SQDCANT,len,wid,thc,gap,den,ymod,sel
Squeeze film damping of a cantilever beam

len         length of the beam in µm
wid        width of the beam in µm
thc         thickness of beam in µm
gap        air gap distance in µm
den        density of the material of the beam in kg/m3
ymod     Young's modulus in GPa
sel          number denoting the selected result.
              Use 1 for quality factor and 3 for damping ratio

Notes

Air film damping plays a significant part in the design of micro electro mechanical devices. If a stationary surface is placed in close proximity to a cantilever, the air in between the cantilever and the surface will be squeezed when the beam moves towards the surface developing a pressure gradient across the width of the beam. This will push the air out of the gap. Alternately, when the cantilever moves away from the surface, the pressure in the gap is reduced and air flows into the gap. The work done in this process would reduce the energy of the cantilever and thereby the air acts as a damper and the process is called squeeze film damping.

Forces on the moving cantilever from gas film can be obtained from linearized Reynolds equation. The coefficient of damping force can be calculated from this provided the oscillating frequency of the cantilever is low and the pressure is near ambient. The damping ratio is calculated from it. This design form can be used to estimate the damping ratio for the first mode of vibration of the cantilever which is up and down displacement. The quality factor is calculated from the damping ratio for slight damping.

The plot shows the variation of damping ratio with the air gap thickness. Using the crosshair tool, the damping ratio for any air gap thickness upto 20µm can be estimated. It can be used to calculate the air gap that would give a damping ratio of 0.7 for optimum damping of a harmonically forced vibration.

Assumptions

-The default material is Silicon and ambient is air with viscosity of 1.8e-5 Pa.sec at 20°C.
-The damping ratio is calculated for the first mode of vibration (normal vibration) of the cantilever.
-The frequency of vibration of the cantilever is low and air pressure is near ambient to keep the squeeze number small.
-The air gap is small compared to the lateral dimensions of the surface.
-The displacement of the beam is small.
-Pressure drops to ambient pressure at the edges of the beam.
-Inertia of fluid is neglected.
-Gas obeys ideal gas law.
-The system is isothermal.
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