Lesson 2. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

Transcription

1 Lesson 2 Thermomechncl Mesurements for Energy Systems (MEN) Mesurements for Mechncl Systems nd Producton (MME) 1 A.Y Zccr (no ) Del Prete

2 A U The property A s clled: «mesurnd» the reference property U s the «mesurement unt» the rto between A nd U tody s lwys performed by clbrted nstrument! the mesurement expresses the mpltude or ntensty of the property A we re studyng Drect mesurements: ndrect mesurements: when there s drect comprson between the mesurnd A nd the unt U when physcl lw s ppled to mesure qunttes other thn the one we re nterested n: for exmple, mesurng velocty v = x/t by mesurng dstnce x nd tme t Mesurements wth clbrted nstruments: by fr the mjorty of the mesurements performed tody the nstrument hs memorzed nsde the unt U Drect nstruments : ndrect nstruments : (only very few) they lwys trnsform the physcl quntty they cqure n nput Anlog nstruments Dgtl nstruments

3 Deflecton nstruments Null-out nstruments ecordng nstruments Bsc MEASUEMENT CHAN: A Sensor or Trnsducer Sgnl condtoner sulzng termnl

4 Frst queston to be nswered: WHAT do we wnt to mesure nd WHY? t s KNOWLEDGE PATH tht leds to new quntttve NFOMATON bout the world surroundng us! wnt we to hve n pproxmte control of physcl quntty? wnt we to do rgorous scentfc mesurement? wnt we to use the vlue of the mesure for n utomtc control? wnt we to know to wht extent cn physcl prmeter vry to set n lrm sgnl? 1. we choose the nstrument ccordng to the extenson rnge of the physcl quntty to be mesured, bsed on the mount of vrton tht s expected for the quntty nd lso on how fst the quntty chnges ts vlue durng the mesurement; 2. we reds the numerc dt on the output devce of the nstrument; 3. by mens of the grduton of the nstrument we ssocte the numerc dt wth the U unts, performng ctully the rel mesurement: A = U 4. t ths pont we stll only hve rw mesurement of the physcl quntty A. We hve to dentfy the mny uncertntes ε ssocted wth the rw dt, correct the dt we obtned nd then swtch to the fnl mesurement: A = ( ± ε) U 5. wth the dffuson of dgtl nstrumentton s now possble to cqure mny repeted mesurements of physcl quntty n. Ths rses the queston of dentfyng the true mgntude of the vlue. We hve therefore to go through sttstcl nlyss of the dt

5 We hve to estblsh the QUALTY of mesurement Hgh qulty mesurements mens beng ble to get dt wth low uncertnty; most of the tmes, ths s lso n expensve procedure! To quntfy the qulty of mesurement we hve to quntfy frst the qulty of the nstrument! To ths extent we cn defne 5 generl metrologcl chrcterstcs tht pply to every mesurng nstrument or mesurng system nd completely descrbe ts performnces! MEASUEMENT SPAN SENSTTY STFFNESS ACCUACY MEASUEMENT APDTY

6 MEASUEMENT SPAN The mesurng spn s the numercl rnge between the mnmum nd mxmum vlues of the mesurnd the nstrument cn pproprtely mesure nd wthn whch the other four nstrument chrcterstcs re vld! Spn = hgh operton lmt low operton lmt Grduton curve : The operton of every nstrument s bsed on physcl lw, ths lw s descrbed by n equton; the sme equton s lso the equton representtve of the grduton curve! f ths equton s of 1st degree ( strght lne) the nstrument s sd lner nstrument! f ths equton s of 2nd degree (prbolc) the nstrument s sd qudrtc nstrument!

7 Exmple: fnd the grduton curve of the Hg thermometer the fundmentl physcl lw (strtng pont) s the lw of volumetrc therml expnson of ll mterls (fluds): T 1 0 T 0 0 T 0 h S T h S 0 T S h 0 output nput (mesurnd) wth Tht s the grduton curve!

8 Grduton curve should NOT be confused wth the CALBATON curve : u s the reference vlue or the ndcton of reference nstrument u b s the rw ndcton of the nstrument under clbrton u u b f ( u b ) s the clbrton curve, e the curve of the dfferences between the reference vlue u nd the «rw» nstrument ndcton u b, for every nstrument output u b. f u - u b < 0 u < u b the nstrument under clbrton overestmtes the mesurnd mgntude (nput) so we hve to subtrct the ndcted devton from u b. f u - u b > 0 u > u b the nstrument under clbrton underestmtes the mesurnd mgntude (nput) so we hve to dd the ndcted devton to u b.

