Blade tip clearance measurement of the turbine engines based on a multi-mode fiber coupled laser ranging system Haotian Guo, Fajie Duan, Guoxiu Wu, and Jilong Zhang Citation: Review of Scientific Instruments 85, 115105 (2014); doi: 10.1063/1.4901601 View online: http://dx.doi.org/10.1063/1.4901601 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Progress toward luminescence-based VAATE turbine blade and vane temperature measurement AIP Conf. Proc. 1552, 903 (2013); 10.1063/1.4819664 Design of advanced automatic inspection system for turbine blade FPI analysis AIP Conf. Proc. 1511, 612 (2013); 10.1063/1.4789103 Modeling turbine blade crack detection in sonic IR imaging with a method of creating flat crack surface in finite element analysis AIP Conf. Proc. 1430, 527 (2012); 10.1063/1.4716272 Crack detection in high-pressure turbine blades with flying spot active thermography in the SWIR range AIP Conf. Proc. 1430, 515 (2012); 10.1063/1.4716270 MULTI‐MODE EXCITATION SYSTEM FOR THERMOSONIC TESTING OF TURBINE BLADES AIP Conf. Proc. 975, 520 (2008); 10.1063/1.2902705
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 115105 (2014)
Blade tip clearance measurement of the turbine engines based on a multi-mode fiber coupled laser ranging system Haotian Guo, Fajie Duan, Guoxiu Wu, and Jilong Zhang State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
(Received 10 September 2014; accepted 3 November 2014; published online 14 November 2014) The blade tip clearance is a parameter of great importance to guarantee the efficiency and safety of the turbine engines. In this article, a laser ranging system designed for blade tip clearance measurement is presented. Multi-mode fiber is utilized for optical transmission to guarantee that enough optical power is received by the sensor probe. The model of the tiny sensor probe is presented. The error brought by the optical path difference of different modes of the fiber is estimated and the length of the fiber is limited to reduce this error. The measurement range in which the optical power received by the probe remains essentially unchanged is analyzed. Calibration experiments and dynamic experiments are conducted. The results of the calibration experiments indicate that the resolution of the system is about 0.02 mm and the range of the system is about 9 mm. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901601] I. INTRODUCTION
Blade tip clearance is the distance between the tip of a rotating blade and the casing which is a parameter of great importance to guarantee the efficiency and safety of the turbine engines.1, 2 The efficiency and fuel consumption of turbine engines are improved dramatically by minimizing the tip clearance in order to reduce leakage flows, while it has to be assured that the blade will not touch the casing in any case to prevent fatal damage.3 The tip clearance varies due to mechanical loads, varying pressure conditions inside the turbine or the differing expansions and contractions of the blades and case over temperature during operation. An accurate online tip clearance measurement is therefore indispensable for optimized and safe operation, especially for the closed-loop active clearance control (ACC) system.4 The blade tip clearance is difficult to acquire in real-time for the following reasons: (1) the environmental temperature of the sensor probe exceeds 2000 ◦ F, (2) the size of the probe is limited, (3) the data acquisition process of a single measurement is limited within several microseconds because of the high velocity of the blade tip along the circumference, (4) a rather high resolution of 0.025 mm is required in a measurement range of several millimeters.5 The eddy current sensors, capacitive probes, and microwave radars are applied for real-time measurement of the blade tip clearance, because they are small, robust, and low cost.6–8 However, these methods will introduce a spatial filtering effect which makes the measurement results sensitive to the geometry of the blade tips.5 Optical sensors can overcome this drawback. Several different optical measurement principles, e.g., laser Doppler position sensor,9 reflective intensity modulation,10 or optical coherence tomography (OCT) measurements11 have been employed for tip clearance measurements. The resolution of the laser Doppler position probe is high, but the complex sensor probe limits the application of this system. The resolution of the reflective intensity modulation based sensor probe is low due to the modal noise at the endface of the transmitting fiber 0034-6748/2014/85(11)/115105/5/$30.00
when multi-mode fiber is utilized, and it takes a minute for data acquisition to reduce the impact of the speckle noise.12 The measurement rate of the OCT method is limited by the speed of mechanical scanning. Therefore, the conventional optical tip clearance sensors do not fully satisfy the requirement of future ACC systems. The laser ranging system based on phase shifting method is used in various applications for it is a non-contact measurement method and can withstand harsh operating environments. It is reported that this method can provide a system resolution of about 10 μm which is high enough for the blade tip clearance measurement.13 In this article, a laser ranging system for blade tip clearance measurement is introduced. A fiber coupled sensor probe isolates the optical receiver from the harsh environment inside the turbine engine. Multi-mode fiber is utilized to collect the light reflected by the blade, so the signal to noise ratio (SNR) is acceptable for high precision tip clearance measurement. The error brought by the multimode fiber is estimated. The measurement range in which the optical power received by the probe remains essentially unchanged is analyzed. Experiments are conducted using the system for clearance measurement.
