- #1
Juanda
Gold Member
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- TL;DR Summary
- I can't find a source giving the derivation of the support span.
The title mentions angular bearings although the concept applies to tapered bearings as well.
They can be assembled in different configurations which results in different properties.
(Picture from this video although the pictures I think are from SKF)
The support span (it might also be called with other terms but that's how I found it described on this page) is very important for bearings. For the 3 configurations, the tandem will have the same support span as "straight" bearings, the back-to-back or O configuration will have the greatest, and the face-to-face or X will have the smallest (even negative as in that picture?).
I have seen in several places some rules of thumb to choose one configuration or the other. I'll focus on X and O. Basically, O is stiffer because of the increased support span. Therefore:
(Picture's source)
I tried using a free-body diagram which clearly shows how the support span makes it more rigid in the case of deep groove bearings or other "straight" bearings but I don't see how the angular bearings change the support span.
In the previous picture, it's evident that by increasing the distance between the bearings, the support span increases which gives the assembly more leverage to counter input forces so it'll be stiffer.
I tried doing a similar diagram with angular contact bearings and I don't see how the equivalent support span grows or shortens depending on the angle of the bearings. The implication is that it is equivalent to "straight" bearings being placed at a different location but I don't see why.
Does it just fall out from the algebra once the equations of equilibrium are in place?
Also, what would be the implications of an X configuration where the support span is negative because the X crosses as in the previous picture?
*NOTE: I know that bearings are usually preloaded so, as the input force increases, all the balls would still have a reaction. To be precise, some balls would see their contact pressure decrease and others would see it increase. I focused only on the increment of pressure which would be equivalent to not preloaded bearings as an attempt to keep the thread clearer.
They can be assembled in different configurations which results in different properties.
(Picture from this video although the pictures I think are from SKF)
The support span (it might also be called with other terms but that's how I found it described on this page) is very important for bearings. For the 3 configurations, the tandem will have the same support span as "straight" bearings, the back-to-back or O configuration will have the greatest, and the face-to-face or X will have the smallest (even negative as in that picture?).
I have seen in several places some rules of thumb to choose one configuration or the other. I'll focus on X and O. Basically, O is stiffer because of the increased support span. Therefore:
- Looking for stiffness? Choose O.
- Looking for compliance? Choose X which is less stiff.
(Picture's source)
I tried using a free-body diagram which clearly shows how the support span makes it more rigid in the case of deep groove bearings or other "straight" bearings but I don't see how the angular bearings change the support span.
In the previous picture, it's evident that by increasing the distance between the bearings, the support span increases which gives the assembly more leverage to counter input forces so it'll be stiffer.
I tried doing a similar diagram with angular contact bearings and I don't see how the equivalent support span grows or shortens depending on the angle of the bearings. The implication is that it is equivalent to "straight" bearings being placed at a different location but I don't see why.
Does it just fall out from the algebra once the equations of equilibrium are in place?
Also, what would be the implications of an X configuration where the support span is negative because the X crosses as in the previous picture?
*NOTE: I know that bearings are usually preloaded so, as the input force increases, all the balls would still have a reaction. To be precise, some balls would see their contact pressure decrease and others would see it increase. I focused only on the increment of pressure which would be equivalent to not preloaded bearings as an attempt to keep the thread clearer.