hydrodynamic lubrication

Can we ignore buoyency? Assume a heavy ball?

Hydrodynamic lubrication requires rotation, so if the ball is sliding, probably not. If it is rotating at a rpm sufficient to get lift, then yes.

In hydrodynamic bearings there is contact between the journal and the bearing until sufficient rpm has been reached to lift off the shaft. If your ball is sliding and not rotating there is now hydrodynamic lubrication, only boundry layer lubrication.

I have to correct the previous comment. A hydrodynamic lubrication occurs when two surfaces witg a relative sliding speed allow a lubricator edge to form. A ball in a groove allows this so that even if it does NOT rotate a hydrodynamic effect could occur and its magnitude depends on the form of the groove. When the ball rolls as in a ball bearing the oil film works under different conditions named elastohydrodynamic lubrication. Ubder pressure the oil viscosity goes up abd offers a resistance to the contact between ball and race. In a journal rotation generates teh sliding relative speed and the difference in diameters allows the oil edge since the shaft takes oil on its surface and "pushes" it in the gap.

I am fully supporting the corrections proposed by nick-name - except for the effect of pressure on viscosity for the hydrodynamic conditions:

Yes, under pressure fluids viscosities are increasing - but for true fluids this effect is so small so it won't be considered in the very most hydrodynamic calculation methods. What makes a surface riding at a fluid film is the friction between the fluids molecules when they are forced to relative movements (from moving surface) ==> the resistance against relative movements of molecules becomes expressed by shear forces. In summary these shear forces are generating the fluid flim pressure (balancing the load) and generating a heat (the power loss from fluid film frictions). The generated heat is warming up the fluid enclosed between the surfaces (the fluid wedge) continuously. If fluids viscosity is significantly dependent on fluid temperature as valid for common oil or gas', the fluid becomes more liquid the longer the wedge. This thermal effects for lowering the fluids viscosity is much, much bigger than the effect of pressure on increasing the viscosity!

I am also of opinion the word lubrication is too less specific to be used in discussions about hydrodynamic effects. The word lubrication easily can lead to confusion because a lot of different technical aspects can be associated with lubrication having nothing to do with hydrodynamic. For the hydrodynamic effects the physical nature of the fluid and contact surfaces are important - lubrication is this discussion becomes important for the case the hydrodynamic effects are insufficient to separate the sliding surfaces fully by the fluid film (e.g. at start and stop moments of the relative movement) ==> viscosity too small, load to high, geometries insufficient, relative sliding speed too small.

What makes the slider separated from the ground? It can be explained from theories of "boundary effects" but you may imagine the following pictures(a non-theoretical approach):

The fluid is sticking at the surface of ground and slider. The fluid molecules in direct contact with the surfaces will remain sticking there. This means, the fluid in slider contact will be moved with slider velocity - and fluid at ground remains at ground (stand still for example). This difference creates a friction between the moving and not moving fluid molecules. Tese friction forces (the gradients of forces) causing other fluid molecules to be pushed into the contact wedge. This way a molecule multi-layer becomes created where the gradients of friction forces from one molecule to the other becomes minimised. If we had choosen a sufficient fluid viscosity (the higher the viscosity the higher the fluid friction resistance) the final fluid film thickness is bigger than the geometrical deviations of the surfaces in actual contact - the slider is "riding" at a fluid film and fully seaprated from the ground (no wear, no hazzle, infenite lifetime ...). If speed increases more again the fluid friction gradients rising and more molecules pushed into the wedge, the fluid film thickness increases (but also the generated temperature).

In case the fluid viscosity is clearly dependent on fluid temperature the warming up of the fluid reduces the viscosity and therefore the friction - this mechanism therefore is reducing the fluid film thickness. This is the first reason for hydrodynamic bearings (fluid = oil) why the bearing temperature needs to be watched.

Albert

The facts written above are all or mostly correct but I do not see the answer to the original post anywhere.

Hydrodynamic lubrication Will lift the ball regardless of the liquid pressure around the ball. The resulting force of the fluids in this system point slightly up from the straight or flat surface as the forces of the fluid on the ball alone are undoing itself as they are the same in all directions. The fact that the ball is immersed will not change the lifting effect of hydro dynamic lubing.

The only thing that will throw this out is:

1) gravity.

