Advanced Materials Research Submitted: 214-1-31 ISSN: 1662-8985, Vol 183, pp 121-126 Accepted: 214-11-3 doi:1428/wwwscientificnet/amr183121 Online: 215-1-12 215 Trans Tech Publications, Switzerland A Research on High-Precision Strain Measurement Based on FBG with Temperature Compensation Zi Wang a, Xiang Zhang b, Yuegang Tan c, Tianliang Li d School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan, Hubei, China; WUT- Birmingham Intelligent Machines Joint Laboratory, Wuhan, Hubei, China a wangziwhut@163com, b 44788927@qqcom, c ygtan@whuteducn, d 49274694@qqcom Keywords: FBG; Temperature Compensation; High-Precision Strain Measurement Abstract FBG (Fiber Bragg Grating) is a new type of optical passive device which can be used in sensing field This paper demonstrates the feasibility and effectiveness of FBG as the new method of strain measurement, and improves the measuring precision Based on the strain sensing property of FBG, the study adopts the differential method of double FBGs to make temperature compensation, and conduct the contrast experiment with resistance strain chip The experimental results show that strain measurement based on FBG agrees well with theoretical calculation The measurement error: no more than 1%, linear fitting correlation coefficient: almost 1, linearity: 17%, sensitivity: 792 / N, hysteresis error: 347%, repeatability error: 333% The results show FBG s performance are superior to resistance strain chip, especially in aspect of measuring precision Therefore, we can conclude that FBG is a feasible and effective method of strain measurement Introduction Strain measurement is the basic item in performance test for the material and structural mechanics, which is of great significance in safety inspection, workload evaluation and safety check [1] How to improve the reliability and precision of strain measurement has been a hot research subject Traditional strain measuring technique is given priority to resistance strain chip However, resistance strain chip has poor durability, susceptible to electromagnetic interference and other defects Besides, long-term measuring is influenced by zero drift which causes serious distortion of measurement results [2] In 1989, Zhang Zhiyou [3] classified the influence factors of strain measurement precision, and provides a theoretical basis for the elimination of these factors Deng [4] in 8 improved the algorithm to eliminate the calculation error of strain measurement, and make the error less than 5% through experiment verification In 9, Yin Fuyan [5] brought a temperature compensation method for resistance strain chip according to the swelling coefficient difference between resistance strain chip and base material, but this method had many limitations like only used for designate materials In 213, to the structural health monitoring of crane, Li Xiangdong et al [6] thought that the resistance strain chip didn t meet the requirements of long-term monitoring, because it could be only used through one test, and the reliability couldn t meet the actual demand FBG (Fiber Bragg Grating) is a new type of optical passive device developing rapidly in recent years, which has the advantages of small volume, anti electromagnetic interference, high reliability and can be used in distributed measurement, etc [7] Its application in the field of strain sensing can overcome the defects of the current electrical sensing system In order to verify the feasibility and effectiveness of FBG as the new method of strain measurement, this paper based on the strain sensing property of FBG, adopted differential method of double FBGs to make temperature compensation, and put up equal strength standard beam to conduct the contrast experiment between FBG and resistance strain chip The results show that FBG with temperature compensation has better performance in measuring precision Therefore, we can conclude that FBG is a feasible and effective method of strain measurement All rights reserved No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, wwwttpnet (ID: 132313675, Pennsylvania State University, University Park, USA-9/5/16,9:18:2)
