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Sommerfeld Number & Hydrodynamic Journal Bearing Calculator

Hydrodynamic journal bearings support high-speed shafts on a self-generated pressurised fluid film without metallic contact.

Shaft journal radius in millimeters (e.g. 25 mm = 50 mm diameter).

Radial clearance between shaft and bushing (typically 0.001 mm per mm of radius).

Rotational speed in revolutions per minute.

Total radial load on the bearing in Newtons.

Axial length of the bearing shell in millimeters.

Viscosity of lubricating oil at operating temperature (e.g. 0.03 Pa·s = 30 cP for ISO VG 32 at 60°C).

Calculated Result
0.4500

Sommerfeld Number (S)

Minimum Oil Film Thickness (h₀)

7.4 µm

Film Thickness Ratio (h₀/C)

0.295

Mean Projected Pressure

2.00 MPa

Lubrication Regime

Full Hydrodynamic Film

Calculation Breakdown

  1. Bearing Pressure EvaluationP = W / (2·R·L) = 2.00 MPa
  2. Dimensionless Sommerfeld ParameterS = (R/C)² · (μ·n / P) = 0.4500
  3. Minimum Fluid Film Clearanceh₀ = 7.4 µm ensures hydrodynamic separation of asperities

What Is the Sommerfeld Number & Hydrodynamic Journal Bearing Calculator?

The Sommerfeld number S is the universal dimensionless parameter governing hydrodynamic journal bearing operation.

It combines geometric clearance ratio, speed, viscosity, and unit load to predict oil film thickness, friction, and eccentricity.

How Does the Sommerfeld Number & Hydrodynamic Journal Bearing Calculator Work?

As the shaft rotates eccentrically within the clearance space, fluid is dragged into a narrowing converging wedge, developing high hydrodynamic pressure that lifts the journal.

S > 0.15 ensures full fluid-film hydrodynamic separation without metal-to-metal wear.

Sommerfeld Number & Hydrodynamic Journal Bearing Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

S = (R / C)² · (μ · n / P), P = W / (2 · R · L), h_0 ≈ C · 0.44 · S^0.5

Raimondi-Boyd classical hydrodynamic lubrication relation linking load, speed, clearance, and oil viscosity.

How to Use the Sommerfeld Number & Hydrodynamic Journal Bearing Calculator

  1. Input shaft radius, bearing length, and radial clearance.
  2. Provide operating RPM, radial load, and oil viscosity at temperature.
  3. Verify that minimum film thickness h₀ exceeds surface roughness asperities (h₀ > 3·Rq).

Step-by-Step Example Calculation

50 mm Diameter Industrial Turbine Journal Bearing

Input Values:

journalRadiusMm:25
radialClearanceMm:0.025
rotationalSpeedRpm:1800
radialLoadNewtons:5000
bearingLengthMm:50
dynamicViscosityPaS:0.03
Worked Steps: Predicts S ≈ 0.45 and comfortable hydrodynamic film thickness h₀ ≈ 7.4 µm.

Understanding Your Result

h₀ indicates minimum clearance at the thinnest point of the oil wedge.

A low Sommerfeld number (S < 0.05) warns of boundary lubrication and premature bearing wipe.

Factors That Affect the Result

  • Oil temperature: Excessive heat thins the lubricant (lower μ), causing h₀ to collapse.
  • Clearance ratio: Machining clearance too loose drops pressure; too tight causes overheating.

When Should You Use This Calculator?

  • Designing sleeve bearings for internal combustion engines, steam turbines, and pumps.
  • Troubleshooting bearing wipe failures and selecting lubricant viscosity grades.

Assumptions & Limitations

  • Assumes steady-state laminar Newtonian fluid flow in a full 360° circular bushing.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard Raimondi-Boyd tribological solution.

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