Hi,
I am trying to obtain the gauge factor equation (G = dR/R*epsilon) from the resistance, electrical conductivity, length, and cross sectional area, A (width and thickness) of material. I have worked the problem several times, however, I feel that I am just throwing G into my equations randomly because I know what the final equation looks like for the gauge factor. Can anyone give me any advice on what I may be doing wrong? I want to validate why I can put the G there in equation (4). I have attached my analytical solution for your review.
Dear Sir
To calculate the Gauge factor in this case is much better to apply total differential
of the formula foe rtesistance than to make a logarithm.
The result depends which elements of the equation You consider as variables
(resulting from inacurate measurements).
The way to calculate G in case You regard L and A as variables is presented in attached page.
Best regards -from
Piotr Wach, Technical Univerity of Opole, Poland
Suggest use basic definition of GF:
1. Gf = (deltR/R)/eps where eps = strain =deltl/L where R =rest resistance
2. Obtain Rstrain using Poisson.s ratio for area vs length
3. deltR =( Rstrain - R)/R maybe simplify
4. Plug into 1 above...
Cheers
Dear Jamel,
welcome!
You overlooked the variation of the conductivity of the material with the strain. The conductivity of the material changes with the stain.
To get dR/R let us write down the expression of the resistance R as:
R =L/ sigma A
Taking the log of both sides then log R= log L - log sigma - logA,
differentiating both sides, and dividing by R, one gets:
dR/R = dL/L- d sigma/sigma - dA/A,
dividing by dL/L the relative stain , one gets:
G= 1- Gsigma- Ga where G sigma is the gauge factor due to sigma, and Gais the gauge factor due to area.. The other note is that dA/A can be never zero as hinted Narasim since dL/L is related to dA/A
So, the guage constant is a summation of multiple gauge constants.
Best wishes
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