Strain gage signal conversion formula

[wimba]

Dear forum users and NI employees,

I am struggling to verify a formula that is used by LabVIEW and DAQmx for the conversion of a strain gage signal to mechanical strain.
The formula given for strain "eps" is (full bridge type III: 4 strain elements, 2x2 in the same direction):

eps = -2*Vr / ( GF * [(nu + 1) - Vr * (nu - 1)] )

see also "10. Full-Bridge III" here: https://www.ni.com/en/shop/data-acquisition/sensor-fundamentals/measuring-strain-with-strain-gages.h...

But if I try to reproduce that formula based on figure 1-15 in the linked web page, I simply get to this:

Vr = Vch/Vex = 1/4 * GF * (-nu*eps + eps - nu*eps + eps)
=> eps = 2*Vr / (GF * [1 - nu])

So either I make a mistake or the given formula is faulty. The other formulas on the linked web page don't quite work out for me either by the way.
As a reference, have a look at this: "Full bridge, 2 longitudinal-2 cross gratings", second to last entry on this page:

me-systeme/dms-bridge

The mentioned NI formula can be found here as well:

NI: Full-Bridge Type III

NI: LabVIEW Help on Convert Strain Gauge Reading VI

The formula I got for "eps" has been posted by an NI employee in a different context (with negative sign):

forum post

Can anyone explain this further?

Have a nice day!

[annav]

Hi Wimba,

can you explain the steps you took to calculate eps? I found the same formula posted for example in the whitepaper also in other sources (e.g. here).

Best Regards,

anna

[wimba]

Hello Anna,

thank you for your reply and thank your for the additional source. Which I don't understand either. Here is what I understand:

I have 4 strain gage elements in the considered strain gage bridge, type III. Two of them measure the strain "eps" (for strain "epsilon"), the other two "-nu*eps" (negative lateral strain, with Poisson ratio "nu"). This is also shown in figure 1-14 and 1-15 in the source.

The standard formula for strain gages transforms as follows (Vr...measured voltage; GF...gage factor):
Vr = 1/4 * GF * (-nu*eps + eps - nu*eps + eps) = 1/4 * GF * (-2*nu + 2)*eps = 1/2 * GF * eps * (1 - nu)  <=>  eps = 2*Vr / (GF * [1 - nu])

Apparently for the NI formula, the components of the total strain are not added as I did above. I just don't see how else to do it.

Have a nice day.

[annav · Accepted solution]

Hi Wimba,

the formula you describe is for bending (Type II) and not for axial (Type III) strain.

You have to take in account that the voltage has to be descriebed as ratios of the restistors.

See the Wheatstone Bridge for that.

Hope that helped.

Anna

[wimba]

Well, I guess you are right, bridge type II is the right one for my version of the formula.

The original problem arose because I am using a strain gage with a configuration that is not represented by either three bridge types: 2 longitudinal and 2 crosswise strain gages in one unit (and not one of each at each side of the measured object, i.e. at tensile and compressive sides). I suppose type II works for that, too.

Thank you Anna, and have a nice day.

[SamMuncy]

Hi

I was searching the site and found your comments. i have attached an NI white paper i have been studying.  Could someone please describe the reason for the negative sign in the half bridge type II strain conversion formula on page 5 0f 8?   Thanks