# Strain Gauges

The **strain gauges** is a transducer used for the measurement of dimensional variations within mechanical systems. Its principle of operation is based on the variation in electric resistance within a conductor with respect to a change in its physical dimensions, usually length.

## Strain Gauges Sensitivity

An indication of the sensitivity of a strain gauge is therefore the ratio between the unit change in the electrical resistance and the unit change in the physical length, as shown in eqn (1); this is known generally as the gauge factor, which is denoted in this book by the symbol G_{f}.

Initially, strain gauges were constructed with a length of metal wire and were consequently somewhat bulky. These days strain gauges are divided in to two main groups: metal (resistive) and semiconductor (piezoresistive).

Metal strain gauges are made of a metal film pattern, typically only a few micro metres thick, bonded to a flexible and electrically insulating backing material such as polyester. This construction (Figure 1), is obtained with techniques similar to those employed in the microelectronics industry to produce film resistors and therefore benefits from the same high reliability and low tolerance values

The gauge factor of metal strain gauges is given by eqn (2), where fl is the Poisson ratio, which relates the increase in the length of a solid object under the effect of a traction force to the reduction of its diameter.

Table 1 lists typical gauge factors for metal strain gauges.

Semiconductor strain gauges, sometimes referred to as piezoresistive strain gauges, are based on thin layers of doped silicon or germanium manufactured into rectangular sections, as shown in Figure 2. The gauge factor for these transducers is given by:

where μ is Poisson’s ratio, p_{c} is the transducer longitudinal piezoelectric coefficient and E is Young’ modulus.

Because of the addition of the P_{c}E term these gauges have a higher gauge factor, that is a higher sensitivity, than metal ones. This is shown in a quantitative format in Table 2.

Semiconductor strain gauges can thus measure lower mechanical strains and therefore lower forces than metal ones by approximately two orders of magnitude. However, they have a lower temperature range and lower mechanical strength than metal ones and are therefore limited in their use to high sensitivity, low temperature and low dynamic range applications.