Reducing friction at interface between a sphere and a plane?

[Twigg]

I have a flat planar part made of crystalline sapphire (about ~2k weight, and polished to a mirror finish) that rests on three ball bearings, and I want to minimize the static friction at these 3 interfaces. The ball bearings are fixed so they cannot roll, and the sapphire part can only slip. (For the sapphire part, the c-axis is along gravity.) The one annoying constraint is that any materials used have to be ultra-high vacuum (UHV) compatible. For example, dry molybdenum disulfide powder is fine but anything containing oil is not fine (except for specialty UHV greases). Bonus points if the materials are also compatible with liquid helium temperatures (4K), but that's not a hard requirement for right now.

I can change the material of the ball bearings (I'm using teflon ball bearings right now), but I can't change the material of the sapphire part. The ball bearings cannot be smaller than 3/32in or bigger than 3/16in (I use 1/8in right now).

I tried coating the teflon balls with TaS2 powder (similar to MoS2 powder, but supposedly lower friction), but I don't feel any improvement sliding the sapphire part around. I also tried applying Apiezon L-grease (a UHV-compatible grease that is recommended for lubrication), and that made a slight improvement.

I believe the geometry the sphere/plane interface results in a lot of stress, and I fear that the lubricants are being "squished" out of the interface. I checked this by coating the ball bearings in grease and TaS2 powder, so they pick up a crusty layer of powder, and putting the sapphire part on top of them. When I did this, I saw that there was a tiny bald spot on the ball bearings where the sapphire part had been. I interpreted this as the weight of the sapphire part was "squishing" out the grease/powder mixture from the point of contact.

Any advice? Sorry, I know it's an oddball situation.

 

[anorlunda]

Any chance of injecting a gas or liquid through the bearings to levitate the sphere? Maybe liquid helium.

 

[Baluncore]

Any advice? Sorry, I know it's an oddball situation.

Hexagonal boron nitride = BN-h = white graphite, an insulator and face powder.

The PTFE balls will flatten slightly due to the load. Dirt will become embedded in the surface of the PTFE ball. Lubricant will be squeezed out of the gap and not replaced, unless it can be coated onto the sapphire plate.

A steel ball, will have less contact area and will embed less dirt than PTFE.

I would consider electrostatic attachment of the lubricant to the steel balls, or to the sapphire plate. It might be possible to have BN-h flow across the ball surface, towards the point of contact with the sapphire plate.

 

[Twigg]

Any chance of injecting a gas or liquid through the bearings to levitate the sphere? Maybe liquid helium.

It wouldn't be possible because of our vacuum requirements. Helium is really hard to pump out and I feel like the amount of flow needed to levitate the sapphire part (is that what you meant?) would be impossible to pump out continuously.

The PTFE balls will flatten slightly due to the load. Dirt will become embedded in the surface of the PTFE ball.

Nominally, the PTFE balls and sapphire part are as clean as we can make them (sonicated in degreaser and then methanol). At least, I feel confident that there isn't any dirt bigger than 50 microns or so, but I haven't checked it under a microscope to look for smaller particles.

A steel ball, will have less contact area and will embed less dirt than PTFE.

So I forgot to mention, but I did try this with stainless (440C) balls of the same dimensions. From what I could feel, the friction was much greater on the stainless balls than the PTFE balls. However, adding L-grease seemed to make a much bigger improvement on the stainless balls; in contrast, it made only a slight improvement on the PTFE balls. (Sorry I don't have any quantitative data for this.)

I would consider electrostatic attachment of the lubricant to the steel balls, or to the sapphire plate.

Is there a good way to increase the electrostatic attraction between the powder and the balls or the plate? I noticed it seems to happen naturally (to an extent) between the TaS2 powder and the PTFE, but it was a really sparse coating.

I've been thinking of adding a thin sheet of low-friction material to the bottom of the sapphire plate. I was going to start with putting pieces of teflon tape (not the plumbing kind, but an adhesive-backed teflon film) on the sapphire plate where it touches the balls as the easiest solution.

 

[Baluncore]

I've been thinking of adding a thin sheet of low-friction material to the bottom of the sapphire plate. I was going to start with putting pieces of teflon tape (not the plumbing kind, but an adhesive-backed teflon film) on the sapphire plate where it touches the balls as the easiest solution.

