SaM ~ Complete Sensor • Load Cell with a Resistive Bridge

Remeber:

A load cell is a sensor for force, it takes a force and changes into a strain, its strucutre is like this:
It uses a full bridge of strain gagues, we can model it as:

We have that:$\begin{array}{l}{\epsilon }_l=\frac{{\sigma }_1}{E}\\ {\epsilon }_t=-\nu {\epsilon }_l\\ {\sigma }_1=\frac{F_1}{A}\end{array}$Where:

• $E$ and $\nu$ are Young and Poisson modulus.
• ${\epsilon }_l$ and ${\epsilon }_t$ are the longitudinal and tranverse strain.
• ${\sigma }_1$ is the stress in the direction of the force $F_1$.

While the strain gauge can be modelled as:$R=R_0(1+G\epsilon )$We put four strain gauges in a load cell, and by changing their orientation (with respect to the direction of $F_1$) we can describe each of them as:$\begin{array}{l}{R}_1=R_0(1+G{\epsilon }_l)\\ R_2=R_0(1+G{\epsilon }_t)\\ R_3=R_0(1-G{\epsilon }_l)\\ R_4=R_0(1-G{\epsilon }_t)\end{array}$Finally remember that a resistive bridge has this equation:$V_{out}=V\left(\frac{R_1}{R_1+R_4}-\frac{R_2}{R_2+R_3}\right)$

If we perform the calculations we obtain the formual of a load brige, refering to the strain:$V_{out}=V\frac{G(1+\nu )}{2}{\epsilon }_l$We can change the equation using force instead of strain:$V_{out}=V\frac{G(1+\nu )}{2}\frac{E}{A}{F}_1$Finally rember that usually $\nu \simeq 0.35$.

==As far as the effect of temperature is concerned, this is a full bridge because the elements are identical, and if they experience the same temperature, they vary in the same way, so the effect of temperature is completely cancelled==. “A full bridge rejects common mode disturbances”

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• Primary Sensor for Force: Takes a force and changes into a strain.

Now we create a full-bridge with four sensors:

• Usually $\nu \simeq 0.35$

==As far as the effect of temperature is concerned, this is a full bridge because the elements are identical, and if they experience the same temperature, they vary in the same way, so the effect of temperature is completely cancelled==.