TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN

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1 HARDMEKO 004 Hardess Measuremets Theory ad Applicatio i Laboratories ad Idustries - November, 004, Washigto, D.C., USA TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN Koichiro HATTORI, Satoshi TAKAGI, Hajime ISHIDA ad Takashi USUDA Natioal Metrology Istitute of Japa, Natioal Istitute of Advaced Idustrial Sciece ad Techology, Tsukuba, Japa Abstract I the early of 003, the traceability system of the Rockwell hardess stadard have bee developed i Japa. The Natioal Metrology Istitute of Japa (NMIJ started to provide the atioal primary hardess stadards, oe of which is the hardess referece blocks, ad the other oe is the accreditatio of the Rockwell hardess tester. I this paper, we preset the detail of ucertaity trasfer betwee the NMIJ ad the secodary stadard laboratories. Keywords: Rockwell hardess, traceability, ucertaity. CALIBRATION SERVICE AND ACCREDITATION PROGRAM IN JAPAN NMIJ started calibratio service of secodary stadard Rockwell testig machie (jcss i 00, ad the Natioal Istitute of Techology ad Evaluatio (NITE also started two accreditatio program of traceability of Rockwell hardess, oe is the traceability of calibratio of testig machies ad the other is calibratio of stadard blocks. The ame of the service is Japa calibratio service system (JCSS. The JCSS accredits compay, supplyig the calibratio service to a customer with the traceable Rockwell hardess values. Because of the traceability system operated uder the measuremet-law of Japa, jcss ad JCSS have some differece. The NMIJ oly calibrates the secodary stadard Rockwell hardess machie o the jcss calibratio system, ad there are o differece of machies betwee calibratio of stadard blocks ad calibratio of testig machie at this poit. The calibrated laboratories declare their calibratio services (calibratio of testig machie/ stadard block ad their ucertaity, after jcss calibratio. The ucertaity sources of Rockwell hardess block issued by secodary laboratory are show i the table that is calculated for the stadard blocks provided by the secodary laboratory. The terms,, 3 ad 4 is determied as the result of jcss calibratio, certified by NMIJ. The ucertaity of stadard ideter is calculated of combiatio of the accidetal error ad ucertaity of atioal primary ideters whe the ideter is compared with the primary ideter. Fially the declared ucertaity of the Rockwell hardess value is tested uder the accreditatio program of the JCSS traceability system coducted by NITE. The NMIJ certified stadard hardess blocks, which are used i this proficiecy test (Fig.. The details of the ucertaity calculatios ad evaluatio of declared ucertaity are preseted as followig sectios. jcss calibratio NMIJ Primary stadard trasfer stadard Blocks commo ideter with calibratio of. test forces. depth 3. compariso of hardess Secodary stadard Fig. schematic of secodary stadard o the jcss calibratio system. JCSS accreditatio Primary stadard Proefficiecy test to evaluate the declared ucertaity usig E value NMIJ stadard blocks Secodary stadard Fig. evaluatio of declared ucertaity through the proficiecy test o the JCSS accreditatio program. Table. The ucertaity sources of the JCSS certified block. Source of ucertaity Prelimiary test force u F0 Total test force u F 3 Depth measurig device u h 4 Hardess compariso with commo ideter u comp 5 Stadard ideter u Id 6 Hardess variatio of the block u block Sources -4 are evaluated by NMIJ 5,6 are evaluated by secodary laboratory.

