MEASUREMENT OF SMALL LINEAR DISPLACEMENTS WITH INDUCTIVE TRANSDUCER

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1 MEASUEMET OF SMALL LIEA DISPLACEMETS WITH IDUCTIVE TASDUCE Vslka Ivanchva, Silvia Kachulkova, ozhida Dzhudzhv 3 and Vladislav Slavov 4 ) Tchnical Univsity of Sofia, Faculty of Automation, 8 Klimnt Ohidski, 000 Sofia, ulgaia, vivanchva@tu-sofia.bg ) Tchnical Univsity of Sofia, Faculty of Elctical Engining, 8 Klimnt Ohidski, 000 Sofia, ulgaia, s_kachulkova@tu-sofia.bg 3) Tchnical Univsity of Sofia, Faculty of Automation, 8 Klimnt Ohidski, 000 Sofia, ulgaia, bojida.djudgv@abv.bg 4) Tchnical Univsity of Sofia, Faculty of Automation, 8 Klimnt Ohidski, 000 Sofia, ulgaia, vladi_s@abv.bg Abstact: This aticl discusss inductiv tansducs and thi application fo lina masumnt. Th functions of convsion a xpimntally dfind and xamind. Ky wods: Lina, nonlctical masumnt, inductiv tansduc,oscillato, fquncy disciminato, Whatston idg.. Elctomagntic induction pincipls Michal Faaday was on of th fist scintists to study th lationship btwn magntism and lcticity. Faaday s Laws can b summaizd as: Th magnitud of an EMF poducd in a conducto is popotional to th at of chang of magntic flux-linkag xpincd by th conducto. Whn a conducto is xposd to a changing magntic fild, an lctic cunt will flow in th conducto. Th EMF givn by th at of chang of th magntic flux is: d Φ = () wh is th lctomotiv foc (EMF) in volts and Φ is th magntic flux in Wbs. Th diction of th lctomotiv foc is givn by Lnz's law. Fo a tightly wound coil of wi, composd of idntical loops, ach with th sam Φ, Faaday's law of induction stats that = d Φ () wh is th numb of tuns of wi and Φ is th magntic flux in Wbs though a singl loop. W can vay th inducd mf by vaying o dφ. Changing is had to do bcaus it is a physical dimnsional chang. It is asi to dφ chang by changing.. Slf inductanc A singl coil of many tuns has inductiv poptis du to th magntic intaction of adjacnt loops in th coil. If th loops a wound in th sam diction th total ffct of this intaction is an inducd back mf that opposs th initial cunt chang. This slf inductanc is a fom of intia sisting cunt chang in th coil. Th slf- inducd mf E can b xpssd in quation fom as follows:

2 = L di (3) wh L is th slf-inductanc and Δi/Δt is th cunt chang p unit tim in th coil. If E is masud in volts and Δi/Δt in amps p scond, th inductanc is givn in hnis, H = V-sc/A. Th ngativ sign is consistnt with Lnz's law and consvation of ngy. Thus w hav an xpssion fo th coil inductanc. L = S o a L = µ 0 µ i (4) wh and - numb of tuns on pimay and sconday coils. If w plac i = imax sinωt in th abov xpssion, w can dduc th tansfom quation fo sconday mf. E = 4, 44 f Φ max 4. Masumnts of vaiations in th valu of inductanc On mthod of dtcting a chang in th valu of inductanc is to us a Whatston idg cicuit at AC (fig.). wh i S = - luctnc. µ 0 µ a Fom th fomula it is sn that th inductanc can b vaid by vaying th paamts, µ, a o i. 3. Mutual inductanc Whn an mf is inducd into a cicuit by a chang of flux that is poducd by a cunt changing in an adjacnt cicuit, th popty is calld mutual inductanc (M). Fig.. Whatston idg cicuit Whn th cicuit is balancd w hav th following quations: s x = (6) Fig.. Mutual inductanc cucuit On fig. an AC souc gnats an altnating cunt in th pimay coil. This poducs an altnating flux in th magntic path which inducs an altnating mf in th sconday coil. If th sconday cicuit w closd, an altnating cunt would flow in it. This is th pincipl of th tansfom. Th inducd mf is th sconday cicuit is givn by: di = (5) S L s L x = (7) Standad inductos a not asy to manufactu, so this mthod is vy sldom usd. It also suffs fom th usual disadvantags of bidg masumnts. 5. lock diagam of an inductiv tansducs sach fo masumnt of small lina s. On figu 3 is shown th block diagam of an inductiv tansduc fo masumnt of small lina s.