II. SYSTEM STRUCTURE
The measurement principle of the laser ranging system is based on phase shifting method.14 The intensity of the laser beam is modulated by a sinusoidal signal. The phase of the reflected light from the target which is related to the location of the target is measured and compared to a reference signal for distance measurement. As shown in Fig. 1, the modulated laser is coupled into a fiber splitter. One output of the splitter transmits the optical power to the sensor probe for the tip clearance measurement as the measurement channel. The fiber collection of the measurement channel is illustrated in Sec. III of the article. The sensor probe sends the light to the blade tip and collects the
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FIG. 1. System structure.
light reflected. Avalanche photo diodes (APDs) are utilized for photoelectric conversion. The light from the sensor probe is received by APD1 and then amplified, downconverted, and sampled with an analog to digital converter (ADC). The other output of the splitter is used as the reference channel. The transmitting fiber of the reference channel from the splitter is directly coupled to the APD2 and the optical path difference and circumstance of this fiber are similar to the measurement channel. The signal received by APD2 is amplified, downconverted, and sampled synchronously. The sensor probe is fixed on the casing of the rotating machine. The ADC begins to sample the signals when the probe detects the arriving of the blade. The blade tip clearance is acquired by calculating the phase difference of the two channels. All-phase fast Fourier transformation is applied for phase detection.15 The arrival time of the blade can also be acquired at the same time which is utilized for blade vibration measurement.16 III. STRUCTURE OF THE SENSOR PROBE
The sensor probe is a key part of the system. The probe will work under high temperature condition and isolate the APD from the harsh environment. It should collect sufficient optical power reflected from the blade in the full measurement range to guarantee the SNR and the precision of the system. As in Fig. 2, the sensor probe consists of the fiber from the splitter (hereafter referred to as the input fiber), a lens, and a receiving fiber. The fiber ends of the input fiber and receiving fiber are fixed at the focal plane of the lens and symmetric about the axis of the lens. The lens collimates the divergent beam output of the fiber and directs it to the blade tip. The reflected light is collected by the same lens and coupled to the receiving fiber. A step-index multi-mode fiber is applied as the receiving fiber for the small diameter of the single-mode fiber makes it
FIG. 2. Structure of the sensor probe.
Rev. Sci. Instrum. 85, 115105 (2014)
difficult to couple the reflected light. The SNR is not acceptable when single-mode fiber is applied. As different modes of the multi-mode fiber have different optical paths, when different modes are excited there will be an extra phase shifting for the modulated light, which will bring a significant measurement error. As illustrated in literature,17 the group velocity of a mode in the multi-mode fiber is presented as Eq. (1) approximately: (l + 2m)2 Vlm = c1 1 − , (1) M where the c1 is the phase velocity of light in the core material, l and m are the indices of the mode which√satisfy that the minimum of l + 2m is 2 and the maximum is M; the M is the total number of the modes which satisfies M 1 and the satisfies 1 which is obtained from Eq. (2): 1 NA 2 n − n2 ≈ , (2) = 1 n1 2 n1 where the n1 and n2 are the refractive indices of the core and the cladding, respectively, and the NA is the numerical aperture of the fiber. For a multi-mode fiber with the length of L, the phase shifting for a modulated light brought by two different modes is presented as Eq. (3): ϕf =
2π Lf 2π Lf − , Vlm1 Vlm2
(3)
where the f is the modulating frequency of the light, Vlm1 and Vlm2 are the group velocities of two different modes. The minimum and maximum values of the group velocities of different modes are c1 and c1 (1 − ), respectively, so the maximum of ϕ f is π Lf N A 2 2π Lf ≈ ϕf max = . (4) c1 1 - c1 n1 The maximum of the phase shifting error caused by the different modes of the multi-mode fiber is presented as Eq. (4). As not only the two modes which have the maximum or the minimum group velocity are exited, the error caused by the different modes will be smaller than the maximum. The measurement range in which the optical power received by the probe remains essentially unchanged is estimated. If it is required that all light reflected by the blade is coupled to the receiving fiber by the lens, the maximum tip clearance between the blade and the lens is obtained from Fig. 3.
