MEASUREMENTS AND INSTRUMENTATION ELE 4101 LECTURE XV
Lecturer: Jomo N. Gill
CONCEPTS TO BE EXAMINED Strain The
strain gauge
Measurements using strain strain gauges
Temperature compensation compen sation
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STRAIN Strain
is the amount of deformation of a body due to an applied force. More specifically, strain (ε) is defined as the fractional change in length, as shown in Figure 1
Fig. 1 3
…cont’d
Strain can be positive (tensile) or negative (compressive). Strain is expressed in in/in or mm/mm. In practice, the magnitude of the measured strain is very small. Therefore, strain is often expressed as microstrain (µε), which is ε × 10 –6
The
resistance of the metallic bar of Fig. 1 is given by:
R
l
A
,
where the quantities have their usual meanings 4
…cont’d A
compressive force causes the length of the metallic bar to decrease and its area to increase. This in turn causes the resistance of the bar to decrease. However, the volume of the bar does not change as it is compressed.
The
new resistance of the bar would be given
by:
R R
l l A A
, 5
…cont’d
It can be shown that the change in resistance is given by:
l
R GF.R , l R / R or GF l / l R / R
where GF is the gauge factor 6
…cont’d For
metals, GF~2. The GF is a measure of the sensitivity of the strain gauge
A larger GF signifies a larger change in resistance for a given strain, and a larger resistance is easier to measure
Semiconductor strain gauges have much higher GFs than metallic strain gauges, but they are very sensitive to temperature variations and are often non-linear 7
THE STRAIN GAUGE
A strain gauge is usually a thin metallic conductor that is firmly attached to a solid object to detect strain in the object. It changes its resistance as it is stretched or compressed. The change in resistance is measured in a bridge circuit
There are two types of strain gauge: the unbonded type the bonded type 8
THE BONDED STRAIN GAUGE
This strain gauge consists of a very fine wire or, more commonly, metallic foil arranged in a grid pattern
9
… cont’d
The grid pattern maximizes the amount of metallic wire or foil subject to strain in the parallel direction, while minimising the strain in the perpendicular direction
The
grid is bonded to a thin backing, called the carrier, which is attached directly to the test specimen. Therefore, the strain experienced by the test specimen is transferred directly to the strain gauge, which responds with a linear change in electrical resistance 10
MEASUREMENTS USING STRAIN GAUGES Wheatstone
bridges are employed to detect the very small resistance change in strain gauges
The strain gauge is used in one or more arms of the bridge, while the source does not usually exceed 15 V, in order to guard against selfheating of the gauges
Temperature
design resistance
compensation is factored into the because temperature influences 11
QUARTER BRIDGE CONFIGURATION
Such a bridge has an active strain gauge, and a dummy strain gauge included for temperature compensation only
12
…cont’d To
determine the strain, Vo with no strain is observed; the bridge can then be balanced at this point by adjusting one of the bridge resistors.
The
gauge is then subject to strain and the output voltage is again observed.
The strain is given by:
4Vr GF(1 2Vr ) 13
…cont’d where
Vout Vout Vr Vin strained Vin unstrained
The
equation for strain factors in non-linearity of the bridge. If we neglect this non-linearity and assume the bridge is initially balanced (Vout, unstrained = 0 V, then . . . .
14
…cont’d
The strain can be approximated as:
4Vout GFVin
Worked example on strain gauge
15
HALF BRIDGE CONFIGURATION
Is more sensitive than the quarter bridge
Is used for measuring bending beams
Utilises
2 strain gauges – one in tension and the other in compression, as shown in the Figure
16
… cont’d Any
changes in temperature will affect both gauges in the same way. Because the temperature changes are identical in the two gauges, the ratio of their resistance does not change, the voltage Vo does not change, and the effects of the temperature change are minimised
The
sensitivity of the half bridge is twice that of the quarter bridge
17
… cont’d
The strain can be approximated as:
2Vout GFVin
18
FULL BRIDGE CONFIGURATION
Utilises active gauges in all four arms
Two
strain gauges in opposite diagonals are in tension and the other two are in compression
Additional temperature compensation is accomplished by placing compensation elements in the excitation lines and output junctions
19
… cont’d
The strain can be approximated as:
Vout GFVin
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CONFIGURABLE GAUGES
Manufacturers of strain equipment have developed instrumentation that performs the basic functions necessary for making a strain measurement
These enable the user to: set the GF directly into the arm resistance scale the output signal zero the bridge calibrate the instrument supply the excitation voltage complete the various possible configurations
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THE P3500 STRAIN INDICATOR
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