3 Fig. 5 shows connct th xpimntal st. Fig.3. lock diagam Fig.4 shows th schm fo sach on th tansfomation functions. Th way it woks is: th inductanc vais th fquncy of an oscillato, whos output is passd though a fquncy disciminato to a dtcto. Th inductiv tansduc bcoms pat of th tund cicuit of th oscillato, and vaying th inductanc by vaying th position of th tansduc will vay th fquncy of oscillation. Th fquncy disciminato contains a cicuit fo convting ths vaiations into voltag vaiations. Ths voltag vaiations a thn amplifid and indicatd on th mt. An inductiv tansduc can b usd with an oscillato, a fquncy disciminato and an amplifi to fom a complt FM systm. Movmnt of th inductiv tansduc vais th fquncy of th oscillato and this fquncy chang is accompanid by a chang in output fom th disciminato, which can b masud and latd to th tansduc position. Fig.4. Schm fo sach on th tansfomation functions Fig. 5. Expimntal st Fig.6. Singl-coil vaiabl inductanc tansduc Fig. 6 shows singl-coil vaiabl inductanc tansduc fo lina s. It consists of a singl coil wound aound an insulating fom. Into it can slid a co of a fit matial with a lativ pmability µ. Th valu of µ is givn by th slop of /H cuv of th fit matial. Sinc th valu of H changs as w push th co into th coil, so th valu of µ may chang if th /H cuv is not lina. Th co is attachd to a od which fits on to th slid of TK94, nabling th position of th co insid th coil to b masud. 6. Masumnt sults Examining th tansfomation functions of th inductiv tansducs fo masumnt of small lina s. Th masumnts w mad und th following conditions: fquncy of th masud signal 476 khz, th opational amplifi gain is st to 0, lina fom 0 to mm.

4 6.. Examining th tansfomation function of a singl inductiv tansduc with a movabl co fo th psnc of hystsis. Th tansduc is xamind on a position of th slid at 55 mm and a chang of th lina fom 0 to mm and fom to 0 mm. Th sults a shown on figu 7 and in tabl. On figu 7 it is obvious that almost a lina tansfomation function can b achivd fo lina s fom 3 to 9 mm and almost th sam valus fo both dictions. Lina Voltag whn having lina fom 0 to mm Tabl Voltag whn having lina fom to 0 mm Absolut o lativ o [mm] [V] [V] [V] % 0 - -,05 0,05 5,00-0,96-0,99 0,03 3,3-0,84-0,88 0,04 4,76 3-0,63-0,67 0,06 6,35 4-0,8-0,38 0, 3,57 4, ,7 0,6 0,0 5,88 6 0,8 0,76 0,04 5,00 Fig Examining th tansfomation function of a singl inductiv tansduc with a movabl co whn th position of th slid is changd to 50 mm. 7,4,9 0, 7,86 8,8,75 0,06 3,3 9,94,93 0,0 0,5 0,89,9 0,0,06,76,79 0,03,70,6,64 0,03,86 3,48,5 0,0,35 4,38,39 0,0 0,7 5,3,3 0 0,00 6,6,7 0,0 0,79 7,4,4 0 0,00 8,4,4 0 0,00 Fig.8. Th sults a shown on figu 8 and in tabl. On figu 8 it is obvious that almost a lina tansfomation function can b achivd fo lina s fom 6 to mm and almost th sam valus fo both dictions. 9,7,7 0 0,00 0,3,3 0,0 0,76,4,39 0,0,4,5,5 0 0,00

5 Lina [mm] Tabl Voltag whn having lina fom 0 to mm [V] 0 3, 3,0,89 3,65 4,5 5,35 6,6 7, 9,6 0,34,48,65 3,8 4 3,05 5 3, 5,5 3,06 6,9 7,6 8,7 9 0,4 9, ,63 -,9 -,53 7. Conclusion. 7. Conclusion. Th pap is ddicatd on th inductiv tansducs and thi application fo masumnt of small lina s in th od of mm. Expimntally a dfind and xamind th tansfomation functions of th inductiv tansduc and it is dfind th lina pat of th tansmission chaactistic. Th tansducs a connctd in a cicuit consisting of sonant cicuit, oscillato, disciminato, amplifi and a voltmt. Ths tansducs can b applid vy succssfully wh it is ndd a pcis dtmination of th location of objcts in th od of µm and mm. It can b usd to dsign a mt movmnt dvic but just fo vy littl movmnts wh th tansfomation function is lina. Acknowldgmnt. Th sachs, th sults of which a psntd in this publication a fundd by intnal comptition TU-0 contact to suppot PhD studnt P "Study and optimization of pocsss fo masuing vibation". fncs: [] Wbst John G., Masumnt Instumntation and Snsos, 999. [] Под общата редакция на проф. Христо Радев Метрология и измервателна техника, том,,3 -София, Софтрейд, 00. [3] Applications-H-Q-Full/dp/ [4] Th Masumnt, Instumntation and Snso, John G. Wbst, 999 by CL Pss LLC. [5]