Calibration of nonautomatic weighing instruments

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1 XVIII IMEKO WORLD CONGRESS Metology fo Sstinble Development Septembe, 7, 006, Rio de Jneio, Bzil Clibtion of nontomti eighing instments Atho : Adin Vâl Ntionl Institte of Metology, Bhest, Romni, din.vl@inm.o Abstt: This ppe desibes the metologil eqiements nd the mesements methods fo libting nontomti eighing instments. It lso my be sefl gideline fo opetos oking in libtion lbotoies edited in vios fields. This ppe is lso intended to enble metology lbotoies to pove given expnded netinty sing sitble poedes. To exmples of libtion methods e given: one fo eletoni eighing instments nd nothe fo the mehnil instments. The desibed methods inlde infomtion egding the mesements stndds sed fo libtion, envionmentl onditions, libtion poedes nd estimtion of the mesement netinty. Keyods: eletoni eighing instments, mehnil eighing instments, mltiple nges nd mlti-intevl instments. Intodtion Clibtion methods nd the evltion of the netinty desibed in the ppe e in ompline ith the OIML Reommendtion OIML R 76- nd ISO-GUM [] (Gide to the expession of netinty in mesements-995). The ombined stndd netinty eslts fom both the type A nd type B evltions of the mesements netinty. The envionmentl oking onditions shll be sitble fo the instment to be libted. The oom hee the blnes e instlled mst be tempete nd hmidity ontolled. It is not lloed to ple blnes ne eqipment tht genetes vibtion o in oom hee dst my ffet them. Also, het tnsmission by sol dition thogh the indos shll be pevented. A. Clibtion of eletoni blnes Befoe libtion, n eletoni eighing instment shold be heked on site to mke se it fntions deqtely fo the intended pplition. The peliminy opetions e: - identifition of the eighing instment (type, model, seil nmbe, et.); - heking the leveling; - ensing tht eletilly poeed instments hve been sithed on fo peiod of lest one ho (pefebly ovenight) nd hve ehed oom tempete; - ensing tht the pn of the eighing instment is len nd in good ondition; - pe-loding fo sevel times the eighing instments to ne mximm pity; - djsting the eo lose to Mx, sing intenl o deqte extenl eights, to llo ompenstion fo hnging envionmentl ftos sh s tempete nd, impliitly, i density. Estimting the expnded netinty is bsed on: - epetbility - esoltion - eentiity - the inflene of tempete vitions t the site of se - y mesements - the stndds eights sed in the y mesements - hysteesis. Repetbility At lest ten epeted mesements mst be pefomed. This test shold be done t o ne the nominl mximm pity of the eighing instment o sing the lgest lod genelly eighed in pplitions. In the se of zeo devition beteen the eighings, the instment shll be eset to zeo, ithot detemining the eo of the zeo indition []. The netinty de to epetbility of the eighing poess,, is given by stndd devition s of sevel eighing eslts obtined fo the sme lod nde the sme onditions. Fo mltiple nge instments, this test shll be ied ot fo eh nge sed, ths fo n mesements: n I I i () = = i = s n hee I i is the indition of the eighing instment nd n is the nmbe of epeted eighings: n I = I i () n i=. Resoltion Fo blnes hving the esoltion d (eql to the sle intevl), the netinty of the onding eo,, fo eh eding I is []: d / d = = () The netinty of the onding effet fo I 0 is given by [6] d I = 0 + d I = L = () Eqtion () is sed fo single nd mltiple nge instments. Fo mlti-intevl instments, fo the diffeent sle intevls d i, the netinty de to the onding effet is:

2 d + d i = (5) hee: d is the smllest sle intevl d i is the sle intevl of the ppopite ptil nge.. Eentiity It is pefeble to se lge eights insted of sevel smll eights. The lod L shll be pplied on the pn in the positions indited in Fig. in seqene of ente, font, left, bk, ight, o eqivlent. Afte the fist mesement, te setting my be done hen the instment is loded. Fo instment hving no moe thn fo points (n ) of sppot, the test lod is / Mx. []. Fig. The lod is fist pled in position nd is sbseqently pled in the othe positions in n bity ode. Aeptble soltion fo netinty de to eentiity, ex is estimted s follos []: ex = (6) hee, is the