Download strain gauge measurement - Measurement Systems Ltd

Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
STRAIN GAUGE MEASUREMENT
INTRODUCTION
There are many possible ways of measuring strain gauges using a Datascan. All methods
measure the change in resistance of the gauge within a bridge circuit and the circuits are all
effectively full bridges.
Where we refer to half or quarter bridges, we are really referring to the number of “arms” of the
bridge which must be supplied by the customer.
THEORY
Strain is defined as the change in length of a component divided by its original length.
It
It is usually measured into microstrain where
Microstrain
___________________________________________________________________________________
1
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
Strain gauges are resistive devices whose resistance changes when strained. They are
attached to the unit under test and so experience the same strain as the unit. They are
designed to be both linear and to have negligible effect on the unit they are attached to.
The behaviour of the gauges is defined by:-
Where G is the gauge factor of particular gauge being used.
Gauges are supplied with a number of initial values, normally 120Ω, 350Ω and 1kΩ. The value
for the gauge factor is supplied by the manufacturer.
BEHAVIOUR IN BRIDGE CIRCUITS
RD
RD
Terms
VE = energisation voltage
VU = unbalance voltage
RD = resistance of “dummy” arms
RG = resistance of strain gauge
VG = voltage across the gauge
VU
VE
RD
RG
VG
NOTE
RG and RD should be chosen to be nominally equal so that the unbalance
voltage is small compared to the energisation voltage.
___________________________________________________________________________________
2
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
If RG is initially equal to RD then:For small variations of RG from RD,
Ignoring terms in
VU
VE
=
∆RG
4RG
RG = RG + ∆RG
(∆RG)2
(RG)
-------------------------------------------------- (3)
Therefore if RG varies from its initial value due to strain, the change in bridge imbalance voltage
is given by equation (3)
From equation (2)
The software within the Datascan computes this value.
The energisation voltage VE is fixed at approx 1.8V.
___________________________________________________________________________________
3
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
Gauge Factors
All calculations performed by Datascan assume a gauge factory of 1 and one active arm in the
bridge.
For different gauge factors the scale and offset facility is used. The scaling value entered
should be the reciprocal of the actual gauge factor multiplied by the number of active arms.
Examples
1)
2)
Gauge Factor
No. of active alarms
Therefore Scale
=
=
=
2.1
1
1
2.1
Gauge Factor
No. of active alarms
Therefore Scale
=
=
=
2.1
2
= 0.47619
1
2.1 x 2
= 0.238095
Initial Offsets
The scale and offset facility is also used to “initialise” the bridge, ie. remove the initial offset.
This is done by programming the channel to have the required “scaling” value but a Ø offset
value. The value which is then measured is used to calculate the offset value required.
Example
1)
Measured value
offset programmed
= 1017.62
= -1017.62
2)
Measured value
offset programmed
= -573.84
= +573.84
___________________________________________________________________________________
4
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
Errors
There are a number of error sources when measuring strain.
1)
2)
3)
4)
5)
Uncertainty of gauge factor. This is typically 1%
Bridge non-linearity
The matching of the dummy arms to the gauge
Measurement errors
Self heating of gauges
Bridge of non-linearity
The calculations performed by Datascan assume that the output of the bridge varies linearly
with strain. This is only true for small deviations when terms in (∆RG/RG)2 can be ignored. The
error introduced with an imbalance of 10000µE is approximately 1%. This can be reduced
significantly by using a suitable conversion polynomial.
Dummy Resistors
The dummy resistors have two effects.
1)
The scaling of the measurements will only be correct if RD1 = RG when the bridge is
initialised. If RD is 1% different then a 0.5% scaling error is introduced.
2)
Changes in RD with temperature are equivalent to straining the gauge. Low temperature
coefficient resistors must be used for arms which must remain constant. (See
temperature Consideration).
___________________________________________________________________________________
5
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
Measurement Errors
The figure for accuracy quoted assumes
1)
The bridge imbalance is less than 20mV so the 20mV range can be used.
2)
Bridge non-linearities are allowed for elsewhere.
3)
Gauge and dummy matching is perfect.
Self Heating
Self heating is minimised with Datascan by only energising the bridge whilst measurements are
being made.
Example
A 120Ω bridge is measured every second using the 16 bit mode.
Current in each arm of bridge
Average power in each arm
of bridge
=
1.8V
240
=
7.5mA
=
I2R x
=
(7.5 x 10-3)2 x 120 x 0.025
=
169µW
25ms
1s
___________________________________________________________________________________
6
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
NUMBER OF ACTIVE ARMS
It is possible to increase the sensitivity of this circuit by replacing some of the dummy arms with
other strain gauges.
Clearly, adding a 2nd gauge as shown
subjected to the same strain as the
first will double the output from the
bridge
In circumstances where you also have
an equal and opposite strain, it is
possible to make all arms of the bridge
active and get 4 times the sensitivity.
___________________________________________________________________________________
7
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
HALF BRIDGE CONFIGURATIONS
If you are a ½ bridge setup, 2 arms of the bridge have been supplied within the Datascan. The
circuit is then:-
Figure: User Half Bridge
Lead resistances RL appear in the two arms of the half bridge and therefore have little effect on
the bridge balance. They do affect the effective energisation voltage VEFF by a small amount.
This can be eliminated using the 5 wire connection to a half bridge.
Example:
If
RL = 1Ω
Then VEFF
&
RG = 350Ω
= 350 x VE
351
=
0.997 VE
This 0.3% error should be seen in context with a typical uncertainty of ± 1% in the value for the
gauge factor.
___________________________________________________________________________________
8
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
QUARTER BRIDGE CONFIGURATIONS
If you are using a quarter bridge setup, 2 arms of the bridge are supplied within the Datascan
unit, you must provide the 3rd dummy and the gauge.
The equivalent circuit is:-
Figure: User Quarter Bridge
Lead impedances RL1 & RL2 appear in opposite arms of the right hand side of the bridge. The
third wire ensures that the voltage measured is the voltage difference between points A and C
of the bridge. If only 2 wires are used, then VU will be measured as the voltage difference
between points A and B and Lead Impedances RL1 & RL2 are both in series with the gauge.
Therefore changes in RL1 & RL2 due to temperature changes are indistinguishable from
changes in RG due to strain if only 2 wires are used.
As for half bridge circuits, the effective energisation voltage is incorrectly measured and so
causes small gain errors. The size of the error is the same as for half bridge circuits.
___________________________________________________________________________________
9
Datascan 7000
Strain Gauge Measurement
___________________________________________________________________________________
TEMPERATURE CONSIDERATIONS
The resistance of a strain gauge will vary either because of being strained or because of
temperature variations.
Typical values for foil gauges
=
0.015% /°C
compared with output change of 0.0002% /µE.
For gauge with these specifications, a one degree change in temperature will cause an effective
strain error of approx 75µE, just because of the change in temperature of the gauge.
Note
Changes in the test objects length due to expansion with
temperature should be allowed for separately
Using a 2nd gauge as a dummy gauge will give significant improvements in these temperature
related effects.
In the diagram above, the dummy is mounted in such a way so that it experiences exactly the
same temperature environment as the gauge, but none of the strain (ignoring Poissons Ratio
Effects).
NOTE
This type of compensation is only available when using full or half bridge modes. In
quarter bridge modes, the dummy is fitted at the Datascan. Precision resistors must
be used for all dummy arms.
___________________________________________________________________________________
10