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Radius of Journal given Sommerfeld Number of Bearing Formula

GoRadius of Journal in Terms of Radial Clearance of Bearing Formula

GoRadius of Journal in Terms of Minimum Film Thickness of Bearing Formula

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

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

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

Radius of Journal given Sommerfeld Number of Bearing Example

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With units

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

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

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

25.4651 = 0.024 \cdot \sqrt{2 \cdot 3.1416 \cdot 2.58 \cdot \frac{0.96}{220 \cdot 10}}

25.4651mm = 0.024mm \cdot \sqrt{2 \cdot 3.1416 \cdot 2.58 \cdot \frac{0.96MPa}{220cP \cdot 10rev/s}}

25.4651 = 0.024 \cdot \sqrt{2 \cdot 3.1416 \cdot 2.58 \cdot \frac{0.96}{220 \cdot 10}}

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Radius of Journal given Sommerfeld Number of Bearing Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r = 0.024mm \cdot \sqrt{2 \cdot π \cdot 2.58 \cdot \frac{0.96MPa}{220cP \cdot 10rev/s}}

Next Step Substitute values of Constants

∴

r = 0.024mm \cdot \sqrt{2 \cdot 3.1416 \cdot 2.58 \cdot \frac{0.96MPa}{220cP \cdot 10rev/s}}

Next Step Convert Units

∴

r = 2.4E-5m \cdot \sqrt{2 \cdot 3.1416 \cdot 2.58 \cdot \frac{960000Pa}{0.22Pa*s \cdot 62.8319rad/s}}

Next Step Prepare to Evaluate

∴

r = 2.4E-5 \cdot \sqrt{2 \cdot 3.1416 \cdot 2.58 \cdot \frac{960000}{0.22 \cdot 62.8319}}

Next Step Evaluate

∴

r = 0.0254650991115349m

Next Step Convert to Output's Unit

∴

r = 25.4650991115349mm

LAST Step Rounding Answer

∴

r = 25.4651mm

Radius of Journal given Sommerfeld Number of Bearing Formula Elements

Variables

Constants

Functions

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

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

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

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

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

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.

Syntax: sqrt(Number)

Other Formulas to find Radius of Journal

Go Radius of Journal in Terms of Radial Clearance of Bearing

r = R - c

Go Radius of Journal in Terms of Minimum Film Thickness of Bearing

r = R - (e + h °)

Go Radius of Journal in Terms of Flow Variable

r = Q cs \cdot 2 \cdot \frac{π}{FV \cdot c \cdot n s \cdot l a}

Other formulas in Journal category

Go Journal Speed in Terms of Sommerfeld Number of Bearing

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

Go Journal Diameter given Unit Bearing Pressure

d = \frac{W r}{p \cdot l a}

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

Q cs = \frac{FV \cdot r \cdot c \cdot n s \cdot l a}{2 \cdot π}

Go Journal Speed in Terms of Flow Variable

n s = Q cs \cdot 2 \cdot \frac{π}{r \cdot c \cdot FV \cdot l a}

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

Radius of Journal given Sommerfeld Number of Bearing evaluator 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 evaluate 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 evaluate Radius of Journal given Sommerfeld Number of Bearing using this online evaluator? To use this online evaluator 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.

FAQs on Radius of Journal given Sommerfeld Number of Bearing

What is the formula to find Radius of Journal given Sommerfeld Number of Bearing?

The formula of Radius of Journal given Sommerfeld Number of Bearing is expressed as 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)). Here is an example- 25465.1 = 2.4E-05*sqrt(2*pi*2.58*960000/(0.22*62.8318530685963)).

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

With 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) we can find Radius of Journal given Sommerfeld Number of Bearing using the formula - 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)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Radius of Journal?

Here are the different ways to Calculate Radius of Journal-

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)

Can the Radius of Journal given Sommerfeld Number of Bearing be negative?

No, the Radius of Journal given Sommerfeld Number of Bearing, measured in Length cannot be negative.

Which unit is used to measure Radius of Journal given Sommerfeld Number of Bearing?

Radius of Journal given Sommerfeld Number of Bearing is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Journal given Sommerfeld Number of Bearing can be measured.

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Radius of Journal given Sommerfeld Number of Bearing Formula

​GoRadius of Journal in Terms of Radial Clearance of Bearing Formula

​GoRadius of Journal in Terms of Minimum Film Thickness of Bearing Formula

Radius of Journal given Sommerfeld Number of Bearing Example

Radius of Journal given Sommerfeld Number of Bearing Solution

Radius of Journal given Sommerfeld Number of Bearing Formula Elements

Other Formulas to find Radius of Journal

Other formulas in Journal category

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

FAQs on Radius of Journal given Sommerfeld Number of Bearing

Variable Name

GoRadius of Journal in Terms of Radial Clearance of Bearing Formula

GoRadius of Journal in Terms of Minimum Film Thickness of Bearing Formula