Journal Bearings Calculator — Sommerfeld Number, Oil Film Thickness & Lubrication Regime (Raimondi-Boyd)

Each panel names its own method, because they do not share one. The journal-bearing engine resolves the Sommerfeld number and eccentricity ratio from the Raimondi-Boyd characteristic tables for an L/D ratio of 1, as tabulated in Shigley's Mechanical Engineering Design, with a continuous Petroff-asymptote blend beyond the tabulated range. That is closely related to DIN 31652 / ISO 7902 but is not the same calculation: DIN and ISO define the Sommerfeld number as its reciprocal (So = 1/(2π·S)) and tabulate against the width-to-diameter ratio, so the displayed S should not be looked up in a DIN table. Viscosity-temperature behaviour follows the ASTM D341 Walther equation over ISO 3448 grades. The rolling-bearing panel follows ISO 281, grease intervals follow the published bearing-maker relubrication bracket (a manufacturer document, not a standard), and oil cleanliness is classified per ISO 4406:1999. The lambda-ratio regime bands are tribology convention with no governing standard. The governing method and all references are shown in the generated PDF report.

The Sommerfeld number S groups viscosity, speed, bearing pressure and the clearance-to-radius ratio into one dimensionless value that fixes where the bearing sits on the Raimondi-Boyd characteristic curve. This tool treats S above 0.3 as full hydrodynamic operation, 0.1 to 0.3 as thin film, and below 0.1 as boundary or mixed. One caution worth knowing: DIN 31652 and ISO 7902 define their Sommerfeld number as So = 1/(2*pi*S), the reciprocal of the S shown here, so a value from this tool must not be looked up directly in a DIN characteristic table. S tells you how well established the wedge is; the film ratio Lambda tells you whether the resulting film is thicker than the surface roughness. The tool reports both and governs on the worse of the two.

The ISO VG grade sets the kinematic viscosity at 40 °C; the actual operating viscosity at your bearing temperature is lower and is predicted by the ASTM D341 Walther equation built into the tool. The DN-value method (bore diameter × rotational speed, in mm·rpm) gives a first-pass recommendation: DN < 25 000 favours higher-viscosity grades (VG 100–220) for film thickness; DN > 200 000 favours lower viscosity (VG 22–46) to limit heat generation. In this tool you simply select the grade and enter the oil inlet temperature, and the dynamic viscosity is derived for you at the mean film temperature — you never convert cSt to mPa.s by hand, and you cannot accidentally type the ISO VG number itself into a field that wants mPa.s. Then read the film ratio: below 3 is boundary, 3 to 10 is mixed, and 10 or above is a full fluid film.

The film ratio Lambda = h_min / sigma compares the minimum oil film thickness against the composite RMS roughness of the two surfaces, sigma = sqrt(Rq1^2 + Rq2^2). For two equally ground surfaces this tool takes sigma = sqrt(2) x 1.25 x Ra, because Lambda is defined on RMS roughness (Rq) and Rq is about 1.25 times Ra for a ground finish — using Ra directly would overstate Lambda by roughly 25 %. This tool uses the strict reading of the convention: below 3 is boundary lubrication and the asperities touch, 3 to 10 is mixed with partial contact, and 10 or above is a full fluid film. Lambda is the acceptance check because it asks the question that actually matters — is the film thicker than the roughness it has to bridge? A criterion expressed as a fraction of the shaft diameter cannot answer that, since it takes no account of surface finish. These regime bands are tribology convention rather than a governing standard, and the tool says so in-product.

Because the honest answer for those geometries is not available from the table it uses. The engine reads the Raimondi-Boyd characteristic data for a length-to-diameter ratio of 1, and that column overstates film thickness for a shorter bearing — by roughly 1.6 times at L/D = 0.5 and 3.1 times at L/D = 0.25, because a short bearing leaks far more oil out of its ends and runs much more eccentric. Rather than return an optimistic number for a geometry the data does not cover, the calculation is refused and says why. Support for the L/D = 1/4, 1/2 and infinity columns is planned; until then, size the bearing near L/D = 1 or use a method that tabulates your ratio.

The h_min greater than or equal to 0.1 % of diameter figure is an in-house design target, shown for reference, and it is explicitly advisory. It is not from any standard, and it cannot be met by a bearing built to the clearance ratio of about c/r = 0.001 that is the usual starting point — the minimum film thickness can never exceed the radial clearance itself, and that target asks for twice it. The acceptance check is the film ratio Lambda, which compares the film against the actual surface finish. If Lambda is 10 or above the film separates the surfaces regardless of what fraction of the diameter it happens to be.

No, and deliberately so. Rolling-bearing L10 fatigue life to ISO 281 lives in the Bearing Analysis tool, which derives the equivalent dynamic load from the radial and axial forces using the ISO 281 X and Y factors and computes the life-modification factor from the viscosity ratio and contamination, rather than asking you to type those values in. This tool covers hydrodynamic plain (journal) bearings. Grease relubrication intervals appear here as a supporting bearing-maker-method calculator because they are commonly needed alongside a lubrication review, and that section states clearly that it applies to rolling bearings rather than to the journal bearing above.

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