Electrical Strain Gages

Strain-gauge

The electrical resistance strain is a metal wire or metal foil strip which is wafer-like and can be stuck onto surfaces like a postage stamp.

Typical bonded strain gages

When a strain gauge is bonded to an object, When a strain gauge is bonded to an object, and theand the object changes in size, the resistance of the object changes in size, the resistance of the strainstrain gauge will change. The resistance R is given by gauge will change. The resistance R is given by thethe expression: expression:

R= R= ρρ l/A l/A

Where:Where:

l is the length of the wire in metersl is the length of the wire in meters

ρρ is the resistivity of the material in ohm is the resistivity of the material in ohm metersmeters

A is the cross-sectional area of the filament in A is the cross-sectional area of the filament in mm22

When strain gauges measure the changing When strain gauges measure the changing dimensions of an object, they are measuring dimensions of an object, they are measuring strainstrain. . Strain is the ratio of the change in dimension of an Strain is the ratio of the change in dimension of an object to the original dimensionobject to the original dimension

Mechanical strain Mechanical strain εε = = ΔΔL / LL / L

When subject to strain, its resistance R changes, the When subject to strain, its resistance R changes, the fractional change in resistance fractional change in resistance ΔΔR/R being R/R being proportional to the mechanical strain i.e. proportional to the mechanical strain i.e.

Electrical strain Electrical strain ΔΔR/R= G . R/R= G . ΔΔL/L L/L

where G is the gauge factor (1.8 – 2.2)where G is the gauge factor (1.8 – 2.2)

R varies between 50 R varies between 50 ΩΩ and 2K and 2KΩΩ

Potential Potential DividerDivider

Potential Divider with differential Potential Divider with differential amplifieramplifier

Wheatstone Bridge

The four arms of the bridge circuit are formed by the resistance R1 to R4.

The corner points 1 and 4 are connected to the input voltage Vin

The corner points 2 and

3 are connected to the output voltage Vo.

1

2

4

3

R2

R

1

R

3

R

4

Vo

Vin

Quarter strain gauge bridge with differential amplifierQuarter strain gauge bridge with differential amplifier

Half strain gauge bridge with differential amplifierHalf strain gauge bridge with differential amplifier

Full strain gauge bridge with differential amplifier

Meter readingMeter reading

Interpretation of results

(Example 1)

(Example 2)

Meter readingMeter reading

Strain Gages - review

Strain = Elongation / Original Length

Change in length = Change in electrical resistance

Electrical Resistance change is very small, too small to be accurately measured using ordinary voltmeters

Wheatstone Bridge

Converts a change in electrical resistance from a strain gage to a change in voltage

Changes in strain are linearly related to a change in voltage output

Voltage change is too small to be accurately measured and for this reason an amplifier is used