lgest diffeene beteen off-ente nd entl loding inditions; The eenti test is not ied ot in the se of eighing instments ith sspended lod eepto.. The effet of tempete vitions, ding the libtion, T is llted fom: 6 T = ( t TK 0 ) L (7) hee: TK is the effet of tempete on the men gdient of the hteisti in ppm/k (estimted o tken fom dt infomtion sheet). t = t mx t min is tempete vition ding the libtion, fo lod L. 5. Mss stndds 5 The eights sed s mesement stndds shll omply ith the speifitions in the OIML R. The tebility of the stndds to the SI nit shll be ensed. The stndds shll be deqtely limtized befoe the libtion (to minimize the effet of onvetion). A themomete kept inside the box ith stndd eights my be helpfl to hek the tempete diffeene. When the indition of the instment is not oeted fo the eos of the eights (the libtion eights e intoded s nominl vles) the netinty of the efeene eights, ef, is estimted s follos: δ i ef = (8) o, hen to o moe eights e sed, δ i ef = (8 ) 5 hee: δ i is the mximm pemissible eo of the i pplied eights When the inditions of the instments e oeted fo the eos of the eights (the libtion eights e intoded s onventionl vles) the stndd netinty fom the libtion etifite ( et ) shold be ombined ith the netinty de to the instbility of the mss of the efeene eight ( stb ) s folloing []: U ef = + et stb = + stb (9) k When to o moe eights e sed fo L, the eqtion beomes: U i ef = + stb k (9 ) U i (k=) is the netinty of the pplied eights fom the libtion etifite. The lltion of the netinty ssoited ith the stbility of the stndd ( stb ) hs to tke into ont hnge in vle beteen libtions, ssmed tht etngl distibtion. This omponent old be eqivlent to the hnge beteen libtions divided by : D mx stb = (0) hee D mx epesents the dift detemined fom the pevios libtions. If pevios libtion vles e not vilble, the netinty fom the libted etifite is onsideed to be n netinty ssoited to the dift. 6. Ay mesements Weighing instments shold be libted thoghot thei nge. When eighing instment is sed only ove pt of its pity, the libtion my be estited to this pt of the mesing nge. In this se, the pt nge tht hs been libted hs to be expliitly mentioned in the libtion etifite nd lso lbel ith this infomtion shold be fixed to the eighing instment. Mesements e mde t bot five eql steps oss the nge of the blne (zeo, 0.5Mx, 0.50Mx, 0.75Mx nd Mx). If the blne is typilly sed fo ptil lod, the y of the sle ond this lod shold be mesed. When : - the eighing instment s djsted befoe mesement, - the density of eights is lose to 8000 kg/m nd - the i density is lose to, kg/m, the indition eo, E I, is obtined fom the diffeene beteen the instment eding I - pon pplition of lod L - nd the vle of this lod (onventionl mss vle o nominl vle). E I = I - L ()

3 The eights e pplied in inesing nd deesing lods. The estimtion of netinty ssoited ith the indition eo tking into ont the inflenes of epetbility ( ), esoltion ( ), efeene eights ( ef ), tempete ( T ) nd hysteesis ( H ). Hysteesis os hen blne displys diffeent eding fo the sme lod, hen the lod is pplied inesing the eight nd deesing the eight. If the diffeene is δ x, the stndd netinty de to hysteesis is given by []: δ x H = = 0,9 δ x () The expession of netinty ssoited ith the detemining the indition eo is: (EI) = ( ) + ( ) + ( ) + ( ) L + ( ) () ef T H The netinty EI shold be llted fo eh vle of the lod sed. Fom eq. (), the eltive stndd netinty n be llted s: (EI) el = (EI) / L () nd the lgest netinty (EI) el mx is tken into ont fo fthe lltions. The indition eo is not the sme hen the eighing instments e libted sing stndd eights nde diffeent onditions. In this se, the eo of indition is: E= I (L+BC)= I L BC= = I L L ( ) ) + dj 0 = Whee BC, the boyny oetion is eql to [8]: dj = I L + L ( 0 ) ) + (5) dj BC = L ( 0 ) ) + (6) hee: = density of the eight = density of the i ding the libtion 0 =, kg/m is the efeene density of the i = efeene (onventionl) density of the djstment eight eql to 8000 kg/m dj = i density t the time of djstment. Povided - the instment hs been djsted immeditely befoe the libtion, dj =, the boyny oetion my be llted s: BC = L ) ) (6 ) - the