FIG. 3. The maximum clearance between the target and the lens.
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FIG. 4. The minimum clearance between the target and the lens.
FIG. 5. The calibration experiment result of 20 mm receiving fiber.
And the maximum clearance is presented as Eq. (5)
merical apertures are 0.18 and the fibers are 62.5 μm core multimode fibers. The length of the receiving fiber is 20 mm, the numerical aperture is 0.22, the diameter of the fiber core is 400 μm, and the refractive index of the fiber core is about 1.55, so the maximum phase shifting caused by the different modes of the receiving fiber is within ±0.0035 rad. The maximum tip clearance measurement error caused by this phase shifting is within ±0.08 mm. The parameter of the fiber probe is as follow: F = 10 mm, s = 1 mm, sin(α 2 ) = 0.22, and sin(α 1 ) = 0.18. According to Eqs. (5)–(7), the dmax = 14.3 mm, dmin = 5.7 mm, and the measurement range is 8.6 mm, which satisfies the requirement of the blade tip clearance measurement. The minimum diameter of the sensor probe is 5.5 mm from Eq. (8) which is small enough for blade tip clearance measurement. The calibration experiments of the system are conducted. In the first experiment, the blade is fixed on a linear translation stage with a precision of 10 μm. The surface of the blade tip is stainless steel surface and the surface roughness is about Ra = 0.03 μm. At the initial position where the tip clearance between the blade and the lens is about 6 mm, the phase difference between the measurement channel and reference channel is measured. And then the change of the tip clearance is measured by the laser ranging system while the blade tip clearance is increased every 0.25 mm by the linear translation stage. The measurement result is as Fig. 5. The maximum absolute value of the measurement error is 0.054 mm and the standard deviation is 0.024 mm which indicates that the error caused by different mode of the fiber is much smaller than the maximum value. The optical power of the receiving channel keeps approximately the same for the full measurement range.
tan(α2 ) × F − tan(α1 ) × F + F. s From Fig. 4, the minimum clearance is acquired. And the minimum clearance is Eq. (6), 2
2
dmax =
tan(α1 ) × F 2 − tan(α2 ) × F 2 + F. s The measurement range is Eq. (7), dmin =
(5)
(6)
2tan(α2 ) × F 2 − 2tan(α1 ) × F 2 . s (7) The minimum diameter of the lens can also be acquired in Fig. 3, drange = dmax − dmin =
Ddiameter = 2tan(α2 ) × F + s.
(8)
The s is the clearance between the two fibers, the α 1 and α 2 are the acceptance angles of the input fiber and the receiving fiber, respectively, the F is the focal length of the lens. The measurement range is lengthened by increasing the focal length of the lens, increasing the difference between the receiving angles of the input fiber and the receiving fiber, or reducing the clearance between the input fiber and the receiving fiber. The size of the sensor probe is mainly determined by the diameter of the lens. The minimum diameter of the sensor probe is obtained from Eq. (8). IV. EXPERIMENTS
In the experiments, a dual frequency He-Ne laser is utilized as the light source whose intensity is modulated with the frequency of 1.089 GHz.18, 19 The wavelength of the laser is 632 nm and the optical power is 1 mW. The split ratio of the fiber splitter is 80:20. Eighty percent of the total optical power is sent to the sensor probe and the remaining power is utilized as the reference signal. The fibers of the splitter are 62.5 μm core multimode fibers. The APDs (Silicon Sensor APD230-8 TO52S3) are in room temperature and the bias voltage of the APDs is 117 V. The signals from the APDs are downconverted to 2.5 MHz and sampled with a 125 MS/s ADC. The length of the all-phase fast Fourier transformation is 511 points which takes less than 5 μs for data acquisition. The lengths of the input fiber of the probe and the transmitting fiber of the reference channel are about 2 m, the nu-
FIG. 6. The calibration experiment result of 3 m receiving fiber.
