A strain gauge is an electrical sensor which is used to accurately measure strain in a test piece. Strain gauges are usually based on a metallic foil pattern. The gauge is attached to the test piece with a special adhesive. As the test piece is deformed, so the adhesive deforms equally and thus the strain gauge deforms at the same rate and amount as the test piece. It’s for this reason that the adhesive must be carefully chosen. If the adhesive cracks or becomes detached from the test piece any test results will be useless.
Strain gauges are used not just for metals; they have been connected to the retina of the human eye, insects, plastics, concrete and indeed any material where strain is under investigation. Modern composite materials like carbon fibre when under development are often constructed with strain gauges between the layers of the material.
The strain gauge is effectively a resistor. As the strain increases so the resistance increases.
In a basic sense a strain gauge is simply a long piece of wire. Gauges are mostly made from copper or aluminium (Figure 1). As the wire in the strain gauge is mostly laid from end to end, the strain gauge is only sensitive in that direction.
When an electrical conductor is stretched within the limits of its elasticity it will become thinner and longer. It is important to understand that strain gauges actually deform only a very small amount, the wire is not stretched anywhere near its breaking point. As it becomes thinner and longer it’s electrical characteristics change. This is because resistance is a function of both cable length and cable diameter.
The formula for resistance in a wire is
For example, the resistance of a copper wire which has a resistivity of 1.8 x 10-8 ?/m, is 1 meter long and has a cross sectional area of 2mm2 would be
Resistivity is provided by the manufacturer of the material in question and is a measurement of how strongly the material opposes the flow of current. It is measured in ohm’s per meter (?/m).
If in our example the cable was then put under certain strain its length would extended to 2 meters, as it was stretched longer it would get thinner, it’s cross sectional area would decrease. In this example to 0.5 mm2 the resistance now would be
As can clearly be seen the resistance is now different, but the resistances in question are very small. This example shows only the difference when the characteristics of the copper wire have changed. It is not practically possible to stretch and extend a piece of copper wire by these amounts. The example merely shows how resistance changes with respect to length and cross sectional area and demonstrates that strain gauges, by their very nature, exhibit small resistance changes with respect to strain upon them.
These small resistance changes are very difficult to measure. So, in a practical sense, it is difficult to measure a strain gauge, which is just a long wire. Whatever is used to measure the strain gauges resistance will itself have its own resistance. The resistance of the measuring device would almost certainly obscure the resistance change of the strain gauge.
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| Figure 2: A Wheatstone bridge | Figure 3: With shunt resistor |
The solution to this problem is to use a Wheatstone bridge to measure the resistance change. A Wheatstone bridge is a device used to measure an unknown electrical resistance. It works by balancing two halves of a circuit, where one half of the circuit includes the unknown resistance. Figure 2 shows a classical Wheatstone bridge, Rx represents the strain gauge.
Resistors R2, R3 and R4 are known resistances. Normally, 120?, 350? or 1000? are used depending on the application. Knowing the supply voltage and the returned signal voltage it’s possible to calculate the resistance of Rx very accurately.
For example if R2, R3 and R4 are 1000? and if the measured signal voltage between measurement points A and B was 0 Volts then the resistance of Rx is
For our example we get
This implies a perfectly balanced bridge. In practice, because the strain gauge goes through different strain levels its resistance changes, the measured signal level between measurement points A and B is not zero. This is not a problem when using a system like the Prosig P8000 as it can accurately measure the voltage between measurement points A and B.
It is necessary to know the relationship between resistance and voltage. Only then can the measured voltage be related to a resistance and, hence, a strain value.
Figure 3 shows the addition of another resistor RS, called the shunt resistor. The shunt resistor is a known fixed value, normally 126,000?.
The Shunt resistor is added for calibration purposes and is a very high precision resistor. By measuring the voltage between measurement points A and B with the shunt resistor across Rx, a voltage with the shunt resistor in place is known. Then by removing the shunt resistor, which is a known 126,000? and measuring the voltage between measurement points A and B again, it’s possible to relate the measured voltage change to a known resistance change. Therefore the volt per ohm value is known for this particular bridge and this particular Rx.
In order to go one step further and calculate the strain from the resistance, the gauge factor must be known. This is a calibrated number provided by the manufacturer of the strain gauge. With this information the sensitivity of the whole sensor can be calculated. That is, the volt per strain is known.
Inside the P8000 the resistors used to complete the bridge are very high precision. This allows the Prosig P8000 to calculate the resistance, and therefore, strain with a high degree of accuracy.
