INSTRUMENTS USED OR MEASURINNG THE MAGNETIC PROPERTIES O ONE KILOGRAM MASS STANDARD IN CENTER OR MEASUREMENT STANDARDS (CMS) Sheu-shi Pn, H. C. Lu nd C. S. Chng Center for Mesurement Stndrds, Industril Technology Reserch Institute ABSTRACT We mesured the volume mgnetic susceptibility nd permnent mgnetiztion of kg mss stndrds re mesured under the circumstnces of CMS mss lbortory. The method nd clcultion of uncertinty described here re referred to the experimentl method nd procedure developed by Dvis; while the distnce between mgnetic smple nd the weighs were mesured with luminium guide nd the distnce ws determined by reding of lser interferometer. The effects of volume mgnetic susceptibility nd permnent mgnetiztion on weights ws rel-time mesured.the degree of rel-time mesured dependent upon the trnsient time of the blnce. These results of susceptibility mesurement were compred to the results of smples when they rrived CMS.. INTRODUCTION The mgnetic susceptometer developed by Dvis[]t the Bureu Interntionl des Poids et Mesures(BIPM).This device ws used to mesure the volume mgnetic susceptibility of the stinless-steel weight stndrds; under the ssumption of liner,homogeneous nd wek susceptibility smples or stndrds. The susceptometer included the smll mgnetic source smple, lifting guge blocks nd high precision commeril blnce. As this type of susceptometer ws widely used ; Severl results of the volume mgnetic susceptibility mesurement on the kg stndrds ws mesured under the erth mgnetic field [,,3] nd shield the erth mgnetic field [4,5].The relevnt investigtions on the mgnetic interctions between weights nd blnces were found [6,7]. The method ws used in ssuming the mgnetic source is the dipole source nd the weight smple is semi-infinite slb. The nerest distnces between mgnetic source nd the weight smple( ) ws evluted by convergent wy. When the guge blocks were used to chnge lifting distnces vlues in discrete wy; we cn get redings of the blnce which showed the mgnetic effects on the stin-steel weight stndrd. About this work, we modified the guge lifting device by combining the luminium slide guide nd compct three xis lser interferometer to mesure the nd the other vlues of lifting heights. During the experiment; the heights of the lifting stinless-steel smples nd the redings of the blnce were recorded by computer simultneously. According these ccess dtum; we could clculted the volume mgnetic susceptibility χ nd the mgnetic effect to the height continuously.. BASIC PRINCIPLES We ssumed the mgnetic field of erth ws uniform in our re of experiment nd ssumed the field produced by the smll cylinder mgnetic disc is dipole field. The dipole field cted on smple with the form of semi-infinite slb nd pproximted the mgnetic flux s being uniformly long its xis. These force equtions cn be expressed s follows []:
where nd µ + χ I m ( H E + M ) Ib + () χ mxi b 4π 3µ χm 4 mx 64π 3π 3m χ, () n V n H mg H mg dv 3π n ρ + 4z ( ρ + z ) V n 4 ρdρdθdz, (3) I b 4π m n ( H mg ) V n z dv n ρ z V n ( ρ + z ) 5 ρdρdθdz, (4) where χ is the effective volume mgnetic susceptibility of the stndrd, the prmeter µ is the 7 vcuum permebility, identiclly equl to 4π N A. And χ H E is n induced mgnetiztion tht hs the sme effect s permnent mgnetiztion M. The prmeter m is the moment of the mgnet nd is the distnce between the center of the mgnet nd the smple, s shown in igure. 3-xis compct interferometer Moving guide Lser bems Lser source HP557C Stoppers Moved Pltform Mgnetic smple Dvis holder Pn Blnce UNT5 Dvis Structure igure: Note how the text is centered under the figure ( The first term in Eq. () is given by + ( nd the second term by ) b. ) The initil force mesurement is mde with the north pole of the mgnet pointing down nd second mesurement is mde (t the sme ) with the north pole
pointing up. As we hve mesured the by lser interferometer directly; so the formul were modified s following: χ I µ m ( χh + M ) I m g mx + E b 4π ( m) ( χh + M ) I m g µ χ mxi + E b 4π + I ( m + m ) g χ mx χ ( m + m ) g /(mxi ) where g is the grvittionl ccelertion in the lbortory. m nd m re the corresponding redings of blnce when the direction of north pole were down nd up. The mesurement principle of cn be shown in ig. [8].This distnces were determined by the verge of the opticl pths X, X nd X 3 mesured by the 3-xis compct interferometer. The uncertinties could be cused by cosine error nd Abbe error were considered. When we mesured the distnce ; the pitch nd yw were mesured.they cn be expressed by X, X, X 3, L nd d: ( X + X 3) / X Pitch ϑ y (5) d X X 3 Yw ϑ x (6) L where L nd d re equl to 4,38 mm(the distnce between the incident lser bems).then the stndrd uncertinty of the mesurement due to the Abbe error, u Abbe, cn be determined by the sum of the yw multiplied by its own Abbe offset nd the pitch multiplied by its own Abbe offset, with X Yw X ϑ X (7) Abbe x Y Pitch Y θ Y (8) Abbe where : Abbe error in yw-direction; X Abbe Y Abbe : Abbe error in pitch-direction; X Y : Abbe offset in yw-direction; : Abbe offset in pitch-direction y 3