122 Advanced Measurement and Test IV Measuring Principle of FBG Strain Sensing Property of FBG FBG has the periodic distribution structure of refractive index in fiber core using ultraviolet exposure technology, as shown in Fig1 When an incident beam of broad-band comes to FBG, a particular wavelength of narrow-band light is reflected due to the periodic distribution structure of refractive index, which satisfies the Bragg scattering conditions [8] by Eq (1): B 2n Where n and are effective refractive index and grid period of FBG, respectively The reflection principle is shown in Fig1 [8] (1) Fig1 The structure of FBG and reflection principle When FBG is under force, the reflected wavelength is determined by strain and elastic-optic effect The relationship between the change of reflected wavelength and strain can be described by Equation (2): B B (1 Pe ) (2) Where P e is valid elastic-optic constant For common optical fiber, Pe equals 22 [8] Temperature Compensating Model for FBG In the application, FBG will be influenced by both temperature and strain In this condition, the relationship between the change of reflected wavelength, temperature and strain can be described by Equation (3): B (1 Pe ) + ( + ) T B Where is thermal expansion coefficient and is thermo-optic coefficient Therefore, in the high precision strain measurement based on FBG, the influence of temperature is not negligible [9] Select equal strength beam as elastomer, which has the character that the strain on the surface of it equal everywhere This structure ensure the tensile stress or compressive stress share the same value in the bonding length range of FBG, and not bring measurement error caused by uneven stress For the sake of temperature compensation, attach double FBGs on the upper surface and lower surface of equal strength beam, respectively One senses tensile stress, the other one senses compressive stress (3)
Advanced Materials Research Vol 183 123 Fig2 The schematic diagram of measurement with FBG According to the knowledge of material mechanics [1], with load F, elastic modulus E, and relevant geometry size, the theoretical calculation of the strain on the surface of equal strength beam can be described by Equation(4): The central wavelength shift of FBG 1 is: The central wavelength shift of FBG 2 is: 6( - ') = Ll F 2 Eb h B1 B1 B2 B2 (1 P) + ( + ) T e FBG1 (1 Pe ) FBG 2+ ( + ) T Where FBG 1=-FBG 2 When Equation (5) minus Equation (6), the real strain can be obtained by the central wavelength shift of FBG with Temperature Compensating Experimental Analysis - = ( 2 1 ) B1 B2 B1 B2 P e Experiment System Conducting the contrast experiment between FBG and resistance strain chip, the schematic diagram and physical map of the experiment system are shown in Fig 3 Resistance strain chip 1 and resistance strain chip 2 constitute half-bridge circuit FBG 1 is stuck to the upper surface of cantilever beam, and FBG 2 is stuck to the corresponding position on the lower surface Change the load by adding or reducing the number of weights which are hung on the free end of cantilever beam As a signal modulation unit, the SDY212 resistance strain gauge is to transfer the output signal of resistance strain into the value of strain, and present it on the PC FBG interrogator is to acquire the FBG s central wavelength shift and record it by using relevant software In the experiments, the central wavelength of FBG 1 B1 wavelength of FBG 2 B2 shown in Table 1 is 1315693nm, the central is 1315553nm The structure parameters of equal strength beam are (4) (5) (6) (7)
Strain / 1e-6 Strain / 1e-6 124 Advanced Measurement and Test IV (a) Fig3 Schematic diagram and physical map of the experiment system (a) Schematic diagram; (b) Physical map (b) Table 1 Structure parameters of equal strength beam E [Pa] h[mm] L [mm] L [mm] b[mm] 2 1 11 5 34 6 45 The initial state is zero load When loading, firstly put on the weight disk (25N), then load step by step, and each weight s weight is 5N, till the maximal load (375N) Next, unload as the reverse process of load The process of load and unload are repeated for 6 times Meanwhile, record each FBG s central wavelength shift and strain value through resistance strain gauge at each step Experimental Results and Analysis Based on Equation(7), we can transfer FBG s central wavelength shift into strain value, and the relation between strain and load is shown in Fig 4 (a) The relation between strains which are measured based on resistance strain chip and load is shown in Fig 4 (b) Obviously, in the repetitive experiments based on two methods, the 6 curves are almost coincided respectively It can be calculated that in the method of FBG, hysteresis error is 347%, and repeatability error is 333% In the method of resistance strain chip, hysteresis error is 164%, and repeatability error is 164% Both two methods have good reproducibility and minimal hysteresis 3 1 1st loading 2nd unloading 3rd loading 4st unloading 5st loading 6st unloading 3 3 1st loading 2nd unloading 3rd loading 4st unloading 5st loading 6st unloading 1-5 1 15 2 25 3 35 4 (a) 5 1 15 2 25 3 35 4 Fig4 The repetitive experimental results of FBG and resistance strain chip (a) FBG; (b) Resistance strain chip The average strain at each load based on two methods and linear fitting are shown in Fig 5 It can be calculated that in the method of FBG, linear fitting correlation coefficient is 1, the linearity is (b)
