Plain bearing sliding speed
Calculates the surface speed of the journal relative to the bearing bush from diameter and rotational speed -- the basis for the PV value and the Sommerfeld number.
Formula
v = pi * d * n / 60
Sliding speed is the surface speed of a point on the journal. It follows from the circumference pi*d and the rotational speed n, converted from revolutions per minute to a speed per second by dividing by 60 (and, depending on units used, by 1000 to convert millimeters to meters).
What this model does not show
The formula v = pi*d*n/60 applies to continuous rotation. For oscillating motion (e.g. swiveling bearing points), average sliding speed must be determined from the swing angle and oscillation frequency -- a rotational speed in the conventional sense does not exist there. There is also no universal maximum permissible v; allowable speeds depend on material pairing, lubrication type and heat dissipation.
Worked example
A shaft with d = 50 mm rotates at n = 1,500 rpm. Circumference: pi x 50 mm ~ 157.08 mm. Sliding speed: v = 157.08 mm x 1,500 rpm / 60 = 3,927 mm/s = 3.927 m/s. For comparison, at the same speed but d = 25 mm, v would be only ~1.96 m/s -- sliding speed scales linearly with diameter.
Common mistakes
- Using rotational speed directly as a velocity, without multiplying by the circumference pi*d.
- Forgetting to convert from rpm to a per-second speed (dividing by 60).
- Applying the formula unchanged to oscillating swivel motion, for which no rotational speed is defined.
Frequently asked questions
What's the difference between rotational speed and sliding speed?
Rotational speed n (in rpm) describes how often the shaft turns per minute, independent of its size. Sliding speed v additionally depends on diameter: at the same rpm, a thicker shaft slides faster along the bearing surface.
Why divide by 60?
Rotational speed n is given in revolutions per minute, but sliding speed is conventionally expressed in meters per second. Dividing by 60 converts from minutes to seconds.
Does this formula also apply to oscillating bearings?
No. Oscillating (swiveling) motion has no continuous rotational speed; average sliding speed must instead be calculated from the swing angle, shaft radius and oscillation frequency.
Is there a maximum permissible v?
No universal one. Permissible sliding speeds depend on the material pairing (e.g. white metal, polymer plain bearings), lubrication type and heat dissipation, and must be checked against datasheets.
How does v relate to the PV value?
The PV value (calculator 56) is the product of specific load p and sliding speed v. Both quantities -- not just their product -- must additionally stay within their own permissible limits.
Does v change during operation?
Yes, whenever rotational speed changes (e.g. during start-up or braking). A complete assessment may need to check several operating points at different speeds separately.