X L X X 3 d Y Guide Reflect Mirror Pln X Guide Moving Axis Bems spots Interferometer Reference Pln igure: Note how the text is centered under the figure 3. SYSTEM SET UP AND EXPERIMENTS The system included the UMT5 blnce, 3-xis compct lser interferometer, the lifting devices in moving guide nd smples lifting pltform (in the figure 3). The moving guide ws used to indicte the distnce between the smple pltform nd top of mgnetic source smple; there were two moving mesure fixed long the moving guide. When the moving guide pproches the mgnetic source on the pn; these moving mesure will be used s the proper stoppers lterntely. As the moving guide touches the top of mgnetic source lightly; the reding of the UMT5 blnce will chnge. The redings corresponding to the lser interferometer nd the blnce will be recorded by control progrm in PC. We cn nlysis from these dtum nd get the distnce. As the response of the blnce ws slow. When we lifts the smple pltform in one new distnce, the sme position will be hold in one minute nd let the redings of blnce be recorded. The redings of blnce, lser interferometer will be recorded simultneously. The cylindricl neodymium-iron-boron mgnet ws used s the source of the mgnetic field; the dimensions of the simple cylinder re nominlly 6 mm in dimeter nd 5 mm in height. The mgnet ws mnufctured by IBS (Mgnet Berlin Germny). The volume mgnetic susceptibilities m of two stndrd smples were determined with respect to working stndrds of the BIPM. 4. RESULT The figure 3 shows when the moving guide pproched nd left the top of mgnetic source; the response of the blnce nd the vlue of ws recorded. When the moving guide touched the top of mgnetic smple; the reding of blnce chnges lrgely. After we nlyzed these mesurements; the distnce ws determined. The results of distnces were presented in tble. The figure 4 expressed the pitch nd yw s the ws mesured. The uncertinties by pitch nd yw were lso evluted; the figure 4 shows the mesurements of pitch nd yw. The figure 5 represented the reding of blnce when the distnce () vried nd north pole of the mgnetic pointed up nd down respectively. The vrition of χ vlue with the distnce () ws shown in figure 6. The vlue of χ vlue decresed s the distnce () incresed. 4
Tble: The result of Sttistics Cosine-Error Abbe Error Totl (-sigm).54 mm.7 μm 5. μm 9. μm 35.4 μm mg 6 5 4 3 4 7 8 7 7 6 4 (time) mm Rd. Pitch nd Yw in mesurement.8.6.4. -. -.4 -.6 Smpling rte(per.34 second) 5
igure 3: The pproching nd leving of the guide igure 4: Pitch nd yw of the distnces mesurements mg N-pole down -.5 - -.5 - -.5-3 - 3.5 3 mm -.5 - -.5 - -.5-3 - 3.5 mg N-pole up 3 mm igure 5: The mesurements of distnces corresponds to the redings of blnce igure 6: The mesurements of χ vlue χ 5. SUMMARY.5..5 We hve modified the mgnetic susceptometer developed by Dvis with the lser interferometer nd proper moving guide system. Although the smples ws confined in low χ nd low externl field used, but the modified mgnetic susceptometer hs three novel differences with the originl 5 5 3 ( mm) mgnetic susceptometer s the following:.the distnces nd were mesured directly by lser interferometer nd proper guiding system..the form of uncertinty evluted ws different from the method of Dvis. 3.The mesurement of χ vlue ws in rel time tht dependent upon the response time of blnce in new equilibrium stte. ACKNOWLEDGEMENTS We would like to thnk Dr. Chris Sutton to give us some good suggestions in mgnetic moment mesurement when he visited in CMS. REERENCES [] R.S.,Dvis, ew method to mesure mgnetic susceptibity,mes. Sci. Technol. 4 (993) pp:4-47 [] R.S., Dvis, Determining the mgnetic properties of kg mss stndrds, J. Res. Ntl. Inst. Stnd. Technol., (995) pp: 9-5 [3] H.C. Lu nd C. S. Chng, Evluting the Mgnetic Property of One Kilogrm Mss Stndrd in Center or Mesurement, APM'3 Proceeding, pp: 57-6 6
[4] J.W. Chung, J.-Y. Do,B.-S. Chon nd R.S. Dvis, ffect of erth mgnetic field on mesurement of volume mgnetic susceptibility of mss, Metrologi,,37,pp: 65-7 [5] J.W. Chung, K.S. Ryu nd R.S. Dvis, Uncertinty nlysis of the BIPM susceptometer, Metrologi, 38 (), pp: 535-54. [6] Michel Glser, gnetic interctions between weights nd weighing instruments, Mes. Sci. Technol. () pp: 79-75 [7] R Dvis nd M Glser, gnetic properties of weights,their mesurements nd mgnetic interctions between weights nd blnces, Metrologi 4 (3), pp: 339-355 [8] Sheu-shi Pn, Chiu-Hsien Chen nd Chi-Sheng Chng,Evlution of the uncertinty due to Abbe error for primry Rockwell hrdness stndrd system, XVII IMEKO World Congress Meterology in 3 rd Millennium June -7,Dubrovnik, Crotis, 3, pp: -4 Addresses of the Authors: Dr. Sheu-shi Pn, Center for Mesurement Stndrds,Bldg. 6, 3 Kung u Rod, Sec., Hsinchu, Tiwn 3, R.O.C. E-mil: sheu.shi.pn@itri.org.tw Hui-Ching Lu, Center for Mesurement Stndrds,Bldg. 6, 3 Kung u Rod, Sec., Hsinchu, Tiwn 3, R.O.C. E-mil: frnceslu@itri.org.tw Dr. Chi-Sheng Chng, Center for Mesurement Stndrds,Bldg. 6, 3 Kung u Rod, Sec., Hsinchu,Tiwn 3, R.O.C. E-mil: ChiSheng.Chng@itri.org.tw 7