MINIATURIZATION OF INERTIAL MAGNETOELECTRIC VIBRATION VELOCITY SENSOR WITH HIGH FREQUENCY RESPONSE AT LOW FREQUENCY BAND

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1 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: MINIATURIZATION OF INERTIAL MAGNETOELECTRIC VIBRATION VELOCITY SENSOR WITH HIGH FREQUENCY RESPONSE AT LOW FREQUENCY BAND XI CHEN SHUIBAO YU College o Mathematic Phyic and Inormation Engineering Zhejiang Normal Univerity Jinhua 34 Zhejiang China. College o Mathematic Phyic and Inormation Engineering Zhejiang Normal Univerity Jinhua 34 Zhejiang China. chenxi@zjnu.cn yb@zjnu.cn ABSTRACT The requency repone o the inertial magnetoelectric vibration velocity enor i limited in the low requency range due to the character o econd order high pa ilter o the tructure. For better perormance in the low requency range the traditional method i to increae the initial ma o the enor which will increae the ize and weight tremendouly. Thi paper preent a requency-elected compenation network to improve the perormance o the requency repone at low requency band keeping the enor in mall ize and light weight. The requency-elected network which i compoed o ampliier reiter and capacitance i connected to the output port o the enor in cacade without any modiication o the enor tructure. Ater compenation the requency band o the enor i lattened and the requency repone till ha the character o econd order high pa ilter while the reonant requency decreae rom Hz to about.9hz. The experimental reult have hown that the enor ater been compenated ha good perormance in the low requency range. Keyword: Magnetoelectric Vibration Velocity Senor Compenation Network Traner Function Reonant Frequency Low Frequency Band. INTRODUCTION Some vibration uch a eimic wave bridge vibration vibration o water turbine have no tatic reerence point relative to inertial pace. Low requency component in thee vibration are alway ignored ince the mall acceleration value could hardly be experienced. But in ome area uch a indutrial machine it i igniicant to monitor low requency vibration which are vital indicator o their health []. Low requency vibration detection in thee ield i mainly baed on high enitivity excellent perormance good reliability inertial enor which ha requency range rom Hz to khz at leat [ 4]. Several kind o enor have been propoed in relevant reearche to detect the abolute vibration (The vibration which ha no tatic reerence point relative to inertial pace) uch a iber optic enor baed on Fiber Bragg Grating (FBG) [5 8] piezoelectric vibration enor [9 ] magnetoelectric velocity enor or accelerometer [ 3]. In every particular application there ha the mot appropriate enor or it [4]. One o the mot widely ued enor in the low requency abolute vibration detection i the inertial magnetoelectric velocity enor which ha the advantage o wide bandwidth (-Hz) low output impedance high reolution and low cot [5 6]. All inertial enor uing an electrical ield hare a baic tructure called pring-ma ytem [7 8]. The inertial magnetoelectric velocity enor with thi tructure ha the character o econd order band pa ilter. In thi cae the meaurement o low requency i limited due to the high requency reonance. To improve the output ignal rom the inertial magnetoelectric velocity enor in the range o low requency one o the method i to increae the inertial ma to decreae the enor reonant requency [9]. A a reult the ize and weight o the enor have been increaed tremendouly. In thi ituation the ma loading can aect the 79

