HYDROSTATIC WEIGHING SYSTEM AT THE INRiM FOR CALIBRATING HYDROMETERS

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1 XVIII IMEKO WORD CONGRESS Metology fo Sustinble Development Septembe, 17 22, 2006, Rio de Jneio, Bzil HYDROSTATIC WEIGHING SYSTEM AT THE INRiM FOR CAIBRATING HYDROMETERS oefice S. 1, Mlengo A. 1 1 Istituto Nzionle di Ricec Metologic (fomely IMGC-CNR, Toino, Itly, S.oefice@imgc.cn.it Abstct: Hydometes e simple but effective instuments fo mesuing the density of liquids. In this wok, we pesent the new hydosttic weighing system developed t the INRiM, fomely IMGC CNR, fo the clibtion of hydometes in the nge 500 kg.m -3 to 2000 kg.m -3. The pptus which uses method to utomticlly lign specific scle-mks fo the clibtion of hydometes, mkes esy the whole clibtion pocedue nd llows to educe the fome uncetinty decled by lbotoy. It consists of vision system, stepping moto, nd softwe to contol the system. The vision system, composed of CCD cme nd fme gbbe, is used to cquie imges. The ovell pefomnce of the pptus is illustted by the ssessment of the uncetinty fo some usul kinds of hydometes sent to the Institute fo clibtion. Keywods: Hydomete, Clibtion, Atificil vision 1. Intoduction Hydometes e eposed to etended immesion times in vious liquids which my ttck the glss, plus they e subjected to mechnicl stess nd bsion though hndling nd clening. Moeove, the ntul geing pocess of the glss futhe esults in minute chnges to the dimensions of the instument. The sum of these fctos, lthough not visible to the eye, my esult in slight chnges in the weight nd/o displcement of the instument nd cuse it to chnge its indiction. The coectness of mesuements nd mesuing instuments is one of the most impotnt peequisites fo the ssunce of the qulity nd quntity of poducts nd sevices, nd the ccucy of the instuments must be consistent with thei intended use. The eltively low pice of hydometes doesn t eclude the need of thei peiodic egul clibtion nd, if equested, peiodic veifiction. Those two diffeent ctions, lthough estblished though septe ules nd metologicl infstuctues nd ctivities, e mostly bsed on the sme mesuing pocedues, tht s e essentil to ssue the integity of the edings, the tcebility to intentionl stndds in the es of density mesuements nd to comply with the equiements of the qulity systems. Diffeently fom the diect compison method whee diffeent stndds, such s liquids o solutions with known density e used, the multipoint pocedue to clibte hydometes bsed on hydosttic weighing (well know s Cuckow s method is in use t most ntionl stndds lbotoies, tht povide clibtion sevices fo efeence hydometes genelly used s lbotoy stndds [1]. 2. Outline of the hydomete clibtion Hydometes of ny nge cn be clibted t diffeent selected gdution mks, by mesuing the buoyncy foce when the hydomete is plced in i nd ptilly immesed in efeence liquid. At fist, the hydomete to be clibted is weighed in i nd then it is sunk into efeence liquid, whose density is known t the efeence tempetue, with the stem connected to n uppe blnce though metl wie (figue 1. The depth of immesion of the hydomete is djusted by mechnicl device so tht the middle of the gdution mk unde clibtion is ligned with the hoizontl sufce of the efeence liquid. To detect coectly the lignment of the hydomete scle the vision by mgnifie o by monito is commonly used. In those situtions whee the nge of the hydomete to be clibted is lowe thn the density of the efeence liquid, supplementy weight, in the shpe of stinless steel ing is dded to the hydomete to cuse it to sink. The hydomete eding is then comped with efeence vlue clculted fom the diffeence in the weighing esults M whee ( 1 1 π γ + M D g s 1 1 π γ M s + D g s [ 1+ β ( T T0 ] + 1 (1

