## How to provide the result of calibrating a force sensor

The best way to communicate the calibration result is to provide the user of the force sensor with a 1st, 2nd or 3rd degree polynomial enabling him / her to calculate the force according to the indication provided by the dynamometer.

For example, in the case of a 2nd degree, the result is expressed as follows:

F = a x D2 + b x D + c

Where:

F is the force applied to the dynamometer in the unit of force (mN, daN, kN, MN) and a, b and c are constants
D = IF - IO is the deformation of the dynamometer by force F
IF = indication at force F
IO = indication at zero force

## The uncertainty of calibrating a force sensor

In the same way, the best way to express calibration uncertainty is:

U (F) = A + B x F
U = uncertainty expanded on force F with an expansion factor k =2
A = constant expressed by force unit
B = constant without dimension

Calibration uncertainty is calculated taking into account at least the following components:

• uncertainty of the forces applied to the force sensor
• resolution of the indication
• indications repeatability
• indications reproducibility
• variation in the indication at force zero before and after the application of a load series
• temperature and its fluctuations during calibration
• interpolation errors.

These different components are evaluated for each force level and the relevant combined uncertainty is calculated. A linear regression according to the force is then applied to these combined uncertainties and the result is expanded with an expansion factor equal to 2.

While the dynamometer provides the results of indications directly in force units, calibration results are generally given in the form of indication errors for each force level, with its associated uncertainty established by taking into account the above-mentioned components.

Calibration results for a dynamometer must be accompanied by all the necessary elements for their understanding, and the proper use of the dynamometer. All calibration parameters must be specified including, in particular, the mechanical assembly for the application of force and the settings of the indicator device connected to the load cell.