测厚仪不确定度.doc

Eddy Current (Magnetic Resistance) Thickness GaugeExpanded Uncertainty of measurement for Eddy Current(Magnetic Resistance) Thickness Gauge1 Method of Measurement(According to JJG818-93 & JJG889-95) The indication error of eddy current (and Magnetic Resistance) thickness gauge is directly calibrated using a series of standard foils which have different thickness and coverage within the range of the thickness gauge being calibrated. For every standard foil, three or five measurements are taken, and indication error is the difference between the average of readings and the value of standard foils. Relative indication error is obtained from the error divided by the thickness of related standard foils. 2 Mathematical model =RHIn formula : indication error of the instrument being calibrated Rindication of the instrument being calibrated Hthickness of related standard foils3 Contributory variances From formula ,we have In formulaC(R)= 1 C(H)= -1 Then 4 Table for summary of standard uncertainty components:4.1 For eddy current thickness gauge H =543Standard uncertainty componentu(xi)Source of uncertaintyValue of standard uncertaintyu(xi)|ci|u(xi)Degrees of freedom u(R) u(R1) u(R2) u(R3)Indication of the instrumentRepeatability of measurementQuantization errorFlatness of base3.75(1/)=1.67 1 1.8112 9 50 u(H)standard foils543(1%/2.00)=2.72 -1 2.7260 u=10.72 uc=3.27 neff=634.2 For eddy current thickness gauge H =1000Standard uncertainty componentu(xi)Source of uncertaintyValue of standard uncertaintyu(xi)|ci|u(xi)Degrees of freedom u(R) u(R1) u(R2) u(R3)Indication of the instrument Repeatability of measurement Quantization error Flatness of base 7.33(1/)=3.28 1 3.36 9 9 50 u(H)standard foils1000(1%/2.00)=5.00 -1 5.00 60 u=36.32 uc=6.02 neff=534.3 For magnetic resistance thickness gauge H =543 Standard uncertainty componentu(xi)Source of uncertaintyValue of Standard uncertaintyu(xi)|ci|u(xi)Degrees of freedom u(R) u(R1) u(R2) u(R3)Indication of the instrument Repeatability of measurement Quantization error Flatness of base 5.83(1/)=3.37 1 3.44 99 50 u(H)Standard foils543(1%/2.00)=2.72 -1 2.72 60 u=19.22 uc=4.38 neff=224.4 For magnetic resistance thickness gauge H=1000mStandard uncertainty componentu(xi)Source of uncertaintyValue of Standard uncertaintyu(xi)|ci|u(xi)Degrees of freedom u(R) u(R1) u(R2) u(R3)Indication of the instrument Repeatability of measurement Quantization error Flatness of base 10.8(1/)=6.24 1 6.28 99 50 u(H)standard foils1000(1%/2.00)=5.00 -1 5.00 60 u=64.42 uc=8.03 neff=223 Calculating components of uncertainty5.1 Uncertainty due to indication of the instrument being calibrated u(R)5.1.1 Uncertainty due to repeatability of measurement u(R1)The repeatability is the standard deviation obtained from 10 repeated measurements. The standard deviation s is evaluated below. For eddy current thickness gauge: For H=543 s=3.75, For H=1000 s= 7.34, In measurement，the mean of five readings is taken, then： For H=543 u(R1)=1.67 (R1)=9 For H=1000 u(R1)=3.28 (R1)=9 For magnetic resistance thickness gauge: For H=543 s=5.83 For H=1000 s=10.80 In measurement，the mean of three readings is taken, then： For H=543 u(R1)=5.83/=3.37 (R1)=9 For H=1000 u(R1)=10.80/=6.24 (R1)=95.1.2 Uncertainty due to quantization error of readings u(R2) The resolution of the instrument is 0.001 mm. The quantization error of reading is regard as rectangular distribution of the half width 0.0005 mm. For it effects results twice，then：(R2)5.1.3 Uncertainty due to the flatness of base u(R3) The flatness of base is 1m. The flatness lies with equal probability within half width 1m, Uncertainty due to the flatness error estimated below. Its relative uncertainty is estimated to be 10%，Degrees of freedom is(R3)=50 By For eddy current thickness gauge For H =543 u(R)=1.81 (R)=12 For H=1000 u(R)=3.36 (R)=9 For magnetic resistance thickness gauge: For H=543 u(R)=3.44 (R)=9 For H=1000 u(R)=6.28 (R)=95.2 Uncertainty due to standard foils u(H) The certificate of standard foils gives expanded uncertainty of measurement U=1.0%， probability lever p=0.95，coverage factor k=2，and degrees of freedom=60， For H=543 u(H)=2.72 (H)=60 For H=1000 u(H)=5.00 (R)=604 Combined standard uncertainty For eddy current thickness gauge For H =543 uc=3.27 For H=1000 uc=6.02 For magnetic resistance thickness gauge For H=543 uc=4.38 For H=1000 uc=8.037 Effective degree of freedom Using Welch-Satterthwaite formula For eddy current thickness gauge For H=543 eff(R)=63 For H=1000 eff(R)=53For magnetic resistance thickness gauge For H=543 eff(R)=22 For H=1000 eff(R)=228 Expanded uncertainty of measurement For the confidence lever =95%，we have For eddy current