2 M, M = eding of the blnce when weighing in i nd in the liquid immesed up to the mesuement point, espectively;, = density of i duing weighing in i nd in liquid, espectively; = efeence density fo weights (8000 kg m 3 ; s Figue 1. The piciple of the hydomete clibtion pocedue in the fist (A nd second (B step. = density of the clibtion liquid; γ, γ = sufce tension of the clibtion liquid nd the liquid in which the hydomete is nomlly used, espectively; d = stem dimete of the hydomete t meniscus level g = cceletion due to gvity; β = volumetic theml epnsion coefficient of the glss fom which the hydomete is mde; T, T 0 = the i tempetue t the time the weighing ws done nd the efeence tempetue, espectively. 3. The epeimentl set-up Two min spects wee tken into ccount in setting up the new INRiM clibtion sttion fo hydometes: the fome is to mke moe esy nd ccute ll mesuing pocedues by mens of n etensive utomtion of the clibtion pocess, the ltte is to eliminte s much s possible opeto's mistkes in detecting coectly the lignment of the hydomete scle mk to be clibted. The doption of n utomtic lignment system [2] composed of CCD cme (piel mti of 604 H 576 V nd fme gbbe, which is used to cquie imges by mens of home-mde imge pocessing softwe, hs llowed us to design hydosttic weighing sttion suitble to clibte hydometes in the nge between 500 kg m -3 up 2000 kg m -3. Fom ou pevious sttion [3] only the weighing system, consisting of commecilly vilble electonic blnce fo hydosttic weighing of 405 g cpcity, nd the envionmentl equipment ( potble pessue gge nd themo-hygomete e unchnged. A lift unit hs been instlled undeneth the concete bse plte upon which the blnce nd the envionmentl equipments e instlled (figue 2.. The unit compises veticl feed bll scew used s single is ctuto, poviding tnsltion up to 67 cm with micomete esolution. A cige holding themosttic tnk is moved veticlly togethe with the CCD cme by the feed bll scew ctuto. A compute-contolled stepping moto is coupled to the feed bll scew; its llows the tnsltion to the desied position without oveshoot, oscilltion, o stedy-stte eo. To chieve this, the ctuto moves vey egully in ode not to distub the hoizontl plne sufce of the efeence liquid; when the liquid level is close to the mk to be clibted, the numbe of steps mde t time is educed to 3 coespond to 6 µm. The 3 lites of efeence liquid e contined in glss vessel suounded by 30 lites of tempetue-contolled ciculting wte t 20 C, lthough diffeent tempetues between 10 C nd 50 C cn be set nd mintined by n etenl themostt bth. A esistnce themomete is housed inside the glss vessel, close to bulb of the hydomete to be clibte, in ode to ensue n ccute mesuement of the liquid tempetue duing the clibtion. Moeove commecilly vilble tensiomete is used fo mesuing the sufce tension of the efeence liquid. To mesue the tempetue duing the weighing of hydometes, both in i nd in liquid, two clibted pltinum esistnce themometes (Pt100 e linked to n.c. bidge, finlly the men dimete of the hydomete stem is detemined by n ccute cllipe, by mesuing it t fou diffeent levels, ppoimtely t ech select mk. Figue 2. Detil of the hydomete clibtion sttion befoe the lift unit is moved towds the hydomete to be clibted..

