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Home » GATE Study Material » Electrical Engineering » Electrical Elements » Strain Gages

Strain Gages

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Strain Gages

       A strain gage is a resistor in which the resistance changes with strain.  A strain gage is a thin piece of conducting material that may look like the drawing below.  (Although, there are also semiconductor strain gages - not covered here.)  It is literally glued on to the device where you want to measure strain.  If you want more information on strain gages, it is a good idea to check with manufacturers.  Here are some good links.
  • Omega Engineering - A nice writeup about strain gage basics.

  • Vishay - Links to catalogs

  • NMB Products - a page on strain gage selection

  • Entran - A page that gives good definitions of strain gage terms

  • efunda - Go to this page if you want a more theoretical treatment of strain gages.

  • PennState - Another learning resource.

        Now, assume that you have a strain gage glued on a device and the device is under stress.  When the device-under-test is put under stress it may elongate or shrink, and the strain gage is sensitive to that small change in geometry.

The small elongation in the strain gage produces a small change in the resistance of the strain gage.  Small as it is, it is what we need to use to get a voltage indicative of the strain in the bar.  To convert that small change in resistance into a usable signal is not impossible, but it takes a little doing.  Often, the strain gage is used is a bridge circuit like this one.

        What are you trying to do in this lesson?

  • Given a sensor - like a strain gage - that changes resistance as some physical variable changes,

    • Be able to use the sensor in a bridge circuit.

    • Be able to choose components for the bridge circuit that will produce good performance.

Sensors In Voltage Divider Circuits

        The kind of sensor that we will examine is a resistive sensor, and to make things specific we will look at using a strain gage to make mechanical measurements of strain.  Here's that sensor (Rs) in a voltage divider with another resistor, Ra.

Let's examine what happens in this circuit.  Some of the things that happen in this circuit include the following.

  • When the sensor resistance changes, the output voltage changes.

  • Although the voltage changes, if the resistance change is small, then the voltage change will also be small.

  • When the supply voltage changes, the output voltage will also change.

  • Let's assume that we have a typical strain gage.  Normally a strain gage has a nominal resistance of either 120Wor 350W.  Here is how a strain gage looks.

  • We need to remember that strain is the fractional change in length in a material when the material is stressed.  It is normally measured in inches/inch (or you could make that furlongs/furlong if you like.)

  • Normally, in most metals, for instance, the strain will not exceed .005 inch/inch.

  • The material will elongate no more than .5 inches in a 100 inch long piece of material.

  • If the maximum strain is .005 (.5%) then the maximum fractional change in resistance will be 1% - and that is far larger than you would expect to see since it is an extreme case.

  • We went into the laboratory where we have some strain gages attached to a ten inch bar of .05" thickness.

    • That's shown at the top of the picture, where the bar extends from the wooden block.

    • We had strain gages on both the top of the bar and underneath the bar so that one would always elongate and the other would compress.

  • The bar is clamped at one end and the other end is free.  Putting 75 cents (three US quarters) on the free end of the bar produced no measurable change in resistance with a 5-1/2 digit ohmmeter.

  • However an overloaded wallet (about 1/2 pound) changed resistance from 350.550Wto 350.520W.  The change in resistance can be very small.

        Now, if we have some sense of the resistance change, then we can think about how we will sense that change.  Because the change is very very small we will have to worry about how we are going to use that very small change in resistance  We have at least a couple of options for how we can make that measurement.

  • We can measure resistance directly.  But as we have seen, the resistance change is very small and ohmmeters will have trouble showing us much.

  • We can put the strain gage in a circuit like a voltage divider, letting the change in resistance cause a voltage change and measure that change.  We will need to check to see if that makes our situation any better.

  • Our problem is complicated by the fact that most devices that are used  for electrical measurements will measure DC voltage.  The ohmmeter is an exception.  But if we want to get our measurements into a computer and we don't want to type them in, we'll probably need a voltage.

  • So, we conclude that the voltage divider (below) is a good idea in some ways.

        Let's compute the output voltage for the voltage divider.

V1 = Vin Rs/( Ra + Rs)

  • The expression for the output voltage is one we have seen many times before.

  • The output voltage from the voltage divider increases as the sensor resistance increases.

        Now, let's compute some typical values.

  • Let's use a source voltage of 5 volts.

  • Assume we have a standard strain gage sensor - a nominal resistance of 350W.

  • We'll choose the same value, 350W, for the other resistor in the voltage divider.

        Now, we can check what happens when the resistance changes by a typical small amount.

  • We will assume that the resistance changes from 350 to 350.03W.  The typical small change we discussed earlier.

  • The question we need to answer is "How much does the output voltage change when the resistance changes from 350 to 350.03W?"

We can compute the output for both cases.

  • When the sensor is unstrained and has a resistance of 350W, the output is:

    • V1 = Vin/2.  Remember we are assuming that Ra = 350W.

  • When the strain gage sensor changes to 350.03W, the output changes to:

    • V1 = Vin*350.03/(350+350.03) = 0.50002142*Vin.

        That's a pretty small change in the output voltage.

  • When the sensor is unstrained and has a resistance of 350W, the output is:

    • V1 = Vin/2.  Remember we are assuming that Ra = 350W.

  • When the strain gage sensor changes to 350.03W, the output changes to:


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