Bearing Power Loss⚠ unverified
Mechanical / Lubrication · Compute the frictional power loss in a bearing
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Bearing load |
| mu | μ | — | 1.0 | Coefficient of friction (dimensionless) |
| r | r | m | 1.0 | Journal radius |
| N | N | 1/s | 1.0 | Rotational speed |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Ploss | W | Power dissipated by friction, in watts (W) |
The science & history
Understanding the Parameters
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Load $F$ and friction coefficient $\mu$ — their product $\mu F$ is the friction force at the journal surface. Both the applied load and the lubrication regime (which sets $\mu$ via the Stribeck curve) scale the loss. Full-film $\mu$ is small ($\sim0.001$–$0.005$) but non-zero — the price of viscous shear.
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Journal radius $r$ — the friction force acts at this radius, so it sets the friction torque ($T_f = \mu F r$) and the surface speed. Larger bearings lose more power for the same load.
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Rotational speed $N$ — power is proportional to speed: the friction force does work over the sliding distance, which per second is $2\pi r N$ (the circumference times revolutions per second). High-speed bearings dominate a machine's parasitic losses.
Derivation (Approaching a Proof)
Power dissipated by friction is the friction force times the sliding velocity (the rotational analogue of $P = Fv$, or equivalently friction torque times angular speed):
$$P_{loss} = F_f\,v = (\mu F)\,(2\pi r N).$$
Here the friction force is $F_f = \mu F$ (friction coefficient times load), and the sliding velocity at the journal surface is $v = 2\pi r N$ — one circumference ($2\pi r$) per revolution, $N$ revolutions per second. Multiplying:
$$P_{loss} = 2\pi F \mu r N.$$
Equivalently, in terms of the friction torque $T_f = \mu F r$ and angular speed $\omega = 2\pi N$, this is just $P = T_f\,\omega$ — the universal rotational-power law. All of this power becomes heat, raising the bearing/lubricant temperature until the heat generated equals the heat rejected (by oil flow, conduction, and convection). That thermal balance sets the operating temperature, which in turn lowers the viscosity (Viscosity Temperature) and can shift the lubrication regime — a coupled loop central to bearing thermal design.
Dimensional check. $[F \mu r N] = \text{N}\cdot\text{m}\cdot(1/\text{s}) = \text{N}\cdot\text{m/s} = \text{W}$ ($2\pi$, $\mu$ dimensionless). ✓
History and Development
Bearing frictional loss as $\mu F v$ (or $T_f\omega$) is elementary but central to machine efficiency and thermal design (Shigley, tribology handbooks). For journal bearings the friction coefficient comes from Petroff/Sommerfeld analysis (Petroff Friction); for rolling bearings, from manufacturer friction-torque models (rolling + sliding + seal + drag). Minimising this loss — through low-friction full-film operation, low-viscosity oils, and rolling elements — is a core goal of drivetrain and machine design, and the reason this heat feeds the same $Q = T\omega$ balance as Heat Generation Bearing.
Related Concepts: Petroff Friction, Heat Generation Bearing, Sommerfeld Number, Stribeck Curve, Friction, Viscosity Temperature
Notes: $P = \mu F\,v = T_f\,\omega$ with $v = 2\pi r N$. All lost as heat — feed into the bearing thermal balance. Friction coefficient from Petroff/Sommerfeld (journal) or a torque model (rolling).