Force Measurement Glossary: Characteristics of Force Transducers

Benefit from our practical on-line glossary to look up the most important technical terms in the field of force measurement:

Fundamental frequency

Like every mass and spring system, force transducers, too, have a resonance frequency. It can be calculated as follows:

With m being the oscillating mass - not to be mixed up with the transducer's mass. The resonance frequency given in the specifications takes into account the force transducer only, not the required loading fittings. Of course the relevant resonance frequency of the whole setup varies with additional masses being installed on the transducer. Therefore, this is only a recommended value. Dynamic design of a test setup always requires the mounting conditions to be taken into account.

Input resistance

The input resistance is the resistance that can be measured at the transducer connections where the excitation is connected. Due to the fact that additional resistors for balancing of the force transducer are connected to the Wheatstone bridge, the input and output resistance values can vary.
When connecting force transducers in parallel, please remember that the resistance of the circuit as a whole is reduced. This total resistance must not exceed the limit specified in the amplifier's operating manual.

Insulation resistance

The resistance between any connecting cable and the spring element is called 'insulation resistance'. It is essential that the insulation resistance corresponds to the value at ambient temperature specified in the data sheet; otherwise the transducer needs to be replaced, since the characteristics no longer are correct.


Linearity describes the real characteristic curve's maximum deviation from the ideal straight line. The value is given in percent relative to the nominal (rated) force.
Often, no linearity error is specified with reference force transducers (U15, Top Class transducers, etc.) that offer maximum accuracy, because in these cases no sensitivity is used but, instead, a polynomial or interpolation points. In this case, the so-called relative interpolation error is specified, i.e. the maximum deviation from the fitting curve.
Furthermore, specifications for reference force transducers indicate the accuracy the force transducer will at least achieve during a calibration. In general, requirements as specified in the international ISO 376 standard are used, therefore, HBM provides corresponding values in its technical data sheets. Hence, the specified linearity refers to the actual value, i.e. it is relative to the measured value.
Force transducers for use in industrial applications or in experimental mechanics comply with VDI/VDE 2638. Here, linearity refers to the nominal (rated) force.


At 20% of its nominal (rated) force (1000 N), a force transducer has a linearity error of 0.2 N. The linearity error relative to full scale is 0.02%. The deviation relative to the actual value needs to be calculated based on 200 N and is 0.1%. This is five times the original value.

In practical applications, the linearity error can be substantially reduced by competently selecting the transducer's calibration range. If a force transducer with a nominal (rated) force of 100 kN, e.g., is used at 50 kN, it can be calibrated in this range. This halves the error, since computation of the linearity error now can be based on the calibration range.

Nominal (rated) displacement

The force transducer is deformed when the force to be measured is applied. The nominal (rated) displacement specifies the deformation at nominal (rated) force. It is an important characteristic because, together with the nominal (rated) force, it determines a transducer's stiffness. The force transducer's stiffness is crucial to its resonance frequency. From the physical point of view it is absolutely permissible to compare a force transducer with a very stiff spring.

Nominal (rated) force

The nominal (rated) force is the force at which the transducer is 100 percent loaded. All transducer specifications are met in this force range. Please keep in mind that tare loads resulting, e.g., from the tare weight of mounting parts also need to be taken into account and that they use up part of the nominal (rated) force. With dynamic loading, it is essential to take into consideration the transducers' oscillation width.

Nominal (rated) temperature range

In the nominal (rated) temperature range the force transducer meets the values given in the specifications.

Operating range of the excitation voltage

The excitation voltage is the force transducer's supply voltage; in general a range is specified. It is essential not to exceed the maximum excitation voltage, since otherwise the permissible voltage at the strain gages will be exceeded. As a consequence, the electrical power will be too high and the strain gage will become too hot. This will result in a change in zero point (temperature effect on zero point) and a change in sensitivity (temperature effect on sensitivity).

Operating temperature range

In the noIn the operating temperature range the force transducer enables measurements to be taken, however, the measurement accuracy is limited.minal (rated) temperature range the force transducer meets the values given in the specifications.

Output resistance

This is the resistance present on the wires connected to the amplifier input. When connected in parallel, the output resistance's tolerance should not exceed 10 ohm; otherwise cross currents could affect the measurement result.

Reference excitation voltage

All measurements for determining the characteristics are taken at reference excitation voltage.

Reference temperature

In the noIn the operating temperature range the force transducer enables measurements to be taken, however, the measurement accuracy is limited.minal (rated) temperature range the force transducer meets the values given in the specifications.

Relative creep

All strain gage-based transducers show a small signal variation under constant loading which approximately has the form of an exponential function. This process is also called "creep upon loading". With the transducer being relieved of the force, the signal changes in the reverse direction inmore or less the same way. This process is also called "creep upon unloading".

The time period during which the value has been determined is specified in addition to the maximum value of the signal variation in percent.
It is essential to keep in mind that the creep influence must not be calculated relative to the nominal (rated) force but, instead, always needs to be calculated relative to the force applied. HBM specifies the creep value after 30 minutes; due to the typical form of an exponential function, this value can be assumed in good approximation as the creep maximum. This value must in no case be linearly extrapolated.

Relatice sensitivity error tension/compression

Force transducers for tensile and compressive loading often have a small characteristic-curve variation for mechanical reasons, depending on whether they are used with tensile or compressive forces.

This parameter describes the maximum difference.

(Relative) breaking force

Either an absolute value or a percent value is specified. The name of this characteristic indicates the possibility that the transducer may break.

Tip: Please refer to the safety instructions given in the transducer's mounting instructions.

