Improved accuracy with HBM force transducers

As a result of many detail enhancements, HBM has improved the accuracy of the U10M force transducer - so what are the advantages of this in practice? U10M has always been a precise sensor, what's more it is also rugged - it is available in many variations right up to protection class IP69, it is rust-proof, insensitive to bending moments and, thanks to the modular system, it can be configured in many ways. Now, properties such as linearity, hysteresis and relative reversibility error, which influence the accuracy of the transducer, have been optimized. The result: less measurement uncertainty for more meaningful test results, less waste in end-of-line tests and lower investment costs for the user.

On error analysis of measurements with force transducers

When taking measurements with force transducers a distinction is made between two error groups: errors that generate a certain output signal irrespective of the force applied to it, and errors whose magnitude is proportionate to the force applied at the moment of observation.

The temperature influence on the zero point is an example of a load-independent error: This measurement deviation outputs a specific value that is independent of the measured force. If such an error is considered relative to the output signal, it can be seen that the influence of the TC0 is always particularly pronounced when just a small percentage of the nominal (rated) force is used. The absolute value is always the same, but increases due to the small useful signal of the relative percentage in this situation. In addition to TC0, the linearity error is also relative to the end value.

Errors that are relative to the actual value (actual-value dependent error) are calculated relative to the actual applied signal. This includes, for instance, the temperature dependency of sensitivity (TCS), creep or even the tolerance of a calibration that may have been implemented.

Error calculation

Errors are now calculated according to the following principle:

  • Every individual error is calculated on the basis of the manufacturer's technical information. (TC0, linearity influence, hysteresis, etc.). Whether the parameter refers to the full-scale value or the measured value to be considered must be borne in mind, i.e. whether it relates to the full-scale value or the actual value. The process parameters must also be considered.
  • The error must now be allocated a statistical factor that results from the type of distribution. Since this step only reduces the calculated measurement uncertainty, it can be dispensed with for assessment - there is no need to go into it any further here.
  • All individual errors are now squared and added together, then the square root of the total is calculated.
  • The result is allocated a factor that determines the probability that the calculated measurement uncertainty will be achieved.

As explained above, full-scale value-related influence quantities are especially important. However, it is also important to keep an eye on the biggest individual error. In the procedure described above, an improvement only makes sense if the biggest influence quantities are optimized in a targeted fashion. Improving just a single feature does not make sense. A good force transducer may have equally good properties.

Which parameters have been optimized?

As part of the U10M improvements, all of the characteristics that result in a real improvement in practice have been optimized. Below you will find a list with brief explanations.

Relative repeatability error

The relative repeatability error describes the reproducibility accuracy of a sensor. How big is the spread of the measurement results if a force transducer is subjected to an equal load repeatedly? The relative repeatability error provides information on this. The lower this value, the better the sensor reproduces and the more reliably the result of its calibration can be transferred into practice.


Linearity describes the deviation of the measured value from an intended ideal uniform characteristic curve of a sensor. The lower the linearity, the more precisely the forces between the calibration points can be identified.

Relative reversibility error (hysteresis)

If a sensor is loaded up to the nominal force with rising force and the force is then removed, you will notice a small difference between the two series of tests with the same force. This difference is the relative reversibility error (hysteresis) of the force transducer. In the case of dynamic measurements with a large force measurement range, the relative reversibility error is a major influencing factor.


Thanks to the elastic aftereffect of the components of a force transducer (spring material and strain gauge), there are minor changes in the output signal with a constant exertion of force. This is irrelevant for many measuring tasks. However, if longer-term monitoring tasks are to be performed, a low creep value is very important.

Temperature coefficient of zero signal (TC0)

TC0 is an important technical property, in many cases the most important one. The value indicates the magnitude of the zero signal of a force transducer when the temperature changes. This information is very important, in particular when small forces are to be measured, because this influence is always significant - no matter which force is being measured. The relative influence rises with diminishing measured values.

What improvements have been achieved by optimizing the U10M force transducer?

All of the errors described above were on the test bench and are influence quantities for every consideration of measurement uncertainties. In detail:

Repeatability error in an unmodified mounting position (% of measured value)

Creep (% of measured value)

Linearity (% of full-scale value)


Hysteresis (% of full-scale value)


At TC0 the already very good values of 150ppm 10K could be improved with a tweak in many applications. To do this, check whether the option "200% calibration" can be applied. This means that an U10M force transducer is calibrated with double the nominal force - e.g. a transducer with a nominal force of 50 kN is calibrated at 100 kN. This means that you also get a doubled output value. With the improvements that have now been incorporated and this option, it has been possible to reduce TC0 to 75 ppm 10K. The mechanical reserves of the U10 allow this without any problems.

But two things must be borne in mind:

  • The input range of the amplifier must be suitable. 5mV/V are necessary to make use of the full calibration force (in our example above 100kN). If smaller forces are to be measured, you can downscale accordingly in a linear fashion.
  • The permissible oscillation bandwidth is lower - i.e. with dynamic loads the peak-peak value may only match the calibration force exactly.

The advantages in application

Usually, when measuring forces, a degree of accuracy required by the question is assumed. The accuracy of the measurement of the force depends not only on the sensor used, but also on the force to be measured - the measurement uncertainty rises the smaller the force. Conversely, the following results: If an accuracy is defined, the measuring range of the force transducer rises with its accuracy.

The advantages of modern technology for practice:

  • Extended measuring range: with high-capacity sensors you can determine smaller forces with a prescribed accuracy (measurements in the part-load range)
  • The requirements of measurement technology are increasing because the requirements of testing are likewise increasing. If we consider the useful life of force transducers, it certainly makes sense to rely on future-proofing - with the currently available accuracy and insensitivity to ambient conditions.
  • Incorporate more spare capacity. The more you can use the lower range of the sensor, the more conservatively you can design your measuring chain. If there is a risk of overload, just choose a slightly bigger sensor. The capacities in accuracy are usually not enough to achieve your goals.
  • Reduce your waste: The transducer's measurement accuracy needs to be assessed to enable the process to be evaluated. To implement a good/bad evaluation, the components may only be judged to be OK when they lie within the setpoint range less the measurement tolerance (symbolized in the diagrams by the blue hatched lines). As can be seen, the number of tolerable parts rises when the measurement accuracy rises (right-hand graph). Expressed in a different way, the number of parts to be rejected is also dependent on the measurement accuracy of the force measurement chain.
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