SDN 002.15 – Bearing Clearances
This document outlines the criteria for calculating bearing clearances for the GNIRS cold mechanisms, and provides some sample calculations.
2. Requirements
The bearing clearances in the GNIRS mechanisms should be set so as to provide proper clearances when the mechanism is cold. In general, this means that the bearing housing should provide an interference fit, and the shaft should have a slip fit to allow for thermal and mechanical compensation. The calculations outlined below can be carried out for other conditions.
It is also desirable to meet these conditions when the mechanism is warm, particularly for the main mechanism axis. Even if this is not possible, it must be possible to assemble the mechanism warm, which means that one should avoid things like press fits of both housing and shaft or excessive interference fits.
3. Calculations
The calculations outlined below cover a representative case (or cases).
3.1 Facts and Assumptions
For these calculations the following facts are and assumptions are used:
·CTE values are taken from SDN0013.02. The calculations below assume a housing of 6061 Al and a bearing material 440C stainless. The shaft is 303 stainless. The differential CTE values are summarized below, where a positive sign means that the first material contracts more than the second:
|
Material
|
% Difference to 80K
|
% Difference to 60K
|
|
6061 Al – 440C Stainless
|
0.216
|
0.226
|
|
303 Stainless – 440C Stainless
|
0.105
|
0.111
|
·Bearing manufacturers suggest (for applications such as these) an interference fit of 0.0000 to 0.0004 inches for the housing. Shrinkage of the bore is stated to be roughly 80% of the interference fit – in this case, 0.0000 to 0.0003 inches. It is possible that this somewhat overestimates the effect for an aluminum housing.
·According to Roger Repp,
§A slip fit can be achieved (with care) with a clearance of 0.0002 inches.
§Shafts
can be machined to ±0.0001
inches.
§Housings can be machined to ±0.0002 inches.
3.2 Calculations
We take the case of a 5/8 inch bearing, which has (when warm) an outside diameter of 0.6250 inches and a bore of 0.2500 inches.
The required shaft diameter is calculated as follows:
When cold, the maximum bore reduction due to the interference fit is 0.00032 in. However, the differential contraction of the shaft relative to the bearing is similar, about 0.00027 in. We require 0.0002 in. clearance. This means that the warm shaft diameter can be at most 0.24965 in., which (allowing for the ±0.0001 in. tolerance) gives a diameter of 0.2496±0.0001 in. Since this diameter also provides a slip fit when warm, it is acceptable.
The required housing diameter is calculated as follows:
The maximum allowable interference is 0.0004 in. The differential contraction between the housing and the bearing is 0.00141 in. (to 60K), so that when warm the minimum clearance is 0.00101 in., for a diameter of 0.62601 in. Allowing for a ±0.0002 tolerance in the housing diameter means that it should be 0.6262±0.0002 in.
Note that there is appreciable play in the bearing housing warm, so this may impact mechanism performance when warm. Also, since both shaft and housing can slide, the bearing should be clamped or spring loaded into the housing so that it does not come out.
3.2.1 Cooling Down
The calculations above are for only the steady date cold and warm cases. Generally, on cool-down and warm-up, the housing may be expected to change first, followed by the bearing itself and then the shaft. On cool-down, if the housing cools completely and neither the bearing nor the shaft has cooled appreciably (the worst case), the interference will be somewhat larger than 0.001 in. This will cause the bearing to shrink onto the shaft, eliminating the slip fit. The bearings in the prototype mechanisms should be examined after the cooling cycle to look for damage. In practice, this scenario is probably too extreme, since once an interference fit develops, the bearing will tend to be thermally coupled to the housing and will cool accordingly.
4. Effects of Shaft Play
For the GNIRS mechanisms, some end play in the shafts of the drive train is allowable, but not in the main mechanism axes. If the mechanism itself is held by friction (and balanced so moments are small), end play in shafts simply acts as another component of backlash and is removed during mechanism operation. (This assumes that the weight of the gears and shafts is less than the forces applied during operation.)
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