instment hs been djsted independent of libtion ( dj is nknon) the boyny oetion my be llted s: 0 0 BC = L (6 ) ith the next ssmptions: dj = 0 nd = Stting fom eq. (6 ) nd (6 ), the eltive stndd netinty ssoited to the boyny oetion ( BC ) my be llted s: BC BC ( ) + ( 0 ) + = (7) = + ( 0 ) (8) Unetinty of i density is detemined oding to []. When the i density is not mesed nd the vege i density fo the site is sed insted, the netinty ssoited to the i density is estimted (oding to hpte C.6.. in []) s: 0, ( ) = [kg/m ] (9) The expession of netinty ssoited ith indition eo (hen the boyny oetion is pplied) is: (EI) = ( ) + ( ) + ( ) + ( ) L + ( ) + ( ) L (0) ef T The netinty (EI) shold be llted fo eh vle of the lod sed. Fom eq. (0), the eltive stndd netinty n be llted s: (EI) el = (EI) / L () nd the lgest netinty (EI) el mx is tken into ont. Unetinty of mesement fo the eighing instment The inflenes of the epetbility nd of the onding eo e ssmed to be independent fom the lod pplied, hile ll the othe omponents e popotionl to the eight vles. The stndd netinties oesponding to the omponents tht e popotionl to the eight vles e expessed s eltive netinties. The ombined stndd netinty is bsed on the pmetes desibed bove (hih n be goped to obtin simplified expession tht old bette eflet the ft tht some of the tems e independent fom the pplied lod, hile othes e popotionl to the eight vle) [5]: H = α + β L () When oetions e pplied to the eo of indition of the eighing instment, the expession fo ombined stndd netinty is: exel Tel = + + L + + ) BC ( EI ) el mx = + L exel + Tel + ( EI ) el mx + () Tel fom eq. () is llted by epling the tempete vition ding libtion (fom eq.7) ith the tl tempete vition eoded ding the se of the blne. When no oetions e pplied to the eo of indition of the eighing instment, the lgest eltive indition eo oss the nge tht is mesed E I el (Mx) shold be dded to, in ddition to (EI)el(mx), s follos:

4 = + + L [ + + ( + E ) ] exel Tel ( EI ) el mx I el( Mx) = + L exel + Tel + ( ( EI ) + E ( ) I el( Mx) ) el Mx + () The expnded netinty fo k= is U = k (5) B. Clibtion of mehnil blnes B. To pn blnes: the blnes ith to pns nd thee knife edges e lso knon s eql-m blnes bese the knife edges sppoting the pns e nominlly eqidistnt fom the entl knife edge. The thee knifeedges e pllel nd lie in the sme hoizontl plne. To-pn blnes e genelly ndmped ith est point being llted fom seies of tning points. Some blnes inopote dmping mehnism (slly mehnil o neti) to llo the diet eding of est point. In ll ses, the eding in tems of sle nits needs to be onveted into mesed mss diffeene. A to-pn blne ndmped is sed hee: less feqently minly de to the mont of time needed to mke eighing omped ith eletoni blnes. Thee e to methods to llte the est point (the eqilibim positions) P fo blnes (the y of the seond is bette thn tht of the fist one): P = (e + e + e )/ o (6) P = (e + e +e +e )/8 (7) hee e e e onsetive edings t the extemity of the sing of the pointe, i.e. hee it hnges its dietion of motion. A libtion poede, [7], is shon in the tble. Tble. Clibtion poede fo to pn blnes No Lods pplied on eeives Redings e e e Eqilibim position div div Diffeene i div left ight 0 0 P L L P L L P L L +s P P 5 6 L L P 6 7 L L P 7 8 L +s L P P 9 0 L L P 0 = P 0-P P L L P = P -P 0 0 P L L P = P -P P 5 6 L L P 6 = P 6-P P 7 8 L L P 8 5= P 8-P P 9 0 L L P 0 6= P 0-P 9 hee: s nd s e dditionl smll eights (sensitivity eights) ith mss m s, sed to detemine the sle intevl of the blne. The sensitivity eights shold be libted ginst sitble mss stndds. L nd L e eights ith nominl msses eql to the minimm pity of the blne. L nd L e eights ith nominl msses eql to the mximm pity of the blne. The folloing tests nd lltions shold be ied ot on egl bsis nd e essentil to the otine opetion of the blne [7]:. Detemining sle intevl hile the blne is loded ith minimm pity. d min =m s / P -P (8). Detemining sle intevl hile the blne is loded ith mximm pity: d mx =m s / P 8 -P 7 (9). Detemining epetbility hile the blne is no loded nd loded ith mximm pity (by detemining the expeimentl stndd devitions): n n ( Poimed Poi ) ( imed i ) R 0 = i= ; R