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V. CONCLUSION
FIG. 7. The fluctuation of the measurement result.
According to Eq. (3), the phase difference caused by two different modes of the receiving fiber is proportional to the length of the fiber. In the second experiment the length of the fiber is 3 m to estimate the measurement error caused by the multi-mode fiber. The experiment steps are as the first one. The experiment result is presented in Fig. 6. The experiment result indicates that the measurement error caused by a 3-mlong multi-mode fiber is less than 0.5 mm within the measurement range. And according to Eq. (3), the measurement error caused by the receiving fiber with a length of 20 mm is less than 0.003 mm within the measurement range. The fluctuation of the measurement result is tested. The tip clearance between the lens and the blade is 10 mm. The measurement result of the ranging system is recorded every 1 s for 1000 s. The standard deviation of the result is 0.019 mm. The fluctuation of the result is plotted in Fig. 7. The dynamic experiment is conducted by using a benchtop test rig. A rotator driven by a motor is utilized and the diameter of the rotator is 160 mm. The probe is fixed and the tip clearances of four blades which are located at 0◦ , 90◦ , 180◦ , and 270◦ of the circumference of the rotator are measured at different rotating speed. The surfaces of the blade tips are also stainless steel surfaces and surface roughness is about Ra = 0.03 μm. The measurement result is as Fig. 8. Thirty tip clearance measurement results of each blade at the rotating speed of 5000 revolutions per minute (rpm) are utilized to calculate the standard deviations, and the maximum standard deviation of the four blades is 0.048 mm. The experiments indicate that the system can be applied for dynamic clearance measurement of the rotator.
FIG. 8. Tip clearance measurement of four blades at different rotating speed.
A laser ranging system for blade tip clearance measurement is presented. The resolution of the system is about 0.02 mm within the measurement range of about 9 mm, and the data acquisition time is about 5 μs. The size of the sensor probe is determined by the minimum diameter of the lens in the probe which is less than 6 mm. Multi-mode fiber is utilized for optical transmission to guarantee that enough optical power is received by the sensor probe. And the fiber also isolates the receiver from the harsh environment inside the turbine. The length of the receiving fiber is 20 mm and the maximum measurement error caused by the different mode of the fiber is estimated. A longer fiber is available for the actual error caused by the fiber will be smaller than the maximum. Even though the optical receiver is not kept remote from the turbine, the temperature outside the turbine is much lower and there is enough space to adopt a cooling system. The sensor probe can operate in high temperature circumstance in the turbine engine if sapphire fibers and sapphire lens are applied. In the experiments the surface roughness of the blade tip is about Ra = 0.03 μm and the measurement error caused by low SNR is reduced by increasing the modulation frequency and optical power of the laser when the blade tip surface is rougher. ACKNOWLEDGMENTS
This work was supported in part by Doctoral Fund of Ministry of Education of China Grant No. 20130032110054. 1 M.
