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# Fits for hollow shafts

If bearings are to be mounted with an interference fit on a hollow shaft it is generally necessary to use a heavier interference fit than would be used for a solid shaft in order to achieve the same surface pressure between the inner ring and shaft seat.
The following diameter ratios are important when deciding on the fit to be used

ci = di/d and ce = d/de
The fit is not appreciably affected until the diameter ratio of the hollow shaft ci ≥ 0,5. If the average outside diameter of the inner ring is not known, the diameter ratio ce can be calculated with sufficient accuracy using the equation

ce = d/[k (D – d) + d]

where

 ci = diameter ratio of hollow shaft ce = diameter ratio of inner ring d = outside diameter of hollow shaft, bore diameter of the bearing, mm di = internal diameter of the hollow shaft, mm de = average outside diameter of the inner ring, mm D = outside bearing diameter, mm k = a factor for the bearing type for self-aligning ball bearings in the 22 and 23 series, k = 0,25 for cylindrical roller bearings, k = 0,25 for all other bearings, k = 0,3
To determine the requisite interference fit for a bearing to be mounted on a hollow shaft, use the mean probable interference between the shaft seat and bearing bore obtained for the tolerance recommendation for a solid shaft of the same diameter. If the plastic deformation (smoothing) of the mating surfaces produced during mounting is neglected, then the effective interference can be equated to the mean probable interference.
The interference ΔH needed for a hollow shaft of steel can then be determined in relation to the known interference ΔV for the solid shaft from diagram 1. ΔV equals the mean value of the smallest and largest values of the probable interference for the solid shaft. The tolerance for the hollow shaft is then selected so that the mean probable interference is as close as possible to the interference ΔH obtained from diagram 2.

## Example

A deep groove ball bearing 6208 with d = 40 mm and D = 80 mm is to be mounted on a hollow shaft having a diameter ratio ci = 0,8. What is the requisite interference and what are the appropriate shaft limits?

If the bearing were to be mounted on a solid steel shaft and subjected to normal loads, a tolerance k5 would be recommended, see table. For a shaft diameter of 40 mm, the mean probable interference ΔV = (22 + 5)/2 = 13,5 μm.

For ci = 0,8 and ce = 40/[0,3(80 - 40) + 40] = 0,77 so that from diagram 3, ΔHV = 1,7.
Thus the requisite interference for the hollow shaft ΔH = 1,7 × 13,5 = 23 μm. Consequently, tolerance m6 is selected for the hollow shaft as this gives a mean probable interference of this order.