Torque Wrench Calibration Presentation

Calibration of a Torque

Wrench as per ISO6789

by

Eddie Tarnow

NLA Test & Measurement Workshop 20 September 2011

Calibration Setup

350,0 N•m

Reference Standard Torque Transducer &

Readout Unit

Unit Under Test Torque Wrench

Force Applied Clockwise Rotation

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

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(x_i)

• Sensitivity coefficients, c_i

• Uncertainty contributor, u(y_i)

• Combine to obtain combined standard uncertainty, u_c(y)

• Expand to obtain an expanded uncertainty, U, at an appropriate level of confidence

Measurement Model

STD

Ind

STD

UUT

T

Corr

T

=

+

Identifying the sources of uncertainty

T

T

T

U

Quantifying the sources of uncertainty

• S_CAL

• 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

Quantifying the sources of uncertainty (2)

• S_CAL

• 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.

Quantifying the sources of uncertainty (3)

• S_CAL

• 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.

Quantifying the sources of uncertainty (4)

• S_RES

• 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 %

Quantifying the sources of uncertainty (5)

• S_CF

• Polynomial Equation Coefficients Table from the Calibration Certificate POLYNOMIAL EQUATION y=a+bx+cx 2 +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

Quantifying the sources of uncertainty (6)

• S_CF

• 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

Quantifying the sources of uncertainty (7)

• U_RES

• 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

Quantifying the sources of uncertainty (8)

• U_REP

• 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

Quantifying the sources of uncertainty (9)

Quantifying the sources of uncertainty (9)

Quantifying the sources of uncertainty (9)

• U_REP

• 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

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(x_i)

• Sensitivity coefficients, c_i

• Uncertainty contributor, u(y_i)

• Combine to obtain combined standard uncertainty, u_c(y)

• Expand to obtain an expanded uncertainty, U, at an appropriate level of confidence

Categorize as type A or type B

• S_CAL - type B, not statistically determined

• S_RES - type B, not statistically determined

• S_CF - type A, statistically determined (standard deviation)

• U_RES - type B, not statistically determined

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(x_i)

• Sensitivity coefficients, c_i

• Uncertainty contributor, u(y_i)

• Combine to obtain combined standard uncertainty, u_c(y)

• Expand to obtain an expanded uncertainty, U, at an

appropriate level of confidence

Uncertainty Budget

Torque Wrench Calibration Uncertainty

Budget.xls

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(x_i)

• Sensitivity coefficients, c_i

• Uncertainty contributor, u(y_i)

• Combine to obtain combined standard uncertainty, u_c(y)

• Expand to obtain an expanded uncertainty, U, at an appropriate level of confidence

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:

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