Calibration uncertainty with torque transducer

[hugom]

Hi,

My lab has a torque transducer+Reading unit used to calibrate torque wrenches.
The last certificate of calibration showed that it is no longer inside its specification (+/-0,3% FS). So I was thinking of correcting the errors through an interpolated polynomial correction (using Excel).
But now I don´t know what should be the uncertainties of my equipament, when I calibrate torque wrenches, in the total uncertainties budget (besides uncertainties associated to resolutions).
Should it be:
Uncertainty associated to the correction of values read by of my transducer+Reading unit
+Uncertainty associated of calibration of my transducer+Reading unit
+Uncertainty associated of drift between calibrations of my transducer+Reading unit

Is it complete ?

Despite the correction, shouldn´t I consider in some way the specified accuracy ot the torque transducer (I´m not even thinking of the specified accuracy ot the reading unit itself) ??

Does anyone have a idea ?

Thank you,
Hugo

[Hershal]

The actual readings themselves come in under Type A, or Random, uncertainty. The standard deviation is used to arrive at the standard uncertainty for the actual measurement indications.

Your type B, or Systemic, uncertainty, will include the influences you mentioned in your post, plus likely others. You will need to account for environmental influences, hysterisis of both the wrench and your system, coupling effects (if the connection of the wrench to the system is loose), and other effects as appropriate.

Hope this helps.

Hershal

[Graeme]

Originally Posted by hugom

My lab has a torque transducer+Reading unit used to calibrate torque wrenches.
The last certificate of calibration showed that it is no longer inside its specification (+/-0,3% FS). So I was thinking of correcting the errors through an interpolated polynomial correction (using Excel).
But now I don´t know what should be the uncertainties of my equipament, when I calibrate torque wrenches, in the total uncertainties budget (besides uncertainties associated to resolutions).
Should it be:
Uncertainty associated to the correction of values read by of my transducer+Reading unit
+Uncertainty associated of calibration of my transducer+Reading unit
+Uncertainty associated of drift between calibrations of my transducer+Reading unit

Is it complete ?

Despite the correction, shouldn´t I consider in some way the specified accuracy ot the torque transducer (I´m not even thinking of the specified accuracy ot the reading unit itself) ??

Does anyone have a idea ?

Thank you,
Hugo

Hugo,

First, a disclaimer: I am not an expert in torque calibration, or any other type of force calibration. But I have been doing other types of calibrations for a long time ...

Your question -- the part about an interpolated polynomial correction -- implies that you do have historical calibration data for your torque transducer and possibly the display unit. Have you plotted the data on a run chart to see what the trend is? I use the reported value as the data point, and the uncertainty from the calibration certificate as both + and - error bars. After I have five data points, I add a moving average with n=5, and upper and lower limit lines calculated from 2 times the standard deviation of those five points.

This does several important things. You can see a trend and estimate at least one future point from that. The most recent moving average can be used as the "assigned value" of the standard. Also, the standard deviation is a measure of the actual performance of the standard, and you can use that value instead of the published performance specification. (Note that for uncertainty analysis, these are Type A values.) Finally, when the next point is plotted you can see immediately if it is reasonable of if there may be a problem. An outlier value that looks reasonable in a data table will jump out at you on a graph.

If you have plotted values and calculated the standard deviation for your transducer and display they can take the place of the published specifications. The only other things I can think of to consider would be environmental effects on the transducer and display as a system. You might be able to do a sensitivity analysis based on your historical temperature and humidity data in the lab and the published specifications of the standards. If it appears to be negligible you could leave it at that; otherwise add it in. Or you may want to set up some sort of experiment to gather data and analyze that.

One thing that is important to do -- since you have at least one data point that shows the transducer as out of specification, you need to have it recalibrated more often than before. You need data to keep track of its behavior. If it is stable at some new level then you can use that information as a correction. If it is no longer stable you probably need to replace it.

Additional Information --
You may also want to look at this document: EA Guidelines on the Calibration of Static Torque Measuring Devices. This is a guide to what needs to be considered in developing a calibration procedure for transducers, including a detailed treatment of uncertainty, but it is not a calibration procedure by itself.

Note that the series of Calibration Guides formerly available from the European cooperation for Accreditation (EA) have recently been transferred to the European Collaboration in Measurement Standards (EUROMET).

[hugom]

Thank you Graeme and Hershal for your advices.

Since I don´t have much calibration history-I only have 2 calibrations for my transducer+reading unit- I´m considering the maximum relative drift between these 2 calibrations+50% as an uncertainty. It gives me a uncertainty of 1,5% of reading value, which is a lot. Do you think there is a better way ?

Graeme, you referred an estimate of the future drift for the calibrated points. But what about the points between them. How do you consider the uncertainty associated to the interpolation ? I have a problem: the interpolation (3rd degree) polynomial correction has a R<0,999. How could I improve it ?

Thank you once again for you help,
Hugo

[Graeme]

Originally Posted by hugom

Since I don´t have much calibration history-I only have 2 calibrations for my transducer+reading unit- I´m considering the maximum relative drift between these 2 calibrations+50% as an uncertainty. It gives me a uncertainty of 1,5% of reading value, which is a lot. Do you think there is a better way ?

Graeme, you referred an estimate of the future drift for the calibrated points. But what about the points between them. How do you consider the uncertainty associated to the interpolation ? I have a problem: the interpolation (3rd degree) polynomial correction has a R<0,999. How could I improve it ?

Hugo,

With only two points, you really don't have enough data yet to be doing any interpolation. Three points would be a minimum and five points would be better. Some people have their standards calibrated more frequently than usual for the first year or two specifically so they can determine the behavior trends more quickly. (That's why patience is such a virtue in this business - it takes so long to get the necessary data.)

With only two data points (calibrations), I would question the value of anything other than a linear interpolation at this time.

The correlation coefficient (R), simply put, is a number that explains how much of the change is explained by the variables in the equation. If R = 0.999, then the equation of the regression line explains 99.9% of the data. Any value of R other than +1 or -1 indicates that there is, at some level, an influence that is not explained in the data you have right now. Since each situation is different, you would have to evaluate what those influences might be. The first thing I would do is calculate the standard deviation of the mean (SDOM) and convert it to a percent of the mean. If the difference between R and 1 is small compared to the SDOM then the effects may be small enough that you may choose to ignore them. If the difference is large compared to the SDOM then you probably should find out what other effects are at work. Note that you have to define "small" and "large" because it varies with your requirements, process and comfort level.

Before doing this, though, you need more data.

Graeme

[hugom]

OK...Thank you Graeme for you help !