BIZOMAT MAKEOS · Engineering
Journal Bearing Friction (Petroff) and Sommerfeld Number
What friction torque, power loss and Sommerfeld number does this lightly loaded journal bearing have?
Unit load, Petroff friction torque, coefficient of friction and power loss of a hydrodynamic journal bearing, with the Sommerfeld number for use with design charts.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Journal diameter | mm | Journal (shaft) diameter. |
| Bearing length | mm | Bearing length. |
| Radial clearance | mm | Radial clearance = (bore − journal) ÷ 2. |
| Oil viscosity at operating temperature | mPa·s (cP) | Dynamic viscosity at the film temperature (centistokes × density in g/cm³ gives mPa·s; see the oil viscosity tool). |
| Speed | rpm | Shaft speed. |
| Radial load | N | Radial load on the bearing. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Journal diameter
- What it is
- The diameter of the journal, the part of the shaft that runs inside the bearing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction torque rises with the cube of the journal radius.
- Get it right
- Enter the diameter; the tool uses half of it as the radius.
What this means: Bearing length
- What it is
- The axial length of the bearing surface that carries the load, along the shaft.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Deduct oil grooves that run round the bearing from the length.
What this means: Radial clearance
- What it is
- The radial clearance: half the difference between bearing bore and journal diameter, the gap on one side when the journal is centred.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.04 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction torque and power loss are inversely proportional to the clearance.
- Get it right
- Do not enter the diametral clearance (bore minus journal); that is twice the radial value.
What this means: Oil viscosity at operating temperature
- What it is
- The dynamic (absolute) viscosity of the oil at the temperature of the oil film in the running bearing.
- Units and format
- Enter a number in mPa·s (cP): mPa·s (cP). The form accepts 0.000001 mPa·s (cP) to 100000 mPa·s (cP). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mPa·s (cP) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction torque, power loss and the Sommerfeld number are directly proportional to viscosity.
- Get it right
- Data sheets often give kinematic viscosity in cSt: multiply by the density in g/cm³ for mPa·s, and use the film temperature.
What this means: Speed
- What it is
- The rotational speed of the journal relative to the bearing.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction torque is proportional to speed and power loss to the square of speed.
- Get it right
- If both parts turn, use the relative speed between them.
What this means: Radial load
- What it is
- The total radial load the bearing carries, from shaft weight, belt pull, gear forces and similar.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The load does not change Petroff torque; a higher load lowers the friction coefficient and Sommerfeld number.
- Get it right
- This is the total load on this bearing, not the load per unit area.
Method and formulas
- Unit load P = W ÷ (d L).
- Petroff torque T = 4π² r³ L μ N ÷ c (N in rev/s); friction coefficient f = 2π² (μN/P)(r/c).
- Sommerfeld number S = (r/c)² μN ÷ P; power loss = 2πN T.
- Example: the default bearing has S = 0.12207, f = 0.0038553 and loses 75.699 W.
Limitations
- Petroff’s equation assumes a concentric journal (light load); at higher loads use the Sommerfeld number with design charts.
- Viscosity must be taken at the actual film temperature.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate friction and heat in sleeve bearings
- Calculate the Sommerfeld number for Raimondi–Boyd charts
- Compare clearances and oils
Who it is for
- Design engineers
- Tribology and lubrication engineers
- Maintenance engineers
What you get
- Unit load
- Petroff friction torque and coefficient
- Power loss
- Sommerfeld number
Interpreting the result
- A larger Sommerfeld number means a thicker film; very small values risk boundary contact.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2326–2337. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Petroff's friction and power loss
In Plain Bearings by the Numbers
What it covers: Derive Petroff's equation for a journal bearing's friction, use the BIZOMAT Petroff tool for torque, friction coefficient, power loss and Sommerfeld number, and correct the result for eccentricity.
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