Sommerfeld number, abbreviated as S or So, a dimensionless number, is used extensively in hydrodynamic lubrication analysis. The Sommerfeld number is very important in lubrication analysis because it contains all the variables normally specified by the designer. It's particularly important in the study of journal bearings.
Sommerfeld Number formula |
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\( S \;=\; \left( \dfrac{ r }{ c} \right)^2 \cdot \dfrac{ \mu \cdot n }{ P } \) (Sommerfeld Number) \( r \;=\; c \cdot \sqrt{ \dfrac{ S \cdot P }{ \mu \cdot n } }\) \( c \;=\; r \cdot \sqrt{ \dfrac{ \mu \cdot n }{ S \cdot P } }\) \( \mu \;=\; \dfrac{ S \cdot P \cdot \left( \dfrac{ c }{ r} \right)^2 }{ n } \) \( n \;=\; \dfrac{ S \cdot P \cdot \left( \dfrac{ c }{ r } \right)^2 }{ \mu } \) \( P \;=\; \dfrac{ \mu \cdot n \cdot \left( \dfrac{ r }{ c } \right)^2 }{ S } \) |
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| Symbol | English | Metric |
| \( S \) = Sommerfield Number | \(dimensionless\) | \( dimensionless \) |
| \( r \) = Shaft Radius | \(ft\) | \(m\) |
| \( c \) = Radius Clearance | \(ft\) | \(m\) |
| \( \mu \) (Greek symbol mu) = Absolute Viscosity | \(lbf - sec / ft^2\) | \( Pa - s \) |
| \( n \) = Shaft Rotational Speed | \(r \;/\; min\) | \(r \;/\; min\) |
| \( P \) = Load per Unit of Projected Bearing Area | \(lbf - ft\) | \(N - m\) |
- Helps in determining the stability and performance of journal bearings by relating the bearing's geometry, operating conditions, and lubricant properties.
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A higher Sommerfeld number generally indicates more stable lubrication conditions with less risk of mechanical contact between the journal and bearing surfaces.
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When S is Very Low - It suggests boundary lubrication or potential for metal-to-metal contact, which could lead to increased wear.
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As S Increases - The lubrication shifts towards full-film or hydrodynamic lubrication where a continuous oil film separates the bearing surfaces
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The Sommerfeld number offering insights into how well a bearing will perform under given conditions.
Sommerfeld Number Applications
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Used in the design and analysis of journal bearings to predict friction, wear, and the load-carrying capacity.
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Helps in choosing appropriate bearing materials, lubricant, and operating speeds for machinery to ensure efficient operation and longevity.