Strain gauge readings can be affected by variations in the temperature of the strain gauge or test piece. The wire in the strain gauge will expand or contract as an effect of thermal expansion, which will be detected as a change in strain levels by the measuring system as it will manifest itself as a resistance change. In order to address this most strain gauges are made from constantan or karma alloys. These are designed so that temperature effects on the resistance of the strain gauge cancel out the resistance change of the strain gauge due to the thermal expansion of the test piece. Because different materials have different thermal properties they therefore have differing amounts of thermal expansion.
So, where temperature change during the test is an issue, temperature compensating strain gauges can be used. However this requires correctly matching the strain gauge alloy with the thermal expansion properties of the test piece and the temperature variation during the test. In certain circumstances temperature compensating strain gauges are either not practical nor cost effective. Another more commonly used option is to make use of the Wheatstone bridge for temperature compensation.
When using a Wheatstone bridge constructed of four strain gauges, it is possible to attach the four gauges in a fashion to remove the changes in resistance caused by temperature variation. This requires attaching the strain gauge Rx in the direction of interest and then attaching the remaining strain gauges, R2, R3 and R4, perpendicular to this. The piece under test however must only exhibit strain in the direction across Rx and not in the perpendicular direction.
It’s important to understand that the R2, R3 and R4 strain gauges should not be under strain, hence their direction. This means the whole bridge is subject to the same temperature variations and therefore stays balanced from a thermal expansion point of view. As the resistance changes due to temperature, all the resistances in all four gauges change by the same amount. So the voltage at measurement point A and B stays constant due to temperature fluctuations. Only the strain in the desired direction, across Rx, in the test piece affects the measured voltage readings.
The Prosig P8000 system has multi-pin inputs, these allow for the connection of strain gauges in all the various different bridge configurations.
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| Figure 4: Quarter bridge | Figure 5: Half bridge |
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| Figure 6: Full bridge | |
The configurations that strain gauges can be used in are,
Quarter Bridge is the most common strain gauge configuration. As can be seen in Figure 4 it is actually a three wire configuration. The rest of the bridge as shown in Figure 2 is completed inside the Prosig P8000 system. Quarter Bridge uses three wires to allow for accurate measurement of the actual voltage across S1.
Half Bridge is not an often used strain gauge configuration. As can be seen in Figure 5 it is actually a five wire configuration. The rest of the bridge as shown in Figure 2 is completed inside the Prosig P8000 system. The main advantage of the Half Bridge configuration is that both the strain gauges S1 and S2 can be attached to the test piece, but perpendicular to each other. Which as previously discussed allows for temperature compensation.
Full bridge is used for situations where the fullest degree of accuracy is required. The Full Bridge configuration is a six wire system, as shown in Diagram-5. The Full Bridge configuration is the most accurate in terms of temperature variation because it can have two active gauges, S1 and S4. The gauges can be configured with S1 and S4 in the direction of interest on the test piece and S2 and S3 perpendicular to this. Further the voltage sense lines have no effective current flow and therefore have no voltage drop, therefore the voltage measured by the Prosig P8000 system is the actual voltage that is exciting the bridge. The reason for this requirement is that strain gauges are often on long wires and all wires have their own resistance. The Prosig P8000 system could be exciting the gauge with 5 Volts for example, but the voltage at the active part of the bridge might be 4.95 Volts because of the resistance of the wires carrying the supply voltage. This small change once measured using the sense lines it can be allowed for automatically in the strain calculations inside the data acquisition system.
Strain gauge measurements with direction
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| Figure 7: Strain gauge rosette |
Strain Gauges can be configured in a particular pattern that allows for the calculation of the overall strain component, this is often referred to as a strain gauge rosette. As shown in Figure 7, three strain gauges are placed either very close together or in some cases on top of each other. These can be used to measure a complex strain, the strain is complex because it has both amplitude and a direction. Using the Prosig DATS software it is possible to calculate the principle component of the strain, the amplitude over time and to calculate the direction as an angle from the reference X axis over time.
The picture of the gage at the top can be misleading by showing only 2 lead wires. One of the bigger sources of error due to temperature is the lead wires. This can be compensated for with a 3-wire lead configuration. In a quarter bridge setup there should be two lead wires from one side of gage and one from the other. These leads should all run together to experience whatever temperature delta is present. The resistance change is then canceled by the bridge circuit. It is stated that 3-wire should be used under the quarter bridge but does not state how it should be laid out. A simple jumper at the connector would do the job but not properly compensate for the temperature and introduce error.
I having a hard time to download and actual browse the pdf file. It took me forever so I finally quit
Mr Church,
Thank you for your comments.
Your points are well made and correct sir. The picture was intentionally a 2 wire system in order to illustrate that the strain gauge at a very basic level is a very long single piece of wire, or more simply a resistor. The first part of the article attempts to explain to the reader what a strain gauge is and how they work in a very basic sense before moving on to more complex actual real world issues.
