Torque Wrench Calibration Presentation

Calibration of a Torque Wrench as per ISO6789 by Eddie Tarnow NLA Test & Measurement Workshop 20 September 2011

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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

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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

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Measurement Model

TUUT = TSTD Ind + CorrSTD

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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

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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.

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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.

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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

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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

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-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

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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

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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

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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

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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

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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

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Uncertainty Budget

Torque Wrench Calibration Uncertainty Budget.xls

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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

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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

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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