2) rotational drag of the ball in case it turns and causing fluid drag on its surface. The resulting force will then have to take into account the direction of the turning of the ball. Turning with the sliding direction will result in a drag force pointing away from the flat surface while turning against the sliding direction will result in a force down wards to the flat surface. Think of a pingpong ball with "effect" from the bat.

Many thanks to all: it "is" useful. But Nick-Name, if the ball is immersed in fluid, apart from the upwards force coming from the surface-fluid-ball interface, the ball-fluid interface at the other side will also exjert a force hindering that the ball experiences an upward displacement...am I right?

Why?

Explain it to me in another way as I think you are wrong!

The fluid exerts force on the ball how? If the density of the ball is less than that if the fluid, the ball wants to go up.

If the density of the fluid is less than the ball's, the ball will go down. If it is equal the ball will float.

What force are you talking about? All forces in a fluid are equal and the same in all directions, the same as in a gas. This is called pressure.

Really not at all definitely sure what it is you are referring to here.

One thing is sure and that is that even under the fluid's surface, the ball will experience an upward force from the hydraulic lubing effect at the ball / plate contact point, as long as the ball is moving along the plate in a flat plane parallel to the plate.

This is not really my field and this is just a comment that might interest some. I have used ultrasonic air bearings for a number of applications. No other lubricant required of course. I don't know if these would be classed as hydrodynamic. The ones I make work at about 35kHz and work very well at normal atmosphere. One or two Watts will support a 50mm diameter ball bearing for example, just a novelty I suppose. I have used them in pressurized dry Nitrogen filled gyros. No gas flow necessary of course and they only need an appropriate AC electrical supply. Its very interesting to watch them skid around on a flat glass plate. They are about as hard to keep them on the glass as a blob of Mercury.

That will be aerodynamic bearings then

I am sure you know but hydro means there has to be a fluid involved. Your ultrasonic bearings are interesting though just for fun. Have you got a website?

"I will be sincerely grateful for any enlightment in this field."

Tribology is the science of lubrication. The (ASME) Journal of Tribology would provide a great deal of enlightenment on the subject.

Journal of Tribology

Hi, the comment in post 7 is correct: there will be a negative lift on the other side where the gap is expanding.

But: if the negative pressure gradient that exists along the ball at this diverging part of the gap is generating a pressure drop that is going below the absolute zero pressure then there will be cavitation in the fluid.

This action is existing in all working hydrodynamic bearings and only by the action of cavitation the positive lift of the converging part of the gap can be used.

This cavitation can be quite severe and destroy the bearing if pure liquids are used as supporting fluids: water, mercury, gallium but no problem with oil as this is a mixture of many different molecules that give no sharp impulses on cavitation.

So if you heavily pressurise a hydrodynamic bearing you will loose all load capacity by preventing cavitation.

In the gap there is laminar flow driven by adherence of the liquid at both sides of the gap and the flow rate is proportional to gap width. So a big gap will transport much more fluid then a small gap. This excess of fluid is generating the pressure buildup as it is streaming backways and sideways.

If there is no rotation of the rotor but sliding there is the same mechanism and the same pressure buidup.

So if driving a car into a water covered street will give the same lift if the wheels rotate or are braked to a standstill!

If the wheels would rotate counterwise then the two actions would subtract and a net lift can be achieved.

This is giving rise to the first instability of hydrodynamic (and aerodynamic) bearings: called half-frequency whirl. This is a forward whirling circular motion with half the rotation frequency and at this condition no tangential lift is remaining and only the remaining radial lift is giving survivability if no big unbalance is causing failure.

If speed can go up further to the speed when the first radial resonance is equal to half the rotation speed there will be a second instability: half frequency whip: not survivable for the bearing as radial and tangential lift is vanishing. Onset of this whirling motion of whip (same direction as in whirl) is typically much faster than in any resonance. I did measurements in an externally pressurised small airbearing where at 1400rev/sec there was no whirling motion detectable (below 10nanometer) and at 4% higher speed the whirl was above 15µm and destroyed the bearing by friction welding.

RHABE

I think we are thinking along slightly different scenarios here.

If I am correct, I think you are talking about a ball in a ball bearing or ball race. In this case it would be covered by a surface at opposing ends and you could apply your explained dynamics.

