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Senta Pessel, winter semester 2011/12

Artikel auf Deutsch

The electrical resistance of a conductor depends on its diameter. If such a conductor is either strained or compressed (its diameter is increased or decreased) its electrical resistance changes. This reaction of electrical conductors to mechanical impact is used in the “strain gauge method”.

General information on strain measurement with strain gauges

A strain gauge is a dilatometer which works on the basis of the geometrical effect mentioned above. Metal strain gauges can either be produced as wire or as foil strain gauges. The third type includes semiconductor strain gauges which work on the basis of the piezoresistive effect.

Strain gauges should only be used within the elastic range of \begin{array}{l}∆l / l ≤ 1 %\end{array} in order to avoid false measurements. The typical range of application is \begin{array}{l}∆l / l ≤ 0.1 %\end{array}. These slight changes in length make detection of even minor changes in resistance in strain gauges possible. More details about this effect can be found in chapter Wheatstone bridge.

As a change in resistance in a strain gauge allows conclusions to be drawn about the strain of a component part, an equation is necessary to calculate the strain from the relative change in resistance. According to [1] the relation between the relative change of the relative resistance \begin{array}{l}∆R / R\end{array} and the strain \begin{array}{l}ε\end{array} can be stated as follows:

\begin{array}{l}\frac{\Delta R}{R}=GF*ε\end{array}

\begin{array}{l}GF\end{array} stands for Gauge Factor. It is the unit of measurement for the sensitivity of a strain gauge. To determine the \begin{array}{l}GF\end{array}, \begin{array}{l}∆R / R\end{array}, \begin{array}{l}ε\end{array} as well as Poisson's ratio \begin{array}{l}μ\end{array} and the relative change in length \begin{array}{l}∆l / l\end{array} can be used. This is described in the following formula:

\begin{array}{l}GF=\left ( \frac{Δ ρ /ρ }{ε}+1+2μ \right )=\frac{Δ R/R}{ε}=\frac{Δ R/R}{Δ l/l}\end{array}

Metal strain gauges

Metal strain gauges are based on geometrical effects. This implies that strain or compression of a conductor leads to a change in its resistance. This change can be made visible for the user using electrical circuits.

The GF is used to define the sensitivity of a strain gauge. As in metals, the relative change in specific resistance is about zero, the following equation is derived to determine the gauge factor: \begin{array}{l}GF=1+2μ\end{array}, based on [1]. Poisson's ratio for metals is usually between 0.2 and 0.5. This results in \begin{array}{l}GF_{max}\end{array}~ 2.

Wire strain gauge

Wire strain gauges consist of wire measuring grids applied on a metal foil. They are attached to the component part for which the strain is to be measured. The metal foil not only simplifies attachment to the component part’s surface, it also ensures that the component part and the strain gauge are not electrically connected. As the production of wire strain gauges is very complex, they have been almost completely ousted from the market by foil strain gauges. Only for measurements in high temperature ranges are they still used. For this, ceramics are used as carrier materials (see also: [2]).

Foil strain gauge

Foil strain gauges are produced from finely rolled metal foils. The foils are typically made from constantan or a Cr-Ni alloy. After rolling the foils, the conductor structures are removed by etching and the resulting measurement grid is applied to a supporting plastic foil. Mass production of these components is possible.

The etching process is very precise, so that for example, rosette strain gauges can also be excised from the metal foils by etching. Configurations of strain gauges placed at different angles to each other are also possible. Dependent on how the strain gauges are configured relative to each other, measurements of strain, shear stress or torque are possible.

 Semiconductor strain gauge

Semiconductor strain gauges consist of semi-conductive materials such as silicon or germanium. They measure strains based on the piezoresistive effect. This means their electrical resistance changes under pressure or tension. In this case, their geometrical deformation does not matter. Due to their high GF (between 100 and 160) semiconductor strain gauges are very sensitive.

Despite their high sensitivity, semiconductor strain gauges are not as popular in the field of strain measurement as metal strain gauges as they are costly and significantly more sensitive to temperature than strain gauges made of metal.

The production of semiconductor strain gauges is similar to the production of computer chips. Technologies developed for computer technology can also be applied to strain gauges, thus micro sensors can be produced from semi-conductive materials. On a large scale, semiconductor strips are attached to foils on the deformation element.

Measurement properties of strain gauges

Cross sensitivity

As a component part does not strain in a single direction only, cross sensitivity occurs. Each strain is also connected with a compression/elongation at 90° to the main strain direction. According to [2] has a strain gauge with a grid length of <3mm a cross sensitivity of <3% of longitudinal sensitivity.

Fatigue behaviour

The fatigue behaviour of strain gauges is important in dynamic measurements. Although the GF (measurement of the sensitivity of a strain gauge) almost does not change in the course of many complete reversals of stress, the zero point of the strain gauge can change significantly. This is due to the metallurgical changes of the strain gauge’s metal structure. According to [2] in 107 complete reversals of stress, a change of the zero point can simulate a strain of up to 0.1%. In order to avoid this effect, it is recommended to use fatigue-resistant strain gauges in the case of applications with frequent complete reversals of stress.

Moisture sensitivity

Moisture can cause carrier materials and glues to swell. This can lead to a large zero drift. If strain gauges are used in areas of high dampness, good moisture-protection is recommended.

Temperature dependency

Temperature can influence the measurement in three different ways:

  • Change in length of the object to be measured and the strain gauge
  • Compression or strain of the strain gauge due to different expansion coefficients of the deformation element and strain gauge.
  • Temperature dependency of electrical resistance

To allow for compensation in temperature, compensation-strain gauges can be used. In this case, an active and a passive strain gauge are built into a bridge circuit. The active strain gauge is connected with a deformation element and records variations in strain and temperature. The passive strain gauge is not directly connected with the deformation element. It has only to collect identical variations in temperature, like the active strain gauge, but not the mechanical deformations. In practice, this works as the passive strain gauge is glued onto the same carrier material as the active strain gauge. The latter, however, is also attached to a carrier material with good thermometric conductivity to remove the mechanical connection. A precondition for a good temperature compensation is that the variations in temperature in component parts have to happen so slowly that the temperatures of both strain gauges can be accommodated.

