Radius of Journal given Sommerfeld Number of Bearing Calculator

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

✖The Radius of Journal is the radius of the journal (which rotates freely in a supporting metal sleeve or shell).ⓘ Radius of Journal given Sommerfeld Number of Bearing [r]

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Formula

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Radius of Journal given Sommerfeld Number of Bearing

Formula

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

Example

`"25.4651mm"="0.024mm"*sqrt(2*pi*"2.58"*"0.96MPa"/("220cP"*"10rev/s"))`

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Radius of Journal given Sommerfeld Number of Bearing Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Journal = Radial clearance for bearing*sqrt(2*pi*Sommerfeld Number of Journal Bearing*Unit bearing pressure for bearing/(Dynamic Viscosity of Lubricant*Journal Speed))
r = c*sqrt(2*pi*S*p/(μ_l*n_s))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Radial clearance for bearing: 0.024 Millimeter --> 2.4E-05 Meter (Check conversion here)
Sommerfeld Number of Journal Bearing: 2.58 --> No Conversion Required
Unit bearing pressure for bearing: 0.96 Megapascal --> 960000 Pascal (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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = c*sqrt(2*pi*S*p/(μ_l*n_s)) --> 2.4E-05*sqrt(2*pi*2.58*960000/(0.22*62.8318530685963))

Evaluating ... ...

r = 0.0254650991115349

STEP 3: Convert Result to Output's Unit

0.0254650991115349 Meter -->25.4650991115349 Millimeter (Check conversion here)

FINAL ANSWER

25.4650991115349 ≈ 25.4651 Millimeter <-- Radius of Journal

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Sliding Contact Bearing » Journal » Radius of Journal given 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

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< 8 Journal Calculators

Radius of Journal given Sommerfeld Number of Bearing

Go Radius of Journal = Radial clearance for bearing*sqrt(2*pi*Sommerfeld Number of Journal Bearing*Unit bearing pressure for bearing/(Dynamic Viscosity of Lubricant*Journal Speed))

Journal Speed in Terms of Sommerfeld Number of Bearing

Go Journal Speed = 2*pi*Sommerfeld Number of Journal Bearing*Unit bearing pressure for bearing/(((Radius of Journal/Radial clearance for bearing)^2)*Dynamic Viscosity of Lubricant)

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

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

Radius of Journal in Terms of Flow Variable

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

Journal Speed in Terms of Flow Variable

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

Journal Diameter given Unit Bearing Pressure

Go Journal Diameter = Radial load acting on sliding bearing/(Unit bearing pressure for bearing*Axial Length of Bearing)

Radius of Journal in Terms of Minimum Film Thickness of Bearing

Go Radius of Journal = Radius of Bearing-(Eccentricity in bearing+Minimum Film Thickness)

Radius of Journal in Terms of Radial Clearance of Bearing

Go Radius of Journal = Radius of Bearing-Radial clearance for bearing

Radius of Journal given 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 Radius of Journal given Sommerfeld Number of Bearing?

Radius of Journal given Sommerfeld Number of Bearing calculator uses Radius of Journal = Radial clearance for bearing*sqrt(2*pi*Sommerfeld Number of Journal Bearing*Unit bearing pressure for bearing/(Dynamic Viscosity of Lubricant*Journal Speed)) to calculate the Radius of Journal, The Radius of Journal given Sommerfeld Number of Bearing formula is defined as product of radial clearance and the square root of the ratio of the product of sommerfeld number and unit bearing pressure to the product of viscosity of lubricant and journal speed. Radius of Journal is denoted by r symbol.

How to calculate Radius of Journal given Sommerfeld Number of Bearing using this online calculator? To use this online calculator for Radius of Journal given Sommerfeld Number of Bearing, enter Radial clearance for bearing (c), Sommerfeld Number of Journal Bearing (S), Unit bearing pressure for bearing (p), Dynamic Viscosity of Lubricant (μ_l) & Journal Speed (n_s) and hit the calculate button. Here is how the Radius of Journal given Sommerfeld Number of Bearing calculation can be explained with given input values -> 25465.1 = 2.4E-05*sqrt(2*pi*2.58*960000/(0.22*62.8318530685963)).

FAQ

What is Radius of Journal given Sommerfeld Number of Bearing?

The Radius of Journal given Sommerfeld Number of Bearing formula is defined as product of radial clearance and the square root of the ratio of the product of sommerfeld number and unit bearing pressure to the product of viscosity of lubricant and journal speed and is represented as r = c*sqrt(2*pi*S*p/(μ_l*n_s)) or Radius of Journal = Radial clearance for bearing*sqrt(2*pi*Sommerfeld Number of Journal Bearing*Unit bearing pressure for bearing/(Dynamic Viscosity of Lubricant*Journal Speed)). 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, Sommerfeld Number of Journal Bearing is a dimensionless number that is used in designing a hydrodynamic bearing, Unit bearing pressure for bearing is the average pressure acting on the contact surface of the bearing, 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.

How to calculate Radius of Journal given Sommerfeld Number of Bearing?

The Radius of Journal given Sommerfeld Number of Bearing formula is defined as product of radial clearance and the square root of the ratio of the product of sommerfeld number and unit bearing pressure to the product of viscosity of lubricant and journal speed is calculated using Radius of Journal = Radial clearance for bearing*sqrt(2*pi*Sommerfeld Number of Journal Bearing*Unit bearing pressure for bearing/(Dynamic Viscosity of Lubricant*Journal Speed)). To calculate Radius of Journal given Sommerfeld Number of Bearing, you need Radial clearance for bearing (c), Sommerfeld Number of Journal Bearing (S), Unit bearing pressure for bearing (p), Dynamic Viscosity of Lubricant (μ_l) & Journal Speed (n_s). With our tool, you need to enter the respective value for Radial clearance for bearing, Sommerfeld Number of Journal Bearing, Unit bearing pressure for bearing, Dynamic Viscosity of Lubricant & Journal Speed and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Radius of Journal?

In this formula, Radius of Journal uses Radial clearance for bearing, Sommerfeld Number of Journal Bearing, Unit bearing pressure for bearing, Dynamic Viscosity of Lubricant & Journal Speed. We can use 3 other way(s) to calculate the same, which is/are as follows -

Radius of Journal = Radius of Bearing-Radial clearance for bearing
Radius of Journal = Radius of Bearing-(Eccentricity in bearing+Minimum Film Thickness)
Radius of Journal = Flow of Lubricant into Clearance Space*2*pi/(Flow Variable*Radial clearance for bearing*Journal Speed*Axial Length of Bearing)

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