How a Lubricant Film Carries a Load

Why this matters

Most people picture lubricant as a cushion between two parts. It is not. A film carries load the way a hydraulic jack does: motion drags oil into a narrowing gap, the gap will not let it all through, and the pressure that builds up is what holds the surfaces apart. Nothing about that mechanism works without motion. Once you see the film as a pressure field generated by speed, a whole class of failures stops being mysterious, starting with the one below, where a machine got quieter, cooler and more efficient and ate its bearings anyway.

Before you go into the fan room

Isolate and lock out under 29 CFR 1910.147 before opening a guard, wait for the wheel to stop turning rather than assuming the contactor drop stopped it, and restrain the spring-loaded motor base before pulling belts, because that base is stored energy under the same standard. Any temperature reading on a running machine is a non-contact infrared reading taken from outside the guard: do not reach past a guard and do not put a contact probe near a rotating shaft. If you touch a bearing housing with a probe, the machine is locked out first, and you do it with sleeves secured and no gloves, because a glove near a turning shaft is an entanglement hazard rather than protection. Fan rooms are loud; use hearing protection where the exposure warrants it under 29 CFR 1910.95. If you clean a bearing with solvent, that is an inhalation route: work with ventilation, follow the SDS you are required to have available under 29 CFR 1910.1200, and if the product calls for respiratory protection it belongs to a written program under 29 CFR 1910.134. Never spin a bearing with compressed air. Compressed air for cleaning is capped at 30 psi with effective chip guarding and personal protective equipment under 29 CFR 1910.242(b), and an unloaded bearing spun by air can burst.

The call

A commercial kitchen exhaust fan, belt driven, on a variable frequency drive fitted eighteen months earlier so the building could turn it down overnight instead of cycling it. Since the retrofit it has run about eight hours a day at full speed and sixteen at roughly 30 percent. Before the retrofit the shaft bearings went about four years. Since, they have been changed twice. The machine is quieter, cooler and cheaper to run, and it is destroying bearings.

What the film actually is

Three things have to be true at once for a lubricant to carry load hydrodynamically: relative motion between the surfaces, a gap that converges in the direction of that motion, and a fluid with enough viscosity to resist being squeezed out sideways. Motion drags fluid into the narrowing gap. Continuity says the same volume has to fit through a smaller space. The only way that happens is for pressure to rise, and that pressure integrated over the contact area is the load capacity.

Take away the motion and all three legs collapse at once. This is why a stationary shaft sits on metal no matter how good the grease is, and why every start begins with contact.

The geometry matters enormously to the numbers, and this is where people carry a relationship one step too far. A journal bearing is conformal: the shaft and the bore have nearly the same curvature, the contact area is large, pressures are on the order of a few hundred psi, and the minimum film runs in the tens of micrometres. A rolling element contact is counterformal: a ball touching a raceway meets it at a point, the loaded area is smaller than a pencil dot, pressures in normal service run roughly 1 to 3 GPa, and the film runs a fraction of a micrometre. Do not carry a journal-bearing intuition into a rolling contact. The mechanism is related; the magnitudes are not in the same universe.

Why the pressure does not just squeeze the oil out

At 1 to 3 GPa, a fluid with the viscosity of motor oil should be gone before it reaches the middle of the contact. Two things save it, and together they are called elastohydrodynamic lubrication.

First, the steel deforms. Under those pressures the ball and the raceway flatten into a small area rather than staying a mathematical point, which spreads the load and lengthens the passage the oil has to traverse.

Second, and more strangely, the oil stiffens. Viscosity rises steeply with pressure. The Barus relation expresses this as an exponential in pressure times a coefficient of around 2 x 10 to the minus 8 per pascal for a typical mineral oil at moderate temperature, which at contact pressure implies a viscosity increase of many orders of magnitude. That relation is fitted at moderate pressures and over-predicts badly at the pressures inside a real rolling contact, so the honest statement is that the oil momentarily behaves more like a solid than a liquid, not that it is precisely some number of times thicker.

The practical consequence of the second effect is the one worth carrying: the film in a rolling contact is almost insensitive to load. In the Hamrock and Dowson central film thickness relation for elliptical contacts, derived under isothermal, fully flooded conditions, the load exponent is about minus 0.073. Double the load and the film gets about 5 percent thinner. That is not a typo. The oil stiffens as fast as the load presses.

The first read: the grease was not the problem

The tech started where most people start. Correct grade against the machine documentation, correct quantity, relubrication interval being kept, no water, no obvious contamination in the purge. Nothing wrong there. If the film had failed because the lubricant was wrong, the same lubricant would have failed before the retrofit too, and it did not.

