Finite Element Analysis of a Fiber Bragg Grating Accelerometer for Performance Optimization

Transcription

1 Finite Element Analyi of a Fiber Bragg Grating Accelerometer for Performance Optimization N. Baumallick*, P. Biwa, K. Dagupta and S. Bandyopadhyay Fiber Optic Laboratory, Central Gla and Ceramic Reearch Intitute, Council of Scientific and Indutrial Reearch (CSIR), Kolkata, India *196, Raja S.C. Mullick Road, Kolkata , India, nandini_b@cgcri.re.in Abtract: Senitivity of a cantilever-ma baed fiber Bragg grating (FBG) accelerometer can efficiently be tailored by altering the ditance between the axi of the FBG enor to the neutral axi of the cantilever. To accomplih that in general, a backing patch i ued to mount the FBG on the cantilever. Ue of finite element analyi to quantify the influence of the material contant (Young modulu) of the backing patch and it thickne on the enitivity i preented in thi paper. It i explicitly hown that for a pecific patch material there i an optimum thickne for which the enitivity happen to be the maximum. Uing thi optimum deign, a enitivity ~ 1062 pm/g ha been experimentally achieved, the enhancement almot by a factor of three a compared to that of the conventional cantilever-ma FBG accelerometer of imilar bandwidth. Keyword: accelerometer, cantilever vibration, fiber Bragg grating. 1. Introduction Fiber Bragg grating accelerometer are widely ued in eimic and civil tructural meaurement where it i required to acquire low frequency, low g ignal under harh environmental condition, without any influence of electromagnetic field, with multiplexing capabilitie [1],[2]. Amongt the variou type of FBG accelerometer, the cantilever baed deign are uitable for low frequency meaurement with high enitivity and low cro-axi enitivity [3]. The cantilever baed FBG accelerometer baically comprie of a vibrating cantilever with a FBG bonded on the urface or attached to it. The bending train of the cantilever i tranferred to the FBG which reult in a wavelength hift proportional to the train. The bending train of the cantilever being proportional to the vertical acceleration, the FBG wavelength hift i a direct meaure of the vertical acceleration. For high enitivity, an inert ma i attached to the cantilever tip. However, the highet achievable enitivity by conventional cantilever-ma deign i inufficient for ignal of ultra low magnitude uch a thoe in eimic and civil tructural meaurement. It i obviou that larger the ditance of the FBG from the urface, higher would be the train experienced by the FBG and thu higher would be the enitivity. In our previou work we achieved an enhancement in enitivity uing a Polyimide backing patch to increae the eparation between the neutral axi of the cantilever and the FBG [4]. Senitivity ~450 pm/g, which wa twice compared to conventional cantilever-ma deign, wa achieved for a pecific cantileverma arrangement with a patch of thickne 150 μ m. The limit up to which the enitivity could be increaed by thi mechanim i an important quetion and ha been dealt with in thi paper. In thi paper the primary objective wa to tudy the influence of patch thickne and alo the Young modulu of the patch material on the enitivity of the FBG-accelerometer, by numerical imulation uing COMSOL Multiphyic (verion-4.2a) finite element analyi oftware. It ha been hown that for a pecific patch material, i.e. having the elatic modulu remaining ame there i an optimum thickne of the patch for which the train enhancement of a particular cantilever ma architecture become maximum and thu the enitivity. Senitivity of the order of 1062 pm/g ha been meaured for a particular configuration with a 1000 μ m teflon patch. 2. Theoretical Background The architecture of the propoed accelerometer i illutrated in figure1. The train experienced by the FBG from [4] and the croreference thereof, may be expreed a,

