ISO 7902 Journal Bearing Calculator — Sommerfeld Number, Film Thickness & Lubrication Regime
ISO 7902 — Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings
ISO 7902 is the international standard for hydrodynamic plain journal bearings operating under steady-state conditions. It establishes the dimensionless Sommerfeld number 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 the Raimondi-Boyd characteristic tables — the same tables that have underpinned journal bearing design practice since Boyd and Raimondi's landmark 1958 paper. 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 implements ISO 7902 (with its German twin DIN 31652) in the journal bearing calculator, running the full Sommerfeld-Raimondi-Boyd analysis in your browser alongside ISO VG viscosity selection, a Stribeck-curve chart, a film-thickness-versus-speed sweep and a shareable PDF engineering report.
Calculators that implement ISO 7902
What ISO 7902 covers
- Sommerfeld number S — the dimensionless parameter combining viscosity, speed, bearing pressure and clearance ratio that characterises hydrodynamic load capacity
- Eccentricity ratio ε and attitude angle φ — read from the Raimondi-Boyd characteristic tables for L/D = 1, with Petroff concentric-bearing asymptote blending beyond the table range
- Minimum oil film thickness h_min and metal-contact-risk thresholds relative to journal diameter
- Friction coefficient, friction torque and bearing power loss derived from the Raimondi-Boyd friction variable fR/C
- Oil flow rate from the Raimondi-Boyd flow variable Q/(r·c·N·L) and adiabatic temperature rise from an energy balance on the oil flow
- Lubrication regime classification — full hydrodynamic (S > 0.3), thin-film (0.1 ≤ S ≤ 0.3) and boundary (S < 0.1) — and film-to-roughness ratio (lambda ratio Λ = h_min / Ra_composite)
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 = Sommerfeld 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.
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 technically equivalent standards — both define the same Sommerfeld-number method and use the same Raimondi-Boyd characteristic tables for circular cylindrical bearings. DIN 31652 is the German national adoption of the ISO standard. They are treated as interchangeable in practice, and the MechanixCalc engine reports compliance with both.
How does bearing length-to-diameter ratio (L/D) affect the calculation?
The Raimondi-Boyd tables in ISO 7902 are tabulated for specific L/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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