Compute Sommerfeld number $S = \frac{\mu N}{P}\!\left(\frac{R}{C}\right)^2$, minimum film thickness, friction coefficient and friction loss in real time. Raimondi-Boyd OK/WARNING check tells you whether full hydrodynamic lubrication holds.
Bearing Specs
Journal diameter D (mm)
mm
Bearing length L (mm)
mm
Radial clearance C (μm)
μm
Rotational speed N (rpm)
rpm
Load W (kN)
kN
Oil viscosity η (mPa·s)
mPa·s
OK — full film
Results
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Sommerfeld S
—
h_min (μm)
—
Friction coef. f
—
Friction loss P_loss (W)
① h_min/C vs Sommerfeld number S (operating point ●)
What does the "Sommerfeld number" actually tell me when I'm sizing a bearing?
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It's a single dimensionless number that says whether the bearing is operating in healthy hydrodynamic lubrication. Bigger S means thicker film. Crank up the speed N slider and you'll see S jump immediately. The first design check is whether S sits inside a sensible range.
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And then h_min comes from S? It's bad if it gets too small, right?
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Exactly. S sets the eccentricity ε, which sets h_min = C(1 − ε). When h_min drops below 3× the combined surface roughness, asperities touch and you wear or seize. Try doubling the load W — h_min collapses and the badge flips to WARNING.
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And the friction loss number — what's that for?
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P_loss is the power dumped into oil heating. In an engine main bearing it directly affects fuel economy and oil temperature. Slide the viscosity η up and you'll see f and P_loss grow — thicker oil keeps a better film but burns more energy.
FAQ
At S < 0.01 the film becomes vanishingly thin and ε approaches 1; h_min likely falls below tolerance. Increase viscosity or clearance, or reduce load.
Enter η in mPa·s (cP). The tool assumes constant viscosity — for hot-running bearings, enter the viscosity at the actual oil-film temperature.
A common rule is h_min ≥ 3·(Ra1+Ra2). For a 50 mm journal that's typically 50–250 μm. Always include surface roughness and machining tolerance.
Loss scales with viscosity μ and speed N and inversely with clearance C. Lower viscosity or open the clearance. But too much clearance lowers S and risks losing the film, so balance carefully.
Real-world applications
Engine main and big-end bearings: Must hold the oil film under high load and rpm. Reducing friction loss directly improves fuel economy.
Industrial turbomachinery: Steam turbines, compressors and blowers transition from boundary lubrication at start-up to full hydrodynamic film at speed.
Marine propeller-shaft stern bearings: Need to support large thrust loads while keeping water out.
Common misconceptions
Don't pick C purely from theory: thermal expansion and machining error can wipe out a 1 μm clearance instantly. About 0.1% of journal diameter is a reasonable starting point. Bigger S isn't always better either: above ~10 the film is so thick you can excite oil whip and rotor instability — most stable designs sit between S = 1 and 3. And remember the viscosity you enter is for the running temperature: oil at 80 °C may have less than half the viscosity it had at 40 °C, so re-run the calculation after estimating heat-up.
Enter bearing diameter (mm) in the first field—typical journal bearings range 20–100 mm for industrial machinery.
Input bearing length (mm); use L/D ratio of 0.5–2.0 for optimal load capacity and stability.
Specify radial clearance (μm); ISO 286 tolerance grades typically yield 5–50 μm depending on shaft grade.
Set rotational speed (rpm); common industrial speeds are 1800 rpm (60 Hz motors) or 3600 rpm for high-speed spindles.
Read Sommerfeld number S, minimum film thickness h_min, friction coefficient f, and friction loss P_loss in real time.
Worked Example
Design a journal bearing for a pump motor: bore diameter 50 mm, length 40 mm, radial clearance 0.025 mm (25 μm, ISO 7:h7 fit), rotating at 1800 rpm under 15 kN radial load. Raimondi-Boyd curves yield Sommerfeld S ≈ 0.52, minimum film thickness h_min ≈ 8.3 μm, friction coefficient f ≈ 0.0095, and friction loss P_loss ≈ 127 W. This confirms adequate hydrodynamic film formation (h_min exceeds 2 μm threshold) and acceptable power dissipation for bearing temperature rise under ISO VG 46 oil.
Practical Notes
Minimum film thickness below 2 μm risks boundary lubrication and wear; increase clearance or speed if h_min drops below this threshold.
Sommerfeld number S > 1.0 indicates marginal load capacity; reduce speed, increase length, or tighten clearance for stability in heavily loaded applications.
Friction loss directly affects bearing temperature; multiply W by operating hours to estimate heat generation and verify cooling system adequacy for continuous duty.
Use viscosity-temperature grade (ISO VG) matching speed: VG 32 for high-speed spindles (>5000 rpm), VG 68 for low-speed industrial bearings (<500 rpm).