9 SENSTTY Cpblty of the nstrument to «sense» smll vrtons of the nput vrble (the mesurnd) how smll cn vrton Δ of the nput be, to get from the nstrument n pprecble output Δu? u We cn certnly wrte tht, for vrtons 0 mens du u, or better lm 0 d du t s mmedtely observed tht, f u = f () s the grduton curve, the senstvty S d of the grduton curve! du d S s the dervtve The senstvty S cn be clculted for every pont of the grduton curve, by mens of the dfferentl rto: t hs therefore lso geometrc menng: t s the slope of the tngent to the grduton curve n the mesurng pont tht s beng consdered. du d

10 Exmples: nstruments wth constnt senstvty re clled lner nstruments! nstruments wth senstvty tht s functon of cn be qudrtc nstruments! nstruments wth senstvty tht s functon of cn be logrthmc nstruments! u k c S du d K 2 du u k S 2k d u k log S du d k Do not confuse the senstvty wth the resoluton of n nstrument, whch ctully s more pproprte concept for dgtl nstruments!

11 STFFNESS The ntroducton of ny mesurng nstrument nto mesured medum lwys results n the extrcton of some energy from the medum, thereby chngng the vlue of the mesured quntty from ts undsturbed stte! Ths crcumstnce mkes perfect mesurement theoretclly mpossble! exmple: T H2O s the sme n the bthtub nd n the glss. The lodng effect of the nstrument s bgger when mesurng T n the glss thn n the bthtub! Every nstrument tht physclly ntercts wth the mesured quntty hs «lodng effect» on the mesurnd nd slghtly chnges ts vlue nstrument desgner cn only «mnmze» ths lodng effect, whch s clled stffness! An nstrument wth low stffness mens n nstrument cpble of dong mesurements wth smll lodng effect! Stffness s sngulr chrcterstc becuse t depends lso on the mesurement envronment nd crcumstnces.

12 Some numercl mens of expressng the lodng effect of the nstrument on the mesured medum would be helpful n comprng competng nstruments t the moment of ther choce or purchse! One prmeter could be the nserton or connecton error done by the nstrument when connectng wth the mesurnd: b b ns where: b s the numercl vlue of the mesurnd before the nstrument nserton; s the numercl vlue of the mesurnd fter the nstrument nserton, nd lso the ctul mesurement returned by the nstrument. Becuse b s vlue tht cn NOT be mesured, ths prmeter my seem useless! Let s go to generlzed defnton of stffness nd nput mpednce : b At the nput of ech component n mesurng system there exsts vrble q 1, the effort vrble, tht crres the nformton content of the mesurement. At the sme nput, however, there s second vrble q 2, ssocted wth q 1, n wy tht the product q 1 q 2 hs the dmensons of power nd represents n nstntneous rte of energy wthdrwl from the precedng element!

13 The generlzed nput mpednce cn then be defned s : Z g q q 1 2 Whle the power drned from the precedng element s : P q Z 2 1 g nd lrge generlzed nput mpednce s needed to keep the power drn smll! These concepts cn be mmedtely ppled to n electrcl exmple: voltmeter mesurng n unknown voltge. As soon s the meter s ppled to the voltge termnls, the electrcl crcut s chnged nd the vlue of s no longer the sme but chnges to nother vlue m. For voltmeter the nput vrble of nterest, the effort vrble (q 1 ), s the termnl voltge m. f we look for n ssocted vrble (q 2 ) whch, when multpled by q 1, gves the power wthdrwl from the voltge termnls, we fnd the meter current m meets ths requrement. q 1 m Thus, the nput mpednce n ths exmple s: Z g m the meter resstnce! q Ths stuton s very mportnt ndeed nd pples lso to the nternl stges of more complex nstrument chn, for exmple, when couplng trnsducer tht mesures physcl quntty A nd outputs voltge or current to the sgnl processng stge tht follows n the mesurement chn. 2 m,

14 Before connectng the voltmeter to the termnls we hve : = 0 wth = 0 After connectng the voltmeter we hve: 0 = ( + v ) wth 0 But the nstrument mesures: = v 0 We commt n error : the connecton error ns 0 0 v v v v 1 1 v 0 f we wsh to keep ths error smll we hve to desgn ether or ns 0 Actng on the trnsducer output resstnce n not so esy therefore, the preferred wy n desgnng the connecton s mkng the nput resstnce v of the sgnl processng stge (voltmeter) very bg! Ths choce prevents the sgnl whch crres the nformton bout the mesurement to degrde further! v

15 Before connectng the mmeter to the termnls we hve : 0 = wth = 0 After connectng the mmeter we hve: 0 = + wth And the nstrument mesures: 0 We commt n error : the connecton error wth becuse the two resstnces nd re now n prllel confgurton // Therefore : And the connecton error becomes : ns ns

16 0 f we wsh to keep ths error smll we hve to desgn ether or ns 0 Hvng t dsposl current genertor wth bg nternl short-crcut resstnce s dvsble but not so esy to obtn from trnsducer whch outputs current therefore, the preferred wy n desgnng the two stge connecton s mkng the nput resstnce of the sgnl processng stge (mmeter) very smll! Ths choce prevents the current sgnl tht crres the nformton on the mesurement to degrde further! So fr, ll the metrologcl chrcterstcs we studed re vld for sttc mesurnd A