Sommerfeld Number of Bearing Calculator

✖The Radius of Journal is the radius of the journal (which rotates freely in a supporting metal sleeve or shell).ⓘ Radius of Journal [r]			+10% -10%
✖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.ⓘ Radial clearance for bearing [c]			+10% -10%
✖The Dynamic Viscosity of Lubricant is the resistance to movement of one layer of fluid over another.ⓘ Dynamic Viscosity of Lubricant [μ_l]			+10% -10%
✖The Journal Speed Value is defined as the speed of the journal of a bearing.ⓘ Journal Speed [n_s]			+10% -10%
✖Unit bearing pressure for bearing is the average pressure acting on the contact surface of the bearing.ⓘ Unit bearing pressure for bearing [p]			+10% -10%

✖Sommerfeld Number of Journal Bearing is a dimensionless number that is used in designing a hydrodynamic bearing.ⓘ Sommerfeld Number of Bearing [S]

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Formula

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Sommerfeld Number of Bearing

Formula

`"S" = ((("r"/"c")^2)*"μ"_{"l"}*"n"_{"s"})/("p"*2*pi)`

Example

`"2.587077"=((("25.5mm"/"0.024mm")^2)*"220cP"*"10rev/s")/("0.96MPa"*2*pi)`

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Sommerfeld Number of Bearing Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
S = (((r/c)^2)*μ_l*n_s)/(p*2*pi)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Sommerfeld Number of Journal Bearing - Sommerfeld Number of Journal Bearing is a dimensionless number that is used in designing a hydrodynamic bearing.
Radius of Journal - (Measured in Meter) - The Radius of Journal is the radius of the journal (which rotates freely in a supporting metal sleeve or shell).
Radial clearance for bearing - (Measured in Meter) - 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.
Dynamic Viscosity of Lubricant - (Measured in Pascal Second) - The Dynamic Viscosity of Lubricant is the resistance to movement of one layer of fluid over another.
Journal Speed - (Measured in Radian per Second) - The Journal Speed Value is defined as the speed of the journal of a bearing.
Unit bearing pressure for bearing - (Measured in Pascal) - Unit bearing pressure for bearing is the average pressure acting on the contact surface of the bearing.

STEP 1: Convert Input(s) to Base Unit

Radius of Journal: 25.5 Millimeter --> 0.0255 Meter (Check conversion here)
Radial clearance for bearing: 0.024 Millimeter --> 2.4E-05 Meter (Check conversion here)
Dynamic Viscosity of Lubricant: 220 Centipoise --> 0.22 Pascal Second (Check conversion here)
Journal Speed: 10 Revolution per Second --> 62.8318530685963 Radian per Second (Check conversion here)
Unit bearing pressure for bearing: 0.96 Megapascal --> 960000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = (((r/c)^2)*μ_l*n_s)/(p*2*pi) --> (((0.0255/2.4E-05)^2)*0.22*62.8318530685963)/(960000*2*pi)

Evaluating ... ...

S = 2.58707682278493

STEP 3: Convert Result to Output's Unit

2.58707682278493 --> No Conversion Required

FINAL ANSWER

2.58707682278493 ≈ 2.587077 <-- Sommerfeld Number of Journal Bearing

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Sliding Contact Bearing » Dimensionless Performance Parameters » Sommerfeld Number of Bearing

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 9 Dimensionless Performance Parameters Calculators

Sommerfeld Number of Bearing

Go 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)

Flow Variable in Terms of Flow of Lubricant in Clearance Space of Journal

Go Flow Variable = (2*pi*Flow of Lubricant into Clearance Space)/(Radius of Journal*Radial clearance for bearing*Journal Speed*Axial Length of Bearing)

Load Coefficient in Terms of Load Acting on Bearing

Go Load coefficient for bearing = Load Acting on Sliding Bearing/(Total Projected Area of Bearing Pad*Pressure of Lubricating Oil)

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

Go Coefficient of Friction Variable = Radius of Journal*Coefficient of friction for journal bearing/Radial clearance for bearing

Radial Clearance in Terms of Coefficient of Friction Variable of Bearing

Go Radial clearance for bearing = Radius of Journal*Coefficient of friction for journal bearing/Coefficient of Friction Variable

Coefficient of Friction in Terms of Coefficient of friction Variable

Go Coefficient of friction for journal bearing = Coefficient of Friction Variable*Radial clearance for bearing/Radius of Journal

Radius of Journal in Terms of Coefficient of Friction Variable

Go Radius of Journal = Coefficient of Friction Variable*Radial clearance for bearing/Coefficient of friction for journal bearing

Flow of Lubricant into Clearance of Journal given Outflow and Flow Ratio Variable

Go Flow of Lubricant = Flow Ratio Variable*Out-Flow of Lubricant

Flow Ratio Variable in Terms of Outflow of Lubricant

Go Flow Ratio Variable = Flow of Lubricant/Out-Flow of Lubricant

Sommerfeld Number of Bearing Formula

What is Sliding Contact Bearing?

The sliding contact bearings in which the sliding action is along the circumference of a circle or an arc of a circle and carrying radial loads are known as journal or sleeve bearings.

How to Calculate Sommerfeld Number of Bearing?

Sommerfeld Number of Bearing calculator 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 calculate 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 calculate Sommerfeld Number of Bearing using this online calculator? To use this online calculator 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. Here is how the Sommerfeld Number of Bearing calculation can be explained with given input values -> 2.587077 = (((0.0255/2.4E-05)^2)*0.22*62.8318530685963)/(960000*2*pi).

FAQ

What is Sommerfeld Number of 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 and is represented as S = (((r/c)^2)*μ_l*n_s)/(p*2*pi) or 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). The Radius of Journal is the radius of the journal (which rotates freely in a supporting metal sleeve or shell), 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, The Dynamic Viscosity of Lubricant is the resistance to movement of one layer of fluid over another, The Journal Speed Value is defined as the speed of the journal of a bearing & Unit bearing pressure for bearing is the average pressure acting on the contact surface of the bearing.

How to calculate Sommerfeld Number of 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 is calculated using 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 calculate Sommerfeld Number of Bearing, you need 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). With our tool, you need to enter the respective value for Radius of Journal, Radial clearance for bearing, Dynamic Viscosity of Lubricant, Journal Speed & Unit bearing pressure for bearing and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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