Strain gauge basics
https://www.youtube.com/watch?v=qHi8FPnWP6E
[00:00] Okay, today we're going to talk about strain gauges.
[00:05] Um, kind of how they work and we'll talk a little bit about how to measure the output of a strain gauge.
[00:11] But, uh, actually we're going to have a separate video on bridge circuits, which is the real the real way you want to go.
[00:18] That's coming up. So, what does a strain gauge do?
[00:21] It gauges strain. Okay.
[00:25] Um, how does it work?
[00:28] Well, let's let's uh let me click here.
[00:32] Basically, you take the uh strain gauge itself.
[00:36] That's this little greenish colored thing here.
[00:38] And a couple more examples over here.
[00:41] And you glue it to the surface that you're going to be straining or stretching or elongating.
[00:47] And as the the base material strains, so does a strain gauge.
[00:53] And you can measure the um effects of that strain in the strain gauge electrically and you know why the
[01:02] gauge electrically and you know why the substrate is deforming.
[01:03] It could be substrate is deforming.
[01:05] It could be force, pressure, whatever.
[01:08] It doesn't matter.
[01:11] You're just measuring how much elongation happens underneath the surface.
[01:14] So basically what happens in the strain gauge is the resistance of the device is a reasonably linear function of its deformation.
[01:19] You have a for a um metallic strain gauge, you essentially have a piece of wire that just gets wound back and forth, back and forth, back and forth, back and forth.
[01:32] So, as you strain it or stretch it like this, you get um you stretch those wires and the resistance those wires change and you can measure the change in resistance.
[01:47] And that was just a change in in the length.
[01:50] You caught that.
[01:52] So that it's active along that way.
[01:55] If I stretch it this way, um I don't really stretch those wires much.
[01:58] So you don't get much indication of strain.
[02:00] And that's a good thing.
[02:01] If I need to measure strain in a couple different
[02:03] measure strain in a couple different directions, I can use a couple of strain gauges.
[02:05] But since they they're fairly directional, I can separate the strain in this direction from the strain in that direction if I use another strain gauge.
[02:15] Sorry. Input is whatever force, pressure, torque to some mechanical thing.
[02:20] It's going to elastically deform whatever we have the strain gauge glued to.
[02:25] That deformation deforms the strain gauge and that results in a change in the resistance of that strain gauge.
[02:31] So, what causes the resistance to change and how does one measure resistance variation?
[02:36] Well, that's where we're going to go.
[02:39] So let's look at the um strain gauge itself and we can say that the resistance of the if we assume that the resistance changes we can say that the resistance at any point in time is the nominal resistance R0 the gauge and relax state plus some change in resistance.
[02:55] And we know that the
[03:03] resistance.
[03:06] And we know that the resistance of a wire is the resistivity row um the length of the wire and the cross-sectional area of the wire.
[03:17] You know this is a material property and these are geometric properties.
[03:23] So we can um essentially rewrite our delta R as the partial of resistance with respect to length times the delta length.
[03:37] So as I change the length, my resistance is going to change.
[03:39] The partial of resistance with respect to area times any change in area and the partial of resistance with respect to resistivity times the delta resistivity.
[03:51] Okay, putting all those together and substituting in, I get my delta R is the resistivity over the area times the change in length minus the resistivity times the length divided
[04:06] the resistivity times the length divided by area squared times the change in
[04:08] by area squared times the change in area.
[04:10] And basically, I'm just taking the area.
[04:10] And basically, I'm just taking the partial derivatives of this and plugging
[04:13] them in over here.
[04:13] and the length over
[04:16] area times the uh change in
[04:20] resistivity.
[04:20] And as we stretch these
[04:23] wires really all all these things happen
[04:26] at the same time um you know just like
[04:29] if I take a rubber band and if I stretch
[04:32] it it gets longer and it gets skinnier,
[04:35] right?
[04:35] So I'm changing the length and I'm changing the
[04:39] cross-sectional area as well.
[04:42] when I stretch it.
[04:44] Same thing happens to
[04:46] these wires.
[04:46] And the other thing that
[04:49] happens as I stretch it is I get a
[04:51] change in the resistivity or
[04:53] conductivity depend how you want to look
[04:55] at it.
