How to Calculate Resolution of a Load Cell

How to Calculate the Resolution of a Load Cell

Per Section 4.14 of JCGM 200:2012, Resolution is the “smallest change in a quantity being measured that causes a perceptible change in the corresponding indication.”??Over the years, this simple definition has become a topic of confusion amongst several people.?This post has pertinent information because anyone who performs calibrations and is accredited to the ISO/IEC 17025:2017 standard and a calibration lab needs to calculate and include the resolution of the instrument as part of the expanded uncertainty reported. The resolution is used as part of the expanded uncertainty to make a statement of conformity if using several guard banding methods.

We hope to simplify how to calculate the resolution of the Unit Under Test so that this can be a simple guidance document.?However, we are first going to briefly discuss why calculating the resolution of the Unit Under Test properly is essential.?

Morehouse reports the resolution of the Unit Under Test on our calibration certificates as well as uses the resolution of what we are testing in the divisor for calculating TUR and reporting Expanded Uncertainty.?In ANSI/NCSLI Z540.3-2006 and ILAC G8, TUR is defined as “The ratio of the span of the tolerance of a measurement quantity subject to calibration, to twice the 95 % expanded uncertainty of the measurement process used for calibration”.?This calculation of TUR is crucial as it is the basis for making statements of conformity as required by ISO/IEC 17025:2017section 7.8.6.1 & 2.

Figure?1?The typical minimum contributors to calculate TUR at the time of calibration

We typically deal with the resolution of the UUT in the denominator, as shown in figure 1 above.?ANSI/NCSL Z540.3 Handbook states, “For the denominator, the 95 % expanded uncertainty of the measurement process used for calibration per the calibration procedure is to be used to calculate TUR.?The value of this uncertainty estimate should reflect the results that are reasonably expected from the use of the approved procedure to calibrate the particular type of M&TE.?Therefore, the estimate includes all components of error that have an influence on the measurement results of the calibration which would also include the influences of the item being calibrated, with the exception of the bias of the M&TE.?The calibration process error, therefore, includes temporary and non-correctable influences incurred during the calibration such as repeatability, resolution, error in the measurement source, operator error, error in correction factors, environmental influences, etc.”?ILAC P-14 addresses resolution as part of the Expanded Uncertainty in section 6.4 that states, “Contributions to the uncertainty stated on the calibration certificate shall include relevant short-term contributions during calibration and contributions that can reasonably be attributed to the customer’s device. Where applicable the uncertainty shall cover the same contributions to uncertainty that were included?in evaluation?of the CMC uncertainty component, except that uncertainty components evaluated for the best existing device shall be replaced with those of the customer’s device.”??

Now that we’ve hopefully made a case for why we need to know the resolution of the UUT, we can discuss various methods for calculating the resolution.?Here at Morehouse, we often ask how you calculate resolution??The answer is that we take the force applied value, divide it by the output of the UUT at the corresponding point, and multiply that number by the readability.?Let’s look at one example.?In Example 1, we have a 10,000 lbf load cell with an output of 4.11235 mV/V and the force-measuring device is read at the fifth decimal?0.00001, and the display counts by 1

Conclusion:

In the five examples provided above, not much changes as far as our formula goes, we either take a single point value of the instruments measured value at capacity, use the formula for the average deflection values, or take the average over all of the points in the measuring range.??We multiply this value by the readability and then multiple by how much the instrument counts by.?The resolution is then used in reporting the Expanded Uncertainty, shown in Figure 2, which complies with ILAC P-14 Policy for Uncertainty in Calibration.??

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