2 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: dynamic characteritic o the tructure to which it i mounted []. The typical practice to eliminate the ma loading eect i to ue the lightet mallet enor that till atiie all the perormance requirement [4]. So it i igniicant to ue eicient method or requency repone improvement at the condition o keeping the light and mall pring-ma ytem. In thi paper we invetigated the amplituderequency characteritic o the inertial magnetoelectric velocity enor. According to it model and traner unction an optimized requency-elected compenation network wa put orward which expand the working bandwidth in the low requency range. Ater compenation it till ha the advantage o at real-time repone light and mall pring-ma ytem.. SENSOR MODEL An inertial magnetoelectric velocity enor i a ma upported on a pring and driven by an external orce. The orce in mall enor i normally generated electromagnetically. The upended ma can either be the magnet with a upporting tructure or in ome cae the coil itel. A mechanical model o the inertial magnetoelectric velocity enor i hown in Fig.. Fig.. Mechanical Model O An Inertial Magnetoelectric Velocity Senor It can be modeled by a imple pring-madamping aembly m i the inertial ma k i pring contant and c i the damping. Suppoing y i abolute coordinate o the inertial ma y i convected coordinate and y repreent the relative coordinate the motion equation can be decribed a 8 According to Newton econd law the kinetic equation can be etablihed a dy dy m c ky dt dt () And the electromagnetic induction equation can be expreed a dy() t dy() t E() t BNL α (3) dt dt B i the magnetic induction intenity N i the number o coil turn L i the average length o ingle-turn coil α BNL i the enitivity. Auming the exciter i making periodic inuoidal vibration y Ainωt (4) Then the olution o equation () can be given by y Ae t+ + A t (5) ω t in( ω ϕ ) in( ω ϕ) A Aω / ( ω ) + ( ω ) (6) tan ϕ ω / ( ω ) (7) Here A ω ' ϕ ' i contant ω ω/ ω i reonant requency ω π k / m (8) i angular requency o the enor c / mk (9) i damping ratio. The irt term in equation (5) will decreae rapidly with the increae o time. Thereore it could be approximately written a ollow y A in( ωt ϕ) () It can be concluded rom equation () that the inertial ma i making inuoidal vibration and the vibration requency i the ame with the meaured object. When ω >> and < i.e. the vibration requency o the meaured object i much larger than the reonant requency o the pringma-damping ytem it can be obtained that A A tanϕ. Hence we have y A in( ωt ϕ) Ain( ωt π) Ain( ωt) () dy dy + () dt dt It mean that the ma i in tatic tate in abolute coordinate while the hell i making the ame movement with the meaured object. For mechanical tructure ake the minimum dy dy dy value o the reonant requency could only be made + () dt dt dt at about 5-Hz at bet. According to equation (8)

3 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: decreaing the value o pring contant k or increaing the inertial ma m could reduce the reonant requency. In gravity ield the diplacement y o the pring can be expreed a mg g g y (3) k ( ω) ( π ) g i contant o gravity acceleration. Suppoing the reonant requency Hz it could be calculated rom equation (3) that the pring tatic elongation i more than 5cm long. Obviouly the ize o the enor i increaed out o the requirement and the tability could hardly be atiied. 3. COMPENSATION Vo α G () H( ) C () C () V + ω+ ω i α + ω+ ω ω i equivalent angular requency o the enor ytem ater been compenated i equivalent damping ratio. (7) 3. Principle o Compenation Appling Laplace tranorm to equation () (3) the traner unction o the enor can be deduced a α H( ) (4) + ω + ω jω ω π. Uing equation (4) the magnitude and phae repone o the enor a a unction o requency and damping ratio can be calculated a hown in equation (5) and (6) repectively H( jω) αλ (5) ( λ) + ( λ ) λ ϕ tan [ ] λ (6) λ /. Equation (4) how that the traner unction ha the character o econd order high pa ilter. A hown in Fig. it i eaible to eek a compenation network connected to the enor in cacade when the compenated enor ytem till ha the character o econd order high pa ilter and the reonant requency o the compenated enor ytem i much lower than the uncompenated one. The traner unction o the compenated enor ytem can be expreed a Fig.. Schematic O Amplitude-Frequency Characteritic Compenation The magnitude and phae repone o the compenated enor ytem a can be calculated a G( jω) αλ (8) ( λ) + ( λ ) λ φ tan [ ] λ (9) λ / i equivalent reonant requency. The traner unction o the compenation network rom equation (7) can be written a + ω + ω C() C () () () HP + CBP + CLP + ω + ω () CHP () + ω + ω () ω CBP () + ω+ ω () CLP () ω + ω + ω Equation () i a econd order all-pa network which requency repone i requency-elected. The principle block diagram i hown in Fig. 3. (3) 8

4 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: Fig. 3. Principle Block Diagram O Frequency- Selected Compenation 3. Realization o Compenation The realization o the requency-elected compenation i hown in Fig. 4. It can be concluded that Fig. 4. Circuit Diagram O The Frequency-Selected Compenation Network V () V () R5 + R6 R4 R5 R3 + R4 R + R R R + + R R + R RC R RRCC R5 + R6 R4 V3() R5 R3 + R4 RC V () R5 + R6 R4 R6 + + R R + R RC R RRCC V4 () V () R5 + R6 R4 R5 R3 + R4 RRCC R + R R R + + R R + R RC R RRCC (4) (5) (6) Suppoing C C C R5 R6 R3 R4 R R R8 R R R then equation (4) (6) can be impliied a V () (7) V () + + RC RC C () V3 () RC V () + + RC RC V 4 () RC V () + + RC RC can be expreed a R V() R V3 () R V4() C () + + R8 V() R9 V() R7 V() R R + + R9 RC R7 RC + + RC RC Comparing equation () with (3) it can be concluded that (8) (9) (3) R R (3) R R C C π RC (3) RR 7 (33) R9 R (34) R7 π RC Equation (3) and (3) mean the equivalent damping ratio and equivalent reonant requency o the compenated enor ytem were determined by the R-C (reitancecapacitance) parameter o the circuit. The damping ratio and reonant requency o the original enor will inluence the ummation actor o the circuit. 3.3 Simpliication o Compenation Network For miniaturization o the enor ytem not only the enor hould be maller but alo the compenation network need be impliied. Suppoing the traner unction o the compenation network can be expreed a + ω + ω C () ω + ω Then the traner unction o the compenated enor ytem can be expreed a (35) 8

