For angular contact ball bearings and tapered roller bearings, the "back-to-back" arrangement is generally used to apply preload for higher rigidity.
This is because shaft rigidity is improved by the longer distance between load centers in the back-to-back arrangement.
Fig. 11-1 shows the relationship between preload given via position preloading and rigidity expressed by displacement in the axial direction of the back-to-back bearing.
In Fig. 11-1, when preload P is applied (inner ring is tightened toward the axial direction), bearings A and B are displaced by δao respectively, and the clearance between inner rings diminishes from 2δao to zero. The displacement when axial load T is applied to these matched pair bearings from the outside can be determined as δa .

## [For reference]How to determine δa in Fig. 11-1

1. Determine the displacement curve of bearing A.
2. Determine the displacement curve of bearing B. ...Symmetrical curve in relation to horizontal axis intersecting vertical line of preload P at point x.
3. With the load from outside defined as T, determine line segment x - y on the horizontal line passing through point x.
Displace segment x - y in parallel along the displacement curve of bearing B.
Determine point y' at which to intersect displacement curve of bearing A.
4. δa can be determined as the distance between line segments x' − y' and xy.

Fig. 11-2 shows the relationship between preload and rigidity in the constant pressure preloading using the same matched pair bearings as in Fig. 11-1.
In this case, since the spring rigidity can be ignored, the matched pair bearing shows almost the same rigidity as a separate bearing with preload P applied in advance.