The second read: the load did not change

Belt tension checked against the drive manufacturer's tension-versus-deflection table with a tension tester, machine locked out, guard off, base restrained. It was within the table.

That result is worth pausing on. A fan's torque falls with the square of speed, so at 30 percent speed the transmitted torque is about 9 percent of full. But belt tension is set at installation and the belt behaves like a spring: the sum of tight-side and slack-side tension stays close to the installed value whatever torque is passing through it. So the shaft load barely fell when the speed fell. Load was constant across the retrofit, and in a rolling contact load is the weakest lever on film thickness anyway.

The third read, and the correction that halved it

Film thickness in that same relation scales with entrainment speed to the power of about 0.68. At 30 percent speed, the speed term alone gives 0.30 to the 0.68 power, which is 0.44. On that basis the film at turndown looked like 44 percent of its full-speed value, and a specific film ratio that had been about 2.2 at full speed would land near 0.97, which is metal-to-metal territory.

That was too big a finding and it was wrong, because the same relation puts inlet viscosity at the same exponent as speed, and the bearings were running cooler. Housing readings were 15 C lower at turndown than at full speed. Note what those readings are and are not: the outer surface of a housing runs below the bearing outer ring, which runs below the oil actually entering the contact, so the absolute number is not the film calculation's input. The difference between two readings on the same housing is reliable, because the offset is roughly constant. A 15 C drop on this VG 100 mineral base with a viscosity index near 95 raises viscosity by roughly 1.8 to 2 times across the 55 to 70 C part of the curve. Take that from your own oil's viscosity-temperature chart; a higher-index or synthetic base has a flatter slope and a smaller effect.

Redo it with both terms. Speed contributes 0.44 and viscosity contributes 1.85 to the 0.68 power, which is 1.52. Net film factor is 0.44 x 1.52, which is 0.67. The specific film ratio goes from about 2.2 to about 1.47, not to 0.97.

What actually failed the bearing

A ratio of 1.47 is a mixed condition, not a boundary one, and mixed conditions do not eat a bearing in nine months on their own. The missing term was the interaction. In the life-modification approach behind ISO 281, the viscosity ratio and the contamination level do not act independently: a given cleanliness level costs very little life when the film is thick and costs a great deal when it is thin. The dust this fan had always ingested through an aging shaft seal had been harmless at a ratio above 2. At 1.47 it was not.

That is the reasoning the machine's owner needed. The retrofit did not introduce a defect. It moved the bearing into a condition where an existing, tolerated defect stopped being tolerated.

The fix, and how they confirmed it

Three changes, in order of what each actually buys.

Seal and clean. Replacing the worn shaft seals and moving to a better-sealed bearing addressed the term that had become expensive. This is the largest lever, and it is the one that would have been invisible from a film calculation alone.

Raise the drive's minimum speed, set by measurement rather than extrapolation. Because temperature feeds back into viscosity which feeds back into film, the closed-form estimate is not trustworthy for setting a minimum. They stepped the minimum up, let the machine reach thermal equilibrium at each step, and recorded housing temperature rise over room air at each one.

Re-tension to the transmitted power, not to the installed default. This barely touches the film, because the load exponent is only minus 0.073, and that is exactly why it is worth stating out loud rather than assuming. What it does buy is fatigue life directly: halving the load multiplies calculated life by eight for a ball bearing at the load-life exponent of 3. Load is a weak lever on the film and a very strong lever on the fatigue clock, and confusing those two is how a re-tension gets credited with fixing a lubrication problem it did not touch.

Confirmation was the housing-to-room temperature difference at each speed step, logged, plus bearing condition at the next scheduled service. The trap they avoided at the start was reading the cooler running as health. Frictional heat generation falls with speed, so a bearing in trouble at turndown runs cooler than a healthy one at full speed. Temperature is a good detector of a change at constant speed and a poor detector of anything across a speed change.

References

• ISO 281 for the rating-life framework and the life-modification approach in which the viscosity ratio and contamination factor interact
• ISO 76 for the static load rating and the calculated contact stress it corresponds to, which sets the scale of rolling-contact pressures
• 29 CFR 1910.147 (hazardous energy and stored energy in a tensioned drive), 29 CFR 1910.242(b) (compressed air for cleaning), 29 CFR 1910.1200 (SDS availability), 29 CFR 1910.134 (respiratory protection program), 29 CFR 1910.95 (occupational noise)
• Lubricant manufacturer viscosity-temperature data for the actual base oil and viscosity index, which sets how much a temperature change is worth
• See related: The Lubrication Regimes and Which One You Are In; What a Bearing Load Actually Is