Strain / 1e-6 Strain / 1e-6 Strain / 1e-6 Advanced Materials Research Vol 183 125 17%, and the sensitivity is 792 / N, zero drift is -6468 To the resistance strain chip, linear fitting correlation coefficient is 1, the linearity is 274%, and the sensitivity is 8138 / N, zero drift is 25 Both methods have good linear characteristics, and FBG can acquire relatively better linear characteristics 3 expermental data linear fit 3 3 expermental data linear fit 1 1-5 1 15 2 25 3 35 4 (a) 5 1 15 2 25 3 35 4 Fig5 Linear fitting for the results of FBG and resistance strain chip (a) FBG; (b) Resistance strain chip Based on Equation(4), we can calculate the theoretical strain at each load The theoretical value, measured value based on two methods and errors are shown in Table 2, the strain-load relation of theory calculation and measurements are shown in Fig 6 It is evident that the measurement method of FBG has a higher measuring precision over resistance strain chip (b) 3 3 theoretical strain measured by resistance strain chip measured by FBG Load (N) 1-5 1 15 2 25 3 35 4 Fig6 The strain-load relation of theory calculation and measurements Table 2 Theoretical value, measured value based on two methods and errors at each load Theoretical strain ( ) Strain measured by resistance strain chip ( ) error Strain measured by FBG ( ) 8 319% -65 94% 25 1987 2 263% 5 29% 75 596 6117 256% 5943 33% 125 9933 1188 247% 991 37% 175 1397 14 251% 13855 56% 225 1788 18329 % 1778 47% 275 21853 224 248% 217 42% 325 25827 26467 243% 25717 29% 375 298 3525 319% 29714 94% error
126 Advanced Measurement and Test IV Conclusions Experimental results show that the measurement method of FBG agrees well with theoretical calculation The relevant data are: measurement error: no more than 1%, linear fitting correlation coefficient: almost 1, linearity: 17%, sensitivity: 792 / N, hysteresis error: 347%, repeatability error: 333% Compared to resistance strain chip, both methods have similar properties, but FBG has a higher measuring precision Therefore, we can conclude that FBG is a feasible and effective method of strain measurement If make a further research on the best bonding process so as to reduce loss when the strain of structure matrix transfer to FBG, we can obtain much higher measuring precision based on the method of FBG as it is now Acknowledgment This research is supported by National High Technology Research and Development Program ( 863 Program) of China The research of key technologies for large rotating machinery safety working (Project No 212AA416) References [1] Jacob, Clement Capacitive strain sensors for measurement of large strain for structural health monitoring MS diss, The University of Texas at Arlington, 21 [2] Jianhua Zhou Study on Strain Transfer Characteristics of Fiber Bragg Grating Sensors MS Diss, Wuhan University of Technology, 21 [3] Zhiyou Zhang The main factors affecting the accuracy of the strain measurement and the solutions Construction machinery and equipment, 1989, 25-28 [4] Yangchun Deng Study on elimination algorithm in large strain measurement with strain gauges calculation error Experimental mechanics, 8, Vol23, No3: 228-233 [5] Fuyan Yin The temperature compensation of the resistance strain gauge and others Weighing Apparatus, 9, Vol38, No9: 4-44 [6] Xiangdong Li The contrast test between FBG and resistance strain chip in structural health monitoring of port crane Hoisting and conveying machinery, 213(6): 11-17 [7] Desheng Jiang, Wei He Review of Application for Fiber Bragg Grating Sensors Journal of Optoelectronics and Laser, 2, Vol13, No4:42-429 [8] Morey W W, Meltz G W, Glenn H Fiber optic Bragg grating sensors SPIE, 1989, 1169: 98-17 [9] Zude Zhou, Yuegang Tan FBG Distributed Sensing in Dynamic Monitoring and Damage Identification of Mechanical System Beijing: Science Press, 213 [1] Mingfa Li, Kaiyin Zhang, Li Huang Mechanics of materials Beijing: Science Press, 7
Advanced Measurement and Test IV 1428/wwwscientificnet/AMR183 A Research on High-Precision Strain Measurement Based on FBG with Temperature Compensation 1428/wwwscientificnet/AMR183121