[04:55] um because I'm and it's material
[05:00] dependent you know some materials
[05:01] exhibit this strongly some don't but as
[05:04] you strain that wire you strain the
[05:07] you strain that wire you strain the interfaces between the crystal interfaces between the crystal boundaries the boundaries between the boundaries the boundaries between the crystals in that metallic substrate and crystals in that metallic substrate and that affects how easily the electrons that affects how easily the electrons can flow and it changes that resistivity can flow and it changes that resistivity typically as you strain it the typically as you strain it the resistivity goes resistivity goes up.
[05:24] So having taken the partial derivatives substituted everything in from there um I can rearrange that and say that my change in resistivity over the base the base resistivity or change in resistance I'm sorry using the word change in resistance over the base resistance is equal to the change in the length over the base length minus change in area over the base area plus the change in resistivity over the base resistivity.
[05:54] resistance and resistivity they're just too close and I can rewrite that as 1 + 2 * V where V is poison
[06:12] ratio and that's the ratio of the ratio and that's the ratio of the transverse to the axial strain that transverse to the axial strain that strain that's the essentially the change in diameter versus change in length as you strain something.
[06:21] And epsilon is our strain and that's that's unitless strain and that's that's unitless because it's and so is poison's ratio.
[06:36] Uh it's basically for example centimeters per centimeter or delta centimeter per centimeter and or delta centimeter per centimeter and or delta inch per inch.
[06:47] So it's the change over the um the percent the fraction change in length.
[06:55] So we got our equation is 1 + 2 coons ratio times the epsilon the strain plus the change in resistivity as a fun over the base resistivity.
[07:06] So we can put those all together in a one simple number because they all tend to go together for any given material which we define as the gauge factor.
[07:09] And our
[07:14] define as the gauge factor.
[07:17] And our gauge factor is basically the change in resistance over the base resistance as a function of the strain.
[07:24] And if we substitute in here, we get with that equation.
[07:30] And we end up with simply our change in resistance over the base resistance is equal to this gauge factor.
[07:35] which is a constant based on on on all of this.
[07:44] um times times the actual strain. Okay.
[07:47] Well, not all of that because the strain is out, but it's a constant based on the material properties and um in the geometry of the device.
[07:57] Obviously, you know, uh the more the more loops I have here in this, the more the my gauge factor is going to increase because my change in length per given strain is is going to be amplified because I'm changing it many more times.
[08:16] because I'm changing it many more times.
[08:16] Okay.
[08:20] So, what are values for gauge factors and things like that?
[08:22] Um, depends on the material.
[08:24] Like I said, there are two primary flavors are metallic strain gauges and semiconductor strain gauges.
[08:29] For metallic gauges, you get a strain factor of about two to 2.22.
[08:37] And we'll play with these numbers in a couple slides.
[08:40] A base resistance 120 ohms plus or minus an ohm is not uncommon.
[08:43] They come in other values.
[08:46] You can give them up to kiloohms as a base resistance.
[08:48] the resistance the actual change in resistance as you strain it from end to end is you know on the order of 2.4 to 4.8 eight just just a few ohms, not very many.
[09:04] Um, they don't take a lot of current, 15 milliamps, 100 milliamps.
[09:08] So, they're fairly low current device.
[09:12] Um, and one good thing about the metallic strain gauges is they're not very sensitive to temperature variation.
[09:15] There they all ex
[09:18] temperature variation.
[09:20] There they all ex that any conductor is going to vary with that any conductor is going to vary with resistivity or conductance with temperature.
[09:22] resistivity or conductance with temperature.
[09:25] Metallic uh conductors are not too bad.
[09:28] Semiconductors change a lot with temperature and that's a problem though.
[09:30] Uh semiconductor strain gauges silicon phos doped with phosphorus arsenic or boron all good healthy stuff right.
[09:35] arsenic or boron all good healthy stuff right.
[09:38] Um yeah but um don't eat them.
[09:44] Okay.
[09:46] Uh gauge factors here you know they're about 20 times larger.
[09:49] Instead of being you on the order of two they're on the order of 100.
[09:50] So um the base resistances tend to be about the same and the downside you know it's nice to get that much bigger signal but the downside is they're sensitive to temperature change and you have to somehow compensate for that different ways of doing it.
[09:54] um the base resistances tend to be about the same and the downside you know it's nice to get that much bigger signal but the downside is they're sensitive to temperature change and you have to somehow compensate for that different ways of doing it.
