Design the hydrodynamic journal bearing that supports a rotating shaft on a self-generated film of oil. Adjust the shaft diameter, bearing length, clearance, speed, oil viscosity and load to see the Sommerfeld number, bearing pressure and whether a load-carrying oil film actually forms — all in real time.
Parameters
Journal (shaft) diameter D
mm
Bearing length L
mm
Radial clearance c
µm
Difference between the bore radius and the shaft radius
Rotational speed N
rpm
Oil viscosity µ
mPa·s
Absolute (dynamic) viscosity at operating temperature
Radial load W
N
Radial force pressing the shaft against the bearing
Results
—
Projected area (mm²)
—
Bearing pressure (MPa)
—
Speed parameter µN/P
—
Clearance ratio r/c
—
Sommerfeld number S
—
Lubrication regime
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Bearing cross-section — oil-film wedge & pressure
The rotating shaft sits eccentrically; oil is dragged into the thin side and builds a pressure wedge. The film is thick opposite the load and thinnest on the loaded side.
The clearance ratio r/c is typically 500-1000. The speed parameter µN/P (the ratio of viscosity·speed to pressure) governs whether hydrodynamic lubrication forms. A high Sommerfeld number means a thick, safe oil film; a low value risks boundary contact.
What is a Journal Bearing and the Sommerfeld Number?
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A journal bearing is just a plain sleeve with no balls inside, right? How can such a simple part carry a heavy shaft?
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Good question. A journal bearing is the simplest of all bearings: a rotating shaft — the "journal" — turning inside a slightly larger cylindrical sleeve. What is remarkable is that, when it is running properly, the shaft and the sleeve never actually touch. Oil dragged into the gap generates its own pressure and floats the whole shaft and its load. We call this hydrodynamic lubrication. Because metal never rubs on metal, an ideally-running journal bearing has almost no wear and an extremely long life.
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Wait — the oil generates its own pressure? Isn't a high-pressure pump forcing it in?
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That is the genius of this bearing. As the shaft rotates, viscosity drags oil along with the shaft surface. The gap narrows on the loaded side into a wedge shape, and the oil gets pushed into that ever-narrowing wedge. The oil cannot escape fast enough, so the pressure builds up high enough to lift the entire shaft and its load. The supply pump only tops the oil up; the load-carrying pressure is generated by the rotation itself.
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I see! So how do you tell whether the shaft is actually floating? There are so many parameters.
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That is exactly where the Sommerfeld number comes in. The German physicist Arnold Sommerfeld showed in 1904 that diameter, clearance, viscosity, speed and load all collapse into one dimensionless number S, written S = (r/c)²·μN/P. It captures the contest between viscosity-and-speed dragging the film in, and pressure squeezing it out. Lower the speed N or raise the load W on the left and you will see S shrink.
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What happens when S is small? A small number doesn't sound dangerous by itself.
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A small S means the oil film is thin — that is the heavy-load, low-speed, low-viscosity case. Below a critical value the high spots on the shaft and bearing surfaces start to touch. That is boundary lubrication, and from there wear accelerates fast and, at worst, the bearing seizes — the metal welds and locks up. A high S, by contrast, means a thick, safe film. In practice you aim for S roughly between 0.05 and 1.0. This tool colours the verdict for you.
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Once you know the Sommerfeld number, what else can you get from it?
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This is the truly powerful part: from S alone you can read almost every property of the bearing. Using the famous Raimondi-Boyd design charts, S gives you the eccentricity ratio (how far off-centre the shaft sits), the minimum film thickness, the friction coefficient and the required oil flow. So journal bearing design always starts with finding S. Use this tool to get S first and check that it lands inside the safe range.
Frequently Asked Questions
The Sommerfeld number S is a single dimensionless group that characterises the operation of a journal bearing, defined as S = (r/c)²·μN/P. Here r/c is the ratio of shaft radius to radial clearance, µ is the oil viscosity, N is the speed in revolutions per second and P is the bearing pressure on the projected area. A high S means a thick, safe oil film; a low S means a thin film and a risk of boundary contact. Once S is known, the classic Raimondi-Boyd charts give the eccentricity, minimum film thickness, friction and required oil flow.
For a typical journal bearing, a Sommerfeld number S roughly in the range 0.05 to 1.0 gives good hydrodynamic lubrication, with the shaft and bearing fully separated by the oil film. Below about 0.05 the film becomes too thin and approaches boundary lubrication, where surface asperities touch and wear and seizure threaten. Far above 1.0 the film is very thick and the load is very light — safe in itself, but watch for oil-film instability such as oil whip in this regime.
Raising the Sommerfeld number S = (r/c)²·μN/P thickens the film. Four levers: (1) switch to a higher-viscosity oil µ, (2) increase the speed N if operation allows, (3) lower the bearing pressure P by enlarging the projected area D·L, and (4) reduce the clearance c to raise r/c. But too much viscosity increases friction loss and heat, and too tight a clearance starves the oil supply, so balance these factors.