5 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: ( ) G () H C () α ω+ ω (36) The magnitude and phae repone o the compenated enor ytem can be calculated a αλ G ( jω) ( λ) ( λ) + λ φ tan [ ] λ (37) (38) Comparing equation (8) with (37) (9) with (38) it could be concluded that the enor ytem uing thee two kind o compenation network ha the ame magnitude repone while the phae repone i revere. Suppoing Hz Hz α the imulation curve o the normalized requency repone beore and ater compenation can be plotted a hown in Fig. 5. The imulation curve o phae repone beore and ater compenation are hown in Fig. 6. Obviouly the enor ha much better perormance in requency repone at low requency band ater been compenated. From Fig. 6 it can be een that there i a correponding time lag aociated with a enor output when compared to the input at requencie near the natural requency o the enor. Data collected uing the enor i ubject to coniderable phae hit when it requency content i around the natural requency o the enor. The maller phae error the more accurate data analyi will be. The compenation network G () tranlate the curve o the phae repone to lower requency direction keeping the curve hape unchangeable. A a reult the compenated enor ha le phae error than the original one at the ame requency point. And both the phae repone o the compenation network G'( ) and G () have the ame phae error. Thereore according to equation (35) the circuit o compenation network could be impliied a hown in Fig. 7. Fig. 5. Simulation Curve O The Normalized Frequency Repone Beore And Ater Compenation ( Hz Hz.77 α ) Fig. 6. Simulation Curve O Phae Repone Beore And Ater Compenation ( Hz Hz.77 α ) Fig. 7. Simpliied Circuit Diagram O The Frequency- Selected Compenation Network 4. EXPERIMENT AND RESULTS Experimental Setup The model o the original enor we manuactured i named a CS-CD-5. The experimental etup ued i hown chematically in Fig. 8. The CS-CD-5 enor with compenation

6 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: network wa rigidly mounted on the vibration table (another commercially available inertial magnetoelectric velocity enor Bently 9 rom GE Meaurement & Control Solution wa alo mounted on the vibration table or comparion tet) which ha the capability o controlling the vibration parameter preciely. The enor wa expoed to inuoidal orce at dierent requencie. The output ignal rom the enor and compenation network were meaured uing a digital ocillocope without any external ignal conditioner or ampliier. damping ratio. The tet reult at mm/ velocity i hown in table. The calculated average value o the reonant requency wa.49hz and the damping ratio wa.53. Thereore the main parameter value o the compenation network can be determined a hown in table. Fig. 9 i a photograph o the actual enor that ha been compenated by requency-elected network. Table I Experimental Data O Frequency Repone For The Original Senor C-Cd-5 Frequency n (Hz) Normalized amplitude A n Fig. 8. Experimental ytem or vibration tet 4. Parameter Determination The nominal reonant requency o the CS- CD-5 enor and the damping ratio i undetermined. The exact value o and can be obtained a ollow: get a group o normalized amplitude A A A 3 An with correponding requencie 3 n ubtituting them into equation (5) we get An (39) + n n n i natural number. Thereore can be derived a equation (4) and (4). n (4) ( ) + ( ) + An 4 4 n n + An (4) n Solving equation (4) and (4) yield n olution o and. The average value o and wa ued a inal reonant requency and Table II Main Parameter Value O The Compenation Network Parameter Value Parameter Value.77 R (kω) (Hz).938 R 7 (kω). R 8 (kω) 7 R 9 (kω) 5.4 R (kω) 7 C ( µ F) Fig. 9. Photograph O The Senor With Frequency- Selected Compenation Network 4.3 Experimental Setup A clear comparion between the theoretical normalized requency repone and the 84