mx = i= (0) n n P 0i e the eqilibim positions hile the blne is not loded P 0i med e the men of eqilibim positions hile the blne is not loded i e the diffeenes beteen eqilibim positions of the blne hen it is not loded nd hen it is loded ith mximm pity i med is the men of i diffeenes. Detemining eos de to the ft tht the to ms of the blne e not eql in length (this test is not pplible to blnes ith single pn, se B, setion to be disssed in). J min = J mx = P + P P + P5 P + P7 P5 + 6 P9 () () Unetinty of mesement fo the eighing instment The stndd netinty is bsed on the desibed bove pmetes s folloing: netinty de to the sensitivity of the blne: nd s min = d min m ( ) s P P () s + P P ( ) s P8 P7 () s mx = dmx + ms P8 P7 hee: s is the netinty of the dditionl smll eights s (sensitivity eights); (P P ) o (P 8 P 7 ) is the hnge in the indition of the blne (de to the sensitivity eights) ith the netinties (P P) o (P8 P7), espetively; d is the sle intevl. Fom eq. () nd (), the eltive stndd netinty n be llted s:

5 s el = s (min, mx) / L (5) nd the lgest netinty s el mx is tken into ont the vine of epetbility : = s = R (6) netinty de to the ineqlity of the to ms lengths (in sle divisions) (7) P6 P7 P5 P9 J = = 0, d J = + ( d) = + ( d) = (in ) (7 ) 0.00 d + ( d) hee: is the vine of the epetbility is the vine of limited esoltion. The esoltion is eql to /0 o /0 of the sle intevl d, the stndd netinty being llted s: 0,d 0,d = = (8) Then, the ombined stndd netinty n be llted s follos: = ( d) + + L = ( d) + + ( L) (9) J selmx J s el mx The expnded netinty is epoting by mltiplying ith the ovege fto k= U = k (0) B. Single pn blnes Displys on these blnes tend to be of the optil viety, the sensitivity of the blne being slly djsted by skilled peson. In the se of single pn, diet eding nlytil blnes, the folloing tests nd lltions shold be ied ot: epetbility, libtion of the seen nd libtion of bilt-in eights.. Repetbility: this test shold be done t o ne the nominl mximm pity of the eighing instment o sing the lgest lod genelly eighed in pplitions. Repetbility is detemined in the sme y s s desibed in setion B, eq. (0).. Clibtion of the seen: on n detemine the y mesements fo the entie seen by the pplition stndd eights t vios points in the nge of the seen (/, /, / nd /) oding to the tble : N o Lod pplied Tble. Clibtion of the seen Eqilibim positions P P P P med P 0imed Diff i 0 P s =/ P = P -P 0 m s 0 P P 0 s =/ P = P -P 0 m s 5 0 P 5 P 0 6 s = / P 6 = P 6-P 0 m s 7 0 P 7 P 0 8 s = / P 8 = P 8-P 0 m s 9 0 P 9 P 0 Mss of sensitivity eight hee: s... s e sensitivity eights hving nominl mss eql to /.../ fom the mximm pity of the seen; m si is the mss of the sensitivity eight pplied; P oi med e the vege eqilibim positions (est points) hile the blne is not loded. The indition eo of the seen ill be llted s follos: E I = i m si V si () hee: is the density of the i nd V si is the volme of the sensitivity eight (ith Vs netinty).. Clibtion of bilt-in eights: the bilt-in eights e sed in ombintion ding the opetion of blne. Fist of ll, it is neessy to identify the bilt-in eights s nominl vles. Idelly the eights bilt into the blne shold be emoved nd libted extenlly. If this is not possible they n be left in the blne nd libted by diling them pon ombintions. A stndd eight S of mss m s nd volme V s is hosen fo libtion, depending on the y of the blne. The steps fo libtion of bilt-in eights e [9]: - eod seen eding t no lod indition I ; - eod seen eding I hen loding ith stndd eight S; - eod seen eding I hen loding ith stndd S (ith volme V s ) nd sensitivity eight of mss m s (ith volme V s ); - eod seen eding I hen the stndd S is emoved nd on pn emins only the sensitivity eight. To llte the mss of the bilt in eight, the next foml n be pplied: I + I I BW = ( + I ms VS + VBW + K ) () hee K is fto sed to onvet the eding in tems of sle nits into mesed mss diffeene. ms Vs K= () I I The foml () n be eded to simple one if the y of the eighing llos it nd it is knon tht K is onstnt fom the pevios mesements: BW = ms VS + VBW + K ( I I) () The vles fo m s, V s, V s, m s, e given in the libtion etifite. Mesement netinty fo the eighing instment To estimte mesement netinty fo the eighing instment the folloing pmetes need to be onsideed:. Unetinty de to the epetbility of the eighing instment,, - given by stndd devition s of sevel eighing eslts obtined fo the sme lod nde the sme onditions, llted s in eq. (6).. Unetinty ssoited ith the indition eo of the seen - llted s follos: (EI) = s s Vs + V (5)