2 . UNCERTAINTY OF FORCE To Estimate the ucertaity of the force, we measured the force at three differet heights ad evaluate the ucertaity as u f 3 3 ( fh, mesured h h fstadard, (. where the h is the umber of measured height ad is the umber of repeat at the same height. f stadard is the ad 47 N for the prelimiary test force ad the total test force, respectively. The total stadard ucertaity of force is calculated by the combiatio of ucertaity of force measurig device, u f, as u. (. f u f u f I this method, the ucertaity of the force is estimated as a total stadard deviatio from the stadard values. The advatage of this method is that it ca be all measured deviatio ca be cosidered, ad the bias compoet ca be also cosidered. The coverage factor is useful whe the ucertaity is give oly by the accidetal error i the measuremet. I additio the treatmet of the effect of o-corrected bias compoet is ot easy. We believe that this method is oe of the best solutios of the ucertaity evaluatio icludig the o-corrected bias compoet. 3. UNCERTAINTY OF THE DEPTH-MEASUREING DEVICE Depth measurig device is evaluated as follows: determiatio of the zero poit as a set positio, where the equivalet of 00HRC. After the depth measurig device is oce moved to the dowward over the 00 m (0 HRC ad after moved to measuremet positio (ex. 00 m. The the measuremet was carried out at each positio that iterval is the 0 m (~0HRC. The corrected depth measurig data was evaluated as, uh 3 ( hij i j hstd i (3. where the i is the positio ad the j is the umber of repeats, ad the is the total umber of measuremet, respectively. The total ucertaity of the depth-measurig device is give by the combiatio of the stadard ucertaity of the depthcalibratio device, u h, ad the ucertaity due to the resolutio of the depth-measurig device (or hardess idicator, u hres ad u h, h uhstd uh uhres u. (4. 4. UNCERTAINTY OF THE INDENTER The ideter characteristic is the most sigificat parameter for measuremet value, eve if the ideter is suitable for the ISO requiremets []. 4. Stadard ideters It is recommeded that the each secodary laboratory should have oe or more stadard ideters. The defiitio of the stadard ideter i the JCSS system is: the ideters a are suitable for the ISO requiremet [] ad b have the correctio values for each hardess levels. The hardess values of the JCSS certified blocks expressed as a corrected hardess values. To determie the correctio values the compariso of the hardess values betwee the atioal primary ideter are carried out usig stable testig machie ad made a sufficiet umber of idetatios to the same blocks []. The correctio values are determied as a bias from the atioal primary ideters. The correctio values are determied 0HRC iterval, from 0 to 65 HRC, typically. The atioal primary ideters also have correctio values. This is based o the followig assumptios that the hardess variatio of each ideter comes from the variatio of the cotact area ad this variatio ca be comparable if the stable testig machie is used to the compariso. 4. Ucertaity of atioal primary stadard ideters The NMIJ has about 30 atioal primary stadard ideters. These ideters have the correctio values, which value is defied as a hardess deviatio from the ideal stadard ideter [3]. The detail of the determiatio of the correctio values is give i the other presetatio[4]. We itroduce it briefly: There are six characteristic parameters for each ideter, the five differet average curvatures (for five differet average agle for the sphere part of the ideter ad oe parameter for the coe agle. May actual shape ideters are prepared ad the hardess measuremet was carried out for each ideter. The multiple regressio aalysis was carried out usig followig model, H i a5 ( p5i a ( pi a6 ( p6i a ( pi 0 i 00..., (5. where H i ad are the hardess values of measured ad ideal for the block, respectively. The parameters p i is the measured characteristic parameters ad a is the coefficiets of the regressio. The error term icludes accidetal error ad the error due to the hardess variatio of the positio. The ideal hardess is estimated, as that is the value of the regressio curve at characteristic parameters set to that of ideal shape ideter, i.e. 00 m for curvature ad 0 for coe agle. The ucertaity of the ideter is determied by the remaied error of the regressio aalysis. The stadard ucertaity of correctio values of the atioal primary stadard ideters is about 0.3 HRC at 60HRC level, ad it depeds o the hardess levels due to the differece of o-uiformity of the blocks. 5. COMPARISON OF HARDNESS VALUES USING COMMON INDENTER

