BOSSDIA,dmem,dbos,thc,pre,pois,ymod,sel
Maximum stress and deflection of a bossed round diaphragm under pressure

dmem    diameter of the diaphragm in µm
dbos      diameter of boss in µm
thc         thickness of the diaphragm in µm
pre        applied pressure in psi
pois       Poisson's ratio
ymod    Young's modulus of the material in GPa
sel         number denoting the selected result.
              Use 1 for maximum stress, 2 for maximum strain and 3 for maximum deflection

Notes

Diaphragms or membranes as it is sometimes called, form the basic structural element of MEMS pressure sensors. They are easy to fabricate, offer good dynamic response and can be used over a wide range of pressures. To improve sensitivity and linearity of a flat diaphragm, the center portion of the membrane is often made thicker so as to form a bossed diaphragm as shown in the figure. Such a diaphragm would exhibit higher stresses for the same deflection or lower deflection for the same stress levels. This makes the bossed design more linear when compared to a flat diaphragm. Also the thin annular area allows concentration of stress to improve the sensitivity of the device. It is particularly useful in sensing low pressure signals. The boss also provides over load protection. The boss ratio 'dbos/dmem' should be greater than 0.15 and thickness ratio 'tbos/thc' should be greater than six for the boss to be effective.

This design interface can be used to determine the maximum stress and deflection of a bossed round diaphragm.  In this analysis the outer perimeter of the diaphragm is held firmly and a uniform pressure is applied from top. The applied pressure will deflect the diaphragm till the elastic forces balance  the pressure. The maximum displacement of the boss is calculated. The radial stress at the outer perimeter and inner perimeter near the boss are same but opposite in sign. The maximum strain corresponds to the maximum radial stress.

The plot shows the deflection of the bossed diaphragm under pressure. The X axis gives the position from the center towards the outer perimeter for the top fiber of the diaphragm. The deflection flattens off where the boss starts. Using the cross hair tool, the defection at any distance from the center can be calculated.

Assumptions

-The default material is Silicon with a Young's modulus of 180GPa and Poisson's ratio of 0.3.
-The diaphragm is assumed to be held rigidly at the outer edges. In reality it may be slightly flexible.
-The property of the material remain constant across the diaphragm.
-The diaphragm is not subjected to any pre-stress and the pressure is the only load acting on it.
-The location of the maximum stress may vary slightly based on the boundary condition.
-Bending effects are considered. Non-linear effects due to tension is ignored.
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Mechanics > Structures > Diaphragms > Round Diaphragm > Bossed Diaphragm

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