(Relative) limit force

As with the operating force, a relative value based on the nominal (rated) force in % or the absolute operating force in N is commonly specified.
If the transducer's limit force is exceeded, the transducer is likely to be no longer suitable for measurement.
Often the force transducer is plastically deformed upon exceeding of the limit force and there is a significant zero point variation. The force transducer may no longer be used and has to be replaced, because the force transducer shows substantially changed specifications. In particular, there is the risk of mechanical limit values such as breaking force and dynamic oscillation width being reduced.

(Relative) maximal operating force

The maximal operating force is specified either as an absolute value in N or relative to the nominal (rated) force Fnom in %. The force transducer will not suffer damage up to the maximal operating force, provided that it is not used several times within this range. The relationship between the output signal and the applied force is repeatable, i.e. the measurement error increases, however, the force can still be assessed.
Force transducers need to be dimensioned such that the maximal operating force is not utilized.

(Relative) permissible oscillatory stress

The relative permissible oscillatory stress specifies the stress up to which the transducer is fatigue resistant. This value is usually specified as a relative quantity based on the nominal (rated) force.
In general, the permissible oscillatory stress is given as a peak-to-peak value, i.e. the difference between the maximum and the minimum force. Force transducers may be stressed with this amplitude both dynamically and alternatingly.
Example: A tensile and compressive force transducer has a nominal (rated) force of 200 kN, the permissible oscillation width is 100%. In this case, the transducer may be loaded between 0 and 200 kN as well as between -100 kN and 100 kN.

Relative reversibility error

The relative reversibility error is the difference of the output signals when measuring the same torque applied in increasing and decreasing steps (see Fig. 4). The specified value is the maximum deviation (according to absolute value) in the measuring range. It is specified as a percentage of the sensitivity C.

The relative reversibility error is a measure of hysteresis, that is, the difference between the characteristic curves determined with increasing and decreasing torque. For determining the relative reversibility error, a load cycle from zero torque through nominal torque and back is recorded. The practical calculation is based on measurements at a number of predefined points in the load cycle (e.g. 0 %, 50 %, 100 % of Mnom).

Hysteresis describes the dependency of the measuring signal on the transducer’s loading history. It is of particular importance if a transducer is used for a wide measuring range and no unloading takes place between acquiring two relevant measurement points. The most extreme case is the use from zero torque up to nominal torque. The effect of hysteresis occurring during a partial load cycle is usually significantly smaller than the hysteresis during a load cycle covering the entire nominal torque range.


The sensitivity indicates the output signal in mV/V which is produced when the transducer is 100 percent loaded, i.e. loaded with its nominal (rated) force. Any zero signal will be deducted. Example: A transducer shows a zero signal of -0.1 mV/V. The sensitivity is 2 mV/V; in this case, the output signal at nominal (rated) force is 1.9 mV/V. 2 mV/V is a very common output signal for force transducers. As described above, strain gage-based force transducers require a voltage supplied by the amplifiers (excitation voltage). A sensitivity of 2 mV/V means that a force transducer produces an output signal of 2 mV at nominal (rated) force, when supplied with one volt. With 5 V excitation voltage, the corresponding output voltage will be 10 mV. A force transducer's output voltage can be calculated as follows:

With U being the output voltage, U0 the excitation voltage, C the sensitivity, F the applied force and Fnom the transducer's nominal (rated) force. This formula assumes that the zero signal is ideally zero.

The transducer's behavior is similar when the force varies, i.e., the transducer from the example is loaded with half its nominal (rated) force to get 1 mV/V at the output. With an excitation voltage of 5 V this corresponds to 5 m V.

A nominal (rated) sensitivity is specified in the technical data sheets. This sensitivity is valid for all force transducers of a type and is therefore given with a tolerance, the so-called "sensitivity tolerance". For this reason, every HBM force transducer comes with a manufacturing certificate specifying the exact sensitivity for the respective transducer.

Tip: Always adjust the amplifier as specified in the manufacturing certificate or according to an existing calibration to ensure optimal measurement accuracy. In this case, the sensitivity tolerance does not affect the error computation.

The transducer can also be ordered with so-called TEDS. A small chip containing the manufacturing certificate's exact specifications is installed in the transducer or in the cable. Amplifiers supporting this feature can read these data and use it for automatic setup.



A transducer's stiffness is calculated from the nominal (rated) force Fnom and the nominal (rated) displacement Snom.

Stiffness is primarily determined by the transducer's design principle and its nominal (rated) force. In physics it corresponds to a spring constant. Stiffness is crucial to the computation of a transducer's resonance frequency.

Storage temperature range

In the noIn the operating temperature range the force transducer enables measurements to be taken, however, the measurement accuracy is limited.minal (rated) temperature range the force transducer meets the values given in the specifications.

Temperature coefficient of sensitivity

Strain gage-based sensors show only a minute change in sensitivity resulting from temperature variation. This is due to the fact that the spring element materials' module of elasticity decreases with increasing temperature - equal force results in higher strain and thus a bigger output signal. The strain gages' gage factor (the sensitivity), too, is dependent on temperature.
With many force transducers the sensitivity's resulting dependence on temperature is compensated for and is thus very small. With both creep and error computation, it is essential that the specified value is always related to the current measured value.

Temperature coefficient of the zero point

In addition to the sensitivity, the zero point slightly varies according to the temperature. The Wheatstone bridge largely compensates for the effect of the individual strain gages. The remaining error is explained by tolerances that cannot be avoided. This small error can be further reduced by appropriate wiring so that modern force transducers have a remaining error of less than 0.05%/10K.

The temperature coefficient of the zero point always needs to be related to the nominal (rated) force, irrespective of what force is measured. For this reason, we recommend using a force transducer with a particularly small TK0 when working under major temperature variations and/or in the partial load range.

Zero signal

The zero signal is the force transducer's output signal prior to installation. When you install the force transducer the signal changes due to pre-stress and the masses of mounting accessories.

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