I don't know what adhesive Teflon tape you are considering, but there is a PTFE sheet material called Turcite B available. It is used to surface the slide ways on machine tools. Turcite, starting at 0.5 mm thickness, is available on the web from eBay, Amazon and AliExpress.

Where a cast iron way is being upgraded to Turcite, only about 1/3 of the original surface area need be covered. If the whole area is covered, a "stick and slip" chatter can occur. Maybe a steel ball on Turcite will show some improvement over a PTFE ball on sapphire.

 

[Twigg]

only about 1/3 of the original surface area need be covered. If the whole area is covered, a "stick and slip" chatter can occur.

Will that affect the static case? The sapphire part isn't supposed to move at all. Sorry if that wasn't made clear in the original post. I know it's a little weird that we need low friction for a part that doesn't move, but regardless our experimental data says low friction = better performance.

Can you think of any materials that are hard (like steel) but have low friction (like teflon) and that can be machined into a ball? I was looking to see if anyone makes a ball out of h-BN or MoS2, but I came up empty. After a quick google search, I found some people make h-BN rods, but I didn't see anyone making balls.

 

[Baluncore]

Can you think of any materials that are hard (like steel) but have low friction (like teflon) and that can be machined into a ball?

BN meets both those requirements, but not at the same time. Cubic BN is one of the hardest materials, chemically deposited onto cutting tools to reduce wear. Hexagonal BN is one of the most lubricious.

Take a tungsten carbide bearing ball for rigidity, coat it with c-BN for hardness, then dust it with h-BN for lubrication.
eBay or Google 'tungsten carbide bearing ball'

If you want to position the sapphire plate on three balls, then eliminate ball surface friction that might bend the sapphire, you might hit the plate with a decaying (ultrasonic?) oscillation. That will reduce hysteresis, relax the contact patches, and reduce the stress in the sapphire plate. Consider sticking a piezo transducer to the bottom of the plate.

 

[Tom.G]

According to this site:
https://www.engineeringtoolbox.com/friction-coefficients-d_778.html

The COF of Sapphire is 0.4

The lowest listed static friction is 0.03, but that is Ice on Steel, clearly not a vacuum option.

The next lowest is Teflon on Teflon (PTFE) at 0.04, either dry or lubricated. That might be doable for you; especially if the support can be a small flat patch rather than a spherical point contact. Since adhesives are problematic, you MAY have to machine a shallow recess to hold teflon blocks in place.

Cheers,
Tom

p.s. Please keep us updated on what you find that works. We like to learn too!

 

[Twigg]

If you want to position the sapphire plate on three balls, then eliminate ball surface friction that might bend the sapphire, you might hit the plate with a decaying (ultrasonic?) oscillation. That will reduce hysteresis, relax the contact patches, and reduce the stress in the sapphire plate. Consider sticking a piezo transducer to the bottom of the plate.

Ok this idea of relaxing stresses in the contact area is really interesting to me, because the effect we're trying to mitigate is a non-reproducible change in the elasticity of the sapphire plate. By non-reproducible, I mean the effect changes every time we pick up the sapphire plate off the ball bearings and put it back down on the ball bearings. The variance in our measurements are higher for ball bearings with higher coefficients of friction.

Can you comment on the origin of these stresses? Even better, do you have some references (or even search terms) I do a literature search with? Thank you!

if the support can be a small flat patch rather than a spherical point contact.

We've been thinking of switching the ball bearings out for rod-shaped stand-offs. It's in the works.

Since adhesives are problematic, you MAY have to machine a shallow recess to hold teflon blocks in place.

If push comes to shove, there are varnishes that we can use as an adhesive. We'd want to avoid this route because the varnish is darn hard to remove once it solidifies. Machining new features in the sapphire plate isn't an option though, as the geometry has already been optimized for other performance metrics with finite-element studies.

Thanks all for your advice so far! I will keep updating the thread as time and circumstance allow.

 

[256bits]

Any advice? Sorry, I know it's an oddball situation.

Why the balls instead of a flatter surface to reduce the deformation of the telfon?

Theoretically, as this is a point contact, the stresses approach infinity. But realistically, materials deform spreading the stress out. You could look up Hertz contact stresses to become familiar with it. As an example,
https://my.mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf

You would be right that the 'lubricant' is being squished out, and would not replenished ( as is done with ordinary steel balls rolling in a bearing assembly - the balls ride on a thin film of lubricant - same for journal bearings, or any other mating parts with lubricant between them ). There probably is still some lubricant on both surfaces, at least within the pits and valleys of each material.

