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Predicting snap-in potentials with COMSOL for a 3D electrostatic actuator

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Hi,

I'm trying to predict the snap-in potential for an electrostatic actuator that consists of an elastomeric membrane (fixed at the edges) with an embedded electrode suspended above a fixed electrode. I recently watched a webinar where the presenter back-calculated the potentials from fixed displacements and was able to find the snap-in potential that way. I'm wondering how you could do this with my particular set up.

Josh

7 Replies Last Post 30.12.2011, 04:30 GMT-5
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 14.12.2011, 15:44 GMT-5
Hi

have you tried to ramp up the potential until the solver fails ? then you should be close to the snap-in value

--
Good luck
Ivar
Hi have you tried to ramp up the potential until the solver fails ? then you should be close to the snap-in value -- Good luck Ivar

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Posted: 1 decade ago 20.12.2011, 18:21 GMT-5
Thanks Ivar. That worked great when dealing with a simple version of my problem where I just had a membrane suspended above a fixed electrode and a fairly significant gap between the two.

Now I have a slightly different scenario. I have a membrane that's deflecting due to an electrostatic force, only I'm dealing with a stable deflection, i.e., the deflection is small enough that no instability arises resulting in "snap-in". Pneumatic pressure is also applied above and below the membrane. Since the material is elastomeric, the lower electrode distorts. I want to predict (i) when the membrane will initially come into contact with the lower electrode, and (ii) how much of the membrane will be in contact with the lower electrode when I increase the potential further.

I've implemented a contact pair in COMSOL, but the membrane moves right on past the lower electrode.

Any ideas? (Model attached)

Josh
Thanks Ivar. That worked great when dealing with a simple version of my problem where I just had a membrane suspended above a fixed electrode and a fairly significant gap between the two. Now I have a slightly different scenario. I have a membrane that's deflecting due to an electrostatic force, only I'm dealing with a stable deflection, i.e., the deflection is small enough that no instability arises resulting in "snap-in". Pneumatic pressure is also applied above and below the membrane. Since the material is elastomeric, the lower electrode distorts. I want to predict (i) when the membrane will initially come into contact with the lower electrode, and (ii) how much of the membrane will be in contact with the lower electrode when I increase the potential further. I've implemented a contact pair in COMSOL, but the membrane moves right on past the lower electrode. Any ideas? (Model attached) Josh


Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 21.12.2011, 04:45 GMT-5
Hi

I see two potential reasons:

1) your parts are not really overlapping, but you are fooled by the automatic scaling of the plot (check the deformation plot scale factor and

set it manually to "1")

2) you have missed something in the contact pair definition and set up (master slave, mesh density ...)

I do not see any other obvious reasons ;)

But I know that contact and intermittent contact modelling is tricky

(PS I'm sitting in a train and not by my COMSOL WS, so I cannot open your model ;)

--
Good luck
Ivar
Hi I see two potential reasons: 1) your parts are not really overlapping, but you are fooled by the automatic scaling of the plot (check the deformation plot scale factor and set it manually to "1") 2) you have missed something in the contact pair definition and set up (master slave, mesh density ...) I do not see any other obvious reasons ;) But I know that contact and intermittent contact modelling is tricky (PS I'm sitting in a train and not by my COMSOL WS, so I cannot open your model ;) -- Good luck Ivar

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Posted: 1 decade ago 23.12.2011, 19:48 GMT-5
I have the scaling set to one, and I tried doing the following as well:

- Increasing the resolution of the mesh in the contact vicinity
- Manually adjusting the search distance for the contact pair (1, 0.1, 0.01, and 0.001 µm)
- Switching the source and destination boundaries

Still no luck...
I have the scaling set to one, and I tried doing the following as well: - Increasing the resolution of the mesh in the contact vicinity - Manually adjusting the search distance for the contact pair (1, 0.1, 0.01, and 0.001 µm) - Switching the source and destination boundaries Still no luck...

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 24.12.2011, 04:39 GMT-5
Hi

indeed having had some minutes to look at your model, I believe it will not work like that, the issue is that you need a mesh for the full system so that you can estimate the electric field and forces, but then you exclude part of the mesh from the solid driving the deformations so you will not observe any deformations. Furthermore, you impose a contact such that the mesh in this region will be squeeze to "0" which is a change of topology that COMSOL (or any other software I know about) cannot handle.