A journal bearing has almost no wear because the oil film fully prevents metal contact, it damps shock and vibration well, runs quietly and tolerates extremely high loads and speeds. Steam turbines, large engine crankshafts and big pumps almost always use journal bearings. Their weakness is that no film forms at start-up and shut-down, when the bearing runs in boundary lubrication, so rolling bearings are better for low-speed, intermittent or hard-to-lubricate duty. As a rule: continuous, high-speed, high-load duty favours the journal bearing.
Real-World Applications
Power-generation turbines and large rotating machinery: The shafts of steam turbines and generators in thermal and nuclear power stations all run on journal bearings. They spin rotors weighing tens of tonnes while floating them entirely on an oil film, allowing the high loads and continuous operation that rolling bearings could never withstand. For these bearings, designers derive the minimum film thickness and eccentricity from the Sommerfeld number and also study the rotordynamic stability — oil whirl and oil whip.
Internal-combustion engine crankshafts and connecting rods: The crankshaft main bearings and connecting-rod big-end bearings of automotive and diesel engines are classic journal bearings. Because the load direction and magnitude swing violently with each combustion stroke, a dynamic design that evaluates the instantaneous Sommerfeld number and film thickness is needed. The bearing shells use conformable materials such as copper-lead or aluminium alloy, with an overlay layer to survive boundary lubrication at start-up.
Large pumps, compressors and blowers: The bearings of fluid machinery that runs continuously for long periods — large water-supply pumps, process compressors, industrial blowers — are chosen as journal bearings. Their quietness and a practically unlimited life when properly lubricated are major advantages. Design keeps the Sommerfeld number inside the safe range while confirming that the bearing pressure stays below the allowable contact stress set by the bearing material.
Bearing troubleshooting: When a bearing "overheats abnormally", "produces noise or vibration" or "the bearing shell has worn or seized", the cause is very often that the Sommerfeld number has fallen and the oil film has broken down. A quick calculation like this tool checks the operating-point S and indicates which of load, viscosity, speed or clearance should be revised. A detailed study also adds a heat balance and an oil-flow calculation.
Common Misconceptions and Pitfalls
The most common misconception is that "a journal bearing is an old type of bearing where metal rubs and wears away". A journal bearing with properly established hydrodynamic lubrication keeps the shaft and bearing fully separated by the oil film, so the metals never touch. Wear is therefore essentially zero and life is practically unlimited. Wear only becomes an issue during the brief boundary lubrication at every start-up and shut-down, and when the Sommerfeld number is so small that the film breaks down. If a journal bearing "wears", that is a sign the design or operating condition is wrong.
Next, assuming the µ in the speed parameter is the kinematic viscosity. The µ used in the Sommerfeld number is the absolute (dynamic) viscosity, in Pa·s (entered here in mPa·s). Using kinematic viscosity (mm²/s = cSt) shifts the result by the density factor. More importantly, viscosity changes strongly with temperature: a mineral oil roughly halves its viscosity for every 10 °C rise. Using the catalogue 40 °C viscosity directly means that at the real operating temperature — often 60-80 °C from shear heating in the film — the film is thinner than assumed, and a design that looks safe on paper slips into boundary lubrication. Always use the viscosity at operating temperature.
Finally, "the bigger the Sommerfeld number, the better" is not true. A higher S does mean a thicker film and less worry about wear. But at an extremely high S — a very light, very fast condition — the shaft sits almost at the centre of the bearing, and the oil film loses the off-centre stiffness that lets it act as a "spring" for the rotor. The film itself can then become unstable, and the shaft can whirl around inside the bearing in a self-excited vibration known as oil whirl or oil whip. Journal bearing design aims for the safe band between the lower limit where the film breaks down and the upper limit where instability appears.
How to Use
Enter journal diameter (mm), bearing length (mm), and radial clearance (μm) using sliders or numeric inputs.
Set rotational speed (RPM) and oil viscosity (cP) for your lubrication fluid—typical machine tool bearings use ISO VG 32 (32 cSt at 40°C).
Read the Sommerfeld number S output; S > 0.6 indicates full film hydrodynamic lubrication, 0.1–0.6 shows mixed regime, and S < 0.1 signals boundary lubrication risk.
Worked Example
Journal bearing for a spindle: diameter 50 mm, length 80 mm, radial clearance 0.05 mm, speed 3000 RPM, oil viscosity 15 cP (ISO VG 10). Projected area = 4000 mm², radial load 2 kN gives bearing pressure P = 0.5 MPa. Speed parameter μN/P = (15×10⁻³ Pa·s × 50 s⁻¹) / 0.5×10⁶ Pa = 1.5×10⁻⁶. Clearance ratio r/c = 25/0.05 = 500. Sommerfeld number S = 0.8, confirming thick-film hydrodynamic operation with minimal wear.
Practical Notes
Industrial spindles (5000–10000 RPM) require lower viscosity oil (ISO VG 10–15) to maintain S > 0.5 and prevent overheating; heavy-duty slow-speed bearings (< 500 RPM) tolerate ISO VG 46–68.
Clearance ratio r/c > 400 increases power loss and heat; precision machine tool bearings target 300–500 for balance between film strength and friction.
Monitor bearing temperature rise above 60°C; viscosity drop at elevated temperature reduces S, potentially shifting to mixed lubrication—select oils with high viscosity index (VI > 90).