[09:57] One would just be to measure the temperature and calculate.
[10:01] Another way when we get to bridge circuits is you will put a uh you arrange the bridge circuit with with
[10:02] nice to get that much bigger signal but the downside is they're sensitive to temperature change and you have to somehow compensate for that different ways of doing it.
[10:04] the downside is they're sensitive to temperature change and you have to somehow compensate for that different ways of doing it.
[10:06] temperature change and you have to somehow compensate for that different ways of doing it.
[10:08] somehow compensate for that different ways of doing it.
[10:10] One would just be to measure the temperature and calculate.
[10:12] Another way when we get to bridge circuits is you will put a uh you
[10:14] Another way when we get to bridge circuits is you will put a uh you arrange the bridge circuit with with
[10:16] circuits is you will put a uh you arrange the bridge circuit with with
[10:18] arrange the bridge circuit with with strain gauges in various places so that the effects of temperature actually just uh cancel each other out.
[10:29] Um so how do you measure resistance?
[10:33] Well, essentially the way a a um multimemeter works or you know regular multimeter for measuring resistance is you have a voltage source.
[10:46] You have your resistance in series with that voltage source and then you measure the current that flows through it and apply apply Ohm's law and we get that the current is the voltage source divided by the resistance plus in our case is this delta R which represents the strain and we can we can juggle the math and draw this but the bottom line here is that um we have some problems if we want to do this.
[11:14] Uh if we use a um strain gauge
[11:18] do this.
[11:18] Uh if we use a um strain gauge like one of those metallic ones, if I like one of those metallic ones, if I assume that my VS = 5 vol uh my R0 assume that my VS = 5 vol uh my R0 = 120 ohms, my delta R equ= 4.
[11:34] With no strain, I measure 8.3 milliamps.
[11:39] And with the strain applied I get you know 8.1 milliamps.
[11:43] So it's not much change in the amperage as a function of that um strain plus I have this big offset.
[11:57] I'm starting out at around 8 milliamps.
[11:59] Okay.
[12:01] Um, I can use a constant current source and measure the voltage variation much like it's just applying Ohm's law rearranged.
[12:09] And here using my numbers again, let me finish the animations.
[12:15] I think that's everything.
[12:17] Um, if I have a 10
[12:21] Um, if I have a 10 milliamp source and I use the same gauge as above, I get 1.20 20 volts in one case and 1.24 volts in the other.
[12:30] So I'm looking for, you know, 0.04 change in voltage out of a 1.2 voltage um baseline.
[12:42] You know, hooking this up to an A to D converter, you're going to get more noise than anything else because you're just it's just not going to work, you know, if you're trying to put that into a um a digital acquisition system.
[12:58] Um, I can also uh you know put it in a voltage divider circuit which which helps a little bit.
[13:10] But um in this circuit, let me just put the math up here.
[13:15] My voltage output is basically a function of both of these resistors because you know Kirkoff's
[13:23] resistors because you know Kirkoff's voltage law.
[13:25] I've got a voltage through here and I uh
[13:30] uh VR1 plus V R0 plus deltar uh equals my voltage source.
[13:39] So I can rearrange all that and I get I get this equation for my output voltage across that.
[13:48] And if our delta R is much smaller than the base resistance, which we know that it is, we can simplify the equation a little bit to look like this.
[13:55] Uh I can plug that in and I oops and I get a little better result.
[14:04] But even so, um let me give you real numbers.
[14:08] If we again we assume VS = 5 R = 120 um our deltar equals 4 I get a difference between
[14:20] between 2.583 volts and
[14:23] 2.583 volts and 250 volts.
[14:27] There's not much signal there.
[14:29] It's it's it's nicely linear which is a good thing.
[14:32] this this bias here you know like in this case this 2.5 volt bias um makes it really difficult to work with uh you get a small difference between you know moderately sized numbers that makes things difficult to work with so obviously there's got to be a better way right I mean there just has to be and it turns out that there is um and in the next video we'll talk about wheat stone bridge circuit and those have a lot of nice properties that essentially get rid of this bias and leave us with just a change in voltage around zero that we can easily amplify and work with and life is much better.
[15:14] So, hope that was interesting or at least didn't put you to sleep.
[15:18] Maybe it didn't talk long enough to put you to sleep.
[15:20] That's it.
[15:20] Thanks.
[15:20] Bye.