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Sommerfeld Number of Bearing Formula

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Sommerfeld Number of Journal Bearing is a dimensionless number that is used in designing a hydrodynamic bearing. Check FAQs

S = \frac{({(\frac{r}{c})}^{2}) \cdot μ l \cdot n s}{p \cdot 2 \cdot π}

S - Sommerfeld Number of Journal Bearing?r - Radius of Journal?c - Radial clearance for bearing?μ_l - Dynamic Viscosity of Lubricant?n_s - Journal Speed?p - Unit bearing pressure for bearing?π - Archimedes' constant?

Sommerfeld Number of Bearing Example

With values

With units

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Here is how the Sommerfeld Number of Bearing equation looks like with Values.

Here is how the Sommerfeld Number of Bearing equation looks like with Units.

Here is how the Sommerfeld Number of Bearing equation looks like.

2.5871 = \frac{({(\frac{25.5}{0.024})}^{2}) \cdot 220 \cdot 10}{0.96 \cdot 2 \cdot 3.1416}

2.5871 = \frac{({(\frac{25.5mm}{0.024mm})}^{2}) \cdot 220cP \cdot 10rev/s}{0.96MPa \cdot 2 \cdot 3.1416}

2.5871 = \frac{({(\frac{25.5}{0.024})}^{2}) \cdot 220 \cdot 10}{0.96 \cdot 2 \cdot 3.1416}

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Sommerfeld Number of Bearing Solution

Follow our step by step solution on how to calculate Sommerfeld Number of Bearing?

FIRST Step Consider the formula

S = \frac{({(\frac{r}{c})}^{2}) \cdot μ l \cdot n s}{p \cdot 2 \cdot π}

Next Step Substitute values of Variables

∴

S = \frac{({(\frac{25.5mm}{0.024mm})}^{2}) \cdot 220cP \cdot 10rev/s}{0.96MPa \cdot 2 \cdot π}

Next Step Substitute values of Constants

∴

S = \frac{({(\frac{25.5mm}{0.024mm})}^{2}) \cdot 220cP \cdot 10rev/s}{0.96MPa \cdot 2 \cdot 3.1416}

Next Step Convert Units

∴

S = \frac{({(\frac{0.0255m}{2.4E-5m})}^{2}) \cdot 0.22Pa*s \cdot 62.8319rad/s}{960000Pa \cdot 2 \cdot 3.1416}

Next Step Prepare to Evaluate

∴

S = \frac{({(\frac{0.0255}{2.4E-5})}^{2}) \cdot 0.22 \cdot 62.8319}{960000 \cdot 2 \cdot 3.1416}

Next Step Evaluate

∴

S = 2.58707682278493

LAST Step Rounding Answer

∴

S = 2.5871

Sommerfeld Number of Bearing Formula Elements

Variables

Constants

Sommerfeld Number of Journal Bearing

Sommerfeld Number of Journal Bearing is a dimensionless number that is used in designing a hydrodynamic bearing.

Symbol: S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sommerfeld Number of Journal Bearing

Radius of Journal

The Radius of Journal is the radius of the journal (which rotates freely in a supporting metal sleeve or shell).

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Journal

Radial clearance for bearing

Radial clearance for bearing is a measured value of the total movement of one ring relative to the other in a plane perpendicular to the bearing axis.

Symbol: c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radial clearance for bearing

Dynamic Viscosity of Lubricant

The Dynamic Viscosity of Lubricant is the resistance to movement of one layer of fluid over another.

Symbol: μ_l

Measurement: Dynamic ViscosityUnit: cP

Note: Value should be greater than 0.

Formulas to find Dynamic Viscosity of Lubricant

Journal Speed

The Journal Speed Value is defined as the speed of the journal of a bearing.

Symbol: n_s

Measurement: Angular VelocityUnit: rev/s

Note: Value should be greater than 0.

Formulas to find Journal Speed

Unit bearing pressure for bearing

Unit bearing pressure for bearing is the average pressure acting on the contact surface of the bearing.

Symbol: p

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Unit bearing pressure for bearing

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Dimensionless Performance Parameters category

Go Coefficient of Friction Variable of Bearing in Terms of Coefficient of Friction

CFV = r \cdot \frac{μ jb}{c}

Go Radius of Journal in Terms of Coefficient of Friction Variable

r = CFV \cdot \frac{c}{μ jb}

Go Radial Clearance in Terms of Coefficient of Friction Variable of Bearing

c = r \cdot \frac{μ jb}{CFV}

Go Coefficient of Friction in Terms of Coefficient of friction Variable

μ jb = CFV \cdot \frac{c}{r}

How to Evaluate Sommerfeld Number of Bearing?

Sommerfeld Number of Bearing evaluator uses Sommerfeld Number of Journal Bearing = (((Radius of Journal/Radial clearance for bearing)^2)*Dynamic Viscosity of Lubricant*Journal Speed)/(Unit bearing pressure for bearing*2*pi) to evaluate the Sommerfeld Number of Journal Bearing, The Sommerfeld Number of Bearing formula is defined as the product of the square of the ratio of the radius of the journal to the radial clearance, and the ratio of the product of viscosity of lubricant and journal speed to unit bearing pressure. Sommerfeld Number of Journal Bearing is denoted by S symbol.

How to evaluate Sommerfeld Number of Bearing using this online evaluator? To use this online evaluator for Sommerfeld Number of Bearing, enter Radius of Journal (r), Radial clearance for bearing (c), Dynamic Viscosity of Lubricant (μ_l), Journal Speed (n_s) & Unit bearing pressure for bearing (p) and hit the calculate button.

FAQs on Sommerfeld Number of Bearing

What is the formula to find Sommerfeld Number of Bearing?

The formula of Sommerfeld Number of Bearing is expressed as Sommerfeld Number of Journal Bearing = (((Radius of Journal/Radial clearance for bearing)^2)*Dynamic Viscosity of Lubricant*Journal Speed)/(Unit bearing pressure for bearing*2*pi). Here is an example- 2.587077 = (((0.0255/2.4E-05)^2)*0.22*62.8318530685963)/(960000*2*pi).

How to calculate Sommerfeld Number of Bearing?

With Radius of Journal (r), Radial clearance for bearing (c), Dynamic Viscosity of Lubricant (μ_l), Journal Speed (n_s) & Unit bearing pressure for bearing (p) we can find Sommerfeld Number of Bearing using the formula - Sommerfeld Number of Journal Bearing = (((Radius of Journal/Radial clearance for bearing)^2)*Dynamic Viscosity of Lubricant*Journal Speed)/(Unit bearing pressure for bearing*2*pi). This formula also uses Archimedes' constant .

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Sommerfeld Number of Bearing Formula

Sommerfeld Number of Bearing Example

Sommerfeld Number of Bearing Solution

Sommerfeld Number of Bearing Formula Elements

Other formulas in Dimensionless Performance Parameters category

How to Evaluate Sommerfeld Number of Bearing?

FAQs on Sommerfeld Number of Bearing

Variable Name