Many quantities are transduced in a displacement and then in an electric signal (pressure, temperature, acceleration). Prof. B.

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1 Displacmn snsors Many quaniis ar ransducd in a displacmn and hn in an lcric signal (prssur, mpraur, acclraion).

2 Poniomrs Poniomrs i p p i o i p A poniomr is basd on a sliding conac moving on a rsisor.

3 Poniomrs Som nos.. Th movmn of h sliding conac can b ranslaional, roaional or implmnd by an hli.

4 Poniomrs al dvics

5 Poniomrs

6 Poniomrs

7 Poniomrs i p o o i In cas of AC powr supply h following modl should b considrd: wih h following assumpions assuring a prvaln rsisiv bhaviour of h dvic. L' 1 C ' 7

8 Poniomrs sponsiviy: i p o o i S D 0 D i S incrass wih

9 Poniomrs Th maimum rsponsiviy is givn by: Th powr is givn by: P 2 p and S ma ma sinc P P ma 2 P ma p Th maimum is: ma P ma p Ohrwis slf-haing phnomna can aris hus compromising h dvic opraions! Th maimum rsponsiviiy valu is S ma ma P ma p S and Sma incras wih p p mus b as high as possibl!

10 Poniomrs Eampl P=0.2 W =1kΩ =0.5in1cm S ma S P V/cm 1 p

11 Poniomrs Singl slid-wir poniomrs show -a coninuous rsisanc variaion; -High rsoluion -low valus and hnc low S valus. Wirwound poniomrs show High sabiliy Low mpraur cofficin Fini rsoluion

12 Poniomrs Wirwound poniomrs has a fini rsoluion Eampl: 500 urns in 1 cm lngh lads o a rsouion of: l cm 210 cm

13 Poniomrs Crm and plasic poniomrs hav: good rsoluion (infini), Long lif High nois du o h surfac roughnss, Mdium mpraur cofficin.

14 Poniomrs Opn Circui bhaviour p S D D 0 i i o OC i Th dvic OC bhaviour is linar!

15 Poniomrs al bhaviour du o load impdnc p i o m m m i p 1 1 i m i m / Thn nominal bhaviour can b obaind if p / m 0 A low p valu is rquird o assur a good linariy! i / Trad off bwn rsponsiviy and linariy! 15

16 Poniomrs Eampl (1/2) In cas of m =10 k, h rsisanc valu in h rang [100, 100 k ] assuring a non linariy rror of 1% of h full scal mus b sarchd for. Considring h P ma valu is consan in h considrd rsisanc rang, h valu assuring h bs rsponsiviy mus b also sarchd for. p i o m 16

17 Poniomrs Eampl (2/2) o c Idally i 0 m m m c In h ral cas 1 i 1 p m 1 i m 2 i i p 1 2 i i p p m m assums null valus for i / =0,1 By fiing m <0.01 h maimum (o incras h rsponsiviy) allowabl valu of p can b found. 17

18 Poniomrs Linarizaion A risor lin can b usd. 1 lin ml / p ml m 1 lin // p 1 i 2 m // p i ml i / 18

19 Poniomrs Linarizaion Wihou linarizaion 0 m m By using h linarizaion rsisor ml m 2 i i p 1 2 i i p p m m assums null valus for i / =0,1 i i i p i p 1 1 lin m i p i i i p lin m ml is null for i / =0,1 ml / and i m m lin i / 19

20 Srain Gaugs Srain gaugs ar basd on h dpndnc of h valu by h dformaion. Two main filds of applicaion: Load forc masurmn; adou sragy for ohr snsors (Prssur, forc, inrial). Th suppor layr allows for asily manag h dvic and provids also lcrical inslualion. 20

21 Srain Gaugs Th oupu rsisanc changs wih h applid srain. Nominal valu 0 A rsisanc variaion +D 0 is princd. A rsisanc variaion -D 0 is princd. 21

22 Srain Gaugs 22

23 Srain Gaugs 23

24 Srain Gaugs Mallic foil: (A) adhsiv bondd o h suppor layr or (C) molcularly bondd ino cramic layr, linar low gag facor (1-2) Smiconducor: (B) adhsiv bondd o h surfac or (D) diffusd, non linar high gag facor (200) 24

