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Explain working of Strain Gauge and also draw the expression for gauge factor.
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The strain gauge has been in use for many years and is the fundamental sensing element for many types of sensors including pressure sensors, load cells, torque sensors, position sensors, et cetera.

In order to explain a strain gauge and its working, we need to first define strain.

• Strain is what happens as a result of stress. If a material is stressed by a force, it often changes shape and gets a little bit longer (if you've pulled it apart) or shorter (if you've pushed it together). Therefore, strain is defined as the change in length the force produces divided by the material's original length.

• A Strain Gauge is a passive transducer that converts a mechanical elongation or displacement produced due to a force into its corresponding change in resistance R, inductance L, or capacitance C.

• It is basically used to measure the strain in a work piece. If a metal piece is subjected to a tensile stress, the metal length will increase and thus will increase the electrical resistance of the material. Similarly, if the metal is subjected to compressive stress, the length will decrease, but the breadth will increase. This will also change the electrical resistance of the conductor

Following is a basic diagram of a bonded strain gauge – Application in Load Measurement –

In engineering, designing anything from a car engine or a bridge to a wind turbine or an airplane wing requires measurement of stress that will be inflicted by the load. Strain gauge simplifies this process by providing accurate data and the engineer does not have to rely on intuition or guesswork.

Gauge factor is defined as the ratio of per unit change in resistance to per unit change in length.

$G_f=\frac{(∆R/R)}{(∆L/L)}$

$\frac{∆R}{R}=G_f×\frac{∆L}{L}=G_f×ε$

where ε=strain= $\frac{∆L}{L}$

$\frac{∆R}{R}=\frac{∆L}{L}+2v×\frac{∆L}{L}+\frac{∆ρ}{ρ}$

∴ Gauge Factor$G_f=1+2v+\frac{((∆ρ/ρ))}{ε}$

where

Term 1 – resistance change due to change of length

2v – resistance change due to change in area i.e. Poisson’s ratio

$\frac{((∆ρ/ρ))}{ε}$ – resistance change due to piezo resistive effect

The strain is usually expressed in terms of micro strain. 1 micro strain = 1 μm/m. If the change in the value of resistivity of a material when strained is neglected, the gauge factor is:

$G_f$ = 1 + 2v

The common value for Poisson's ratio for wires is 0.3. This gives a gauge factor of 1.6 for wire wound strain gauges. Poisson's ratio for all metals is between 0 & 0.5. This gives a value of 2.

Example – A resistance wire strain gauge uses a soft iron wire of small diameter. The gauge factor is +4.2. Neglecting the piezo resistive effects, calculate the Poisson's ratio.

Solution –The gauge factor is given by equation, $G_f$ = 1 + 2v = 4.2

Poisson's ratio = v = (4.2 -1)/2 = 1.6

Strain gauges are broadly used for two major types of applications and they are:

• Experimental stress analysis of machines and structures.

• Construction of force, torque, pressure, flow and acceleration transducers.

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