Calculation
PR = μ · F · uW
Friction power, together with the cooling surface, sets the bearing's operating temperature and thus indirectly the ηeff to use.
PR = μ·F·uW
Plain bearing friction power loss
Friction power, together with the cooling surface, sets the bearing's operating temperature and thus indirectly the ηeff to use.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Friction power loss PR — Mechanical power converted to heat in the lubricant film.
- Friction coefficient μ — Friction value from μ/ψ and the Sommerfeld number; typically 0.001 to 0.01 for hydrodynamic journal bearings.
- Bearing force F — Resultant radial force acting on the bearing.
- Shaft surface speed uW — Shaft journal surface speed, uW = π·dW·nW.
Example
μ = 0.005, F = 5,000 N and uW = 3.93 m/s give PR ≈ 98.3 W.
Assumptions and limits
Steady-state operation at constant μ; transient start-up and mixed friction with a much higher μ are not captured.
Understand Plain bearing friction power loss
This calculator determines the friction power dissipated as heat in a plain bearing from the friction coefficient, bearing force and shaft surface speed.
What does this quantity describe?
The friction power loss PR = μ·F·uW describes the mechanical power converted to heat by internal friction in the lubricant film. Together with the cooling surface and ambient temperature, it determines the bearing's operating temperature and thus indirectly the effective viscosity ηeff to use.
Think of the friction heat between two surfaces sliding past each other: the greater the contact force and the faster the relative motion, the more heat is generated — in a well-lubricated plain bearing, however, this friction is very low thanks to the load-carrying oil film.
Formula and variables
PR = μ · F · uW
PR = μ · F · uWμ = PR / (F · uW)uW = PR / (μ · F)
| Symbol / input | Meaning |
|---|---|
| Friction power loss PR | Mechanical power converted to heat in the lubricant film. |
| Friction coefficient μ | Friction value from μ/ψ and the Sommerfeld number; typically 0.001 to 0.01 for hydrodynamic journal bearings. |
| Bearing force F | Resultant radial force acting on the bearing. |
| Shaft surface speed uW | Shaft journal surface speed, uW = π·dW·nW. |
Choose the inputs correctly
μ is the friction coefficient (determined from μ/ψ and the Sommerfeld number via TB 15-12), F the radial force acting on the bearing, and uW the shaft journal's surface speed (uW = π·dW·nW).
How to use the calculator
Determine μ via the Sommerfeld number and TB 15-12, then enter μ, F and uW to get PR.
Worked example
μ = 0.005, F = 5,000 N and uW = 3.93 m/s give PR = 0.005 · 5,000 N · 3.93 m/s ≈ 98.3 W.
Understand the result and units
PR ≈ 98 W is the power released as heat in the bearing, which must be removed via bearing cooling (housing, oil circuit) to avoid too high an operating temperature and thus too great a drop in oil viscosity.
μ is dimensionless, F is given in N and uW in m/s; PR results in watts.
Friction power as part of the bearing's heat balance
In steady-state operation, the friction power PR generated in the lubricant film must equal the heat power removed via housing, oil circuit and any external cooling. If cooling is insufficient, oil temperature rises until a new equilibrium is reached — usually at a lower viscosity ηeff, which in turn worsens the Sommerfeld number and minimum film thickness. Friction power is thus not just a loss quantity but also a feedback element in the overall plain bearing design.
Typical applications
Friction power loss is used for the thermal design of plain bearings, e.g. sizing the cooling or oil circuit of turbine, gearbox and crankshaft bearings.
Assumptions, limits and common mistakes
The formula applies to steady-state operation at constant friction coefficient μ. During start-up or under mixed friction (insufficient lubricant film), μ is much higher, and the actual friction power can substantially exceed the steady-state value calculated here.
Common mistake: A common mistake is taking μ from a table for a different operating regime (e.g. mixed friction instead of hydrodynamic lubrication), which substantially distorts the calculated friction power.
Frequently asked questions
Where do I get the friction coefficient μ?
From μ/ψ and the Sommerfeld number via a chart or table such as TB 15-12; typical hydrodynamic values range from 0.001 to 0.01.
What happens to the generated friction power?
It is removed as heat via the housing, oil circuit or external cooling, and determines the bearing's operating temperature.
Does the formula apply during start-up?
No, start-up usually involves mixed or boundary friction with a much higher μ than steady-state hydrodynamic operation.
How does PR relate to viscosity?
Excessive friction power heats the oil, lowering ηeff, which feeds back into the Sommerfeld number and film thickness.
How do I reduce friction power?
Lower bearing force, lower surface speed or a more favorable width ratio reduce μ and thus PR, usually at the cost of load capacity or size.