The post is however reffering to a single ball on a single flat plane, which is then submerged in a liquid. The poster than argues that when the ball is sliding along this plane, the pressure of the liquid on the ball is counter working the lift of the hydrondynamic lubing action between ball and plate. Now this sounds wrong to me as the pressure of the liquid is also working on the ball in all other directions and the lift of the lubing only works upwards away from the plate.

Therefor I conclude that the first assumption made in post 7 is incorrect, but in a ball race it would be correct as you have the opposing surface as well.

Please elaborate with me on this point.

Hi case 491,

you are correct regarding the hydrostatic pressure, this is acting on all sides.

On the lower part (of the sphere) it is higher as on the upper part, the total difference is giving boyancy or not.

My arguments refer only to the dynamic part of the pressure (caused by relative sliding or rolling both giving the same lift).

The sliding of the ball will give lift by transport of fluid into the narrowing gap and the excess fluid giving rise to pressure as the fluid is escaping lengthwise and sidewise.

But this pressure rise will be with negative sign at the other side (the side of pressure buildup is where the velocity vector points at, the side of negative pressure at the rear of the velocity vector!) If there is cavitation at the rear side then there will be a substantial pressure buildup in total if surrounding hydrostatic pressure is high enough no lift capacity results.

These arguments are valid in one single contact (plane to ball or plane to cylinder or ball to raceway...) or in two or more contacts per ball.

If with two contacts as on a ball in a ball bearing these two contacts act contrary to each other with different stiffness (delta-Force/delta-displacement) as curvature is different. In a hydrodynamic bearing there can be 1, 2 or more "contacts", very often from 7 to 13, there is no contact between shaft and housing at ordinary good operation. If with multiple "contacts" in a hydrodynamic bearing you can think about many springs distributed around the shaft, each having its stiffness and displacement and in total adding up to support the load (or not at touch down).

In ball bearings - as stated by someone else above - the situation is changing a bit as the pressures in the contact zones are mostly well above 1 Kbar, so compessibility of oils will give compression of typically 50% and elasticity has to be added to theories.

In very thin oil films there has to be taken into account also capillary forces.

If cavitation is existing in ball bearings at the rear of the rolling contact then the oil is converted into an oil mist similar to to the action of carwheels on wet streets at considerable velocity.

RHABE

Rhabe, in my opinion your discussions goes far away from the initial question. Case had given a lot details, and so far I can see from profound knowledge.

The guest was asking what would happen to an fully immersed ball, moved along a not moving flat ground. This question includes two models:

1.) A ball moved through an open fluid (not limited by surrounding surfaces). For this scenario the ball for sure will not get any hydrodynamic lift perpendicular to direction of movement. The hydrodynamic forces are identical in all directions and therefore they are in a balance without effect on the ball - except in the plane of movement, where the "flow resistance" of the ball becomes effective (what makes it required to spend a force for moving the ball.

2.) A ball moved along a flat surface.
If a flat surface comes close to the ball now, the equilibrium of fluid forces at the ball becomes disturbed by the "hydrodynamic effects" between ball and ground. Nevertheless the two effects are independent overlaid. Thus we can forget the scenario 1., except the fact that ball weight becomes reduces by the density of the fluid. The hydrodynamic forces can be calculated by using the hydrodynamic (elastohydrodynamic) theory. Theoretically there will be a reaction force in the contact (sliding) zone trying to lift the ball. If this is sufficient to prevent the ball from friction contact with ground surface is quite another matter (the conditions are bad for a contact geometry ball>flat surface (if relative speed would be high enough, or ball material is not heavy ...).
At this point it need to be defined whether the ball is allowed to rotate under the impact of hydrodynamic forces or not, because this would make a severe difference!

In case the ball would be rotated around its own gravity centre by an independent drive (active rotation) the scenario would change completely.

Albert

Hi, where is the difference to the first part of my answer (one contact point)?

Same explanation, other words.

I have stated the necessary condition to get hydrdynamic lift: cavitation.

This is missed by most statements and is limiting or preventing lift.

So deep down at the bottom of the sea there will be problems as in ordinary hydrodynamic bearings if the outlet oil is restricted too much and the feeder pump is pressurizing the bearing .

RHABE