SaM - Accelerometer

Remeber:

An accelerometer is just simple mass-spring-dumper system with two masses:

We want to find the relation between the acceleration ${\ddot{x}}_s$ and the displacement $x_s$, such that by measuring the displacement we can measure the acceleration, so to calculate it we need:

1. Find the Lumped parameter system of this mechanical system (with the two masses):
   
2. Find the Thevenim Equivalent:
   
   Simplifying the Thevenim resistance, since $m_B\gg m_S$, so we exclude it from the load, since a parallel between $m_S\parallel m_B\simeq m_S$, also remember that $F_{ext}=m_B\cdot a$.
3. After applying the simplifications:$H(s)=\frac{m_S}{m_S\cdot s+\lambda +\frac{k}{s}}$
4. Transform into Bode form, to finally obtain the transfer function for a mounted accelerometer:$\frac{R(s)}{A(s)}=\frac{m_S}{k}\frac{1}{\frac{m_S}{k}{s}^2+\frac{\lambda }{k}s+1}$

We can draw two graphs, the Munted Behaviour graph, and the Unmounted Behaviour graph:

• Where the first one (Mounted Behaviour, blue graph), assumes that $m_B\gg m_S$, so we can simplify the calculation.
• While the second one (Unmounted Behaviour, blue graph), does not make this assumption, and we have that: the gain $\left(A_{DC}=\frac{m_s}{k}\right)$, the natural frequancy $\left({\omega }_0\right)$ and dumping ratio $\left(\zeta \right)$ all depend on $m_B$, which is not good, this means that every time you change the body on which the sensor is placed, you need to re-calibrate it.

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Memory Card

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==I have a flat gain and obviously that means that the operating range in the frequency domain is up to a maximum frequency ${\omega }_{MAX}$==

==The sensor has to be used mounted on a large object, otherwise the $A_{DC}$ will depend on the mass of the body ⇒ the sensor will have to be re-calibrated each time the change of the body sligtly changes (not good)==.