Reducing friction at interface between a sphere and a plane?

Twigg said:

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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.



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).

Dullard said:

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

Baluncore said:

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 your input on this! I really appreciate you spending the time.
One final update on this thread. 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 ball bearings, so there is never 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. 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. 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 your input on this! I really appreciate you spending the time.

In layman's terms, friction is a force that resists one surface from sliding or rolling over another. Therefore, it can be said that friction only occurs when two surfaces are in relative motion, such as when a crankshaft is rotating in a journal bearing or when a ball bearing is rolling along its raceway.

A microscopic view of these surfaces in relative motion reminds us that each surface contains tiny, jagged asperities (rough and uneven surfaces), no matter how closely these surfaces are machined.

Without some form of separation, such as that formed by a lubricant film, these surface asperities may seize upon contact. At the very least, some abrasion, adhesion and/or ploughing of these asperities will take place as the movement occurs.

Factors That Affect Friction

A number of factors affect the frictional conditions at the interface between these two surfaces in relative motion. These factors are:

• Surface Finish — The number, roughness and even the directional contact points of the asperities on the surfaces can dramatically affect the frictional coefficient.

• Temperature — Both ambient and operational temperature can affect friction. For example, temperature is a critical element in whether an anti-wear or extreme pressure additive will be effective in certain applications.

• Operational Load — Friction varies directly with load. A load exceeding the designed capacity will dramatically increase the frictional coefficient.

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• Relative Speed — Increasing the speed beyond that which is safely specified will dramatically increase friction.

• Nature of the Relative Motion between the Surfaces — Sliding motion versus rolling motion can affect the coefficient of friction.

• Lubricant Characteristics — These characteristics are the base oil, the viscosity of the base oil and the additives combined with the base oil for the particular formulation.

The challenge is to reduce the coefficient of friction as much as possible by either eliminating the factors that may have an adverse effect on the surface in relative motion or at the very least controlling those factors.

Reducing Friction

There are several ways to reduce friction:

1. The use of bearing surfaces that are themselves sacrificial, such as low shear materials, of which lead/copper journal bearings are an example.

2. Replace sliding friction with rolling element friction, such as with the use of rolling element bearings.

3. Improve overall lubrication either by changing viscosity, using differing or improved additives or through the use of different lubricants themselves, i.e., synthetics, solids, etc.

Surface Interaction

It is important to understand how two metal surfaces within a machine interact with each other.  All metal surfaces have some degree of surface roughness.  Regardless of how smooth a surface may appear, each metal surface has high points and low valleys. 

The high points are called the surface asperities.  When the two surfaces move past each other, it is the asperities on one surface that come in contact with the asperities on the other surface.  

The number and height of the asperities on the surfaces dramatically affect the friction between the surfaces.  It is the job of the lubricant to keep these asperities apart and prevent them from contacting each other, thus lowering or eliminating metal-to-metal contact and friction. 

Without an adequate oil film to separate the metal surfaces, metal-to-metal contact occurs, asperities from the two surfaces weld together and then are ripped apart from each other by the motion of the surfaces sliding against each other, causing adhesion (smearing) and abrasion (cutting).  In severe cases, the two pieces of metal may weld and seize to each other.

If the oil film is sufficient to keep the surfaces separated but is too high a viscosity for the speed of the moving surfaces, then some drag or internal resistance within the fluid (fluid friction) will occur.  This can be thought of as friction caused by layers of oil being forced to slide past each other.

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