Torque Transducer Calibration Calculator

Evaluate the calibration of a torque transducer in one direction according to EURAMET cg-14 (v.01, July 2007), sections 4.4.5 to 5.5 and Appendix E. Enter the torque levels, the readings of two increasing runs in the first mounting position and one increasing run in each of two further mounting positions, the resolution and the reference torque uncertainty. The calculator returns the mean indication, the expanded relative uncertainty and the expanded uncertainty at each calibration point, together with the cubic fitting coefficients. No class is assigned. The form is preloaded with the worked example of Appendix E.

Calibration data

Torque unit 1 lbf ft = 1.3558179483314004 N m

Resolution r (mV/V) In indication units, zero or greater

Expanded relative reference torque uncertainty W_ref, k = 2 (%) In percent, zero or greater

Readings are signed indications in mV/V. Enter at least five distinct positive torque levels; leave unused rows completely empty.

Level	Torque M (N m)	Run 1, position 1 (mV/V)	Run 2, position 1 (mV/V)	Run 3, position 2 (mV/V)	Run 4, position 3 (mV/V)
Initial zero	0	Run 1 initial zero reading (mV/V)	Run 2 initial zero reading (mV/V)	Run 3 initial zero reading (mV/V)	Run 4 initial zero reading (mV/V)
1	Level 1 torque M (N m)	Level 1 run 1 reading (mV/V)	Level 1 run 2 reading (mV/V)	Level 1 run 3 reading (mV/V)	Level 1 run 4 reading (mV/V)
2	Level 2 torque M (N m)	Level 2 run 1 reading (mV/V)	Level 2 run 2 reading (mV/V)	Level 2 run 3 reading (mV/V)	Level 2 run 4 reading (mV/V)
3	Level 3 torque M (N m)	Level 3 run 1 reading (mV/V)	Level 3 run 2 reading (mV/V)	Level 3 run 3 reading (mV/V)	Level 3 run 4 reading (mV/V)
4	Level 4 torque M (N m)	Level 4 run 1 reading (mV/V)	Level 4 run 2 reading (mV/V)	Level 4 run 3 reading (mV/V)	Level 4 run 4 reading (mV/V)
5	Level 5 torque M (N m)	Level 5 run 1 reading (mV/V)	Level 5 run 2 reading (mV/V)	Level 5 run 3 reading (mV/V)	Level 5 run 4 reading (mV/V)
6	Level 6 torque M (N m)	Level 6 run 1 reading (mV/V)	Level 6 run 2 reading (mV/V)	Level 6 run 3 reading (mV/V)	Level 6 run 4 reading (mV/V)
7	Level 7 torque M (N m)	Level 7 run 1 reading (mV/V)	Level 7 run 2 reading (mV/V)	Level 7 run 3 reading (mV/V)	Level 7 run 4 reading (mV/V)
8	Level 8 torque M (N m)	Level 8 run 1 reading (mV/V)	Level 8 run 2 reading (mV/V)	Level 8 run 3 reading (mV/V)	Level 8 run 4 reading (mV/V)
9	Level 9 torque M (N m)	Level 9 run 1 reading (mV/V)	Level 9 run 2 reading (mV/V)	Level 9 run 3 reading (mV/V)	Level 9 run 4 reading (mV/V)
10	Level 10 torque M (N m)	Level 10 run 1 reading (mV/V)	Level 10 run 2 reading (mV/V)	Level 10 run 3 reading (mV/V)	Level 10 run 4 reading (mV/V)

Results

Torque M (N m)	Mean indication X (mV/V)	Expanded relative uncertainty W (%)	Expanded uncertainty U (mV/V)

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Coverage factor k = 2. This is the increasing calibration uncertainty at the time of calibration; dynamic effects, long term stability and coupling effects are not included. Use a separate evaluation for other uncertainty components.

How the calculation works

Choose the torque unit and enter at least five distinct positive torque levels M, enough for the cubic fitting curve.
Enter the initial zero reading of each run and the increasing reading at every level: runs 1 and 2 in the first mounting position, run 3 in the second position and run 4 in the third position.
Enter the resolution r of the indicating device in mV/V and the expanded relative uncertainty of the reference torque W_ref in percent at k = 2.
Press Calculate to obtain X, W and U at each calibration point and the coefficients A, B and C.

Corrected readings and mean indication

The initial zero of each run is subtracted from that run's readings. With x₁ and x₂ the corrected readings of runs 1 and 2 in the first position, and x₃ and x₄ those of the second and third positions:

X = (x₁ + x₃ + x₄) / 3 p = |x₁ − x₂| (repeatability) s = √( ((x₁ − X)² + (x₃ − X)² + (x₄ − X)²) / 2 ) (reproducibility)

Fitting curve

Following section 4.4.6.7, the mean indications are fitted by least squares with a cubic polynomial through the origin, without an intercept term. Xa is the fitted value at each calibration point.

Xa = A·M + B·M² + C·M³

Expanded relative uncertainty

W = 2·√( (Wref/2)² + (100·p/X/√2)² + (100·s/X/√3)² + (100·(X − Xa)/Xa/√6)² + 2·(100·r/X/√12)² ) U = |X| · W / 100

W is in percent and U in mV/V. The resolution term appears twice because both the zero reading and the loaded reading are affected by the finite resolution. All values are computed at full double precision; only the display is rounded.

Scope and limits

The calculator covers one torque direction with increasing torque only and does not assign a class. A mean indication or fitted value of zero makes the relative terms undefined, so such points are rejected, as are fits whose normal equations are singular. Dynamic effects, long term stability and coupling effects are outside this evaluation and must be assessed separately. Results should be checked against the guideline before they are used in a calibration certificate.