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Q&A: Calibration Curve

Following is the transcript from a question and answer session conducted with a Cooper Instruments technical engineer.

Q: What is a calibration curve?

A: A calibration curve is the performance curve of the transducer; that is to say, its output in relationship to the range of applied loads from a no load condition to that of a full scale load.

If you were to measure the output of a 100 LBF load cell and record the output at 0, 25, 50, 75 and 100 LBF, theoretically you would have a curve much like the one in fig 1. As this is a perfect example, the performance curve is a straight line. In real world conditions however, there will always be a slight error that will prevent a straight line, but depending on the amount of error, the performance could possibly be accepted as straight. Whether the performance is good or not, the resulting performance representation is considered a “curve”.

Q: How is it calculated?

A: As shown above, the calibration curve is not calculated but rather it’s measured. Some calibrations are calculated if, during a calibration, the lab is unable to apply certain data points or force points. In cases like this, the laboratory can turn to statistical tools to calculate what the performance is most likely to be at these unmeasured points. It is; however, always best to stay away from extrapolating data unless absolutely necessary.

Q: Most indicators offer a 2-point calibration: what does that mean?

A: An indicator is a device that allows the user to equate a desired engineering unit to the output of the transducer. Most indicators allow for what is called a 2-point calibration, meaning you can define only 2 points on the calibration curve and the meter assumes a straight (linear) curve. So, if you follow the recommendations in the manual, you will use a no load condition of your transducer and define it as your zero load point. The second point is usually your full load point, and in the case found in Fig 1, the full scale would be defined as 100. Consequently, when the meter reads exactly half the value of the full scale point, the meter will report 50.

Q: What are the limitations of a 2-point calibration?

A: The limitation to a 2 point calibration is that it assumes your transducer is performing at a theoretical (perfect) level. You’ve heard the saying “nature abhors a straight line”? Well, this is a very true saying, and applies to transducer performance just as much as it does to rivers and streams. Now, the effect of the lack of linearity depends on the errors due to inaccuracies and on the user’s quality requirements.

Let’s assume that the 100 LBF transducer in our example performs with a nonlinearity specification of ±1% at half scale, and the 2 point indicator has been calibrated at 0 Lbf and 100 Lbf, when 50 Lbf is applied, the display will read 50, but the actual force is in the range of 49 to 51 Lbf. So due to the 2-point calibration, the inaccuracy of the performance curve is hidden.

So in short, the limitation of a 2 point calibration is the inability to compensate for nonlinear performing load cells, yielding inaccurate readings.

**It’s important to note that a load cell will always perform within OEM specification limits when new. However, after prolonged use and age the performance will begin to degrade, and a 2 point calibration may not be able to compensate for this change.

Q: How does using a multi-point calibration linearize a load cell’s

performance?

A: Now that we know there can be an amount of error between 2 points of a curve, it stands to reason that if we shorten the distance between the points, the smaller the errors will be had between those same points.

So, if we calibrate our meter with more than 2 points, we will begin to reduce the measured errors and improve the performance of the load cell system. In Fig-2 below you can see the same 2 point calibration curve in the blue dotted line. Compare this curve with that of the individual data points. You can see an error grows up to the halfway point and then reduces as it gets to the highest data point.

If we were to use a 5-point calibration method on this instance, you would get a performance more on the lines that the black line represents. Fig-3 demonstrates the new calibration curve with the red dotted line, when applying the multi-point calibration for 5 points.

Q: How does a linearized performance prolong the useful life of a load cell?

A: As the load cell ages with use, the linear performance will decay. With the use of a 2 point calibration, there will be a point where the load cell will not maintain the performance needed and may eventually get to a point where the errors cannot be compensated for.

With the use of an indicator with multi-point calibration functionality, the errors can be compensated for and performance can be maintained.

Q: What solutions can Cooper Instruments offer when an indicator with 2-point calibration is not sufficient for the user’s application?

A: Cooper Instruments offers several products with multi-point calibration

options:

The DFI INFINITY B, M3, M5 and 7i all allow for multi-point calibration. We also offer the DSC USB, which has software that allows for multi-point calibration. Our sales representatives would be happy to help you select the right product for your application.

As always, if you have any questions related to this material, our support staff at Cooper Instruments is available to help. Contact them by calling (800) 344-3921 or emailing sales@cooperinstruments.com.

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