How an oil film carries load

In 1883 Beauchamp Tower was measuring friction in a railway axle bearing for the Institution of Mechanical Engineers when he drilled an oil hole in the top of the bearing’s cap, in the middle of the loaded zone. Oil welled out of the hole instead of running in. When he plugged it, the plug was pushed out. A gauge fitted to the hole showed a pressure far higher than anything the oil supply could produce, high enough to carry the axle’s load. The shaft was floating on oil it was pumping for itself.

Osborne Reynolds explained the result three years later in a paper that founded the theory of lubrication. This chapter follows his explanation: how a fluid dragged into a narrowing gap builds pressure, how a turning shaft creates its own narrowing gap by moving off centre, and how the three regimes of lubrication, boundary, mixed and full film, arise. It introduces the running case, FB-75’s fan bearings, and ends with a supplier’s suggestion that a heavier oil would reduce the bearings’ friction.

The wedge

Take two surfaces separated by oil, one stationary and one sliding, and tilt them so that the gap narrows in the direction of sliding. The moving surface drags oil with it, because oil sticks to both surfaces and the layers in between are sheared, as in Chapter 1 of Viscosity by the Numbers. If the gap were uniform, the oil carried in at the wide end would leave at the other end at the same rate. But the gap narrows, so the shear flow at the narrow end can carry less oil than enters at the wide end. Something must make up the difference, and that something is pressure: oil pressure rises inside the gap until it pushes back against the incoming flow and squeezes extra oil out at the narrow end and at the sides. The pressure, acting over the surface area, carries load.

Figure 1A converging oil film generates pressure

Three things are needed: relative sliding, a viscous fluid between the surfaces, and a gap that converges in the direction of sliding. Take any one away and the pressure vanishes. That is why a stationary shaft cannot carry its load on a film, why a bearing with no oil wipes, and why a gap that diverges generates suction, not pressure.

Reynolds wrote this balance between shear-driven flow, pressure-driven flow and gap shape as a single equation, the Reynolds equation, which every hydrodynamic bearing calculation since has solved in one form or another. The calculations in this book use one of its classic approximate solutions, for bearings that are short compared with their diameter.

How a journal makes its own wedge

A journal bearing has no tilted pad. Its shaft, the journal, turns in a slightly larger bore, and the clearance between them, a few hundredths of a millimetre, is the same all round when the journal is centred. A centred journal generates no pressure, because a uniform gap has no wedge. Under load, though, the journal is pushed off centre. The gap then narrows on one side and widens on the other, and the narrowing side is a wedge into which the turning journal drags oil. Pressure builds there and pushes the journal back. The journal settles at the position where the film’s pressure exactly balances the load.

The offset of the journal’s centre from the bore’s centre is the eccentricity, and divided by the radial clearance it is the eccentricity ratio, from 0 for a centred journal to 1 for a journal touching the bore. A lightly loaded or fast bearing runs nearly centred; a heavily loaded or slow one runs close to the bore. Chapter 4 calculates where FB-75’s journals settle and how thin the film is at its narrowest.

The family of plain bearings

“Plain bearing” covers a wide family, from a greased bronze bush in a hinge to the tilting-pad bearings of a power station turbine. They differ mainly in how much of their life they spend in a full film and in how the oil reaches them.

Figure 2Common kinds of plain bearing

Kind	Usual lubrication	Usual regime	Typical use
Dry or polymer bush	None, or solid lubricant in the material	Boundary	Pivots, linkages, slow or oscillating motion
Oil-impregnated sintered bush	Oil held in the pores	Boundary to mixed	Small motors, fans and appliances
Greased bronze or steel bush	Grease, topped up	Boundary to mixed	Pins, slow heavy pivots
Oil-ring or bath-lubricated sleeve	Oil lifted from a sump by a ring	Full film in running	Fans, pumps, motors, FB-75
Pressure-fed sleeve	Oil pumped in from a system	Full film	Engines, compressors, large motors
Tilting-pad journal or thrust	Pressure-fed or flooded	Full film	Turbines, high-speed or heavily loaded shafts
Hydrostatic	Oil supplied under high pressure	Full film even at rest	Machine tool ways, telescopes, very slow heavy shafts

The distinction that matters most for calculation is between bearings that run on a full hydrodynamic film and those that do not. A full-film bearing is designed by calculating the film, as Chapters 3 to 7 do; a bush that runs in boundary or mixed lubrication is chosen by its material’s limits on load, speed and their product, as Chapter 2 does. Using one method on the other kind of bearing is a common and costly error.