W. Wiseman and T.-H. Guo, “An investigation of life extending control techniques for gas turbine engines,” in Proceedings of IEEE American Control Conference (IEEE, 2001), pp. 3706–3707. 2 A. von Flotow, M. Mercadal, and P. Tappert, “Health monitoring and prognostics of blades and disks with blade tip sensors,” in IEEE Aerospace Conference Proceedings (IEEE, 2000), Vol. 6. 3 R. Ciorciari, A. Lesser, F. Blaim, and R. Niehuis, “Numerical investigation of tip clearance effects in an axial transonic compressor,” J. Therm. Sci. 21(2), 109–119 (2012). 4 S. B. Lattime and B. M. Steinetz, “High-pressure-turbine clearance control systems: current practices and future directions,” J. Propul. Power 20(2), 302–311 (2004). 5 J. Geisheimer and T. Holst, “Novel sensors to enable closed-loop active clearance control in gas turbine engines,” Proc. SPIE 9083, 908310 (2014). 6 M. Violetti, J.-F. Zürcher, J. Geisheimer, and A. K. Skrivervik, “Design of antenna based sensors for blade tip clearance measurement in gas turbines,” in Proceedings of the Fourth European Conference on Antennas and Propagation (IEEE, 2010), pp. 1–4. 7 A. Steiner, “Techniques for blade tip clearance measurements with capacitive probes,” Meas. Sci. Technol. 11(7), 865–869 (2000). 8 L. Du, X. Zhu, and J. Zhe, “A high sensitivity inductive sensor for blade tip clearance measurement,” Smart Mater. Struct. 23(6), 065018 (2014). 9 T. Pfister, L. Büttner, J. Czarske, H. Krain, and R. Schodl, “Turbo machine tip clearance and vibration measurements using a fibre optic laser Doppler position sensor,” Meas. Sci. Technol. 17(7), 1693 (2006). 10 I. García, J. Beloki, J. Zubia et al., “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors 13(6), 7385–7398 (2013). 11 A. Kempe, S. Schlamp, and T. Rösgen, “Low-coherence interferometric tip-clearance probe,” Opt. Lett. 28(15), 1323–1325 (2003). 12 J. Zubia et al., “Improvements in the design of an optical sensor for tipclearance measurements in turbines,” in 16th IEEE International Conference on Transparent Optical Networks (ICTON) (IEEE, 2014). 13 A. Pesatori, M. Norgia, C. Svelto, M. Zucco, M. Stupka, and A. D. Marchi, “High-resolution mode-locked laser rangefinder with
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harmonic downconversion,” IEEE Trans. Instrum. Meas. 61(5), 1536–1542 (2012). 14 B. Journet, G. Bazin, and F. Bras, “Conception of an adaptive laser range finder based on phase shift measurement,” in Proceedings of IEEE Industrial Electronics, Control, and Instrumentation (IEEE, 1996), Vol. 2, pp. 784–789. 15 X. Huang, Z. Wang, and L. Ren, “A novel high-accuracy digitalized measuring phase method,” in Proceedings of the 9th IEEE International Conference on Signal Processing (IEEE, 2008), 120–123.
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niques for turbomachinery vibration,” J. Eng. Gas Turbines Power 120(4), 784–791 (1998). 17 M. C. Teich and B. E. A. Saleh, Fundamentals of Photonics (Wiley Interscience, 1991), Chap. 8. 18 S. L. Zhang, M. X. Wu, and G. F. Jin, “Birefringent tuning double frequency He-Ne laser,” Appl. Opt. 29(9), 1265–1267 (1990). 19 K. Seta and T. O’ishi, “Distance meter utilizing the intermode beat of a He-Ne laser,” Appl. Opt. 29(3), 354–359 (1990).
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 115105 (2014)
Blade tip clearance measurement of the turbine engines based on a multi-mode fiber coupled laser ranging system Haotian Guo, Fajie Duan, Guoxiu Wu, and Jilong Zhang State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
(Received 10 September 2014; accepted 3 November 2014; published online 14 November 2014) The blade tip clearance is a parameter of great importance to guarantee the efficiency and safety of the turbine engines. In this article, a laser ranging system designed for blade tip clearance measurement is presented. Multi-mode fiber is utilized for optical transmission to guarantee that enough optical power is received by the sensor probe. The model of the tiny sensor probe is presented. The error brought by the optical path difference of different modes of the fiber is estimated and the length of the fiber is limited to reduce this error. The measurement range in which the optical power received by the probe remains essentially unchanged is analyzed. Calibration experiments and dynamic experiments are conducted. The results of the calibration experiments indicate that the resolution of the system is about 0.02 mm and the range of the system is about 9 mm. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901601] I. INTRODUCTION
Blade tip clearance is the distance between the tip of a rotating blade and the casing which is a parameter of great importance to guarantee the efficiency and safety of the turbine engines.1, 2 The efficiency and fuel consumption of turbine engines are improved dramatically by minimizing the tip clearance in order to reduce leakage flows, while it has to be assured that the blade will not touch the casing in any case to prevent fatal damage.3 The tip clearance varies due to mechanical loads, varying pressure conditions inside the turbine or the differing expansions and contractions of the blades and case over temperature during operation. An accurate online tip clearance measurement is therefore indispensable for optimized and safe operation, especially for the closed-loop active clearance control (ACC) system.4 The