Calculating the radial load acting on matched bearings

When matched tapered roller bearings, arranged face-to-face or back-to-back, are mounted together with a third bearing, the bearing arrangement is statically indeterminate. In these cases, the radial load Fr acting on the bearing pair must be calculated first.

Matched bearings arranged face-to-face

For matched bearings, where two bearings are arranged face-to-face (fig. 1), it can be assumed that the radial load acts at the geometric centre of the matched bearings, as the distance between the pressure centres of the two bearings is short when compared with the distance between the geometric centres of the set and the other bearing. In this case, it can be assumed that the bearing arrangement is statically determined.

Matched bearings arranged back-to-back

The distance a between the pressure centres of two matched bearings arranged back-to-back is significant when compared with the distance L between the geometric centres of the matched bearings and the other bearing (fig. 2). Therefore, it is necessary to calculate the magnitude of the load acting on the bearing pair and also the distance a1 at which the load acts. The magnitude of the radial load can be obtained using: where
 Fr radial load acting on a bearing pair [kN] Kr radial force acting on the shaft [kN] L distance between the geometric centres of the two bearing positions [mm] L1 distance between the centre of bearing position I and the point of action of the force Kr [mm] a distance between the bearing pressure centres [mm] (→ product table) a1 distance between the geometric centre of the matched bearings and the point of action of the radial load Fr [mm] (→ diagram 1, calculation factor Y2 → product table) The distance a1 can be determined from diagram 1 by making an initial assumption for Fr and if necessary followed by several iterative calculations. 