Journal Bearing Sommerfeld Number Calculator
Sommerfeld number calculator for the hydrodynamic journal bearing: calculates the dimensionless Sommerfeld number So from specific load, relative clearance, viscosity and speed -- the central figure of plain-bearing theory in DIN 31652-1 and ISO 7902, here in an explicitly named convention.
Formula
So = pL * psi^2 / (eta * omega), omega = 2*pi*n
The Sommerfeld number combines load, geometry, and lubrication state into a dimensionless figure. Under this definition, So rises with specific load and the square of relative clearance, and falls with viscosity and speed. Together with width-to-diameter ratio b/d, the ISO 7902-2 characteristic functions then determine eccentricity and minimum film thickness.
What this model does not show
The ranges So ≤ 1 (high speed), 1 < So < 3 (medium load), and So > 3 (heavy load) are literature classifications for the definition used here, not universal approval limits. For its 360° bearing, the cited TU Dortmund problem identifies So < 1 with possible oil-whirl instability and So > 4 with possible mixed lubrication due to insufficient film. Reliability of the actual bearing follows only from the ISO 7902-2 characteristic functions and the permissible hlim, Tlim, and plim values under ISO 7902-3.
Worked example
Recalculation of the published TU Dortmund worked solution: F = 100 kN, b = 40 mm, and d = 50 mm give p = F/(b*d) = 50 MPa. From dL = 50.1 mm and d = 50 mm, psi = 0.1/50 = 0.002. With eta = 0.3 Pa*s = 300 mPa*s and n = 3,000 rpm, omega = 2*pi*3,000/60 = 314.159 rad/s. Thus So = 50e6*0.002^2/(0.3*314.159) = 2.122. This is in the medium-load range 1 < So < 3 and reproduces the published reference value 2.122.
Common mistakes
- Comparing a figure defined with radial clearance, rotational frequency instead of angular speed, or a different reference area directly with the value computed here.
- Using eta at room temperature instead of at the actual operating film temperature.
- Concluding directly from a single Sommerfeld number that a bearing is 'safe' or 'unsafe' without consulting the characteristic functions (which also depend on b/d).
Frequently asked questions
Which Sommerfeld number convention does NormCalc use?
So = pL*psi^2/(eta*omega), with pL in Pa, diametral relative clearance psi, eta in Pa*s, and omega = 2*pi*n in rad/s. These are exactly the variables used by the cited TU Clausthal notes and TU Dortmund worked solution.
Why do Sommerfeld number definitions differ between sources?
Some presentations use radial rather than diametral clearance, rotational frequency rather than angular speed, or a different reference area. These choices introduce fixed factors, so formula, variable definitions, and units must accompany any quoted value.
Which concrete value ranges apply here?
TU Clausthal gives an approximate practical overall range of 0.1 ≤ So ≤ 150 and classifies So ≤ 1 as high-speed, 1 < So < 3 as medium-load, and So > 3 as heavy-load. For its 360° bearing, the TU Dortmund problem associates So < 1 with possible oil whirl and So > 4 with possible mixed lubrication. These are guidance ranges, not a stand-alone safety proof.
What does a high or low Sommerfeld number mean?
At fixed b/d, a smaller value under this definition means relatively low load or high viscosity/speed; the journal tends to run more centrally, and very small values can make a circular bearing dynamically unstable. A larger value means relatively high load or low viscosity/speed; eccentricity rises and minimum film thickness tends to fall.
Is the Sommerfeld number alone sufficient for approval?
No. It is an intermediate quantity. Actual eccentricity epsilon and minimum film thickness h_min only follow from the full ISO 7902-2 characteristic functions, which additionally depend on the width-to-diameter ratio b/d.
Which viscosity should I use?
The dynamic viscosity at the actual operating film temperature, not at room temperature or the datasheet reference temperature. Use the Dynamic/kinematic viscosity conversion and Lubricant viscosity vs temperature calculators to determine it.
What comes after the Sommerfeld number?
With an eccentricity epsilon determined from the ISO 7902-2 characteristic functions, it can be calculated using the Minimum journal-bearing film thickness calculator.
Is there a complete design including the heat balance?
Yes: the Hydrodynamic journal bearing to DIN 31652 calculator inverts the characteristic function So = f(ε, B/D) numerically, derives film thickness, friction power and oil flow from it and iterates the bearing temperature with the temperature-dependent viscosity – for convection cooling or pressure-fed lubrication.