PULLIN IN OF A TILTED MIRROR. Jan Erik Ramstad and Osvanny Ramos. Problem: How to find pullin Geometry shown in the figures Objective: Run simulations with Coventor and try to find pull in. Compare simulated results with analytical approximations. CoventorWare Analyzer. Mirror Design.
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PULLIN IN OF A TILTED MIRROR
Jan Erik Ramstad and Osvanny Ramos
CoventorWare Analyzer
Mirror Design

e
e
2
2
AV
AV
=
>
F
k
elec
2
3
2
2
g
g
CoventorWare Analyzer
Mirror Design
The parallell plate capacitor analogy (continued)
CoventorWare Analyzer
Mirror Design
Derivation of formulas for the mirror design
CoventorWare Analyzer
Mirror Design
Derivation of formulas for the mirror design (continued)
...and analyzing the stability of the equilibrium
Difficult analytically!
CoventorWare Analyzer
Mirror Design
Alternative analytical solution:
CoventorWare Analyzer
Mirror Design
Alternative analytical solution (continued):
0.4
CoventorWare Analyzer
Graph of normalized capacitance vs angle
Mirror Design
47V
Original geometry:
1.5
40V
20V
20V
Graph: Red line is analytical approximationDotted points are measured results from Coventor
40V
47V
CoventorWare Analyzer
Graph of normalized capacitance vs angle
20V
Varying k by reducing hinge thickness
0.2
1.5
15V
10V
10V
15V
Graph: Red line is analytical approximationDotted points are measured results from Coventor
20V
0.2
CoventorWare Analyzer
Graph of normalized capacitance vs angle
Varying the distance from the electrodes
35V
2.5
20V
30V
20V
30V
Graph: Red line is analytical approximationDotted points are measured results from Coventor
35V
Pull in not found
CONCLUSIONS
 We didn’t find pullin regime in our simulations.
 Instead of the parallel capacitor where , in the tilted capacitor the pullin depends on the characteristics of the system.
 The fitting of the curve was not easy. Our measured results were very sensitive to how the curve looked. The curve might have something different than a third degree polynomial dependency on the angle.
 Nonlinearities of the forces not taken into account for the analytic calculations.
50 V