Strain Transfer of Bonded FBG Sensor for Coal Mining Similar Model

Transcription

1 Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP. 0-8 Strain Traner o Bonded FBG Senor or Coal Mining Similar Model Guiua Zang Scool o College, Xi an Univerity o Science and Tecnology, Xi an 70054, Cina zangguiua@xut.edu.cn Abtract-To accurately monitor te train o a ot wit low trengt, a new train traner model i propoed or te ubtrate FBG enor. In te train traner model, te mecanical propertie o te ot are taken into conideration. Te train relationip between te iber core and te ot i obtained. Te teoretical approac wa veriied by numerical imulation and experimental reult. Te inluence o te mecanical parameter o te ot on te train traner are analyzed. It i concluded tat te train traner rate increae nonlinearly wit te increae o te ear modulu o te ot. Te ear modulu o te ot a dierent inluence in dierent train range; or te low trengt ot, te mecanical parameter o te ot ave great inluence on te train traner rate. Tee reult provide teoretical guideline or te FBG enor application in low trengt ot. Keyword- Fiber Bragg Grating; Strain Traner; Similar Model; Mecanical Parameter I. INTRODUCTION A te main tet metod o rock mecanic, coal mining imilar model ave great potential to analyze te ormation tre in underground mining engineering []. In te mining imilar model, we can evaluate te movement o overburdened trata by monitoring te internal train []. Te iber Bragg grating enor (FBG) metod wa adopted to monitor internal train, and a been teted or eaibility in coal mining model [3-5]. Te new metod o FBG baed on imilar material wa developed to monitor train in tunnel excavation [6]. However, reearc on FEG-baed mine model i till limited. It i neceary to tudy te train traner o te ubtrate FBG enor or coal mining in a imilar model. Tere are two popular type o FBG available: cylindrical embedded FBG and ubtrate FBG. Te train traner o cylindrical embedded FBG a been tudied by many reearcer [7-9]. It wa aumed tat tere i identical train in te iber core and te ot [0]; owever, tere are dierent train in te iber core and te ot []. Ti i becaue te adeive layer and te coating layer can conume energy. Similarly, te ame train rate a been conidered between te FBG center and te ot []. However, tere i till limited reearc on train traner or te ubtrate FBG enor. A main reaon or ti i te aymmetry o te ubtrate FBG enor, wic increae te diiculty o analyi. A train traner model o a ubtrate iber enor wa etablied to evaluate te interaction between te ot material and te iber core [3-5]. Te inite element metod (FEM) wa ued to imulate te inluence o te geometric parameter o te adeive layer o te ubtrate FBG enor [6]. However, in toe analye, it wa aumed tat te mecanical propertie o te ot did not inluence train traner. Monette ound tat te train traner o FBG wa related to te elaticity modulu o te ot [7], but tey did not provide te deinite relationip between te train traner and te elaticity modulu o te ot. Tereore, we mut conider te mecanical caracteritic o te ot in order to improve te ubtrate FBG train traner model to predict train in coal mining model. Ti tudy propoe an improved train traner model o te ubtrate FBG wic i uitable or a coal mining model. From te propoed model, a teoretical ormula i derived and ued to predict te train traner relationip between te coal mining model and te iber core in conideration o te mecanical propertie o te ot. Ten, a numerical imulation by FEM and practical experiment are conducted to validate te teoretical prediction. II. THEORETICAL METHODS A model o te ubtrate FBG enor or a coal model i own in Fig.. Te train traner between te iber core and te ot i derived baed on te ollowing aumption: ) Material o all layer o te enor are iotropic and elatic. ) Only te coal model i ubjected to te uniorm axial tre. 3) All te interace are perectly aligned, and diplacement exit only in te axial direction. 4) Te middle layer can alo react to te model, tereby reducing te model train. Te dept o inluence o middle layer on te model i =mm

2 Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP. 0-8 Adeive layer Fiber Core Subtrate layer Adeive layer Hot-Coal model (a) Cro-ection x y σ σ +dσ τ σ τ σ +dσ σ σ +dσ τ σ σ +dσ τ a a σ a σ a +dσ aj τ a (b) Stre ditribution o te longitudinal ection o te ubtrate FBG enor Fig. Model o te ubtrate FBG enor or coal model In Fig., σ, τ and u repreent te axial tre, ear tre and diplacement, repectively; denote te tickne; E and G repreent Young modulu and te ear modulu, repectively; ubcript,,, a and repreent adeive layer, FBG layer, ubtrate layer and adeive layer, repectively; r repreent te radiu o te iber core; b i te tickne o te enor; L i te lengt o te enor; τ, τ, τ a, τ a are te ear tre between te adeive layer and FBG layer, te adeive layer and te ubtrate layer, te ubtrate layer and adeive layer, and te ubtrate layer and te ot tructure, repectively. Under te above aumption, te orce equilibrium equation or adeive layer i expreed a ollow: d ( b r ) r b 0 () were d b r b r () Similarly, te orce equilibrium equation or te FBG layer, ubtrate layer and adeive layer are expreed a ollow: - -