blade tip clearance is difficult to acquire in real-time for the following reasons: (1) the environmental temperature of the sensor probe exceeds 2000 ◦ F, (2) the size of the probe is limited, (3) the data acquisition process of a single measurement is limited within several microseconds because of the high velocity of the blade tip along the circumference, (4) a rather high resolution of 0.025 mm is required in a measurement range of several millimeters.5 The eddy current sensors, capacitive probes, and microwave radars are applied for real-time measurement of the blade tip clearance, because they are small, robust, and low cost.6–8 However, these methods will introduce a spatial filtering effect which makes the measurement results sensitive to the geometry of the blade tips.5 Optical sensors can overcome this drawback. Several different optical measurement principles, e.g., laser Doppler position sensor,9 reflective intensity modulation,10 or optical coherence tomography (OCT) measurements11 have been employed for tip clearance measurements. The resolution of the laser Doppler position probe is high, but the complex sensor probe limits the application of this system. The resolution of the reflective intensity modulation based sensor probe is low due to the modal noise at the endface of the transmitting fiber 0034-6748/2014/85(11)/115105/5/$30.00
when multi-mode fiber is utilized, and it takes a minute for data acquisition to reduce the impact of the speckle noise.12 The measurement rate of the OCT method is limited by the speed of mechanical scanning. Therefore, the conventional optical tip clearance sensors do not fully satisfy the requirement of future ACC systems. The laser ranging system based on phase shifting method is used in various applications for it is a non-contact measurement method and can withstand harsh operating environments. It is reported that this method can provide a system resolution of about 10 μm which is high enough for the blade tip clearance measurement.13 In this article, a laser ranging system for blade tip clearance measurement is introduced. A fiber coupled sensor probe isolates the optical receiver from the harsh environment inside the turbine engine. Multi-mode fiber is utilized to collect the light reflected by the blade, so the signal to noise ratio (SNR) is acceptable for high precision tip clearance measurement. The error brought by the multimode fiber is estimated. The measurement range in which the optical power received by the probe remains essentially unchanged is analyzed. Experiments are conducted using the system for clearance measurement.
II. SYSTEM STRUCTURE
The measurement principle of the laser ranging system is based on phase shifting method.14 The intensity of the laser beam is modulated by a sinusoidal signal. The phase of the reflected light from the target which is related to the location of the target is measured and compared to a reference signal for distance measurement. As shown in Fig. 1, the modulated laser is coupled into a fiber splitter. One output of the splitter transmits the optical power to the sensor probe for the tip clearance measurement as the measurement channel. The fiber collection of the measurement channel is illustrated in Sec. III of the article. The sensor probe sends the light to the blade tip and collects the
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FIG. 1. System structure.
light reflected. Avalanche photo diodes (APDs) are utilized for photoelectric conversion. The light from the sensor probe is received by APD1 and then amplified, downconverted, and sampled with an analog to digital converter (ADC). The other output of the splitter is used as the reference channel. The transmitting fiber of the reference channel from the splitter is directly coupled to the APD2 and the optical path difference and circumstance of this fiber are similar to the measurement channel. The signal received by APD2 is amplified, downconverted, and sampled synchronously. The sensor probe is fixed on the casing of the rotating machine. The ADC begins to sample the signals when the probe detects the arriving of the blade. The blade tip clearance is acquired by calculating the phase difference of the two channels. All-phase fast Fourier transformation is applied for phase detection.15 The arrival time of the blade can also be acquired at the same time which is utilized for blade vibration measurement.16 III. STRUCTURE OF THE SENSOR PROBE
The sensor probe is a key part of the system. The probe will work under high temperature condition and isolate the APD from the harsh environment. It should collect sufficient optical power reflected from the blade in the full measurement range to guarantee the SNR and the precision of the system. As in Fig. 2, the sensor probe consists of the fiber from the splitter (hereafter referred to as the input fiber), a lens, and a receiving fiber. The fiber ends of the input fiber and receiving fiber are fixed at the focal plane of the lens and symmetric about the axis of the lens. The lens collimates the divergent beam output of the fiber and directs it to the blade tip. The reflected light is collected by the same lens and coupled to the receiving fiber. A step-index multi-mode fiber is applied as the receiving fiber for the small diameter of the single-mode fiber makes it
FIG. 2. Structure of the sensor probe.