For me you need some ALE for your "soft regions", to have the mesh therein deformed driven by the solid physics. Then you need to set a minimum gap in your contact region to avoid that the thin mesh gets too squeezed, it must contain a finite thickness (even small a few um or nm should do)

check the model library for a few examples (and the model gallery)

--
Good luck
Ivar
Hi indeed having had some minutes to look at your model, I believe it will not work like that, the issue is that you need a mesh for the full system so that you can estimate the electric field and forces, but then you exclude part of the mesh from the solid driving the deformations so you will not observe any deformations. Furthermore, you impose a contact such that the mesh in this region will be squeeze to "0" which is a change of topology that COMSOL (or any other software I know about) cannot handle. For me you need some ALE for your "soft regions", to have the mesh therein deformed driven by the solid physics. Then you need to set a minimum gap in your contact region to avoid that the thin mesh gets too squeezed, it must contain a finite thickness (even small a few um or nm should do) check the model library for a few examples (and the model gallery) -- Good luck Ivar

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Posted: 1 decade ago 28.12.2011, 21:03 GMT-5
Think I partially figured it out.

Using a simpler, 2D axis symmetric model with a stiff lower electrode, I used ALE as per your suggestion. I designated "free deformation" in the regions above and below my deflecting membrane.

Second, I defined a minimum gap distance between the contact pair of 1E-7 m.

Third , I used a fine mesh in the contact region with the source side of the contact pair (stiff, lower electrode) meshed finer than the destination (deflecting membrane).

Fourth, I made sure that the height of the cells of the mesh in the gap region were initially set to the height of the gap. I.e., the gap contained a mesh of only one row of cells. I observed that if I had two or more cells stacked on each other then the solver crashed sooner.

At this point, the membrane is able to establish contact with the lower electrode and then even increase the area of contact with greater electric potentials.

HOWEVER, increasing the potential beyond a certain threshold leads to "inverted mesh elements" near the initial point of contact between the membrane and the lower electrode. I also noticed that the membrane seems to be impinging beyond the minimum boundary I set up for the contact pair.

Any idea what could be going wrong? (Updated model attached).

Josh
Think I partially figured it out. Using a simpler, 2D axis symmetric model with a stiff lower electrode, I used ALE as per your suggestion. I designated "free deformation" in the regions above and below my deflecting membrane. Second, I defined a minimum gap distance between the contact pair of 1E-7 m. Third , I used a fine mesh in the contact region with the source side of the contact pair (stiff, lower electrode) meshed finer than the destination (deflecting membrane). Fourth, I made sure that the height of the cells of the mesh in the gap region were initially set to the height of the gap. I.e., the gap contained a mesh of only one row of cells. I observed that if I had two or more cells stacked on each other then the solver crashed sooner. At this point, the membrane is able to establish contact with the lower electrode and then even increase the area of contact with greater electric potentials. HOWEVER, increasing the potential beyond a certain threshold leads to "inverted mesh elements" near the initial point of contact between the membrane and the lower electrode. I also noticed that the membrane seems to be impinging beyond the minimum boundary I set up for the contact pair. Any idea what could be going wrong? (Updated model attached). Josh


Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 30.12.2011, 04:30 GMT-5
Hi

Are you sure you have solved each physics independently (by replacing the expected effect of the others by an apropriate BC) and that each one solves OK, that everything is required for each physics.

For me applying every physics everywhere is not really required for your case.

then know that contact is "approximated" by a non linear pressure or spring force, that there are 2 methods propsed (see the doc and on the forum) and that intemittent contact is the most delicate to model

--
Good luck
Ivar
Hi Are you sure you have solved each physics independently (by replacing the expected effect of the others by an apropriate BC) and that each one solves OK, that everything is required for each physics. For me applying every physics everywhere is not really required for your case. then know that contact is "approximated" by a non linear pressure or spring force, that there are 2 methods propsed (see the doc and on the forum) and that intemittent contact is the most delicate to model -- Good luck Ivar

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