3 Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP. 0-8 were d It i aumed tat tere are identical train gradient in all layer: Becaue E i greater tan E and E, equation ()-(6) obtain: (3) r d a (4) d a a a (5) a d d d d a (6) E r d a E ( + ) (7) E b a E ( + ) = a E b E r d (8) r d E b (9) E r d (0) It i aumed tat te ear tre o every layer i linear by it dept; ear tre expreion are,,. a r y. were y a. were + y a a. ( ) - r = y a a r r a = ( y a ) a a a a a a () () = ( y ) (3) For te coal model, τ i linear wit te dept o te ot. Wen y n c j m, m 0 ; wen y n c j, m mj. Tu, we obtain: - -

4 Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP. 0-8 were a + a y a a. du Subtituting ormula (4) into = G dy ( y) (4) a a and integrating wit repect to y, we obtain: r d ( E E ) b a du G dy G(u -u a) dy a a a ( a ) a y dy (5) Dierentiating ormula (5) wit repect to x, we obtain: r d a ( E E ) (6) b Similarly, te train traner equation or te ubtrate layer, adeive layer and FBG are c G According to equation (6)-(9), we obtain: E a a ( + ) Ga E b,,, repectively. E r d (7) E d (8) E G d Were E E r a E ( + ) k G E b G a Te general olution o ormula (0) i a ollow: E r r r d (9) G b d g x k g x k x a ( )( ) 4 ( ) - ( ) - ( ) (0) r E ( ) r r r E E a ( )( ) b G b 4 G kx ( x) C e C e ( x) () kx were C and C are te integration contant determined by boundary condition. Te boundary condition are given a ( L) ( L) 0. Tu, C and C can be expreed a: C = C () co( kl) Subtituting equation () into equation (), we obtain: co(kx) ( x) ( x) - co (kl) (3) - 3 -

5 Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP. 0-8 Along te iber lengt, te train traner rate i expreed a: ( x) co(kx) - ( x) co(kl) (4) Te average train traner rate i expreed a: L co(kx) - ( x) co 0 (kl) in(kl) = =- ( x) L kl co (kl) From equation (5), we can obtain te average train traner rate related to te mecanical parameter o te ot and te ubtrate layer. (5) A. Numerical Validation III. NUMERICAL VALIDATION AND PARAMETER ANALYSIS Numerical analyi wa conducted to validate te teoretical prediction wit ANASYS otware. Due to te geometry, only al o te ubtrate FBG i analyzed. Fig. ow te inite element model. All parameter are lited in Table. Adeive layer Subtrate layer Optical iber Adeive layer Matrix Fig. Finite element model TABLE ASSIGNED PARAMETERS OF THE FBG MODEL Parameter Value Radiu o iber core, r ( m ) 6.5 Young modulu o iber core, E (GPa) 7 Poion ratio o iber core, 0.7 Young modulu o adeive layer, E (MPa) 5 Sear modulu o adeive layer, G (MPa) 0 Tickne o adeive layer g (mm) 0. Young modulu o ubtrate, E (MPa) 0 5 Sear modulu o ubtrate, G (GPa) 40 Tickne o ubtrate, ( mm ) 0. Young modulu o adeive layer, E a(mpa) 5 Sear modulu o adeive layer, G (MPa) a 0 Young modulu o coal model, E (MPa) 7 Sear modulu o coal model, G (MPa)

6 Strain traner Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP. 0-8 Tickne o adeive layer Lengt o FBG enor, L(c ) (mm) a 0. m 4 Te enor and te ot are modeled wit olid 85, and all model element demontrate linear elatic beavior. An axial load o 6N i applied to te ot. Fig. 3 ow te axial train nepogram o te iber core by ANASYS. Fig. 3 Axial train nepogram o te iber core by te ANASYS teoretical reult FEM reult Ditance along te iber/m Fig. 4 Strain traner rate comparion o teoretical analyi and ANASYS reult In Fig. 4, te train traner rate by ANASYS are compared wit tat obtained by equation (4). A can be een in Fig. 4, te two curve are nearly identical, and teoretical reult agree wit ANASYS reult. Te average train traner rate i a calculated by ANASYS. Te value in Table are ubtituted into equation (5) to obtain te teoretical ANASYS reult Tere i 0.9% train relative error between te teoretical reult and te ANASYS reult. It teoretic i urter own tat te teoretical prediction are in good agreement wit te ANASYS reult. B. Parametric Analyi Baed on teoretical analyi, te inluence rate o parameter on te train traner rate are dicued. Te parameter repreent te mecanical propertie o te ubtrate layer and te ot layer. Te parameter o te iber core and adeive layer are lited in Table, and will be ued in te ollowing ubection to imulate te eect o G and E on te average train traner rate. Fig. 5 ow te average train traner rate a a unction o te ear modulu o te ot layer. A can be een, te train traner rate increae wit an increaing ot ear modulu, and ti tendency become more rapid wit maller ear modulu value. Wen te ear modulu cange in te range o 0 to 500 MPa, te lope o te curve varie greatly and te ot ear modulu a great inluence on te train traner rate. Wen te ear modulu o te ot i more 500 MPa, te curve i mooter and te ot ear modulu a little inluence on te train traner rate. Reult indicate tat wen te value o te ot ear modulu i mall, te ot ear modulu mut be conidered a an important parameter in te application o FBG enor. A own in Fig. 5, te average train traner rate decreae wit an increae in te elatic modulu o te ubtrate layer

