiber-based dynamic measurement model for 3D tip clearance

2.1 Space model of 3D tip clearance

2.2 Sensing principle for 3D tip clearance using two-circle coaxial optical fiber bundle

2.3 Demodulation principle for 3D tip clearance using signals from three units

2.4 Establishment of dynamic measurement system for 3D tip clearance

3. Design of dynamic optical fiber measurement system for 3D tip clearance

3.1 Design of the optical probe for 3D tip clearance

3.2 Design of the hardware processing circuits of the measurement system

3.3 Design of the measurement software in the processor

3.4 Entity of measurement system for 3D tip clearance

4. Dynamic measurement for 3D tip clearance of simulated rotating blade

5. Conclusion

Funding

Acknowledgments

References

Cited By

Figures (21)

Tables (3)

Equations (17)

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