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Extending Transducer Calibration Range by Extrapolation Technical Note

Figure 1 Extrapolation Methods
Figure 3 Extrapolation Error vs. Extrapolation Ratio

By LaVar Clegg


Force and torque transducers must be calibrated in a laboratory in order to be useful in their intended application. Applications of transducers range from basic process measurements to critical calibration of other transducers or equipment. The laboratory calibration consists of loading the transducer with known masses and lever arms, or using a comparison method where load is generated by hydraulic or pneumatic means and the transducer under test is compared to a reference transducer. In either method, the cost of calibration equipment rises rapidly with increasing capacity.

Many calibration laboratories have the means to calibrate force up to about 10,000 lbf and torque up to about 20,000 lb-in, but capability for higher ranges is scarce. In fact, there are a very limited number of laboratories in the United States that have the capability for force over 200,000 lbf and torque over 100,000 lb-in.

There has been a practice in the past by some manufacturers of transducers to calibrate a high capacity transducer at partial capacity, leaving the owner to go on hoping and guessing for the sensitivity of the upper end of the capacity. This gives rise to the concept of extrapolating the partial capacity calibration to full capacity, thereby providing the possibility for an increase in confidence in the extended range.

The Problem

Strain gage transducers are basically linear. That is, the output follows the input at a near constant ratio. The nonlinearity is routinely measured and typically is in range of ± 0.10%FS or less. This provides for the ability to interpolate values between calibration points with near zero error. However, the same is not true for extrapolation, which is really estimating values that are beyond the observable range. Conventional wisdom has it, and logically so, that extrapolation is not a valid method of calibration. Extrapolating is similar to forecasting, and that idea helps one realize the liability of it.

The various methods of extrapolation are not all equal. The purpose of this paper is to explore a method that has reasonable validity when economic considerations do not permit a full capacity calibration.

Download the Technical Note below to learn more about:

  • Extrapolation Methods
  • Linear (0 and Last Point) Extrapolation
  • Linear (Last 2 Points) Extrapolation
  • Polynomial Regression
  • Conditions for a Valid Extrapolation with Degree 2 Polynomial
  • Uncertainty of Extrapolated Results
  • Actual Cal Lab Results
  • Effect of Extrapolation Ratio
  • How to Perform Polynomial Regression with Microsoft Excel