Rev. Sci. Instrum. 85, 115105 (2014)
difficult to couple the reflected light. The SNR is not acceptable when single-mode fiber is applied. As different modes of the multi-mode fiber have different optical paths, when different modes are excited there will be an extra phase shifting for the modulated light, which will bring a significant measurement error. As illustrated in literature,17 the group velocity of a mode in the multi-mode fiber is presented as Eq. (1) approximately: (l + 2m)2 Vlm = c1 1 − , (1) M where the c1 is the phase velocity of light in the core material, l and m are the indices of the mode which√satisfy that the minimum of l + 2m is 2 and the maximum is M; the M is the total number of the modes which satisfies M 1 and the satisfies 1 which is obtained from Eq. (2): 1 NA 2 n − n2 ≈ , (2) = 1 n1 2 n1 where the n1 and n2 are the refractive indices of the core and the cladding, respectively, and the NA is the numerical aperture of the fiber. For a multi-mode fiber with the length of L, the phase shifting for a modulated light brought by two different modes is presented as Eq. (3): ϕf =
2π Lf 2π Lf − , Vlm1 Vlm2
(3)
where the f is the modulating frequency of the light, Vlm1 and Vlm2 are the group velocities of two different modes. The minimum and maximum values of the group velocities of different modes are c1 and c1 (1 − ), respectively, so the maximum of ϕ f is π Lf N A 2 2π Lf ≈ ϕf max = . (4) c1 1 - c1 n1 The maximum of the phase shifting error caused by the different modes of the multi-mode fiber is presented as Eq. (4). As not only the two modes which have the maximum or the minimum group velocity are exited, the error caused by the different modes will be smaller than the maximum. The measurement range in which the optical power received by the probe remains essentially unchanged is estimated. If it is required that all light reflected by the blade is coupled to the receiving fiber by the lens, the maximum tip clearance between the blade and the lens is obtained from Fig. 3.
FIG. 3. The maximum clearance between the target and the lens.
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FIG. 4. The minimum clearance between the target and the lens.
FIG. 5. The calibration experiment result of 20 mm receiving fiber.
And the maximum clearance is presented as Eq. (5)
merical apertures are 0.18 and the fibers are 62.5 μm core multimode fibers. The length of the receiving fiber is 20 mm, the numerical aperture is 0.22, the diameter of the fiber core is 400 μm, and the refractive index of the fiber core is about 1.55, so the maximum phase shifting caused by the different modes of the receiving fiber is within ±0.0035 rad. The maximum tip clearance measurement error caused by this phase shifting is within ±0.08 mm. The parameter of the fiber probe is as follow: F = 10 mm, s = 1 mm, sin(α 2 ) = 0.22, and sin(α 1 ) = 0.18. According to Eqs. (5)–(7), the dmax = 14.3 mm, dmin = 5.7 mm, and the measurement range is 8.6 mm, which satisfies the requirement of the blade tip clearance measurement. The minimum diameter of the sensor probe is 5.5 mm from Eq. (8) which is small enough for blade tip clearance measurement. The calibration experiments of the system are conducted. In the first experiment, the blade is fixed on a linear translation stage with a precision of 10 μm. The surface of the blade tip is stainless steel surface and the surface roughness is about Ra = 0.03 μm. At the initial position where the tip clearance between the blade and the lens is about 6 mm, the phase difference between the measurement channel and reference channel is measured. And then the change of the tip clearance is measured by the laser ranging system while the blade tip clearance is increased every 0.25 mm by the linear translation stage. The measurement result is as Fig. 5. The maximum absolute value of the measurement error is 0.054 mm and the standard deviation is 0.024 mm which indicates that the error caused by different mode of the fiber is much smaller than the maximum value. The optical power of the receiving channel keeps approximately the same for the full measurement range.
tan(α2 ) × F − tan(α1 ) × F + F. s From Fig. 4, the minimum clearance is acquired. And the minimum clearance is Eq. (6), 2
2
dmax =
tan(α1 ) × F 2 − tan(α2 ) × F 2 + F. s The measurement range is Eq. (7), dmin =
(5)
(6)
2tan(α2 ) × F 2 − 2tan(α1 ) × F 2 . s (7) The minimum diameter of the lens can also be acquired in Fig. 3, drange = dmax − dmin =
Ddiameter = 2tan(α2 ) × F + s.
