ISO 7902 Journal Bearing Calculator — Sommerfeld Number, Film Thickness & Lubrication Regime
ISO 7902 — Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings
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ISO 7902 is the international standard for hydrodynamic plain journal bearings operating under steady-state conditions. It establishes a dimensionless Sommerfeld number So as the key load-capacity parameter and defines how to determine the eccentricity ratio, minimum oil film thickness, friction coefficient, friction torque, power loss and oil flow rate from its own tabulated characteristic functions, given in ISO 7902-2 against both eccentricity ratio and the width ratio B/D. The standard applies to circular cylindrical bearings, the most common geometry in rotating machinery, and covers the full range from lightly loaded near-concentric operation through to heavily loaded near-contact conditions.
It is the calculation method specified by machinery OEMs for gearbox journals, compressor crankpin bearings, electric-motor sleeve bearings, pump sleeve bearings and any hydrodynamic plain bearing in rotating equipment where a documented, defensible load-capacity calculation is required. MechanixCalc's journal bearing calculator solves the same physics by a DIFFERENT published route — the Raimondi-Boyd characteristic tables (L/D = 1) as tabulated in Shigley Ch. 12, with a Petroff-asymptote blend beyond the table — alongside ISO VG viscosity selection, a Stribeck-curve chart, a film-thickness-versus-speed sweep and a shareable PDF engineering report. It is not an ISO 7902 or DIN 31652 proof; see the note on the characteristic number below before comparing a displayed value against a table in either standard.
What ISO 7902 covers
- Sommerfeld number So — the dimensionless group combining bearing pressure, relative clearance, viscosity and angular velocity that characterises hydrodynamic load capacity (ISO 7902-1)
- Eccentricity ratio ε and attitude angle β — tabulated in ISO 7902-2 against So AND the width ratio B/D, so a bearing is read at its own B/D rather than at a single reference ratio
- Minimum oil film thickness h_min, and the permissible operational limits for film thickness, specific bearing load and bearing temperature given in ISO 7902-3
- Friction coefficient, frictional power loss and the heat balance for both convective and lubricant-cooled bearings
- Lubricant flow rate — the pressure-fed and self-circulating cases — and the resulting temperature rise
- NOT ISO 7902, but layered on top of it in MechanixCalc: the Raimondi-Boyd L/D = 1 characteristic tables (Shigley Ch. 12) used in place of ISO 7902-2's B/D-resolved functions, the Petroff concentric asymptote blend beyond the table range, the S-threshold regime split (full hydrodynamic S > 0.3, thin-film 0.1 ≤ S ≤ 0.3, boundary S < 0.1) and the lambda ratio Λ = h_min / Ra_composite — all tribology convention or textbook practice, with no governing clause
Parts of the standard
- ISO 7902-1Calculation procedure
- ISO 7902-2Functions used in the calculation procedure
- ISO 7902-3Permissible operational parameters
Governing formulas
S = (μ · N_rps / p) · (r / c)²where S = bearing characteristic number (dimensionless); μ = dynamic viscosity at operating temperature (Pa·s); N_rps = journal rotational speed (rev/s); p = mean bearing pressure = W / (L · D) (Pa); r = journal radius (m); c = radial clearance (m); W = radial load (N); L = bearing length (m); D = journal diameter (m). High S → full hydrodynamic; low S → boundary/mixed regime. ⚠️ This is the Raimondi-Boyd / Shigley form, which MechanixCalc computes and displays. ISO 7902-1 and DIN 31652-1 define their Sommerfeld number So as the RECIPROCAL group, So = p·ψ²/(η·ω) with ψ = c/r — so So = 1/(2π·S), and the direction inverts: a HIGH So is the heavily-loaded end. Do not read the displayed S against an ISO 7902 or DIN 31652 table without converting.
h_min = c · (1 − ε)where h_min = minimum oil film thickness (m or mm); c = radial clearance (m or mm); ε = eccentricity ratio (dimensionless, 0 = fully concentric, 1 = journal touching bore); ε is determined by interpolation in the ISO 7902 / Raimondi-Boyd S-table for L/D = 1.
T_f = 4π² · μ · N_rps · r³ · L / cwhere T_f = friction torque (N·m); μ = dynamic viscosity (Pa·s); N_rps = journal speed (rev/s); r = journal radius (m); L = bearing length (m); c = radial clearance (m). This is the limiting form as S → ∞ (ε → 0); the full Raimondi-Boyd table gives the friction variable fR/C for any S, and the friction coefficient follows as f = (fR/C) · (c / r).
Frequently asked questions
What is ISO 7902 used for?
ISO 7902 defines the calculation procedure for hydrodynamic plain journal bearings under steady-state conditions. It establishes how to determine the Sommerfeld number, eccentricity ratio, minimum oil film thickness, friction coefficient, power loss and oil flow rate for a circular cylindrical bearing. The method is used to verify that a proposed combination of journal diameter, bearing length, radial clearance, oil viscosity, load and speed produces adequate oil film separation between the shaft and bearing bore — preventing metal contact and ensuring acceptable wear life.
What is the Sommerfeld number and what does it tell me?
The Sommerfeld number S groups viscosity, speed, bearing pressure and the clearance ratio into one dimensionless parameter. A high S (above about 0.3) indicates full hydrodynamic lubrication: the oil wedge fully separates the shaft from the bore, friction is low and wear is negligible. A low S (below about 0.1) indicates boundary lubrication: the oil film is insufficient, metal contact occurs and wear is severe. S falls as load rises or speed drops, so checking S at start-up (low speed) and overload conditions is essential.
What is the difference between ISO 7902 and DIN 31652?
ISO 7902 and DIN 31652 are closely equivalent standards covering circular cylindrical hydrodynamic journal bearings by the same dimensionless-group method, and are treated as interchangeable in practice. Each tabulates its OWN characteristic functions (So against both ε and the width ratio B/D) — those tables are not a republication of the 1958 Raimondi-Boyd ASLE charts, though the two describe the same physics. MechanixCalc does NOT report compliance with either: its journal engine reads the Raimondi-Boyd L/D = 1 column as tabulated in Shigley Ch. 12, displays the reciprocal characteristic number, and uses a house film-thickness band rather than ISO 7902-3's h_lim. Use it as an engineering calculation, not as evidence of ISO 7902 or DIN 31652 conformance.
How does bearing length-to-diameter ratio (L/D) affect the calculation?
Characteristic tables for journal bearings are given for specific L/D (or B/D) ratios, with L/D = 1 (square bearing) being the most widely published reference case. Shorter bearings (L/D < 1) have lower load capacity and higher side leakage; longer bearings (L/D > 1) carry more load but generate more heat. The MechanixCalc journal bearing engine uses the L/D = 1 tables with a Petroff-asymptote blend at high Sommerfeld numbers. If your L/D departs significantly from 1, treat the result as a conservative first estimate and consider full Reynolds-equation CFD for the final design.
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