Induced Axial Force at tapered bearings

[ttjahjowidodo]

Dear Experts,

Currently I am simulating a vibratory response of a gearbox housing consisting shafts and gears supported by single-row-tapered bearings. My problem arose when I tried to calculated the transmitted forces from the gears to the bearings.
Referring to SKF documents (SKF Catalogue Link), the induced axial forces on the bearings, which are due to the radial forces, are calculated and presented for the case when there is no preload and zero clearance.
In my case, the bearings are obviously preloaded with significant forces.
My question is simply: how to calculate the transmitted forces to the housing (through bearings) in a case of the existance of the preloads.

Thanks in advance to all.

 

[israelkk]

At first iteration calculate how much the outside diameter of the bearing is supposed to expand due to the radial forces in the bearing. If the bearing "expanded" outside diameter is larger than the minimum housing bore then calculate how much peripheral load is needed to "shrink" the bearing outside diameter of the bearing to fit into the housing. However, the same force will tend to expand the housing bore. Therefore, a trial and error calcualtions will give you the force that will shrink the bearing such that it will fit in the expanded housing bore.

 

[volpegrigia]

In a preloaded set of tapered roller bearings without external loads, the net axial force is 0, though there is strain at the interfaces where the preload is applied (flanges, bolts, etc.).

The thrust forces in a tapered roller bearing arrangements using a specific bearing size are a fixed proportion of the applied loading. Preload is part of the loading condition.
So, if one knows the loading applied, one can determine the equivalent load and the forces transmitted to the housing.

The formulae shown in the various catalogs (SKF, FAG, Timken, etc.) only show the induced loads for bearings at 0 or positive clearance and not preload. When preload is present, the magnitude of preload affects the way the load distributes itself within the bearing and thus affects the various components. In order to do this, you have to solve the load distribution within the bearings and to do so you must know the internal geometry (i.e. number of rollers, roller length, contact angle(s) etc.) and such information is not easily obtained.

If you want to design your own code to solve these problems, you can get all of the formulae from these books:
1: Ball and Roller Bearings: Theory, Design and Application - Braendlein, Eschmann, Hasbargen, Weigand - Wiley (expensive but eccellent)
2: Rolling bearing analysis - Harris - Wiley (3rd or 4th edition). It is out of print but you should be able to get it used.
3: analysis of stresses and deflection - Jones (it was published in 1946, You may be able to find it used.).

Any of these books have all of the math. If you simly need a loading evaluation, contact the bearing manufacturer and they will run the calculation for you.

Good luck!