Force measurement systems can involve a number of different physical principles but their performance can be described by a number of common characteristics and terms, and the behaviour of a system or transducer can be expressed graphically as a response curve - by plotting the indicated output value (eg voltage) from the system against the force applied to it. The terms used are sometimes applied independently to the force transducer, the force measurement system as a whole, or some other part of the system and it is important to establish, for any given application, the way in which the terms are being used.

An idealised response curve is shown in fig 1 - where the force applied increases from zero to the rated capacity of the force measurement system and then back again to zero. The deviation of the response curve from a straight line is magnified in the figure for the purposes of clarity.

Characterising the performance of a force measuring system is commonly based on calculating such a best-fit least-squares line and stating the measurement errors with respect to it.

Vertical deviation from this line is referred to as non-linearity and generally the largest value is given in the specifications of a system.

The difference of readings between the increasing and decreasing forces at any given force is defined as hysteresis. The largest value of hysteresis is usually at the mid-range of the system.

Sometimes non-linearity and hysteresis are combined into a single figure - usually by drawing two lines parallel to the best-fit line such that they enclose the increasing and decreasing force curves as shown. The maximum difference (in terms of output) is then halved and referred to as the ±combined error.

Any difference between the indicated value of force and the true value is known as an error of measurement (although note that strictly a 'true' value can never be perfectly known or indeed defined and the concept of uncertainty takes this into account). Such errors are usually expressed as either a percentage of the force applied at that particular point on the characteristic or as a percentage of the maximum force - see the difference between '% reading' and '% full scale reading'.

The rated capacity is the maximum force that a force transducer is designed to measure.

Full-scale output, also known as span or rated output, is the output at the rated capacity minus the output at zero applied force.

Sensitivity is defined as the full-scale output divided by the rated capacity of a given transducer/load cell.

The ability of a force measurement system to measure force consistently is covered by the concepts of repeatability and reproducibility. Repeatability is defined broadly as the measure of agreement between the results of successive measurements of the differences of output of a force measurement system for repeated applications of a given force in the same direction and within the range of calibration forces applied. The tests should be made by the same observer, with the same measuring equipment, on the same occasion (ie successive measurements should be made in a relatively short space of time), without mechanical or electrical disturbance, and calibration conditions such as temperature, alignment of loading, and the timing of readings held constant as far as possible.

Although many manufacturers quote a value for repeatability as a basic characteristic of a transducer, it can be seen from the definition that it should not be considered as such. The value obtained for a given force transducer, in a given force standard machine, will depend not only on the inherent characteristics of the device such as its creep and sensitivity to bending moments, but also on temperature gradients, resolution and repeatability of the electrical measuring equipment, and the degree to which the conditions of the tests are held constant, all of which are characteristics of the test procedure. The value of repeatability obtained is important as it limits the accuracy to which the other characteristics of the force transducer can be measured.

In contrast to repeatability, reproducibility is defined as the closeness of the agreement between the results of measurements of the same force carried out under changed conditions of measurement. A valid statement of reproducibility requires specification of the particular conditions changed and typically refers to measurements made weeks, months, or years apart. It would also measure, for example, changes caused by dismantling and re-assembling equipment. The reproducibility of force measurement systems is clearly important if they are to be used to compare the magnitude of forces at different times, perhaps months or years apart. It will be determined by several factors, including the stability of the force transducer’s many components, the protection of the strain gauges or other parts against humidity, and the conditions under which the system is stored, transported, and used.

A force measurement system will take some time to adjust fully to a change in force applied, and creep of a force transducer is usually defined as the change of output with time following a step increase in force from one value to another. Most manufacturers specify the creep as the maximum change of output over a specified time after increasing the force from zero to the rated force. Fig 2 shows an example of a creep curve where the transducer exhibits a change in output from F₁ to F₂ over a period of time from t₁ to t₂ after a step change between 0 and t₁.  In figures this might be, say, 0.03 % of rated output over 30 minutes.

Creep recovery is the change of output following a step decrease in the force applied to the force transducer, usually from the rated force to zero. For both creep and creep recovery, the results will depend on how long the force applied has been at zero or the rated value respectively before the change of force is made.

The frequency response of a force transducer is affected by the nature of the mechanical structure, both within the transducer and of its mounting. A force transducer on a rigid foundation will have a natural frequency of oscillation and large dynamic errors occur when the frequency of the vibration approaches the natural frequency of oscillations of the system.

The effect of temperature changes is felt on both the zero and rated output of the force measurement system. The temperature coefficient of the output at zero force and the temperature coefficient of the sensitivity are measures of this effect for a given system. A force measurement system may need to be kept at constant temperature, or set up well in advance, to settle in to the ambient conditions if high accuracy measurements are required. In some cases the temperature gradients within the measurement installation create a problem even when the average temperature is stable.

Other influence quantities such as humidity, pressure, electrical power changes, or radio-frequency interference may have analogous effects to those of temperature and may be considered in a similar manner.

In general, a force transducer has two interfaces through which a force is applied. These may be the upper and lower loading surfacesof a compression force transducer or the upper and lower screw threads of a tension device. In some load cells, one or both interfaces are part of the elastic element to which the strain gauges are bonded; in other transducers the interfaces may be remote from the elastic element.

At each interface, there will be a force distribution which will depend on the end loading conditions.  A change in these loading conditions, therefore, may cause a change in the force distribution resulting in a change of the sensitivity of the transducer, even though the resultant force at the interface remains unchanged. The International Standard BS EN ISO 376 concerned with the calibration of proving devices for the verification of materials testing machines recognises the importance of end loading conditions by requiring compression proving devices to pass a bearing pad (or similar) test. In this test, a device is loaded through a flat steel pad and then through each of two steel pads that are conically convex and concave respectively by 1 part in 1 000 of the radius. Depending on the design of the transducer, the change of sensitivity caused by a change of end loading conditions can be quite large; some precision compression load cells with low creep, hysteresis, and temperature coefficients can show differences of sensitivity in the bearing pad test of 0.3 %, others less than 0.05 %. 

True axial alignment of the applied force along the transducer’s principal axis, and the loading conditions across that surface are major factors in the design of a reliable and accurate installation of a force measurement system. Force transducers used to measure a single force component are designed to be insensitive to the orthogonal force components and corresponding moments, provided these are within specified limits, but although the error due to small misalignments may be calibrated statistically, the alignment of force relative to the transducer axis may vary through the load cycle of a typical application giving potentially large and unquantifiable errors of measurement. Users of force measurement systems should adhere to manufacturers' recommendations for alignment when installing force transducers.