SaM ~ Complete Sensor • Accelerometer with a Resistive Bridge

Remeber:

Suppose to have an accelerometer where we measure the strain via a strain gauge, here’s a simple structure:

• All the springs and dumpers can be “merged” together in a single spring.
• ==The mass can move in every direction and we don’t exit from the elastic regime==.
• The resistances values will be:$\begin{array}{l}{R}_{1,3}=R_0\left(1-G\left(\frac{m_s}{K\cdot l}a\right)\right)\\ R_{2,4}=R_0\left(1+G\left(\frac{m_s}{K\cdot l}a\right)\right)\end{array}$Where: $\frac{m_s}{K\cdot l}a={\epsilon }_l$
• Also we have to consider that the strain gauges are pre-deformed so:$\begin{array}{l}{R}_{1,3}=R_0\left(1-G\left(\frac{m_s}{K\cdot l}a\right)+G{\epsilon }_0\right)\\ R_{2,4}=R_0\left(1+G\left(\frac{m_s}{K\cdot l}a\right)+G{\epsilon }_0\right)\end{array}$

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• All the springs and dumpers can be “merged” together in a single spring.
• ==The mass can move in every direction and we don’t exit from the elastic regime==.

Where:

• $r_{\infty }$ : regime value of the elongation.
• $A$ : amplitude of the acceleration.
• $m_S$ : sismic mass.
• $K_{eq}$ : elastic constant of the equivalent system.
• $K_S$ or $K$ : elastic constant of a single sensor/spring.
• $l$ : length of the spring.
• ${\epsilon }_1$ : strain in the single $x$ direction we are considering.
• ${\epsilon }_l$ : longitudinal strain.
• ${\lambda }_{eq}$ : equivalent damp coefficient.
• $G$ : the strain gauge factor.

So I have an output, which is linearly related to the acceleration.

Actually, since they are pre-deformed, I have to add to this deformation, due to acceleration, the ones which were impressed at the beginning, so $+G{\epsilon }_0$ :