6 The bove expession inldes the pmetes desibed: (epetbility), (esoltion), (netinty of the i density), s (netinty of the sensitivity eight), V si (volme of the sensitivity eight ith Vs netinty).. Unetinty of the bilt-in eights - llted stting fom eq. () o (): I + I I + I (6) BW = A + s + ( VBW VS ) + VBW + ) + K ) + K V [( I + I) ( I + I )] S BW= A + s + ( VBW VS ) + + ) + K I I) + K V V ( I I) BW S (7) Sine n expeimentl stndd devition nnot be llted fo single mesement to estimte A, dt obtined fom pevios epetbility evltions n be sed, ths eslting pooled stndd devition. Stndd netinty of the efeene eight, s is llted oding to eq. (9) fom bove. The ombined stndd netinty n be llted s follos: hen oetions e pplied to the eo of indition, the expession fo ombined stndd netinty is: = ) (8) BW ( ( EI ) hen no oetions e pplied to the eo of indition, the indition eo oss the ptil seen nge tht is mesed E I shold be dded to, in ddition to (EI), s follos: = E ) (9) BW ( ( EI ) I The expnded netinty fo k= ill be: U = k (50) Conlsions This ppe estblished metologil eqiements fo the libtion of nontomti eighing instments nd povided sefl infomtion fo opetos oking in edited libtion lbotoies in vios fields, in ode to detemine the mss of podts. - A lbotoy shold not ttempt to mke mesements ith n netinty of x sing n instment tht hs the edbility x. If the se ishes to pply no oetions, to obtin n netinty of x, he shold hve blne ith edbility of 0.x, to be se tht e no goss eos pesent. - The blne inditions e lose to the onventionl mss thn to the te mss, on mny osions, the indition being dietly sed s the onventionl mss. This is nomlly not vlid fo mss (te mss). In ent se, it is neessy to onvet the eighing eslt fom the onventionl mss to the te mss (in setion B desibed bove, the eighing eslt is tnsfomed dietly in te mss). - When libted instment is sed, the libtion netinty stted in the libtion etifite of tht instment hs to be tken into ont hen epoting the mesement netinty ssoited ith ny mesement eslts, bt it shold be emembeed tht the libtion netinty epesents only one pt of the mesement netinty stted in ent pplitions of the lbotoy. Othe ontibtions to the mesement netinty tht hve to be tken into ont e the inflene of the boyny oetion, the inflene of the popeties of the podt tht is eighed (evpotion, hygosopi behvio, eletostti hging, et). - Mehnil blnes hve genelly been epled by eletoni blnes, hih often offe bette esoltion nd e esie to se. The elibtion peiod fo ll of them (mehnil nd eletoni) n be diffeent fo eh type, being inflened by sh ftos s the sge of the eeives, opeto skill nd the envionment in hih the blne is loted. As genel gideline, blne shold be elibted yely, ntil the stbility of opetion is estblished. Refeenes [] Intentionl Reommendtion OIML R76 - Nontomti eighing instments, Annex A. pp 68-7 [] Intentionl Reommendtion N o Weights of lsses E, E, F, F, M, M,M h. 6, pp [] Gide to the expession of netinty in mesement (ISO, Genev, 995), Annex F pp 5. [] Intentionl Doment OIML D 8 Conventionl vle of the eslt of eighing in i pp 7-9, 00 [5] Doment 089, Edition 00 Otobe 000 Speifi eqiements elting to the libtion of nontomti eighing instments, h , pp 9-. [6] DKD R-7-, Clibtion of non-tomti eighing instments, isse 98, h.5 [7] NTM Veifie blnńelo l., şi 5 h.5, pp 5- [8] EA -0 /8 EA Gidelines on the libtion of nontomti eighing instments, (dft) Jly 00, h., pp nd. [9] Rndll M.Shoonove: Ai Boyny Coetion in High-Ay Weighing on Anlytil Blnes. Anl. Chem. 98, 5,

A NOTE ON THE POCHHAMMER FREQUENCY EQUATION

A note on the Pohhmme feqeny eqtion SCIENCE AND TECHNOLOGY - Reseh Jonl - Volme 6 - Univesity of Mitis Rédit Mitis. A NOTE ON THE POCHHAMMER FREQUENCY EQUATION by F.R. GOLAM HOSSEN Deptment of Mthemtis