Oil film in bearings

Why does a fast-spinning shaft ride on a film of oil while the same shaft turning slowly grinds metal on metal?

A steel shaft sits in a bronze shell with a few hundredths of a millimetre of clearance and a supply of oil. Turn it slowly by hand and you can feel the metal dragging. Bring it to three thousand revolutions a minute under a load of tonnes and the surfaces separate completely: nothing touches, nothing wears, and the bearing runs for decades.

The oil is the same oil at both speeds, and the load is often higher at speed. So the separation cannot be something the oil does by being oil. Speed is doing it — but how does turning something faster hold it up?

Begin with what the oil is obliged to do. Oil wets both surfaces and does not slip at them, so the layer touching the shaft moves at the shaft's speed while the layer touching the shell stands still, and everything between is sheared. So the shaft drags oil along with it, and the amount dragged through any cross-section is roughly half the surface speed times the gap.

Now the crucial step. Suppose the gap narrows in the direction of motion. Upstream, where it is wide, drag carries a certain amount in; downstream, where it is narrow, drag can carry less out. More is arriving than can leave.

Oil is essentially incompressible, so where does the excess go? It cannot pile up and cannot disappear. It must be forced back against the direction of drag, and the only thing that can do that is a pressure higher inside the narrowing region than at either end. So a converging gap with viscous fluid dragged into it generates pressure by itself. Nobody pumps it. Integrate that pressure over the bearing's area and you have a load capacity.

Look at what that argument required, because the requirements are the answer: viscosity, or nothing is dragged; relative motion, or there is no drag; and convergence, or flow in equals flow out and no pressure is needed.

That third requirement kills the folk explanations. If the mechanism were "oil is slippery" or "the oil fills in the roughness", a perfectly parallel gap between two flat surfaces would work fine. It does not: a strictly parallel film generates no pressure and carries no load at all. Which is why large thrust bearings use tilting pads that pivot to take up a slight taper, and why a plain journal bearing must run eccentric, the shaft settling off-centre so the loaded side is a converging wedge.

The second folk account — "the oil pump pressure lifts the shaft" — yields to arithmetic. Take a connecting-rod bearing twenty millimetres wide on a fifty-millimetre journal, a projected area of a thousandth of a square metre, carrying twenty kilonewtons: a mean film pressure of twenty megapascals, some two hundred atmospheres, with the peak higher still. An engine's oil gallery runs at a few bar. The pump is not lifting anything; it delivers oil and carries away heat, while the film makes its own pressure fifty times over. Bearings that are held up by supply pressure exist — turbine jacking-oil systems — and need that external pump precisely because at low speed the self-generated pressure is absent.

So the low-speed case answers itself. Halve the speed and the drag flow halves, so the pressure the wedge generates falls, so the shaft sinks closer to the shell until the gap is narrow enough to rebuild it. Keep slowing and the film thins toward the height of the surface roughness. When the tallest asperities touch, load begins to be carried by metal contact and friction rises by two orders of magnitude.

Three refinements, including one that undercuts my own account.

First, the collapse is a threshold rather than a slope. Rising friction is not itself catastrophic; what makes it so is that contact generates heat, heat thins the oil, thinner oil makes a thinner film, and a thinner film means more contact — a loop that runs away in seconds, which is why a bearing that has begun to touch fails rather than degrades. The condition is written as the ratio of minimum film thickness to combined surface roughness, full separation conventionally taken above about three and boundary contact below about one. Those are conventions, placed differently by different sources — the weakest link here, and I would not treat either as physical.

Second, the account above is incomplete in a way that matters. It assumes steady motion into a fixed wedge, yet an engine's main bearings survive loads that reverse several times per revolution, so the wedge is destroyed and rebuilt constantly. A second effect carries the load through those moments: when two surfaces approach, the oil cannot escape instantly, and squeezing it out generates pressure with no sliding at all. Squeeze-film action is why dynamically loaded bearings work despite failing my converging-wedge requirement at every reversal.

Third, the load-bearing claim: the film's load capacity comes from pressure generated by dragging a viscous fluid into a narrowing gap, so it depends on viscosity, speed and geometry, and not at all on any slipperiness of the oil. That is why those three appear together in the Sommerfeld or Hersey grouping — viscosity times speed divided by load — and why a bearing can be rescued by speeding it up, loading it less, or using a thicker oil.

• How elastohydrodynamic lubrication carries gear teeth, where contact pressures deform the metal.
• Why bearings go unstable in oil whirl and whip, and what tilting pads do about it.

Every term the collection defines is gathered in the glossary.