2 ε 3 + d f )( L x) x) = a (1) 2 2 ( ω 0 ω ) L ( F. 3 where urface. d f i the ditance of the FBG from the variation. For a fiber of radiu r, directly mounted on the urface, + r) ε FS = ε (4) 0.5d For a fiber of radiu r, mounted on a patch of thickne, p + r + p) ε FP = ε (5) 0.5d Figure 1. FBG-accelerometer geometry The train experienced by the FBG w.r.t. the train at the urface of the cantilever ε S can therefore be expreed a + d f ) ε F = ε (2) 0.5d The accelerometer enitivity (wavelength hift of FBG per unit acceleration) i given by Δλ 1.2 ε F S = = (3) a a where Δ λ i the FBG wavelength hift. The factor 1.2 i due to the fact that the train enitivity for FBG with peak wavelength in the C band regime, i about 1.2 pm / με in general. From eqn. (2-3), it i evident that larger the ditance of the FBG from the urface, higher i 2 2 the enitivity. The term ( ω in the 0 ω ) denominator of the expreion for ε F ( x ) indicate a frequency dependence of the accelerometer enitivity which i uual for a vibrating cantilever ytem [5]. The enitivity i nearly contant for frequencie much le than the reonance frequency. It gradually increae up to reonance and fall abruptly at frequencie beyond that. Baed on the fact, in practice, the feaible frequency range of operation of thi cla of accelerometer i in general up to half the reonance frequency to avoid large enitivity Thu ratio of the train experienced by the FBG mounted on a patch to the directly mounted FBG (the enhancement factor) may be repreented a ε FP + r + p) IF = = (6) ε + r) FS In [4] eqn.(6) wa ued to predict the train enhancement factor which clearly ha a linear dependence with patch thickne and experimenting with a 150 µm patch we could get enhancement factor IF a predicted by eqn.(6). It may be noted that both the contituent term ε FP and ε FS of eqn.(6) are dependent on the train ditribution ε on the urface of the cantilever. Now if the urface train i aumed to be contant even though it i loaded with a patch of thickne p then eqn. (6) i ufficient to predict the enhancement factor but would not be o imple if the urface train happen to change due to the modification of the cantilever by adding a part in the form of a patch. In that circumtance it i then required to numerically analyze the train variation at the cantilever urface for thi added tructure to quantify it influence on the overall enitivity enhancement. Thi in fact, a mentioned earlier form the bai of the preent paper and i elaborated in the ubequent ection. 3. Model uing COMSOL Multiphyic The geometry in figure1 wa analyzed uing numerical imulation with COMSOL Multiphyic (verion 4.2a) Finite Element Modeling oftware. The geometry compried of a 40mm x 10mm x 0.32mm tainle teel

3 (SS316) cantilever mounted on a fixed aluminum block, a 15gm tainle teel inert ma attached at the cantilever tip, a 15mm x 3mm patch fixed on the cantilever and a polyimide coated ilica fiber with diameter 150 μ m, hoting the FBG enor of length 4mm, wa mounted on the patch. It i conidered that the center of the FBG enor i at 5 mm from the fixed point of the cantilever. It i aumed that a 10 μ m thick layer of adheive connect the cantilever and the patch. A zoomed view of the patch mounted on the cantilever with adheive and a fiber attached on it with the adheive i hown in figure 2. The material propertie were decribed uing the databae available in goodfellow. Figure 3. Meh of the FBG-accelerometer. The cantilever dimenion were choen o a to have a low frequency, low g accelerometer. The effect of the patch material propertie and the patch thickne on the train enhancement and reonance frequency were tudied. 4. Simulation Reult 4.1 Effect of variation of patch thickne on train enhancement Figure 2. Zoomed cro-ection of the FBGaccelerometer. The Solid Mechanic Phyic interface wa ued and a Linear Elatic Material Model wa aumed for a Frequency Domain tudy. The equation governing the Frequency Domain tudy were 2 ρω uˆ. ˆ σ = Fv ˆ, ˆ σ = ˆ (7) ˆ Sˆ = ˆ 0 C : ( ε ε 0 ε inel ) L 1 T ε = [( uˆ) + uˆ] 2 u where i the diplacement in the three û = v w direction, ŝ i the tre tenor, ε i the total train tenor, Fˆ i the force, ω i the angular frequency and ρ i the denity. The mount and the crew were aigned fixed contraint, the remaining domain and boundarie being free. Body load for the cantilever, patch and the inert ma were applied in the negative z direction. The initial diplacement value were zero. A phyic-controlled normal meh compriing of free-tetrahedral element wa generated by the oftware (figure 3). The above geometry wa analyzed for the three patch material teflon, polyimide and aluminum. Teflon and polyimide have very low Young modulu compared to teel and are widely ued a backing patch for mounting FBG enor. Aluminum patch wa alo taken into conideration in our tudy to comprehend the pecific cae where the Young modulu of the patch i appreciably high a compared to that of the material generally ued a a backing patch like teflon or polyimide. The patch thickne wa varied upto 2200 μ m. The excitation frequency wa canned upto 10Hz and excitation amplitude wa fixed at 1g(0-p). Auming that the FBG i located 5mm from the cantilever pivot, the train experienced by the FBG in με i plotted againt varying patch thickne at excitation frequency 10Hz for the three different patch material e.g. teflon, polyimide and aluminum in figure 4. It i intereting to oberve that the train experienced by the FBG increae with the increae of the patch thickne up to a certain extent and then decreae with further increae of the patch thickne. It may alo be oberved that both enitivity and maximum allowable patch thickne are inverely related with the Young modulu of the patch material. The value conidered are 0.5GPa, 2.5GPa and 70GPa for teflon, polyimide and aluminum repectively.