One thing to look at is superlubricity.
https://www.sciencedirect.com/science/article/abs/pii/S0301679X21001547#:~:text=Superlubricity can be divided into two,[4], [5], [6], [7], [8] ].&text=Superlubricity can be divided,[6], [7], [8] ].&text=be divided into two,[4], [5], [6], [7],
discusses glycerin and water, although that seems to not work as well in a vacuum.

Another study, ( an original they say for liquid lubrication in a vacuum ), as it is a fairly new field, using an acid and water, whereby the hydrogen bonds hold the water from evaporating so that a low Cof can be achieved for a long time in a vacuum.
https://www.sciopen.com/article/10.1007/s40544-018-0212-z

 

[jrmichler]

By non-reproducible, I mean the effect changes every time we pick up the sapphire plate off the ball bearings and put it back down on the ball bearings. The variance in our measurements are higher for ball bearings with higher coefficients of friction.

The reasons for this are the effect of friction combined with deflection caused by Newton contact stress. The following are two good sources to learn about this:

Precision Machine Design, by Alexander H. Slocum, available from Society of Manufacturing Engineers: https://cart.sme.org/PersonifyEbusiness/Store/Product-Details/productId/118130#.

Principles and Techniques for Designing Precision Machines, Ph.D. Thesis by Layton Carter Hale. Available online as a PDF from multiple sources. Here's one such source: https://dspace.mit.edu/handle/1721.1/9414.

My hazy recollection is that the Hale thesis is the better source, but both are good.

 

[Twigg]

Why the balls instead of a flatter surface to reduce the deformation of the telfon?

Why indeed. The original argument for this design choice is that you can't control where the point of contact will be on a flat surface, so point contact will be easier to model and will allow us to achieve a higher level of symmetry in the constraining forces. That idea is being re-evaluated.

Principles and Techniques for Designing Precision Machines, Ph.D. Thesis by Layton Carter Hale. Available online as a PDF from multiple sources. Here's one such source: https://dspace.mit.edu/handle/1721.1/9414.

Page 205 had exactly what I needed to confirm my hunch. Thank you!!!

Any advice as far as reducing the nonrepeatable frictional stress from mounting the sapphire plate, besides reducing coefficient of friction?

The ultrasonic relaxation sounds plausible but risky (there are other things permanently and rigidly attached to the sapphire plate that I don't want to hit with ultrasonic). I might start with a tranducer in the audio frequency band (speaker?).

 

[Baluncore]

Can you comment on the origin of these stresses? Even better, do you have some references (or even search terms) I do a literature search with? Thank you!

I have no specific references, just some experience with stress relief by hitting things.

Remember that you must display unto them the instruments of torture, before they will recant.

During and immediately after welding cast iron, while some components of the material are still plastic, the weld area is tapped gently, with a hammer, to release local stresses as the material cools. The low amplitude vibration adds to the greatest local stresses, and so relieves those stresses in a direction towards a lower stress state. The aim is to avoid having stresses "frozen" into the material, as that would directly reduce the strength of the bulk material, and can result in open cracks.

Another relaxation process analogy might be with the demagnetisation of a magnetic material, through the use of a degaussing coil with a diminishing oscillatory field.

The ultrasonic relaxation sounds plausible but risky (there are other things permanently and rigidly attached to the sapphire plate that I don't want to hit with ultrasonic). I might start with a tranducer in the audio frequency band (speaker?).

I am not advising abuse of the equipment, but a more gentle seduction of the instrument. You would do well to identify the possible resonant modes present in the sapphire slab assembly, and what the natural frequency of those modes might be. The sapphire plate might be over-damped, preventing the vibration needed to relax the ball contacts.

The fundamental problem appears to be that the weight of the sapphire slab sets too high a static frictional force against the balls. Horizontal stresses can remain, up to that stiction limit, unless something can be done to anneal the situation.

I expect that forces of evil, less than the contact stiction, will accumulate in the ball contacts as the temperature of the sapphire slab and the ball support structure changes over time. The relaxation process may need to be repeated periodically as the experiment continues. Maybe your laboratory is just too quiet to relieve the stress through normal background noise.

If the oscillatory motion was vertical, the slab could momentarily jump off the balls, then it would land in a new position, having reduced the horizontal static frictional forces in the process. By reducing the amplitude of the induced motion, the stresses introduced by the initial larger amplitude disturbance are reduced by the later smaller movements.

