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# Tolerances for seats on hollow shafts

When a bearing is mounted on a hollow shaft using an interference fit, the shaft experiences more elastic deformation than a solid shaft. As a result, the effectiveness of the fit is less than for the same size solid shaft. The effectiveness of an interference fit on a hollow shaft depends on certain diameter ratios (fig. 1):
• the diameter ratio of the hollow shaft ci = di / d
For diameter ratios ci ≤ 0,5 the reduction of effectiveness is negligible.
• the diameter ratio of the bearing inner ring ce = d / de
When the average outside diameter of the inner ring de is not known, the diameter ratio can be estimated from

where  ce diameter ratio of the bearing inner ring d bearing bore diameter [mm] D bearing outside diameter [mm] k adjustment factor 0,25 for self-aligning ball bearings in the 22 and 23 series 0,25 for cylindrical roller bearings 0,3 for other bearings
For shaft diameter ratios ci > 0,5 the diameter tolerance determined for a seat on a solid shaft should be adjusted to achieve the same effectiveness of the fit on the hollow shaft. This can be done with the following procedure.
1. Determine the mean probable interference for the tolerance selected for a seat on a solid shaft, ΔS (→ Tolerances and resultant fits).
2. Determine the required increase of interference for the seat on the hollow shaft from diagram 1 based on the diameter ratios ci and ce.
3. Calculate the required mean probable interference for the seat on the hollow shaft and select the tolerance class accordingly.

## Example

A 6208 deep groove ball bearing with d = 40 mm and D = 80 mm is to be mounted on a hollow shaft with a diameter ratio ci = 0,8. What is the appropriate tolerance class for the shaft seat?

The bearing is subjected to normal loads, and a tolerance class k5 is appropriate for a seat on a solid shaft.

• The diameter ratio of the bearing inner ring is

• The mean probable interference on a solid shaft is
ΔS = (22 + 5) / 2 = 13,5 μm (→ table 1, k5 for a 40 mm shaft diameter)

• The increase in interference for the seat on the hollow shaft is
ΔHS = 1,7 (→ diagram 1, ci = 0,8, ce = 0,77)

• The requisite interference for the seat on the hollow shaft is
ΔH = 1,7 x 13,5 = 23 μm

• The appropriate tolerance class for the seat on the hollow shaft is m6 (→ table 1, mean probable interference, (33 + 13) / 2 = 23 μm)