3 To determie the total ucertaity of testig machie of secodary laboratory, we compare the measuremet values of same blocks usig commo ideter. The total deviatio from the primary hardess tester icludig test cycle effect is evaluated through the compariso. 5. Hardess compariso usig 4d method The NMIJ adopted the followig method for the hardess compariso, the method had developed by the oe of the authors, ad we call it 4d method. Geerally, the hardess varies getly i the block. Therefore the differece of measured values will be very small with decreasig the iterval of two idetatios. Because of the hardess chage due to the pre-performed idetatio, the limit of actual distace betwee the two idetatios will be 4 times of diameter of idetatio. This iterval betwee the idets is the origi of the ame of this method. I the 4d method, the hardess differece betwee two idetatios ca be regarded as a accidetal error. The theoretical of this compariso ca be calculated as follows: The hardess values of secod idetatio, H i ad correspodig referece idetatio, H i is give by, Hi H i m m pij ij ik (6. where is the ideal hardess value of the block, p i is the hardess variatio depedig o the idet positio i, m is the hardess variatio due to the differeces of machies, i is the accidetal error ad, deote the referece ad secod idetatios, respectively. The hardess differece of the correspodig poit is give by, H i H i Hi m m pij ik ij, (7. ad the mea value of the hardess differece is, H m m. (8. Here, we eglect terms of the mea values of the p i ad i, usig after th measuremets usig, pi i 0 ad i i 0. (9. The stadard deviatio of the compariso usig 4d method will be expressed as ( H i H ( i i pij ik ij. (0. Cosider the idepedece betwee p i ad i, ij ad ik.. It ca be assumed that the amplitude of the accidetal error will be the same. We obtai, i ( pij i pij (. O the other had, the compariso of the hardess values is carried out usig the mea hardess values of the block. We also calculate the deviatio of the mea hardess compariso. The mea hardess values are give by, H i H i m m (. Here the mea terms of the p i ad i are eglected. The differece betwee the mea values m ad m is give by the same as that obtaied by the 4d method, H m m. (3. The stadard deviatio of the mea hardess value for the referece H i is give by,. ( Hi H i ( pij ij ( pij i i i (4. Here we use the result of above discussio, the cross terms ca be eglected ad the amplitude of stadard deviatio of the accidetal error is set to the. The total stadard deviatio of the mea hardess compariso is give by the addig the two idepedet deviatios of two measuremets, pi i i. (5. The stadard deviatio of the 4d method is decreased whe the correlatio betwee the p ij ad p ik becomes strog. The result of 4d method is correspodig to that of mea hardess compariso if the o-correlatio is observed, it is the worst deviatio limit of the 4d method. We also check the validity of the method, experimetally. 5. experimetal evaluatio of validity of 4d method The atioal primary hardess tester SHT-3 Rockwell hardess tester was used i the experimet. SHT-3 is the lever-amplified dead weight type ad the holographic gages used to depth measurig device. The omial hardess levels are 64, 60, 40, 30 ad 0 HRC. The hardess measuremet was carried out four times; the itervals of the measuremets are about oe-week for the d measuremet, about four-moths for the d-3rd ad oe-week for the 3rd- 4th measuremet. Table shows the typical example of measuremet obtaied the 40HRC block. The d-4th idetatio data are obtaied by the measuremet usig 4d method aroud the st idet. The hardess variatio of the each measuremet poit is show i the Fig. 3. The coectig lie shows a measured hardess observed i the same day. The hardess variatio depedig o the measuremet positio shows the similar tedecy. That meas the correlatios betwee the idetatios may be strog.