Hydrostatic bearings deserve a word because they look similar and work differently. Their pressure comes from an external pump, fed into pockets in the bearing surface through restrictors, and it carries the load whether the shaft turns or not. They need a pump, filtration and a supply that must never fail, and they are used where a hydrodynamic film cannot form, at zero or very low speed, or where extreme stiffness and accuracy are needed. Tower’s oil hole, which let film pressure escape, is a reminder that a hydrodynamic bearing’s oil feed must never be placed where the film is generating its pressure, a point Chapter 7 returns to.

Three regimes of lubrication

The film does not appear all at once. When a machine starts, its journal sits on the bottom of its bore, touching through the peaks of the surface roughness on both parts, with nothing but adsorbed oil and additive films between them. As it speeds up, the wedge begins to work and the film thickens until it separates the surfaces completely. Each stage has its own friction and its own wear.

Figure 3The three regimes of lubrication in a plain bearing

Regime	Film	Friction	Wear	Where FB-75 meets it
Boundary	Thinner than the surface roughness; load carried by contact	High, set by the surface films and materials	Possible	Starting from rest; turning by hand
Mixed	About the size of the roughness; load shared by film and contact	Falling steeply with speed	Light	The first seconds of a start and the last of a stop
Full film (hydrodynamic)	Many times the roughness; no contact	Low, rising slowly with speed and viscosity	Almost none	Normal running at 1,480 rpm

Stribeck plotted friction against speed for bearings at the start of the twentieth century and found the curve that now carries his name: high friction at low speed, falling steeply to a minimum as the film forms, then rising slowly as the full film’s viscous shear grows with speed. The useful variable for the horizontal axis, often called the Hersey number, groups the viscosity, speed and unit load: viscosity times speed divided by unit load. A higher Hersey number means a thicker film.

Figure 4Reading the Stribeck curve from left to right

1. 1Rest and very low speedBoundary friction; surfaces in contact through their roughness
2. 2Rising speed or viscosityThe wedge builds pressure; contact falls; friction drops steeply (mixed)
3. 3Minimum frictionThe film just separates the surfaces; little margin
4. 4Normal design pointFilm several times thicker than needed; friction rising slowly
5. 5Very high speed or viscosityFull film throughout, but viscous shear makes friction and heat climb

A well-designed bearing runs to the right of the minimum, where a disturbance that thins the film, such as a load spike or a hot spell, moves it towards lower friction rather than into contact. That margin is what Chapters 4 to 6 quantify.

Viscosity is what the wedge uses

The pressure in the wedge is proportional to the oil’s dynamic viscosity: double the viscosity and, at the same speed and geometry, the film carries double the load, or carries the same load with the journal closer to centre. Viscosity, the property the companion book explains from the motion of molecules, is therefore the material property of the film, much as Young’s modulus is the material property of a spring. And because it falls steeply with temperature, a bearing’s capacity and its temperature are tied together, the theme of Chapter 6.

Speed works the same way as viscosity, because the wedge’s pumping is proportional to how fast the journal’s surface drags the oil. Load works the other way: the heavier the load, the further the journal must move off centre to generate enough pressure, and the thinner the film becomes. The bearing’s dimensions enter through its clearance and its length. A tighter clearance makes a sharper wedge for the same eccentricity, and a longer bearing loses less oil from its ends, so both raise the film’s capacity, though each has costs that Chapters 5 and 6 weigh. These four influences, viscosity and speed against load and geometry, are combined in a single number, the Sommerfeld number, in Chapter 4.

What the film needs from the machine

A film a few hundredths of a millimetre thick is easily upset by things that have nothing to do with the bearing’s calculation. Five conditions decide whether the calculated film exists in practice.

Figure 5What a hydrodynamic film needs from the machine around it

• Do: AlignmentA journal tilted in its bore pinches the film at the bearing's ends; misalignment of a few hundredths of a millimetre across the length matters
• Do: GeometryRound, straight, smooth journals and bores; out-of-roundness and taper eat into a thin film
• Do: Clean oilParticles larger than the thinnest film pass through the gap only by scoring or embedding
• Do: Enough oilThe wedge must be fed continuously, or it runs dry from the inlet side
• Do: Temperature in rangeHot oil thins the film; Chapter 6 finds where the balance settles
• Avoid: Treat the calculated film as a guaranteeIt is the film in an ideal bearing; the machine decides how much of it is left

Particles show how directly these conditions bite. Any hard particle larger than the thinnest part of the film, 28.6 µm in FB-75’s bearings when running and only a few micrometres during starts and stops, must either be pushed into the soft white metal lining, where it embeds harmlessly, or be dragged through the gap, where it scores the journal. White metal’s ability to swallow such particles, called embeddability, is one of the reasons it is used, and Chapter 9 discusses it. Clean oil, a clean assembly and a sealed housing remain the first line of defence.

