Uncertainty calculation for calibration of compression machine as per ISO 7500

[+974San]

Dear,

Can someone provide guidance on the uncertainty parameters that should be considered when calibrating a compression machine using a load cell? According to ISO 7500, factors such as repeatability, resolution, and the transfer standard (including the uncertainty of the master equipment, drift, temperature, and the linear approximation of the polynomial curve) must be taken into account. Specifically, could someone explain how to incorporate the linear approximation of the polynomial curve into the uncertainty parameters?

 

[NotMe]

I have not read 7500-1, but probably you will find your answer in GUM (Guide to express uncertainty in measurements). It contains the general framework.

 

[+974San]

Yes. General uncertainty parameters are mentioned in GUM, however, linear approximation of the polynomial curve is not highlighted. Looking for that particular parameters in order to incorporate that in the uncertainty calculations.

 

[NotMe]

Linear approximation of the polynomial curve is usually called Taylor expansion. Sometimes it is also called nonlinearity of a gauge. Thus, this is commonly analysed by checking the "linearity of the gauge".

 

[AllTheThings]

I would also take a look at Morehouse (Free Morehouse Force and Torque Calibration Books | Morehouse Instrument Company, Inc.). They (well, Henry) are one of the best references out there for force calibrations. The Force cal book for Technicians goes into some of the ASTM E74 math, and how to handle polynomial fits. Might even be worth dropping him an email with the specifics...He seems to be pretty approachable. Also, rice lake puts out a pretty good reference: https://www.ricelake.com/media/zegphd55/m_us_22054_lc-wm_handbook_reva.pdf, but it is more sales-y.

One option is to get an indicator/readout that can handle polynomials. Then you can just ignore needing to generate a linear approximation entirely. But that is spendy.

Realistically, assuming you are within the center 80% of a load cell's range, and calculating your linear approximation only with points from that range, a linear approximation vs. a polynomial fit will probably be a negligible contributor to uncertainty for that calibration. The difference is likely in the tenth or less of a percent of full scale at most. Mounting hardware and pins, cosine errors (especially in compression), temperature, repeatability/squareness of the force stand, and other factors will probably matter much more than the error induced by approximating a curve with a linear best fit via least squares...

It doesn't mean you can ignore it, but you may (for the purposes of uncertainty calculations) be able to take the stated nonlinearity of the master load cell as declared by the manufacturer, and just use that as the input for your uncertainty term.