Torque Wrench Calibration Presentation
February 5, 2017 | Author: mythee | Category: N/A
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Calibration of a Torque Wrench as per ISO6789 by Eddie Tarnow NLA Test & Measurement Workshop 20 September 2011
© NMISA 2011
Calibration Setup 350,0 N•m
Clockwise Rotation Unit Under Test Torque Wrench
Reference Standard Torque Transducer & Readout Unit
Force Applied
Top View of Setup © NMISA 2011
Calibration Scenario • The Unit Under Test Torque Wrench is a Type II class A tool (adjustable click type) and has a full scale of 350 N•m. • It has a setting dial resolution of 2 N•m • We are to calibrate it according to ISO 6789 which requires a calibration point at full scale (100 % of range) viz. at 350 N•m and the estimation of the measurement uncertainty at this point
© NMISA 2011
GUM Steps • • • •
Model the measurement Identify and quantify the sources of uncertainty Categorize as type A or type B Manipulate appropriately to obtain • Standard uncertainties, u(xi) • Sensitivity coefficients, ci • Uncertainty contributor, u(yi) • Combine to obtain combined standard uncertainty, uc(y) • Expand to obtain an expanded uncertainty, U, at an appropriate level of confidence • Report the result
© NMISA 2011
Measurement Model
TUUT = TSTD Ind + CorrSTD
© NMISA 2011
Identifying the sources of uncertainty
TSTD
SCal
TUUT
URes
URep
SRes SCF
TUUT © NMISA 2011
Quantifying the sources of uncertainty • SCAL • Calibration Results Table from the Calibration Certificate APPLIED TORQUE (N•m)
MEAN UUT CALCULATED TORQUE (N•m)
UNCERTAINTY OF MEASUREMENT (± N•m)
0,0
0,0
0,1
99,9
100,0
0,3
199,9
200,2
1,0
299,8
300,5
1,0
399,8
400,8
1,0
499,7
501,1
1,0
599,7
601,5
1,0
699,6
701,8
1,0
© NMISA 2011
Quantifying the sources of uncertainty (2) • SCAL • This is the uncertainty due to the accuracy of the Reference Standard Torque Transducer, which is not perfect • Corrections must first be applied, or the uncertainty increased, to take the error into account (largest error on values either side of the calibration point was +1,0 N•m) • The Reference Standard Torque Transducer used has a full scale of 700 N•m and was calibrated in 100 N•m steps (See calibration certificate) • Therefore we will have to use the polynomial equation to determine the actual torque generated by the UUT at 350 N•m since it is a measurement point in between 300 N•m and 400 N•m. • Since we have to interpolate a value we will use the largest reported uncertainty from the calibration certificate for the values on either side of the calibration point which is ± 1 N•m.
© NMISA 2011
Quantifying the sources of uncertainty (3) • SCAL • Since we will be using the polynomial to interpolate a value at 350 N•m, we DO NOT need to correct for the + 1 N•m error at 399,8 N•m. • Therefore total uncertainty for the “accuracy” of the Reference Standard Torque Transducer is ±1 N•m • This is treated as normal at 95,45% Level of Confidence • The divisor is the coverage factor k which for 95,45% LOC is 2 • The degrees of freedom are always ∞ or 100 % Reliable due to the source of traceability being accredited and reputable.
© NMISA 2011
Quantifying the sources of uncertainty (4) • SRES • This is due to the resolution of the Reference Standard Torque Transducer Readout Unit • We must first determine the “effective resolution” • The least significant digit displayed is 0,1 N•m • Resolution is always treated as a Rectangular distribution source of uncertainty and this is the range. • The semi-range is therefore (0,1 N•m/2)=0,05 N•m • The divisor is √3 • The degrees of freedom are always ∞ or 100 % Reliability
© NMISA 2011
Quantifying the sources of uncertainty (5) • SCF • Polynomial Equation Coefficients Table from the Calibration Certificate POLYNOMIAL EQUATION POLYNOMIAL COEFFICIENTS
2
y=a+bx+cx +dx NORMAL FUNCTION
3
INVERSE FUNCTION
a
2,71846 x10
-2
b
9,99825 x10
-1
1,00017
c
-7,89039 x10
-6
7,95708 x10
-6
d
5,16535 x10
-9
-5,22137 x10
-9
Standard Error of the polynomial curve fit for a Level of Confidence of 68,27% and 4 degrees of freedom
± 0,045 N•m
© NMISA 2011
-2,70765 x10
± 0,045 N•m
-2
Quantifying the sources of uncertainty (6) • SCF • This is the additional uncertainty which results from the interpolation calculation to determine the torque generated by the UUT at a point in between the calibration points of the Reference Standard Torque Transducer • It is obtained directly from the calibration certificate as the “Standard Error of the polynomial curve Fit” value = ± 0,045 N•m • This is treated as a normal distribution at a 68,27% Level of Confidence • The divisor is the coverage factor k which for 68,27% LOC is 1 • The degrees of freedom are also obtained directly from the calibration certificate = 4 © NMISA 2011