3 The pocedue of clibtion is mnged by the opeting pogm which hs the functions: i to contol the stepping moto nd djust by the movement of the glss vessel fo the lignment of the hoizontl plne with the pticul sclemk nd ii to pocess imges fom the cme by the nlysis of the imge pofile contolled to n ccucy of 0,1 piel (figue 3. In shot, fte the hydomete hs been hung up below the blnce nd hs been weighed in i, the themosttic bth with the efeence liquid is moved towds the hydomete, thus llowing its ptil immesion. The hydomete eding by CCD cme consists in obseving the mks of the hydomete unde clibtion fom below the sufce of the liquid nd in ligning the middle of the mk to be clibted with the hoizontl plne tngentil to the liquid sufce. The djustment llows fo the most ccute lignment tht is equied nd emoves the opeto's mistkes in detecting coectly the lignment of the hydomete mk to be clibted. In the cuent pocedue, five independent weighing-ini sequences nd five independent hydosttic weighings t ech one of the stted levels of immesion e mde espectively. The density of the efeence liquid is detemined s function of tempetue ove the nge 18 C to 22 C by hydosttic weighing of zeodu sphee of known mss nd volume. In ode to check the stbility of the density ove the time nd the possible contmintion, the density of the liquid is mesued befoe nd fte the clibtion of ech hydomete by mens of vibting tube densimete. 4. Uncetinty budget Usully hydometes e clibted t sevel gdution mks of the scle (nomlly thee o fou nd fo ech of them the devition, o the coection C is clculted C = (2 whee is clculted by the eqution (1 which is elted to the density of the liquid in which the hydomete would feely flot t the scle eding. Consequently the Figue 3. Digitl cquied imge of hydomete to be clibted nd nlysis of pofile ound the designed mk. best ccucy chieved in the clibtion of hydometes is minly due to how both the quntities nd e estimted. The coection, s given in eqution (2, my be eithe positive, negtive, o zeo, nd the stndd uncetinty ssocited with the estimte of coection cn be epessed s 2 n C 2 u ( c C = u ( i (3 i= 1 i whee the input estimtes i of the input quntities in the equtions (1 nd (2 e ssumed to be uncoelted [4]. Relibility of clibtion s well s the level of uncetinty is stictly connected with the hydomete to be clibted, s well s with equipment nd pocedue used in the mesuement. The evlution of the input quntities e detiled s follows on the bse of the INRiM equipments: Weighing of the hydomete in i nd in the liquid. The weighings of the hydomete in i nd in the efeence liquid e pefomed by mens of n vilble commecil blnces with esolution of 0,01 mg. To educe the influence of line difts, sevel weighing cycles cn be cied out with diffeent subsequent weighings; the usul stndd uncetinties in the weighings e u( = 0,10 mg in i nd u( = M M 0,15 mg in the liquid espectively. The stndd uncetinty ssocited with the weight of the clibted hydomete both in i nd in the liquid is obtined fom contibutions due to the blnce clibtion nd the efeence stndds clibtion, but lso fom the epetbility, lineity, hysteesis, difting of the mesuements. Moeove in geement with the eqution (1 the stndd uncetinty ssocited with the density of the stndd weights must be consideed. b Atmospheic buoyncy. The mesuement of i density is necessy to llow buoyncy coections to be mde when comping weights of diffeent volume, of diffeent mteil o when mking mss mesuements to the highest ccucy. In genel the i density is clculted by mens of envionmentl mesuement of tempetue, pessue nd humidity, detemined duing the weighings, using the eqution ecommended by the CIPM (Comité Intentionl des Poids et Mesues [5]. The cbon dioide concenttion is not mesued, the vlue of 0,04 % with n uncetinty of 0,02 % (ectngul pobbility distibution is dopted. The stndd uncetinty contibution of the density of i usully esults to be ( = u 0,003 kg m -3. c Tempetue influence. Theml conditions ply n impotnt ole duing the whole pocedue, liquid density chnges nd density gdients due to non-unifom tempetue might hve significnt effect on hydomete mesuement esults even in tempetue contolled set-up. Unfotuntely, significnt tempetue gdients cnnot lwys be voided fo pcticl esons, e.g. insufficient unifomity nd stbility of the efeence liquid nd diffeences between the liquid nd mbient tempetue [6]. The tempetue effect should be chnges the ppent weight of the hydomete nd the density of the efeence

