Sommerfeld Number Calculator for Journal Bearings
For mechanical engineers sizing hydrodynamic journal bearings who need the Sommerfeld number S = (r/c)² μN/P — together with the Hersey number μN/P from the same inputs — before matching a design point against a Stribeck chart.
This tool calculates the Sommerfeld number S and the Hersey number (μN/P) for hydrodynamic journal bearings. The Sommerfeld number S = (r/c)^2 mu N / P and the Hersey number mu N / P are both derived from your inputs.
Journal Bearing Analyzer
Sommerfeld Number S
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Hersey Number μN/P
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Projected Pressure P: --- MPa
Geometry Ratio r/c: ---
Disclaimer: for preliminary estimation only, not a substitute for review by a qualified/licensed engineer.
How to Use This Tool
- Enter the shaft radius r and the radial clearance c in mm — the r/c ratio appears immediately below the results.
- Enter the lubricant's dynamic viscosity μ in Pa·s and the shaft speed N in rpm.
- Enter the bearing load W in N, then the bearing length L and diameter D in mm to fix the projected pressure P.
- Read the Sommerfeld number and Hersey number from the headline badges and compare them with your Stribeck chart, converting the chart's units first.
FAQ
- Q: What is the Sommerfeld number formula for a journal bearing?
- A: S = (r/c)² × μN/P, where P is the projected pressure load/(L·D) — this tool applies exactly that formula and reports S alongside the Hersey number μN/P from the same inputs.
- Q: Does the Sommerfeld number use rpm or revolutions per second?
- A: Revolutions per second — the speed field takes rpm and the tool divides by 60 before evaluating μN/P; many Stribeck charts quote the Hersey number with N in rpm and P in psi, so compare only against a chart in the same units.
- Q: What is the difference between the Sommerfeld number and the Hersey number?
- A: The Hersey number is μN/P alone; the Sommerfeld number adds the geometry factor (r/c)², so for a given bearing the two differ by exactly the square of the radius-to-clearance ratio.
- Q: Which units should viscosity and pressure be in for the Sommerfeld number?
- A: Dynamic viscosity μ in Pa·s, projected pressure P in Pa from load/(L·D), and radius r and clearance c in the same length unit — the result is then dimensionless, which is why this tool takes load in N and length and diameter in mm.