# Calculating surface speed at bearing points

#### Lars Butenschön | 24. June 2021

To correctly design plain bearings, you primarily need two fundamental parameters: the sliding speed (v in metres per second) and the load to be carried (p in N/mm²). Together, they give you the pv value, which is an important quantity in the selection of plain bearings. Calculating the load or surface pressure is relatively simple, but calculating surface speed requires a few more formulae and parameters. This blog post will cover the most frequently encountered movement cases and the calculations they require.

#### Calculating surface speed at bearing points with rotating movement

For applications in which the shaft performs complete rotations in the bearings, the peripheral speed at the bearing’s inner diameter must be calculated. This requires the relevant bearing diameter and the number of rotations per unit of time (ideally rpm). Then we just plug the values into the formula.

**The formula: v(u) = π * d * n**

Since the standard units used in the area of plain bearings are mm and rpm, the formula requires conversion factors.

**Formula with conversion: v(u) = ( π * d * n ) / ( 1000 x 60 )**

For a bearing with a 20mm diameter (d) and a rotation speed (n) of 100rpm, the calculation for surface speed is:

v(u) = π * d * n => v(u) = 3.142 * 0.002m * 1.667 1/s = 0.01m/s (numbers rounded to two decimal points)

One source of error is unit conversion. In practice, bearing diameter is often given in mm and rotation speed in rpm. The first must be converted into metres and the second into rotations per second. The formula returns peripheral speed in metres per second.

#### Calculating surface speed at bearing points with pivoting or oscillating movement

Another frequent plain bearing operating mode is swivelling or oscillating movement. This occurs in hinges or applications with other types of pivoting movement. The shaft rotates in alternating directions at the bearing point. The angle representing the difference between the two end positions is the pivot angle. In these applications, movement frequency and pivot angle are often the only known quantities. But the calculations for these applications also require peripheral speed, or the speed at which the shafts move relative to each other. The formula takes into account the angle and is therefore a bit more complicated.

**The formula: v(u) = ( n * ꞵ * d * π ) / 360**

Here, ꞵ is the pivot angle. Adapted to bearing diameter in mm and pivot cycles per minute:

**v(u) = (n * ꞵ * d * π) / (60 * 1000 * 360)**

This formula can be used to calculate the surface speed for pivoting applications.

#### Calculating surface speed and pv value made easy

If you don’t want to do painstaking surface speed calculations by hand, there is another option: the iglidur plain bearing expert. This free tool enables you to perform calculations very simply without disclosing your personal data. At the same time, the program shows the right polymer plain bearing and its potential service life.

Do you need help designing your plain bearing? We would be happy to advise you, help you determine the various parameters, and recommend bearing solutions that would work.