4 Table. The hardess observed usig 4d method for 40HRC block. Idet positio st 0 week d week 3rd 6 weeks 4th 7 weeks Average Idet positio Fig. 3. The hardess observed usig 4d method. st d Table. Oe-way aalysis of variace for 40HRC block. Idet positio factor ss dof variace p value betwee groups E-05 withi groups rd Measured day factor ss dof variace p value betwee groups E-0 withi groups The result of oe-way aalysis of variace is show i table. We regardig that the lie data ad the row data as the same group i the aalysis of idet positio ad measured day i the table, respectively. The 4d method ad the mea hardess compariso are correspodig to the idet positio ad the measured day i the table, respectively. The aalysis idicates that the effect of testig machie istability depedig measuremet day is much smaller tha that effect of the hardess variatio of the block. The calculated stadard deviatios of these comparisos are 0.06 HRC for 4d method ad 0.5 HRC for the mea hardess compariso ad that is directly reflected the ucertaity of the calibratio. The ucertaity of the trasfer block usig hardess compariso is estimated as about 0.07 HRC. As the largest ucertaity source, the ideter is eglected because the ideter is commoly used i the compariso. The result of oe-way aalysis obtaied other hardess levels are show i table 3. The p values of the compariso 4th is small exceptig 60HRC block that is because the 60HRC block is very good so that the measured rage of hardess variatio was very small (0.HRC. The the effect of 4d method looks slightly small. Table 3. The oe-way aalysis of variace for 4d method. 64HRC factor ss dof variace p value betwee groups E-0 withi groups HRC factor ss dof variace p value betwee groups E-0 withi groups HRC factor ss dof variace p value betwee groups E-03 withi groups HRC factor ss dof variace p value betwee groups E-0 withi groups Fially the ucertaity of hardess compariso usig 4d method is give by, ucomp _ ( H i i Hi. (6. where, the hardess value, H i is compared with correspodig referece-idetatio, H i ad is the umber of idets. The the ucertaity of compariso is determied after combied with the ucertaity of trasfer stadard block, u comp_. comp ucomp _ ucomp _ u (7. The u comp_ is cosidered a lower limit of ucertaity, if the measuremet values equal to the stadard oe ad is about 0.07 HRC that is determied by the direct calibratio result of NMIJ without ideter ad discussed stadard deviatio of the block usig 4d method. The ucertaity of compariso will be expected about 0.09 HRC usig u comp_ =0.07 HRC ad u comp_ = 0.06 HRC whe the same tester is used i the compariso. 6 PROFICIENCY TEST 6. Proficiecy test to evaluate the declared ucertaity As metioed at sectio, the declared ucertaity is evaluated by the blid test coducted by the NITE. The stadard block certified by the NMIJ is used i the test. Geerally the a ideter is selected from the atioal primary stadard ideters, arbitrary, to determiatio of the

5 hardess of block, ad that meas the hardess values of the block is dispersed artificially. The hardess of the block is determied as a mea value of the six idetatios; we perform oe idetatio for each sectio. The secodary laboratory also perform six idetatios for each sectio, the idetatio positio is selected arbitrary iside the sectio. The sectio of the block is show i the fig M Fig. 4 The sectio of the block. 6. The evaluatio of the JCSS ucertaity I this subsectio, we show the result of the simulative hardess blid test, performed at 0, 40 ad 60HRC levels. The hardess levels of compariso are selected to cover the Rockwell hardess rages. The calculated JCSS-equivalet ucertaity is evaluated experimetally usig E value, H E (8. U NMIJ U JCSS Here, the U NMIJ ad U JCSS are the expaded combied ucertaities usig coverage factor (k=. The U NMIJ is our declared expaded ucertaity of the Rockwell hardess block calibratio. The U JCSS is the calculated expadig ucertaity followig the metioed method. The sesitivity coefficiets of the ref.