4 liquid. In the pesent pptus, the stndd uncetinty contibution of the tempetue, consideing lso its stbility nd unifomity ound the hydomete to be clibted, esults to be u ( T = 0,01 C. d The efeence liquid. The density of the buoynt liquid depends minly on tempetue. The density uncetinty contibution of the efeence liquid minly depends on the method used fo mesuing the density, othe mino contibutions include the evpotion effect nd the compessibility which e usully tken to be negligible. Howeve the stndd uncetinty contibution of the Nonne used s the buoynt liquid is usully ( = u 0,005 kg m -3. Its sufce tensions is detemined fom diect mesuement by using the plte o the ing method with stndd uncetinty ( = u γ 0,2 mn m -1. e Stem dimete. An ccute clipe o suitble instument with esolution between 0,01 nd 0,1 mm is usully used to mesue the dimete of the stem of the hydomete to be clibted. The uncetinty contibution, tking into ccount the uncetinty of the cllipe nd the epeimentl stndd devition of the mesuements of the dimete t the scle mk, is u( D = 0,1 mm. f Epnsion coefficient of hydometes. Hydometes e usully mde of glss mteil with nominl cubic coefficient of theml epnsion β of C -1 with n uncetinty of C -1 (ectngul distibution. g Gvity influence. The clibted hydometes e weighed in i nd in the liquid t diffeent heights. It is not nomlly necessy to mke coections fo vitions in gvittionl cceletion, the stndd uncetinty contibution due to the gvittionl cceletion is u( g = m s -2. h Opeto effects nd eding eos. Humn eos which cn include inccute edings o mislignments of the scles on the stem of hydomete e not pesent becuse n utomtic lignment is dopted to djust the veticl position of the hydomete (o of the bth so tht the designed mk intesects the liquid sufce coectly. The utomtic vision system mkes bette the epetbility in the coect lignment being ble to disciminte the sme position in 0,1 piel. The min components in the eding uncetinty cn come fom the sensitivity of hydometes, the epetbility in the coect lignment nd fom the pespective eo. The lignment intoduces n uncetinty u contibution (eding eo ( = 0,02 mm which is not dependent fom the distnce between the mks. 5. Epeimentl esults The ssessment of the individul contibutions llows us to evlute the uncetinty fo some usul kinds of hydometes sent to INRiM fo thei clibtion. In obtining the combined stndd uncetinty diffeent esults e epected, tht minly comes fom the vlue of the lest scle division nd the nge of hydomete to be clibted. Genelly, fo ech kind of hydomete, the distnce between mks is ppoimtely constnt ove the whole nge. Sevel fetues of inteest emege fom this, in pticul bout the weight tht the contibutions due to the density of efeence liquid, the tempetue of clibtion nd the edings ehibit in the whole ssessment of uncetinty. Tble 1 compes the vlue of the individul components of the eltive uncetinty s function of the combined stndd uncetinty fo hydometes hving diffeent scle division vlues fom 0,1 kg/m 3 to 1 g/m 3 nd mk distnce bout 1 mm. The tempetue stongly ffects the uncetinty though the theml epnsion coefficient of the efeence liquid, so tht only the density uncetinty nd the eding uncetinty hve the getest impotnce. It is inteesting lso to elize tht fo high esolution hydometes (division of 0,1 kg/m 3 the density uncetinty contibution of the liquid is the min Reltive components of the uncetinty u ( i Division / kg m -3 0,1 0,2 0,5 1 Weighing in i, u ( M 0,002 0,002 0,005 0,006 Weighing in the liquid, u ( M 0,027 0,025 0,058 0,084 Ai density, ( 0,010 0,008 0,003 0,001 u Tempetue of liquid ound hydomete, u ( T 0,577 0,474 0,210 0,070 Density of the buoynt liquid, ( 0,333 0,274 0,121 0,040 u Dimete of the hydomete stem, u ( D 0,008 Negligible Negligible 0,024 Sufce tension of the buoynt liquid, ( 0,016 0,023 0,034 0,041 u γ Gvittionl cceletion, u ( g Negligible Negligible Negligible Negligible Redings eo, u ( 0,027 0,204 0,569 0,734 Combined stndd uncetinty u c ( C / kg m -3 0,012 0,013 0,020 0,035 Tble 1. Evlution of the eltive individul uncetinty contibutions to the combined stndd uncetinty in clibting hydometes with diffeent scle division vlues: fom 0,1 kg/m 3 to 1 kg/m 3 nd mk distnce bout 1 mm in the density nge close to 1000 kg/m 3.