7 Average train traner Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP. 0-8 Ti i a conequence o te act tat te mall ot elatic modulu augment te eiciency o load traner rom te ot material to te iber core. For te coal mining model, te low trengt material neceitate tat we conider te inluence o te mecanical parameter o te ot on te train traner E=ePa E=9.5e0Pa G /Pa x 0 9 Fig. 5 Average train traner rate in te ear modulu o te ot IV. EXPERIMENT VALIDATION Laboratory tet are perormed uing FBG enor to veriy our teoretical analyi. Te experimental model i own in Fig. 6. Fig. 6 Experiment model Tree ubtrate FBG enor, FBG, FBG and FBG3, were embedded in te trata o te coal mine model to obtain te train o te coal model. For comparion, tree dial indicator were placed near te correponding FBG enor to obtain te diplacement o te trata. Te tree dial indicator are DI, DI and DI3. Fig. 7 ow tat te wavelengt it o FBG and te diplacement o DI vary wit te mining ditance. It can be een tat te diplacement vary linearly wit te wavelengt it, wit a linear correlation coeicient R i 0.9, allowing comparion o reult between te FBG and dial indicator

8 diplacement o DI/mm wavelengt it o FBG/pm Journal o Baic and Applied Pyic Aug. 05, Vol. 4 I. 3, PP diplacement o DI wavelengt it o FBG mining ditance/cm Fig. 7 Wavelengt it o FBG and diplacement o DI varying wit mining ditance Te ot train i te ratio o te diplacement recorded by te dial indicator to te dept o correponding trata. Te experimental average train traner rate i te ration o te iber train by te FBG enor to te ot train. In te experiment, te train traner rate o FBG, FBG and FBG3 were 0.7, 0.7 and 0.3, repectively. Te average train traner coeicient o tree enor wa 0.6. Tere wa a 0% train relative error between experimental experiment reult and wit te teoretical reult, wile te error wa 0.9% between te teoretical and FEM reult. Te value in Table are ubtituted into te train traner ormula by Zou [9] were tey neglect te inluence o te mecanic parameter o te ot. Te average train traner rate wa 0.8, wit a 75% between teoretical reult by Zou [9] and te experimental reult. Tereore, tere i a great dierence in train traner rate wen te mecanical parameter o te ot i or i not taken into conideration. Te reult in our teoretical model i cloer to te experiment reult, tu te mecanical parameter o te ot cannot be neglected or te coal mining model. Summarily, our teoretical prediction i in agreement wit te ANASYS reult. Te teoretical model can predict te actual train o te coal mining model. Tereore, baed on te teoretical model, te FBG can be ued to accurately meaure te train in te coal model. V. CONCLUSION FBG a great potential or analyi o te internal train o te coal mining model. Ti paper propoed a train traner model or a coal mining imilar model by introducing te mecanical propertie o te ot to teoretically predict te train traner relationip between te iber core and te coal mine model. Finally, we arrived at te ollowing concluion: () In te conideration o te mecanic parameter o te ot, te train traner rate between te iber core and te ot i teoretically obtained. () Te teoretical reult are validated by ANASYS and experiment. Tere i 0.9% train relative error between te teoretical reult and te ANASYS reult. (3) Te ear modulu o te ot a dierent inluence in dierent train range. Wen te ear modulu o te ot i le tan 500MPa, it a great inluence on te train traner rate. Wen te ear modulu o te ot i more tan 500MPa, it a little inluence on te train traner rate. (4) For te low trengt ot, we mut conider te inluence o te mecanical parameter o te ot on te train traner. For te ig trengt ot, we can neglect te inluence o te mecanical parameter o te ot. ACKNOWLEDGMENTS Ti work wa upported by National Natural Science Foundation o Cina (57480). Autor are grateul or te upport. REFERENCES [] Zuo Bao-ceng, Cen Cong-xin, Liu Cai-ua, et al., Reearc on imilar material o imulation experiment, Rock and Mecanic, vol. 5, no., pp ,

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