Hi friends,

In this article, I am going to describe you strain gauge working principle, gauge factor and strain gauge load cell working.

A strain gauge is a passive transducer, that converts mechanical displacement into the change of resistance. A strain gauge is a thin wafer-like device that can be attached to a variety of materials to measure applied strain. These are used as a fundamental sensor in many types of sensors like pressure sensors, load cells, torque sensors etc.

# Strain Gauge Working Principle

The foil type strain gauges (Figure #1) are very common in which a resistive foil is mounted on a backing material. These are available in a variety of shapes and sizes for different applications. The resistance of the foil changes as the material to which the gauge is attached undergoes tension or compression due to change in its length and diameter.

This change in resistance is proportional to the applied strain. As this change in resistance is very small in magnitude so its effect can be only sensed by a Wheatstone bridge. This is the basic strain gauge working principle.

A circuit diagram is shown in Figure #2. In this circuit diagram, a strain gauge is connected into a Wheatstone bridge. This circuit is so designed that when no force is applied to the strain gauge, R1 is equal to R2 and the resistance of the strain gauge is equal to R3. In this condition the Wheatstone bridge is balanced and the voltmeter shows no deflection.

But when strain is applied to the strain gauge, the resistance of the strain gauge changes, the Wheatstone bridge becomes unbalanced, a current flows through the voltmeter. Since the net change in the resistance is proportional to the applied strain, therefore, resultant current flow through the voltmeter is proportional to the applied strain. So, the voltmeter can be calibrated in terms of strain or force.

In the above circuit, we have used only one strain gauge. This is known as ‘quarter bridge’ circuit. We can also use two strain gauges or even four strain gauges in this circuit. Then this circuit is called ‘half bridge’ and ‘full bridge’ respectively. The full bridge circuit provides greater sensitivity and least temperature variation errors.

## Gauge Factor of Strain Gauge

The gauge factor of strain gauge is defined as the unit change in resistance per unit change in length.

i.e. gauge factor Gf = (∆R/R)/( ∆l/l)

where, R = nominal gauge resistance,
∆R = change in resistance,
l = length of the specimen in an unstressed condition,
∆l = change in specimen length.

It can be proved mathematically,

Gauge factor, Gf = 1 + 2v + (∆ρ/ρ)/(∆L/L)

If the change in resistivity due to strain is almost negligible, then

gauge factor of strain gauge,  Gf = 1 + 2v

Where, v is Poisson’s ratio. It may be defined as the ratio of strain in the lateral direction to the strain in the axial direction. The Poisson’s ratio for most metals lies in the range of 0 to 0.5 and this gives a gauge factor of 2 approximately.

## Strain Gauges Rosettes

The shape of a strain gauge is selected according to the strain to be measured. The different shapes of strain gauges may be used to measure strain in axial, biaxial or multiaxial directions. If a simultaneous measurement of strains in more than one direction is required, multi-element strain gauges are used.

These multi-element strain gauges are called ‘strain gauges rosettes’. In the two element strain gauges, both the elements are kept at 90o. This type of strain gauges is used in force transducers. The three element strain gauges rosettes are used to determine the direction and magnitude of principle strain resulting from complex structural loading. The most popular type has 45o, or 60o (Figure #5) angular displacement between sensing elements.

## Strain Guge Load Cells

A load cell is a force measurement device. In a load cell, a transducer is used to convert force into a proportional electrical signal. There are different types of load cells like hydraulic, pneumatic and strain gauge load cells. In the industry, mostly strain gauge load cells are used. In these load cells, strain gauges are used to sense the force and produce a proportional electrical signal.

A schematic arrangement of a strain gauge load cell is shown in Figure #4. In this load cell, four strain gauges are connected to the load cell. These are further connected to a Wheatstone bridge. This system is so designed that under normal condition, Wheatstone bridge remains balanced and hence voltmeter shows no deflection.

But when we apply a load to the load cell, deformation takes places in strain gauges. This deformation in strain gauges changes their resistances. This makes Wheatstone bridge unbalanced. And the voltmeter shows a reading. As the unbalance in the circuit is proportional to the load, therefore, the voltmeter can be calibrated in terms of force or load.

## Characteristics of Strain Gauges

For a satisfactory operation a strain gauge should have the following characteristics:

• It should have a high value of gauge factor. With the high value of the gauge factor, we can get a high sensitivity of the system.
• It should have a high value of resistance as it minimizes the effect of unwanted variations of resistance in the measurement circuit.
• It should have low resistance temperature coefficient. It is very necessary to minimize errors due to temperature variations.
• It should not have any hysteresis effects.
• It should have linear characteristics. variations in resistance should always be proportional to the variations in the strain.

Thanks for reading about “strain gauge working principle”.

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Categories: Instrumentation

### 1 Comment #### Erika Brady · June 25, 2019 at 1:21 am

I like that you mention how there are different types of load cells that can be used to measure force, such as hydraulic, pneumatic, or strain gauges tools. Knowing the right one to use could ensure that it works for your project and anything else you might need it for. It could also help if you ever need force measurement tool repair services so you can ensure you visit the right professional who is experienced with the type of load cell you have so it’s fixed correctly.