Quantifying the sources of uncertainty (7) • URES • This is due to the resolution of the UUT Torque Wrench scale. (How it influences the setting of the wrench to a specified torque) • Typically this would be the smallest graduation on the UUT setting dial which for this UUT is 2 N•m • This is the range of the rectangular distribution • Therefore the semi-range is (2 N•m/2)=1 N•m • The divisor for Rectangular Distributed uncertainty contributors is √3 • The degrees of freedom for resolution is always ∞ or 100 % Reliability
© NMISA 2011
Quantifying the sources of uncertainty (8) • UREP • This results from the variability in the measurement results obtained after repeating the measurement 5 times. • It can be dealt with either as “repeatability” or as “reproducibility” • “Repeatability” – all conditions remained the same during the repeated measurements • “Reproducibility” – any one or more of the conditions changed during the repeated measurements • Different approaches can be used to repeat the measurement • Take 5 measurements at one setting sequentially • Take 5 sets of measurements from zero to full scale © NMISA 2011
Quantifying the sources of uncertainty (9) Repeatability 20 % Meas 1
20 % Meas 2
20 % Meas 3
20 % Meas 4
20 % Meas 5
20 % Mean
60 % Meas 1
60 % Meas 2
60 % Meas 3
60 % Meas 4
60 % Meas 5
60 % Mean
100 % Meas 1
100 % Meas 2
100 % Meas 3
100 % Meas 4
100 % Meas 5
100 % Mean
© NMISA 2011
Quantifying the sources of uncertainty (9) Reproducibility 20 % Meas 1
20 % Meas 2
20 % Meas 3
20 % Meas 4
20 % Meas 5
20 % Mean
60 % Meas 1
60 % Meas 2
60 % Meas 3
60 % Meas 4
60 % Meas 5
60 % Mean
100 % Meas 1
100 % Meas 2
100 % Meas 3
100 % Meas 4
100 % Meas 5
100 % Mean
© NMISA 2011
Quantifying the sources of uncertainty (9) • UREP • Treating as “Repeatability” (as per ISO 6789) • We use the ESDM • ESDM = ESD/SQRT (n) = 0,98/sqrt (5) = 0,436348 N•m • Treating as “Reproducibility” (preferred option but contrary to ISO 6789) • We use the ESD • ESD = 0,98 N•m
© NMISA 2011
GUM Steps • • • •
Model the measurement Identify and quantify the sources of uncertainty Categorize as type A or type B Manipulate appropriately to obtain • Standard uncertainties, u(xi) • Sensitivity coefficients, ci • Uncertainty contributor, u(yi) • Combine to obtain combined standard uncertainty, uc(y) • Expand to obtain an expanded uncertainty, U, at an appropriate level of confidence • Report the result
© NMISA 2011
Categorize as type A or type B • • • • •
SCAL - type B, not statistically determined SRES - type B, not statistically determined SCF - type A, statistically determined (standard deviation) URES - type B, not statistically determined UREP - type A, statistically determined (standard deviation)
© NMISA 2011
GUM Steps • • • •
Model the measurement Identify and quantify the sources of uncertainty Categorize as type A or type B Manipulate appropriately to obtain • Standard uncertainties, u(xi) • Sensitivity coefficients, ci • Uncertainty contributor, u(yi) • Combine to obtain combined standard uncertainty, uc(y) • Expand to obtain an expanded uncertainty, U, at an appropriate level of confidence • Report the result
© NMISA 2011
Uncertainty Budget
Torque Wrench Calibration Uncertainty Budget.xls
© NMISA 2011
GUM Steps • • • •
Model the measurement Identify and quantify the sources of uncertainty Categorize as type A or type B Manipulate appropriately to obtain • Standard uncertainties, u(xi) • Sensitivity coefficients, ci • Uncertainty contributor, u(yi) • Combine to obtain combined standard uncertainty, uc(y) • Expand to obtain an expanded uncertainty, U, at an appropriate level of confidence • Report the result
© NMISA 2011
Reporting the result • The final result is calculated using the “Normal Function” polynomial coefficients • This is because we want to know the true torque applied to the Reference Standard Torque Transducer when it reads the mean measured value of 350,7 N•m • The calculated interpolated value was 349,938089 N•m • The calculated measurement uncertainty was ± 1,794160789 N•m • Rounding the uncertainty to two significant digits gives ± 1,8 N•m • Rounding the interpolated value to the same number of digits gives 349,9 N•m • The measurement result is then reported as: 349,9 N•m ± 1,8 N•m at a Level of Confidence of 95,45% © NMISA 2011
Graphical Representation of results
© NMISA 2011
Conclusions • Both methods in this case prove that the UUT is well within the allowable ± 4% of Maximum (± 14 N•m) • Using the ESDM (In accordance with ISO 6789) results in the smallest uncertainty (unrealistic??) • Using the ESD (contrary to ISO 6789) results in the largest uncertainty (realistic??) • Always use the polynomial for calibrations using the laboratory Reference Standard Torque Transducer • This will correct for any error on the Reference Standard eliminating the need to apply corrections • This will solve the problem of the “Applied Torque” not being exactly at the nominal values
© NMISA 2011
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