5 Reltive components of the uncetinty u ( i Rnge / kg m Weighing in i, u ( M Negligible 0,001 0,005 Weighing in the liquid, u ( M 0,028 0,046 0,058 Ai density, ( Negligible Negligible 0,003 u Tempetue of liquid ound hydomete, u ( T 0,117 0,173 0,210 Density of the buoynt liquid, ( 0,068 0,100 0,121 u Dimete of the hydomete stem, u ( D Negligible Negligible Negligible Sufce tension of the buoynt liquid, ( 0,029 0,027 0,034 u γ Gvittionl cceletion, u ( g Negligible Negligible Negligible Redings eo, u ( 0, , ,569 Combined stndd uncetinty u c ( C / kg m -3 0,017 0,019 0,020 Tble 2. Evlution of the eltive individul uncetinty contibutions to the combined stndd uncetinty in clibting hydometes with scle division vlue 0,5 kg/m 3 nd mk distnce bout 1 mm in the density nges of kg/m 3, kg/m 3, nd kg/m 3 souce leding to totl uncetinty, but its impotnce fll unde bout 50 % fo hydometes with division of 0,5 kg/m 3 nd becomes somewht negligible fo hydometes with division of 1 kg/m 3, fo which the eding uncetinty is the pedominnt pt of the whole uncetinty. The Tble lso shows tht the combined stndd uncetinty vlues e educed bout of 50 % comped with those obtined by mens of the fome pptus [3]; tht minly depends on the utomtic lignment. Tble 2 consides the vlues of the individul components of the eltive uncetinty s function of the combined stndd uncetinty fo hydometes hving sme scle division vlue of 0,5 kg/m 3, mk distnce bout 1 mm nd density nges of kg/m 3, kg/m 3, nd kg/m 3 espectively. The Tble lso shows tht the eltive uncetinties due to the liquid density, the weighing in the liquid nd the tempetue e incesing with the density nge while the eltive uncetinty due to the edings eo deceses. Tht detemines substntil constncy of the eltive combined stndd uncetinty fo the whole nge. This lst considetion e lso pplicble to hydometes hving diffeent scle divisions. 5. Conclusion The mesuement by hydometes nd the ccucy of mesued dt depend by the usul conditions unde which they e used, thei egul clibtion is the most impotnt peequisite fo ect nd tceble mesuement of density. The clibtion pptus hee pesented hs been designed t the INRiM to mke esie nd moe ccute ll mesuing pocedues. The utomtic lignment method intoduced in clibting hydometes educes eos cused by limited opeto skills o ttention when clibtion is pefomed mnully nd, in pticul, eduction of the ovell uncetinty. In obtining the combined stndd uncetinty diffeent esults e epected, tht minly come fom the vlue of the lest scle division nd the nge of hydomete to be clibted. Genelly, fo ech kind of hydomete, the distnce between mks is ppoimtely constnt ove the whole nge. The the hydosttic pptus of the INRiM hs been evluted fo some kinds of hydometes usully clibted t the Institute. Clibtion uncetinty is minly ffected by the individul contibutions of the density of the efeence liquid, the tempetue of clibtion nd the epetbility in the lignment of the mk to be clibted. The density uncetinty of the efeence liquid is the most impotnt tem fo high esolution hydometes (div. 0,1 kg/m 3, but its impotnce flls unde bout 50 % fo hydometes with division of 0,5 kg/m 3 nd becomes somewht negligible fo hydometes with division of 1 kg/m 3, fo which the lignment (eding uncetinty is the pedominnt contibution of the totl uncetinty. Consideing hydometes with the sme scle division nd diffeent density nges, the eltive uncetinty esults bout constnt ove the whole nge. The best eltive uncetinty in the commecil hydometes usully clibted t the INRiM esults to be between bout fo hydometes with division 1 kg m -3 6 nd fo hydometes with division 0,1 kg m -3. REFERENCE [1] oefice S nd Mlengo A Clibtion of hydometes submitted to Mes. Sci. Technol. [2] oefice S nd Mlengo A An imge pocessing ppoch to clibtion of hydometes Metologi, 41, 2004, [3] oefice S, Heinonen M nd Mdec T Biltel compisons of hydomete clibtions between the IMGC-NE nd the IMGC-MIKES Metologi 37, 2000, [4] GUM Guide to the Epession of Uncetinty in Mesuement ISO, Genev (1993. (Repinted [5] Dvis R S Eqution fo the density of moist i Metologi, 29, 1992, [6] Heinonen M nd Sillnpää S The effect of density gdients on hydometes Mes. Sci. Technol., 14, 2003,