4 Figure 4. Simulated train experienced by FBG on teflon, polyimide and aluminum patch for 10Hz excitation frequency and 1g (0-p) amplitude. For a teflon patch, the maximum train a experienced by the FBG i 963 με at 10 Hz which correpond to a wavelength hift of ~ 1156 pm (conidering 1.2 pm/ με wavelength hift) when the patch thickne i 1100 μ m. With a polyimide patch the maximum train achieved at 10Hz i 798 με for a patch thickne of 600 μ m, while that with aluminum it i 364 με for 100 μ m patch thickne. For thi architecture the train experienced by an FBG when mounted directly on the cantilever ha been found to be 317 με at 10Hz. Now a the train experienced by the FBG a a function of the patch thickne for different patch material and alo the ame without any patch ha already been computed, it i traightforward to obtain the enhancement factor (ay IF 1 ) for individual cae by taking the ratio of the two quantitie. It i thu apparent that the variation of the enhancement factor a a function of the patch thickne will be imilar in nature to thoe a depicted in figure 3-5 and only the amplitude will be reduced by a contant factor. Which mean the enitivity enhancement factor will increae with the increaing thickne of the patch up to a certain point and beyond that will gradually decreae with further increae in the patch thickne. The reult can be interpreted uing figure 5. We have computed the urface train ε [for x=5mm] a a function of the patch thickne (figure 5 i for a teflon patch) for different excitation frequencie with 1g (0-peak) excitation amplitude and a particular cae for 10 Hz i hown by the olid dot in the figure. Figure 5. Simulated plot of enhancement factor without the effect of urface train IF, decrement factor DF, IF x DF and enhancement factor with the effect of urface train IF 1 at 10Hz. It i found that the urface train of the cantilever decreae linearly with patch thickne and may be een a a decrement factor ay DF. The enhancement factor IF a a function of patch thickne uing eqn. (6), where the effect of urface train wa not conidered explicitly, i hown by the olid quare in the ame figure 6. The product of IF and DF i hown by the olid triangle which cloely matche with the computed enhancement factor IF 1 for thi particular cae a explained in the previou paragraph and i hown by the inverted triangle. Thu the two factor IF and DF contribute to practical IF 1 i.e. their product ha a maxima at a particular patch thickne and the effective train on the patch beyond a certain thickne decreae. However, it may be oberved that thi effect i not predominant up to ~250 μ m patch thickne. A a reult the plot for IF 1 and IF are cloe to each other up to thi thickne and i almot linear a obtained in [4], where a 150 m μ polyimide patch wa ued. 4.2 Strain ditribution along the fiber and optimal FBG location In a baic cantilever baed accelerometer where FBG i ued to meaure the bend induced urface train the FBG i in general glued near to the fixed point of the cantilever to maximize the enitivity within the permiible range. In general for a rectangular cantilever the urface train linearly decreae along the length of the cantilever from the fixed point to the tip.