25 Srain Gaugs: marials Consanan - Consanan is a coppr-nickl alloy and h mos commonly usd alloy usd for srain gaug marics. Consanan has a vry sabl rsisanc ovr a larg mpraur rang, making i h prfc choic for gnral-purpos gaugs. Consanan can b procssd o provid mpraur compnsaion for a variy of cofficins of hrmal pansion. Consanan-basd gaugs ar gnrally h las pnsiv of h srain gaug alloys, du o hir wid-scal usag. Annald Consanan - Annald Consanan alloy is usd whn larg srains, usually ovr 5%, ar pcd. This alloy will princ rsisanc drif undr high cyclic srain, so gaugs ha us annald Consanan should no b usd in cyclic loading applicaions. Isolasic - Isolasic alloy is usd for dynamic srain masurmns and cyclic loading applicaions. Gaugs ha us isolasic alloys hav a largr gaug facor han gnral purpos gaugs, and provid a largr signal o nois raio. Isolasic alloy is snsiiv o hrmal ffcs, so i is bs usd in mpraur-conrolld nvironmns Karma - Karma alloy gaugs ar rmly sabl ovr im and ar appropria for long rm monioring applicaions. Karma alloy provids br accuracy a rm mpraurs han gnral purpos gaugs, bu is difficul o soldr. Karma alloy can b procssd o provid mpraur compnsaion for a variy of cofficins of hrmal pansion. 25

26 Srain Gaugs: marials Consanan alloy (by WIKIPEDIA) Of all modrn srain gaug alloys, consanan is h olds, and sill h mos widly usd. This siuaion rflcs h fac ha consanan has h bs ovrall combinaion of propris ndd for many srain gaug applicaions. This alloy has, for ampl, an adqualy high srain snsiiviy, or gaug facor, which is rlaivly insnsiiv o srain lvl and mpraur. Is rsisiviy is high nough o achiv suiabl rsisanc valus in vn vry small grids, and is mpraur cofficin of rsisanc is no cssiv. In addiion, consanan is characrizd by good faigu lif and rlaivly high longaion capabiliy. Howvr, consanan nds o hibi a coninuous drif a mpraurs abov 65 C (150 F); and his characrisic should b akn ino accoun whn zro sabiliy of h srain gaug is criical ovr a priod of hours or days. Consanan is also usd for lcrical rsisiviy haing. 26

27 Srain Gaugs: an applicaion 27

28 Srain Gaugs How o choos h Srain Gaug? mallic alloy suppor Grid lngh and configuraion Nominal rsisanc prcision sabiliy mpraur srain lyf im nvironmn 30

29 Srain Gaugs 31

30 Srain Gaugs 32

31 Srain Gaugs Transvrsal snsiiviy Th capabiliy o prciv srain in h prpndicular dircion as rspc h nominal dircion. Bold lmns rduc such snsiiviy. 33

32 Srain Gaugs 34

33 Srain Gaugs 35

34 Srain Gaugs An aial forc, F, producs a srss,, which is rlad o h dformaion (srain),, by h Young modul, Y : F A Y Y dl l is dimnsionlss (srain/lngh). (1 microsrain=1=10-6 m/m).

35 ) ( ) ( G G G G L dl G In cas of smiconducor: d d Typ p Typ n 0 unsrssd 25 C 37 Srain Gaugs Which is h rlaionship bwn D/ 0 and?

36 Srain Gaugs Th Gag facor l 2 D A 4 1 da DdD; 2 da dd dl 2 2 A D l D Is h Poisson coff d d d dl (1 c(1 2 ) 2 ) l G (1 c(1 2 ) 2 ) l [ ] A l dl d A A dl d da l A C is h Bridgman consan l 2 A d c da dv V 2 D V l 4 dv DldD D 2 4 dv dd dl 2 V D l d dl c(1 2 ) l 2 dl l dl (1 2 )

37 Srain Gaugs Eampl SG spcificaions: G=2.0, =120 Ω, Y=210 GPa). Find D in cas of =810 6 Pa. G l l Y G l l 2 ( )

38 Srain Gaugs Bnding Srss Masurmn 1-gag Sysm As illusrad blow, bond a srain gag on h op surfac of a canilvr wih a rcangular scion. If load W is applid o h unfid nd of h canilvr, h sraingag bonding si has h following surfac srss σ: σ = ε Y Srain ε is obaind hrough h following quaion: ε = 6WL/(Ebh 2 ) whr: B is h canilvr widh, h is h canilvr hicknss L is h disanc from h load poin o h cnr of srain gag This approach can b adopd for h sak of SG characrizaion by: - using known Loads L -prforming h D masurmn O To sima h applid Load in cas a calibrad SG is usd.

39 Srain Gaugs Tmpraur ffcs T 1 T 2 T 3 41

40 Dummy snsors Srain Gaugs 42