Sommerfeld Number of Bearing Calculator

Sommerfeld Number Formula:

\[ S = \frac{\left(\frac{r}{c}\right)^2 \times \mu_l \times n_s}{p \times 2\pi} \]

Radius of Journal:

Radial Clearance:

Dynamic Viscosity:

Pa·s

Journal Speed:

rad/s

Unit Bearing Pressure:

Sommerfeld Number:

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1. What is the Sommerfeld Number?

The Sommerfeld Number is a dimensionless parameter used in hydrodynamic bearing design that characterizes the operating conditions of a journal bearing. It relates bearing geometry, lubricant properties, and operating conditions.

2. How Does the Calculator Work?

The calculator uses the Sommerfeld Number formula:

\[ S = \frac{\left(\frac{r}{c}\right)^2 \times \mu_l \times n_s}{p \times 2\pi} \]

Where:

\( S \) — Sommerfeld Number (dimensionless)
\( r \) — Radius of Journal (m)
\( c \) — Radial Clearance (m)
\( \mu_l \) — Dynamic Viscosity of Lubricant (Pa·s)
\( n_s \) — Journal Speed (rad/s)
\( p \) — Unit Bearing Pressure (Pa)

Explanation: The Sommerfeld Number represents the relationship between hydrodynamic forces and bearing load capacity in journal bearings.

3. Importance of Sommerfeld Number

Details: The Sommerfeld Number is crucial for predicting bearing performance, including friction characteristics, load capacity, and stability of hydrodynamic bearings. It helps in determining optimal operating conditions.

4. Using the Calculator

Tips: Enter all values in SI units (meters for length, Pa·s for viscosity, rad/s for speed, and Pa for pressure). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of Sommerfeld Number?
A: Typical values range from 0.001 to 10, depending on bearing design and operating conditions.

Q2: How does Sommerfeld Number affect bearing performance?
A: Higher Sommerfeld Numbers indicate better hydrodynamic lubrication conditions with thicker oil films and lower friction.

Q3: What are the limitations of this calculation?
A: The calculation assumes isothermal conditions, Newtonian fluid behavior, and steady-state operation.

Q4: How is radial clearance measured?
A: Radial clearance is the difference between the bearing radius and journal radius, typically measured in micrometers.

Q5: Can this be used for all types of bearings?
A: This formula is specifically designed for hydrodynamic journal bearings and may not apply to other bearing types.