5 Therefore, apparently it eem that the enitivity of the FBG will alo have linear dependence with repect to it location along the length of the cantilever. However, while corroborating experimental reult with the prediction it ha been oberved that the apect require a more careful tudy to identify the bet FBG location for maximum train ening. In practice a length of ~10-12 mm fiber i glued on the cantilever urface for thi purpoe which hot the FBG of length ~ 4-5 mm at ome location along it length. Strain ditribution along the fiber when glued on top of a patch ha been computed for varying length of the fiber. One reult for a 12 mm fiber itting on a teflon patch of thickne 500 µm and 1000 µm ha been hown in figure 6. The train ditribution related with the bending of the cantilever due to vibration for a 10Hz, 1g (0-p) inuoidal excitation ignal ha been hown in the figure. The train ditribution wa found to be parabolic in nature with a maximum at ome point from the fixed point and alo over a few millimeter the train i almot uniform. Hence care mut be taken to localize the FBG a cloe to the maximum train location a poible. Any deviation from thi location may caue a decreae in enitivity i.e. a reduced train induced wavelength hift. Alo ignificant chirp may be generated along a long length FBG due to the non-uniform train ditribution along the FBG. Ue of a mall length FBG would alleviate the problem. Figure 6. Simulated Strain along the fiber core for a teflon patch of 500 μ m and 1000 μ m for 1g (0-p) excitation amplitude at 10Hz. Simulation with Optiwave for a 4mm long FBG how that thi variation of train a found in the preent cae along the FBG i equivalent to a chirp of ~.01nm and thi amount of chirp doe not degrade the pectral characteritic of the FBG. 5. Concluion and Future Scope To the bet of our knowledge thi i for the firt time a detailed finite element analyi to undertand a practicable concept of uing a backing patch to enhance the enitivity of the cantilever-ma baed FBG accelerometer ha been reported. The work thoroughly explored the influence of patch material (Young modulu) and patch thicknee on the train tranfer to the FBG enor. In agreement with the numerical analyi, enitivity ~1062 pm/g ha been experimentally achieved with a particular accelerometer configuration with 1000 μ m teflon patch. Thi value i about 3 time a compared to a imilar FBG-accelerometer without patch. The effect of the patch material and the patch thickne on the vibration characteritic of the FBG accelerometer alo require a through invetigation and i of our future target. Further experiment with different patch thicknee and at different excitation frequencie will be carried out to corroborate the imulation reult. The complete numerical analyi and the experimental reult will be preented in our forthcoming paper. 6. Reference 1. M. D. Todd, G. A. Johnon, B. A. Althoue, and S. T. Vohra, Flexural beam-baed fiber Bragg grating accelerometer, IEEE Photonic Technology Letter, Volume 10, No. 11(1998) 2. T. A. Berkoff and A. D. Kerey, Experimental demontration of a fiber Bragg grating accelerometer, IEEE Photonic Technology Letter, Volume 8, No. 12 (1996) 3. Wu, J., Maek, V., Cada, M., The poible ue of fiber Bragg grating baed accelerometer for eimic meaurement, Canadian Conference on Electrical and Computer Engineering, page number (2009) 4. N. Baumallick, I. Chatterjee, P. Biwa, K. Dagupta, S. Bandyopadhyay, Fiber Bragg Grating Accelerometer with Enhanced Senitivity, Senor and Actuator A: Phyical, Volume 173, Iue 1, page number (2012)

6 5. P. F. C. Antune et al, Optical fiber accelerometer ytem for tructural dynamic monitoring, IEEE Senor Journal, Volume 9, No. 11, page number (2009) 8. Acknowledgement The author thank COMSOL Support Team for aiding in imulation.