If the motion induced was horizontal, the contact patches with asymmetric stresses would tend to become more evenly balanced, rounder, with a more parabolic pressure field.

 

[Twigg]

Quick update:

Tl;dr: Grease works, dry powders don't.

I measured coefficients of friction for different ball bearing materials, and recorded them. Some of the notable points are:

• PTFE ball on sapphire (dry): $\mu_s=0.129\pm0.009$
• PTFE ball on sapphire (greased): $\mu_s=0.028\pm0.001$
• PTFE ball on PTFE tape (dry): $\mu_s=0.121\pm0.003$
• PEEK ball on sapphire (dry): $\mu_s=0.151\pm0.008$
• PEEK ball on sapphire ($\mathrm{MoSe_2}$ powder): $\mu_s=0.163\pm0.003$
• Stainless ball on sapphire (dry): $\mu_s=0.201\pm0.007$
• Stainless ball on sapphire (greased): $\mu_s=0.098\pm0.002$

I tried other combinations, but these are enough to give you the jist of it. The coefficient of static friction was calculated from the critical angle of an inclined plane that causes the sapphire plate to slip.

Weirdly, other data suggests that we are still seeing effects of unrelaxed frictional forces in the case of greased PTFE on sapphire, even though the coefficient of friction is 4 times less. We haven't seen any changes in the other observables between greased and ungreased PTFE, but maybe we just haven't gathered enough statistics yet. Unclear. Will update when I have more information.

 

[Dullard]

I really like Baluncore's idea: Rattle it occasionally.

Keeps going through my head: magnets. If you could 'float' the balls magnetically...

Also: Can you suspend it via 3 wires, rather than 'parking' on 3 balls?

 

[Twigg]

One final update on this thread.

Ok this idea of relaxing stresses in the contact area is really interesting to me, because the effect we're trying to mitigate is a non-reproducible change in the elasticity of the sapphire plate. By non-reproducible, I mean the effect changes every time we pick up the sapphire plate off the ball bearings and put it back down on the ball bearings. The variance in our measurements are higher for ball bearings with higher coefficients of friction.

After taking a truly painful amount of data, we found that the magnitude of non-reproducible changes in the elasticity of the sapphire plate are linearly related to the coefficient of static friction between the sapphire plate and the ball bearings. In other words, if I plot standard deviation of elasticity vs coefficient of friction, I get a very clear linear trend. Consequently, we found that PTFE ball bearings with L-grease is the winning combination. So, at the very least, I know I have been barking up the right tree.

@Baluncore's suggestion of forcibly relaxing the pent-up strain in the sapphire plate is the most appealing to me right now. The problem is that the sapphire plate is flat and featureless where it sits on the ball bearings, and so if you smack it (or something near it) it will just slip (and that's bad because we need it to stay aligned with nearby structures). I would like to add some additional constraints to keep the sapphire plate from slipping off to one side, but I don't have time for that right now (since it could compromise other figures of merit and start a whole new sad adventure). I found a computational paper that actually simulates a procedure for relaxing built up strain in a spherical indenter by applying a driving oscillatory force horizontally. It seems really similar to degaussing, just like Baluncore was saying. The only new thing I took away from it is that the applied force has to (initially) exceed the frictional force and cause slipping.

Another, interesting (but not helpful to me) idea I found in the literature is to cut flexures around the surface that the ball bearings contact on. This will allow the contacting surface to deform and follow with the ball bearings, so there is never a relative motion between the two (which would lead to a shear strain). Here's the paper that discusses this strategy. Unfortunately, cutting thin flexures into a piece of hard, brittle sapphire is probably impossible (definitely ill-advised). Might be useful to someone else.

Also: Can you suspend it via 3 wires, rather than 'parking' on 3 balls?

It's a good idea, just requires a lot of hard work just to test it. I'm trying to make do with what I've got. You know how these hard projects go... bandaids and duct tape

You would do well to identify the possible resonant modes present in the sapphire slab assembly, and what the natural frequency of those modes might be.

I would guess that these modes would be almost entirely compressional modes of the ball bearings, since they're a mere 1/8" sphere of teflon as opposed to the chunky, rock-hard sapphire plate. I get answers ranging from 10Hz (using the Hertzian contact radius as my length scale) to a few hundred Hz (using the ball radius as the length scale). It's unclear to me if inertial forces would help or hurt the relaxation process.

Thanks all for you input on this! I really appreciate you spending the time.