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
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 VU VE = energisation voltage VU = unbalance voltage RD = resistance of dummy arms RG = resistance of strain gauge VG = voltage across the gauge 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
If RG is initially equal to RD then:- For small variations of RG from RD, RG = RG + RG Ignoring terms in ( RG) 2 (RG) VU = RG -------------------------------------------------- (3) VE 4RG 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
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) Gauge Factor = 2.1 No. of active alarms = 1 Therefore Scale = 1 = 0.47619 2.1 2) Gauge Factor = 2.1 No. of active alarms = 2 Therefore Scale = 1 = 0.238095 2.1 x 2 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 = 1017.62 offset programmed = -1017.62 2) Measured value = -573.84 offset programmed = +573.84 4
Errors There are a number of error sources when measuring strain. 1) Uncertainty of gauge factor. This is typically 1% 2) Bridge non-linearity 3) The matching of the dummy arms to the gauge 4) Measurement errors 5) 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
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 = 1.8V 240 = 7.5mA Average power in each arm of bridge = I 2 R x 25ms 1s = (7.5 x 10-3 ) 2 x 120 x 0.025 = 169µW 6
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 2 nd 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
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 & RG = 350Ω Then VEFF = 350 x VE = 0.997 VE 351 This 0.3% error should be seen in context with a typical uncertainty of ± 1% in the value for the gauge factor. 8
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 3 rd 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
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 2 nd 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