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Hydrodynamic Journal Bearing Sommerfeld Number Calculator

Hydrodynamic journal sleeve bearings support rotating turbomachinery shafts on a continuous self-pressurizing lubricating fluid wedge without metal-to-metal contact.

Outside diameter of the rotating shaft journal.

Axial length of the cylindrical journal bearing (typically L/D = 0.5 to 1.5).

Radial difference between bearing bore radius and shaft radius (typically 0.001 × D).

Operating rotational velocity of the shaft.

Total external radial force supported by the bearing.

Dynamic viscosity of the oil at operating temperature (1 mPa·s = 1 cP; typically 15 to 40 for ISO VG 32/46).

Calculated Result
S = 0.209

Dimensionless Sommerfeld Number

Sommerfeld Number (S)

0.209

Minimum Oil Film Thickness (h₀)

0.01 mm (10.0 µm)

Hydrodynamic Film Regime

Full Hydrodynamic Thick Film

Unit Bearing Pressure (P)

1.4 MPa

Estimated Friction Coefficient (f)

0.0086

Calculation Breakdown

  1. Unit Bearing Pressure EvaluationP = W / (L × D) = 3500 N / (0.05 m × 0.05 m) = 1.4 MPa
  2. Sommerfeld Dimensionless FormulationS = (r/c)² × (μ × n_s / P) = (625)² × [ 0.025 × 30.0 / 1400000 ] = 0.209
  3. Hydrodynamic Film ThicknessEstimated h₀ ≈ 10.0 µm (Clearance: 40 µm)

Journal Bearing Operating Metrics

Interactive visualization based on your current inputs

Value
0.010203040Sommerfeld S (×10)Pressure (MPa)Film h₀ (µm)Clearance (µm)Speed (kRPM)ParameterValue

What Is the Hydrodynamic Journal Bearing Sommerfeld Number Calculator?

The Hydrodynamic Journal Bearing Sommerfeld Number Calculator evaluates fluid film lubrication safety, operating pressure, and oil film thickness in sleeve bearings.

How Does the Hydrodynamic Journal Bearing Sommerfeld Number Calculator Work?

It computes unit projected pressure and determines the dimensionless Sommerfeld number S to verify full hydrodynamic thick-film separation.

Hydrodynamic Journal Bearing Sommerfeld Number Calculator Formula & Variables

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

S = \left(\frac{r}{c}\right)^2 \frac{\mu \cdot n_s}{P}, \quad P = \frac{W}{L \cdot D}, \quad h_0 \approx c \left(1 - \varepsilon\right)

Fundamental dimensionless hydrodynamic grouping relating geometric clearance, fluid viscosity, shear speed, and unit loading.

How to Use the Hydrodynamic Journal Bearing Sommerfeld Number Calculator

  1. Enter shaft diameter and bearing axial length.
  2. Specify radial clearance and rotating shaft RPM.
  3. Input applied radial load and lubricant dynamic viscosity.

Step-by-Step Example Calculation

50mm Industrial Pump Journal Bearing

Input Values:

journalDiameterMm:50
bearingLengthMm:50
radialClearanceMm:0.04
shaftSpeedRpm:1800
appliedRadialLoadN:3500
oilDynamicViscosityMpaS:25
Worked Steps: Generates Sommerfeld S = 0.210 with 1.40 MPa unit pressure, maintaining a safe 10.2 µm minimum oil film thickness.

Understanding Your Result

Sommerfeld Number (S): Master dimensionless criterion for hydrodynamic stability.

Minimum Film Thickness (h₀): Narrowest gap between rotating journal and bearing wall in micrometers.

Lubrication Regime: Classifies operation into thick-film hydrodynamic, moderate, or boundary risk.

Factors That Affect the Result

  • Higher shaft RPM and higher oil viscosity generate stronger hydrodynamic wedge lift.
  • Excessive clearance c weakens peak pressure generation.

When Should You Use This Calculator?

  • Steam and gas turbines, high-speed centrifugal compressors, engine crankshaft main bearings, and electric generator pedestals.

Assumptions & Limitations

  • Assumes steady-state laminar Newtonian lubricant flow without thermal viscosity breakdown across the arc.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Conforms to Raimondi & Boyd (1958) and Shigley Mechanical Engineering Design principles.

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