The running case: FB-75’s bearings

This is an illustration. FB-75’s journals are 80 mm in diameter in bearings 60 mm long, turning at 1,480 rpm. Each bearing carries 6.0 kN. Three numbers summarise the duty.

Figure 6FB-75's journal bearing duty

1.25 MPaUnit load6,000 N ÷ (80 × 60) mm²

6.20 m/sJournal surface speedπ × 0.080 m × 1,480 ÷ 60

28.6 µmThinnest oil film when runningat about 66 °C

0.75Length ÷ diameter60 ÷ 80

The film is thick compared with the surfaces it separates. The journal is ground to a roughness average (Ra) of 0.4 µm and the white metal bore is fine-bored to 0.8 µm Ra. Converting each to a root-mean-square roughness, about 1.25 times the average for typical machined surfaces, and combining them as the square root of the sum of squares gives a composite roughness of about 1.12 µm. The film is 28.6 ÷ 1.12 = about 26 times thicker: a full film with a wide margin. That ratio, the film thickness ratio, appears again in Chapter 9, where the KEVOS® film thickness ratio tool calculates it.

The error: a heavier oil to cut friction

This is an illustration. During a review of the plant’s energy use, a lubricant supplier proposed changing FB-75’s bearings from VG 68 to VG 100, arguing that “a heavier film reduces friction and wear”. The maintenance planner asked the reliability engineer to check the claim before the change.

The engineer recognised the argument as belonging to the left-hand side of the Stribeck curve, where more viscosity does reduce friction by thickening a film that is not yet complete. FB-75’s bearings run far to the right of the minimum, with a film 26 times the roughness. There, friction is viscous shear, and more viscosity means more friction. At the same 66 °C, the VG 100 oil, with 100 mm²/s at 40 °C and 11.2 mm²/s at 100 °C, would have a dynamic viscosity of 26.4 mPa·s against the VG 68’s 19.1 mPa·s, and the calculation of Chapter 4 gives a friction loss of 287 W per bearing against 217 W, 32% more.

Figure 7FB-75's drive-end bearing on VG 68 and on VG 100

Oil	Running temperature	Friction loss	Thinnest film
VG 68, as now	66.1 °C	217 W	28.6 µm
VG 100, same temperature	66.1 °C	287 W	32.6 µm
VG 100, after the heat balance settles	70.9 °C	246 W	30.3 µm

The extra heat would not stay put. With the housing’s fixed ability to shed heat, the bearing would settle 4.8 K hotter, at 70.9 °C, where the heavier oil thins and the loss settles at 246 W, still 13% more than now. In return the film would thicken by 6%, from 28.6 to 30.3 µm, an improvement the bearing did not need. The change was not made. The engineer’s note to the planner made the general point: in a bearing running in full film, a heavier oil increases friction; it helps only a bearing whose film is too thin, and the way to know which applies is to calculate the film.

Bringing it together

A hydrodynamic bearing works because a sliding surface drags viscous oil into a converging gap, raising a pressure that carries the load. A journal creates its own converging gap by running off centre. Friction and wear depend on how the film compares with the surface roughness: boundary, mixed or full film, along the Stribeck curve. FB-75’s bearings run in full film, 28.6 µm thick against 1.12 µm of roughness, where friction comes from viscous shear and a heavier oil adds to it. The next chapter turns to the bushes that never reach a full film, and the screening checks used for them.

Exercise: a coarser bore

A replacement bearing shell for FB-75 arrives with its white metal bored to 1.6 µm Ra instead of 0.8 µm. Estimate the new composite roughness and film thickness ratio at the running film of 28.6 µm, and say whether the coarser finish matters in running. Where might it matter more?

Worked answer. This is an illustration. The root-mean-square roughnesses are about 1.25 × 0.4 = 0.5 µm for the journal and 1.25 × 1.6 = 2.0 µm for the bore. The composite is √(0.5² + 2.0²) = 2.06 µm, and the film thickness ratio is 28.6 ÷ 2.06 = 13.9, still a full film with a wide margin. In running, the coarser bore makes little difference. It matters more at starting and stopping, where Chapter 9 shows the film is a few micrometres thick: there, the coarser peaks touch at a higher speed and for longer. A fitter would also expect the coarse peaks to be worn down in the first hours of running, which is why a bearing maker’s specified finish should be insisted on.