7 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: experimental one beore and ater compenation i hown in Fig.. It how that the experimental normalized requency repone i very cloe to the theoretical one. Some experimental data deviated rom the theoretical curve i due to an approximation o the R C value. The normalized requency repone beore compenation ha mall reonant peak and wa lattened ater been compenated. Experimental comparion between 9 and compenated CS-CD-5 were alo carried out. The main parameter or comparion are lited in table 3. The enor CS-CD-5 we ued or compenation ha much maller ize and weight than 9 but higher reonant requency. However the reonant requency o the CS-CD-5 enor decreae rom Hz to.93 Hz ater been compenated while it till keep the mall ize and light weight. Table III Main Parameter For Comparion Between 9 And Compenated C-Cd-5 Parameter 9 CS-CD- 5 Compenated CS-CD-5 Height (mm) Diameter (mm) Weight(g) Frequency Repone (Hz -3dB) Senitivity (mv/(mm - ) Hz) Dynamic Operating Range (mm).54.. Fig.. Output Waveorm Quality Comparion Between 9 And Compenated CS-CD-5 At Sinuoidal Excitation O Hz 4mm/S The comparion o the output waveorm quality between 9 and compenated CS-CD-5 at dierent requencie with the ame inuoidal excitation velocity i hown in Fig. -4. Obviouly the compenated CS-CD-5 ha better perormance in requency repone in the low requency range. It hould be pointed out that the output waveorm o 9 ha little ditortion at.4hz while the compenated one o CS-CD-5 till ha good waveorm quality. Both 9 and compenated CS-CD-5 output waveorm were ditorted eriouly at.hz. However the output waveorm o compenated CS-CD-5 can till relect the characteritic o inuoidal vibration while the one o 9 i ubmerged in noie. Fig.. Output Waveorm Quality Comparion Between 9 And Compenated CS-CD-5 At Sinuoidal Excitation O Hz mm/s Fig.. Experimental And Theoretical Frequency Repone Beore And Ater Compenation (.49 Hz.938 Hz ) 85

8 th February 3. Vol. 48 No. 5-3 JATIT & LLS. All right reerved. ISSN: E-ISSN: ACKNOWLEDGEMENTS Thi work wa upported in part by the Science and Technology Hall o Zhejiang Province in China under Grant 9C36. REFRENCES: Fig. 3. Output Waveorm Quality Comparion Between 9 And Compenated CS-CD-5 At Sinuoidal Excitation O.4Hz mm/s Fig. 4. Output Waveorm Quality Comparion Between 9 And Compenated CS-CD-5 At Sinuoidal Excitation O.Hz mm/s. 5. CONCLUSION The inertial magnetoelectric velocity enor ha the character o econd order high pa ilter and the reonant requency cannot be very low according to the mechanical model. Since the requency repone cannot meet the demand in the low requency range the cope o application i limited. To improve the perormance at low requency a requency-elected network or amplitude-requency characteritic compenation wa developed. Experimental veriication wa perormed and ound to be in good agreement with the theoretical analyi. At the circumtance o unchanging the original enor tructure the requency-elected network improved the requency repone in the low requency range by changing the R C parameter o the circuit. Thereore it till ha the character o mall ize and light weight. It can meet the demand in vibration meaurement epecially in the low requency range. [] T. K. Gangopadhyay Propect or Fibre Bragg Grating and Fabry-Perot Intererometer in ibre-optic vibration ening Senor and Actuator A vol. 3 n. pp [] T. C. Liang Y. L. Lin Ground vibration detection with iber optic enor Optic Communication vol. 85 n. 9 pp [3] Y. Itakura N. Fujii T. Sawada Baic characteritic o ground vibration enor or the detection o debri low Phyic and Chemitry o the Earth Part B vol. 5 n. 9 pp [4] D. Peer C. Hatzeld R. Werthchützky Development o an electrodynamic velocity enor or active mounting tructure Procedia Engineering vol. 5 pp [5] J. Wu V. Maek M. Cada The poible ue o iber Bragg grating baed accelerometer or eimic meaurement Canadian Conerence on Electrical and Computer Engineering (Page: Year o Publication: 9 ISBN: ). [6] N. Baumallick I. Chatterjee P. Biwa et al. Fiber Bragg grating accelerometer with enhanced enitivity Senor and Actuator A vol. 73 n. pp [7] L. H. Kang D. K. Kim J. H. Han Etimation o dynamic tructural diplacement uing iber Bragg grating train enor Journal o Sound and Vibration vol. 35 n. 3 pp [8] F.Xie J. Ren Z. Chen et al. Vibrationdiplacement meaurement with a highly tabilied optical iber Michelon intererometer ytem Optic & Laer Technology vol. 4 n. pp [9] T. Li Y. H. Chen J. Ma Frequency dependence o piezoelectric vibration velocity Senor and Actuator A vol. 38 n. pp [] A. Yu P. Jiang Z. L. Wang Nanogenerator a el-powered vibration enor Nano Energy. vol. n. 3 pp

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