NMISA 2011

Calibration of a Torque

Wrench as per ISO6789by

Eddie Tarnow

NLA Test & Measurement Workshop

20 September 2011

NMISA 2011

Calibration Setup

350,0 Nm

Reference Standard Torque Transducer &

Readout Unit

Unit Under Test Torque Wrench

Force Applied

Clockwise Rotation

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 Nm.

It has a setting dial resolution of 2 Nm We are to calibrate it according to ISO 6789 which requires

a calibration point at full scale (100 % of range) viz. at350 Nm 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

STDIndSTDUUT CorrTT +=

NMISA 2011

Identifying the sources of uncertainty

TUUT

TUUT UResTSTDSCal

SRes

SCF

URep

NMISA 2011

Quantifying the sources of uncertainty

SCAL Calibration Results Table from the Calibration Certificate

APPLIED TORQUE

(Nm) MEAN

UUT CALCULATED TORQUE (Nm)

UNCERTAINTY OF MEASUREMENT

( Nm) 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 Nm)

The Reference Standard Torque Transducer used has a full scale of 700 Nm and was calibrated in 100 Nm steps (See calibration certificate)

Therefore we will have to use the polynomial equation to determine the actual torque generated by the UUT at 350 Nm since it is a measurement point in between 300 Nm and 400 Nm.

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 Nm.

NMISA 2011

Quantifying the sources of uncertainty (3)

SCAL Since we will be using the polynomial to interpolate a

value at 350 Nm, we DO NOT need to correct for the+ 1 Nm error at 399,8 Nm.

Therefore total uncertainty for the accuracy of the Reference Standard Torque Transducer is 1 Nm

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 Nm Resolution is always treated as a Rectangular

distribution source of uncertainty and this is the range. The semi-range is therefore (0,1 Nm/2)=0,05 Nm 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 CertificatePOLYNOMIAL

EQUATION y=a+bx+cx2+dx3

POLYNOMIAL COEFFICIENTS

NORMAL FUNCTION

INVERSE FUNCTION

a 2,71846 x10-2 -2,70765 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 Nm 0,045 Nm

NMISA 2011

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 Nm

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 Nm

This is the range of the rectangular distribution Therefore the semi-range is (2 Nm/2)=1 Nm 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 %Mean

60 %Meas 1

60 %Meas 2

60 %Mean

100 %Meas 1

100 %Meas 2

100 %Mean

20 %Meas 4

60 %Meas 4

100 %Meas 4

20 %Meas 3

60 %Meas 3

100 %Meas 3

20 %Meas 5

60 %Meas 5

100 %Meas 5

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 Nm

Treating as Reproducibility (preferred option but contrary to ISO 6789) We use the ESD ESD = 0,98 Nm

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 polynomialcoefficients

This is because we want to know the true torque appliedto the Reference Standard Torque Transducer when it reads the mean measured value of 350,7 Nm

The calculated interpolated value was 349,938089 Nm The calculated measurement uncertainty was

1,794160789 Nm Rounding the uncertainty to two significant digits gives

1,8 Nm Rounding the interpolated value to the same number of

digits gives 349,9 Nm The measurement result is then reported as:

349,9 Nm 1,8 Nm 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 Nm)

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