[5] is used i the ucertaity calculatio. Two differet testers are used i the evaluatio, oe of which is the (A NMIJ primary hardess machie, SHT-3, ad the other oe is the (B commercially available tester, which oe of the participated machie for the roud robi test of the JCSS program. The features of that is the lever-amplified dead weight type ad the prelimiary test force is applied by the sprig. The result of the tester A is show i table 5. The ucertaity equivalet to the jcss certificate is determied usig metioed ucertaity estimatio. The uit of ucertaity i the tables are HRC. The ucertaity of the hardess compariso is determied experimetally usig 4d method ad commo ideter. The determied ucertaity of compariso i the table 5(a is about HRC, which value is almost same expected i the 5.. The total ucertaity of tester A idicated the table 5(b, ad is equivalet to the ucertaity of JCSS calibratio of block. I the jcss is ot ivolvig the ucertaity of ideter, the the ucertaity of the ideter is combied at here. Fially the result of the JCSS ucertaity is tested by the E value. The differece of hardess betwee the stadard hardess blocks ad the hardess of tested machie is about 0., which is caused by the differece of ideter i this case. The E values are less tha 0.3. I the table 6, we show the result obtaied by the commercial tester usig the metioed calibratio scheme. The expected ucertaity, show i the table 6(b, is equivalet to that of JCSS calibratio of blocks. The machie used i this evaluatio is ot suitable for the ISO part 3[], however, the all E values show less tha, ad that is earby the E = 0.5. These results show the metioed scheme may estimate the ucertaity of Rockwell hardess correctly. Table 5. The simulative estimatio of total ucertaity for NMIJ primary hardess tester (A, uit of ucertaity is HRC. (a The ucertaity equivalet to the jcss Source of ucertaity 0HRC 40HRC 60HRC Prelimiary test force, u F Total test force, u F Depth measurig device, u h Hardess compariso with commo ideter, u comp Comb. std. Ucertaity Exp. std. Ucertaity (k= (b Total ucertaity of simulative d machie (JCSS Source of ucertaity 0HRC 40HRC 60HRC Machie (jcss for A Stadard ideter, u std o-uiformity of blocks, u b Comb. std. Ucertaity Exp. std. Ucertaity (k= (c E Source of ucertaity 0HRC 40HRC 60HRC Differece of Hardess Exp. ucertaity of d Lab Exp. ucertaity of NMIJ E value Table 6. The simulative estimatio of total ucertaity for commercial type hardess tester (B, uit of ucertaity is HRC. (a Expected ucertaity of commercial tester (B Source of ucertaity 0HRC 40HRC 60HRC Machie (jcss for B Stadard ideter, u std o-uiformity of blocks, u b Comb. std. Ucertaity Exp. std. Ucertaity (k= (b E Source of ucertaity 0HRC 40HRC 60HRC Differece of Hardess Exp. ucertaity of d Lab Exp. ucertaity of NMIJ E value

6 7. CONCLUDING REMARKS The traceability of Rockwell hardess ad ucertaity trasfer system i Japa is preseted. The ucertaity calculatio method is verified two differet simulative experimets. We also verify the validity of this ucertaity trasfer method through the actual JCSS accreditatio program. The Rockwell hardess traceability system i Japa is just started. The JCSS accredited compaies are rapidly icreased ad may compaies are waitig jcss calibratio. Because of the jcss allows oly the direct calibratio of machie by the NMIJ. We are tryig to develop aother ucertaity estimatio system usig their certified calibratio devices ad certified hardess blocks. REFERENCES [] ISO6508-,3,"Metallic materials -Rockwell hardess test -". [] H. Ishida et al., "The characters of the Rockwell diamod ideters ad tatalizatio method" J. Mater. Test. Res., No.3, pp.9-6, 978. [3] H. Yao et al., "Characterizatio of stadard Rockwell diamod ideters ad method of establishig stadard ideters", proceedigs of the roud-table discussio o hardess testig 7th, IMEKO, Lodo, pp. 6-50, 996. [4] S. Takagi et al., Direct Verificatio ad Calibratio of Rockwell Diamod Coe Ideters, proceedigs of Hardmeko 004, submitted to Hardmeko 004. [5] Europea co-operatio for Accreditatio, EA-0/6, "EA Guidelies o the Estimatio of Ucertaity i Hardess Measuremets", 00 [6] The detail of JCSS system please refer: Authors: Dr. Koichiro Hattori, NMIJ, AIST Address: AIST Tsukuba Cet.3, Umezoo -- Phoe: , FAX: Mr. Satoshi TAKAGI, NMIJ, AIST, Address: AIST Tsukuba Cet.3, Umezoo -- Phoe: , FAX: Mr. Hajime ISHIDA, NMIJ, AIST Address: AIST Tsukuba Cet.3, Umezoo -- Phoe: , FAX: Dr. Takashi USUDA, NMIJ AIST Address: AIST Tsukuba Cet.3, Umezoo -- Phoe: , FAX:

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