As the article tries to show in figure 4 the classical quarter bridge configuration is in fact a 3 wire system. The wires connecting to the gauge in figure 4 should be the same length and as your rightly state they should follow the same route, for the reasons you state. By following these points the bridge will be balanced by virtue of the fact the resistance of the lead wires will be the same.
Your point about the lead wiring running together is a valid point, in most cases this sort of point is glossed over, but with experience and wisdom with strain gauges these things are learnt. Thank you for sharing your knowledge with our readers.
A strain gauge has two fixed resistors R3 and R4 of 150? each and a variable resistor R2 which is 110? at zero strain and 110.75? with the strain (R1=Rg). The gauge factor is 2.54. How to determine the strain, where the strain gauge is attached? Can you help me on this problem? Thank you sir…
Hello Mok,
Thank you for your question.
It really sounds like your trying to do it all in one giant step. Perhaps you should break the problem down into smaller chunks.
A strain gauge is like a resistor, a strain gauge bridge is made of 4 resistive elements.
All the resistors in the bridge should be of the same value, 120 Ohms is often used in industry. The resistors must be the same value to balance the bridge. There are other techniques to balance a bridge, but for clarity in this case we’ll assume the bridge must be balanced by the four resistors having the same resistance.
When you have setup your bridge you should attach the active strain gauge (assuming you have only one active element in your bridge) to the area where you are interested in knowing the strain. I am afraid we cannot offer advice about where to attach your gauge.
You should then be able to read back a value of zero volts from your bridge, then when your material under test has some forced applied, which produces a strain in the area your gauge is attached, you’ll see the voltage from the bridge change to something other than zero. This voltage change is proportional to the strain in that gauge.
You simply then use the bridge and gauge factor, supply voltage, output voltage and non-deformed and deformed gauge resistance values to calculate the strain.
What could cause large spikes (+ and -, some to infinity) in strain gauge readings? I am using strain gauges to measure the force required to cycle through exercise bikes at different levels of resistance. The resulting graphs reveal trends of required force but there are so many spikes and variations it is not accurate enough. The gauges are electrically grounded. They are subjected to vibration during the testing.
Hello Alex,
Thank you for asking a question on our blog.
Strain gauges are effectively wires, and long wires at that. They can behave like aerials and pick up electrical signals from any other sources, for example mains electricity at 50Hz is quite a common source of noise.
The sample rate you choose is very important. You must use a sample rate that reflects what you’re looking for. If you are studying the human body and motion on a bicycle we are talking a few Hz at most. For example, an effective bandwidth of 10Hz would need a sample rate of 24Hz. If you sample higher you will simply be collecting noise, you will gain no useful information below 10Hz.
Now perhaps 24Hz is not high enough for your application or is not practically possible. In this case you should consider using a low pass filter on your captured data. This will remove the effects of the high frequency noise you are seeing. The result will be the dynamic strain you are looking to study.
Hello!
Thank you for your helpful article about the strain gauges.
I would like to ask you a question. Is it possible to measure vibrations with the strain gauges? I do not want to use an accelerometer because they are too big for my application (I wanted something like the surface bonded strain gauges).
Thank you in advance!
Hello Nick,
Thank you for asking a question on our blog.
You pose an interesting question.
Strain and Acceleration are not commonly compatible types.
I am sceptical that you will be successful in this endeavour.
Acceleration, Displacement and Velocity are all related. For example an accelerometer will traditionally measure displacement and convert it to acceleration internally. The strain in the material is not really related to the acceleration.
A Strain Gauge will measure the strain in the material it is adhered to. This is not necessarily the acceleration of the component.
There may be a relationship between strain and vibration. You could measure the strain and draw a conclusion on the possible acceleration level. But you would need to first measure and categorise the relationship between the strain and vibration.
In my experience I would advise against it and try to find a way to use an accelerometer for your application.
hi
i am doing mechanical engg.in final year now.we are trying to fabricate a dynamometer to measure torque using electrical strain gauges.but we are facing the problem of slip rings.that we cannot afford them.could you please suggest any idea how to use strain gauges on a rotating shaft to measure torque with any altrnative to slip rings or any other techinique.thanx
Hello Ayesha
I am not a strain gauge expert, but I will pass your question to some of our tech guys and see what they say.
Hello Ayesha,
Thanks for asking a question on our blog.
I think you may have hit a technical barrier there, you have to pass the signals through a medium that allows for the mechanical rotation, if you just used cables they would soon become twisted and fail.
I have colleagues who have used wireless sensors, but these are even more expensive.
I would suggest that you need to find a mechanism in your budget.