The application of the passive strain gauge at an angle of 90° can also lead to the desired decoupling of the passive strain gauge for the actually targeted measurement. However, the precondition for this would be that the component part shows minor to no strain orthogonal to the strain that is to be measured.

If only local strains are to be determined, it is possible to apply a self-temperature-compensation strain gauge. This is characterised by its thermal expansion coefficient that is matched with that of the deformation element. i.e. for each application, material-specific temperature-compensation strain gauges are necessary.

Wheatstone bridge

The Wheatstone Measurement Bridge (also: Wheatstone Bridge) is used to determine DC resistances and small ohmic resistances.

It is built from four resistors that together form a closed ring or a circle. If they are arranged in a square, to complete a bridge circuit, a voltage source has to be inserted on one diagonal and an voltmeter on the other.

Depending on how many of the four resistors are employed to actively measure resistances, it is known as a quarter, half or full bridge. With strain measurement using strain gauges, bridge circuits are used, because if a strain gauge is built into an electric circuit, it functions as an ohmic resistor. If connected with other resistors in a bridge circuit, more detailed measurements can be taken, as well as temperature compensation and stronger measurement signals can be achieved.

Strain gauge quarter-bridge

In the case of a quarter-bridge, only one of the deployed resistors is an active strain gauge that can register strain. The other three are basic ohmic resistors. As shown in [3] the following connection accounts for the output voltage displayed on the voltmeter. (if R ≫ ∆R):

\begin{array}{l}U_{AB}=\frac {U_0}{4}ε*GF\end{array}

However, in this type of circuit there is no temperature correction performed. This can lead to false measurements, particularly with small strains. To realise temperature compensation, one of the ohmic resistors of the quarter-bridge is replaced by a passive strain gauge. It is built exactly like its strain gauge neighbour, only it cannot determine strains. Its change in resistance results solely from changes in temperature. If the circuit is built like this the change in temperature is negligible.

Strain gauge half-bridge

A half-bridge is a measurement apparatus with two active strain gauges. If it is possible to attach these to a component part so that they are exposed to opposite strains, the measured resistances sum. A typical use of such circuits is for example the attachment to a cantilever. If such cantilevers are bent downwards, an even state of stress will occur in which the material on the upper side of the cantilever is strained yet on the bottom side is compressed. Due to the summing of changes in resistance of both strain gauges, small strains in a half-bridge are significantly more recognisable than in quarter-bridges. Specific temperature compensation is not required in this kind of circuit as with the use of two strain gauges it is already in the system.

Corresponding to [3] the output voltage of the half-bridge can be determined as follows:

\begin{array}{l}U_{AB}=\frac {U_0}{2}ε*GF\end{array}

Strain gauge full-bridge

Full-bridges are generally used in load transducers. They have an integrated wooden cylinder in which a known connection between the acting force and the resulting strain exists. Thus, a connection can be drawn between the measured strain on the acting force. A full-bridge has high accuracy at good temperature compensation for such use. The output voltage of a full-bridge is determined as follows:


The use of strain gauges in wireless sensor technology

The use of strain gauges in wireless sensor technology is not markably different to cabled applications. As with “cabled” use, strain gauges have to be configured in bridge circuits and attached to the to be measured component part. As it makes wireless technology easier, for the investigation of large buildings from outside the importance of moisture-protection for the sensors is increasing.

The most important issue that occurs with the use of wireless strain gauges is the power supply of the strain gauge. As with measurements using strain gauges for the detection of changes in stress, for wireless strain gauges, there must also always be sufficient energy available. In [5] it is emphasised that in the field of strain measurement, it can be crucial to be able to reprogram strain gauge sensors via radio even after installation. On one hand, this results from the necessity to factor in the “subtraction” of the collected pre-installation strains before sending the raw data and on the other, it is sometimes necessary to readjust a strain gauge even during measurement.

This is the reason why for most strain gauges an “intelligent” interface has been created that allows for external control as well as for “self-administration”. In order to save energy, it is also important that the wireless sensor can be controlled via software. There are different approaches to reduce the energy consumption of a wireless strain gauge.

One is to provide the strain gauge with pulsed energy. In [5] for example, it is proposed that instead of constant measurement, to only carry out ten measurements per second thus reducing electric power consumption.

Another approach of [5] is to control the sensor nodes from a base station. The normal state of a node would then be “sleep” for example, i.e. a state of minimal energy consumption. After waking, the following example scenarios are possible:

  • Wake up, wait for instructions, as instructed collect or send data, sleep
  • Wake up, collect data if an event or exceeding of a threshold is detected, sleep
  • Wake up, periodically send data, sleep

In fig. [8] a wireless sensor node that is also equipped with a semiconductor strain gauge is shown.

Fig. 8: Wireless sensor mote with semiconductor strain gauge [4]



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  2. Schiessle, E.: Sensortechnik und Meßwertaufnahme. Vogel Business Media, 1992.
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  4. Große, C. U.; Krüger, M.: Inspection and Monitoring of Structures in Civil Engineering;
  5. Arms, S.W.; Townsend, C.P.; Galbreath, J.H.; Newhard, A.T.: Wireless Strain Sensing Networks. 2nd European Workshop on Structural Health Monitoring, München, 7. - 9. Juli 2004.
  6. Schöne, A.: Meßtechnik. Springer Berlin, 1994.