Plain bearing friction power
Calculates friction force, friction torque and friction power of a plain bearing from a supplied friction coefficient, load, diameter and speed -- the friction coefficient itself is explicitly a required input, not a universal figure.
Formula
PR = mu * F * u (equivalently: M = mu*F*d/2, PR = M*omega)
Friction force and torque follow directly from the friction coefficient mu and the load F; friction power follows either from friction force times sliding speed or equivalently from friction torque times angular velocity. Both paths give the same result and are both reported here for cross-checking.
What this model does not show
Friction coefficient mu is not a material constant; it depends on the lubrication regime (Stribeck curve: boundary, mixed and full-film friction), and therefore on viscosity, speed, load, clearance and temperature -- it must come from measurement or a manufacturer figure valid for the specific operating point. The computed friction power also generates heat that lowers film temperature and therefore changes viscosity -- this shifts the operating point (and mu itself) away from this static snapshot; a full thermal balance (heat removal through housing and lubricant) is a separate check not included here.
Worked example
mu = 0.02 (assumed for mixed friction), F = 5,000 N, d = 50 mm, n = 1,500 rpm. Friction force: 0.02 x 5,000 N = 100 N. Friction torque: M = 100 N x 0.025 m = 2.5 N*m. Sliding speed (as in calculator 55): v ~ 3.927 m/s. Friction power via force: PR = 100 N x 3.927 m/s ~ 392.7 W. Cross-check via torque: omega = 2*pi*1,500/60 ~ 157.08 rad/s, PR = 2.5 N*m x 157.08 rad/s ~ 392.7 W -- both paths agree.
Common mistakes
- Adopting a 'typical' friction coefficient found online unchecked for one's own operating point, without checking the lubrication regime and operating conditions.
- Assuming friction power is constant over the operating time, even though viscosity and therefore mu can change due to the heat generated.
- Confusing friction torque with friction force (a factor d/2 difference, plus different units N vs. N*m).
Frequently asked questions
Where do I get the friction coefficient mu?
From a measurement on the actual bearing or from a manufacturer figure valid for the present lubrication regime (boundary, mixed or full-film friction), the material pairing and the operating conditions -- not from a generic table value.
What is the Stribeck curve and why does it matter here?
The Stribeck curve shows friction coefficient mu as a function of a dimensionless figure combining viscosity, speed and load. It shows that mu varies strongly with the operating point (high in boundary friction, low in full-film friction) -- so a single 'friction coefficient' is valid only for exactly one operating point.
Why do the two calculation paths (force x speed and torque x angular velocity) agree?
Both are mathematically equivalent formulations of the same power: PR = F_R*u = (F_R*d/2)*(u/(d/2)) = M*omega, since u = omega*d/2. In the calculator they serve as a mutual cross-check.
How does friction power affect viscosity?
Friction power converts to heat, which warms the film and lowers its viscosity (see calculator 51/52). Lower viscosity in turn changes the Sommerfeld number and the resulting friction coefficient -- a self-influencing (thermally coupled) loop.
Does this calculator compute the bearing's actual operating temperature?
No. It only returns friction power for a given, assumed friction coefficient. A thermal balance with heat removal through the housing, lubricant flow and ambient conditions is a separate calculation step not covered here.
How does friction power relate to the PV figure?
The PV value (calculator 56) is an approximate, area-based indicator of thermal duty without a known friction coefficient. Friction power here is the actual, absolute power loss once a specific friction coefficient is known -- a more precise but more data-intensive figure.