(8)
The s is the clearance between the two fibers, the α 1 and α 2 are the acceptance angles of the input fiber and the receiving fiber, respectively, the F is the focal length of the lens. The measurement range is lengthened by increasing the focal length of the lens, increasing the difference between the receiving angles of the input fiber and the receiving fiber, or reducing the clearance between the input fiber and the receiving fiber. The size of the sensor probe is mainly determined by the diameter of the lens. The minimum diameter of the sensor probe is obtained from Eq. (8). IV. EXPERIMENTS
In the experiments, a dual frequency He-Ne laser is utilized as the light source whose intensity is modulated with the frequency of 1.089 GHz.18, 19 The wavelength of the laser is 632 nm and the optical power is 1 mW. The split ratio of the fiber splitter is 80:20. Eighty percent of the total optical power is sent to the sensor probe and the remaining power is utilized as the reference signal. The fibers of the splitter are 62.5 μm core multimode fibers. The APDs (Silicon Sensor APD230-8 TO52S3) are in room temperature and the bias voltage of the APDs is 117 V. The signals from the APDs are downconverted to 2.5 MHz and sampled with a 125 MS/s ADC. The length of the all-phase fast Fourier transformation is 511 points which takes less than 5 μs for data acquisition. The lengths of the input fiber of the probe and the transmitting fiber of the reference channel are about 2 m, the nu-
FIG. 6. The calibration experiment result of 3 m receiving fiber.
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V. CONCLUSION
FIG. 7. The fluctuation of the measurement result.
According to Eq. (3), the phase difference caused by two different modes of the receiving fiber is proportional to the length of the fiber. In the second experiment the length of the fiber is 3 m to estimate the measurement error caused by the multi-mode fiber. The experiment steps are as the first one. The experiment result is presented in Fig. 6. The experiment result indicates that the measurement error caused by a 3-mlong multi-mode fiber is less than 0.5 mm within the measurement range. And according to Eq. (3), the measurement error caused by the receiving fiber with a length of 20 mm is less than 0.003 mm within the measurement range. The fluctuation of the measurement result is tested. The tip clearance between the lens and the blade is 10 mm. The measurement result of the ranging system is recorded every 1 s for 1000 s. The standard deviation of the result is 0.019 mm. The fluctuation of the result is plotted in Fig. 7. The dynamic experiment is conducted by using a benchtop test rig. A rotator driven by a motor is utilized and the diameter of the rotator is 160 mm. The probe is fixed and the tip clearances of four blades which are located at 0◦ , 90◦ , 180◦ , and 270◦ of the circumference of the rotator are measured at different rotating speed. The surfaces of the blade tips are also stainless steel surfaces and surface roughness is about Ra = 0.03 μm. The measurement result is as Fig. 8. Thirty tip clearance measurement results of each blade at the rotating speed of 5000 revolutions per minute (rpm) are utilized to calculate the standard deviations, and the maximum standard deviation of the four blades is 0.048 mm. The experiments indicate that the system can be applied for dynamic clearance measurement of the rotator.
FIG. 8. Tip clearance measurement of four blades at different rotating speed.
A laser ranging system for blade tip clearance measurement is presented. The resolution of the system is about 0.02 mm within the measurement range of about 9 mm, and the data acquisition time is about 5 μs. The size of the sensor probe is determined by the minimum diameter of the lens in the probe which is less than 6 mm. Multi-mode fiber is utilized for optical transmission to guarantee that enough optical power is received by the sensor probe. And the fiber also isolates the receiver from the harsh environment inside the turbine. The length of the receiving fiber is 20 mm and the maximum measurement error caused by the different mode of the fiber is estimated. A longer fiber is available for the actual error caused by the fiber will be smaller than the maximum. Even though the optical receiver is not kept remote from the turbine, the temperature outside the turbine is much lower and there is enough space to adopt a cooling system. The sensor probe can operate in high temperature circumstance in the turbine engine if sapphire fibers and sapphire lens are applied. In the experiments the surface roughness of the blade tip is about Ra = 0.03 μm and the measurement error caused by low SNR is reduced by increasing the modulation frequency and optical power of the laser when the blade tip surface is rougher. ACKNOWLEDGMENTS
This work was supported in part by Doctoral Fund of Ministry of Education of China Grant No. 20130032110054. 1 M.
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