Bearing Ball FEA simplified modelling

[RigidRay]

Dear colleagues,

I want to know the proper way to model bearing balls correctly which installed between two beam tracks, is it spring (if so how to define its stiffness) or haw could it modelled as a compression only member in FEA.

Kind Regards,
Ray

 

[rb1957]

i'd suggest a rigid beam (RBE) and a gap element (to permit only compression loading)

 

[GregLocock]

It rather depends on what you need from the model. I've seen non linear springs used, to give the hertz stiffness and clearance effects, for preload calcs.

Cheers

Greg Locock


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[flash3780]

I've always felt that a half-cosine load is a sufficient representation of a bearing load, especially when the area of interest doesn't include the bearing itself. Some researchers, have found that a [link=http://mechanicalhacks.wordpress.com/2011/03/01/bearing-loads-cosine-and-gencoz-distributions/]Gencoz distribution can be more accurate[/url].

That said, I've worked with a major aerospace company whose standard practice was to use a "spoke method", invoking CONTAC52 elements in Ansys tied to a central node to which the load is applied. I believe that it is necessary to set the real constant for the gap to the radius of the bearing raceway to get this to work. Good luck.

//signed//
Christopher K. Hubley
Mechanical Engineer
Sunpower Incorporated
Athens, Ohio

 

[crisb]

I had a similar problem recently (with a circular track) and ended up doing a contact analysis including the balls. Initially I did an axisymmetric model with one ball, with an approximation of the loading. Then moved on to a 180 degree model with symmetry. Obviously it was a big model and that gave its own problems with mesh quality, solution time etc.

 

[johnhors]

Chris H. a couple of points, firstly your post has moved away from the simple 1D approach to a full 3D modelling effort for the bearings. (each ball bearing was modelled with a single spring or gap element with earlier posts).

Secondly, having ventured into the 3D modelling world, the "spoke" (or "wagon wheel") method, (I suspect you know already) is not capable of applying a smooth continuous pressure to the bearing surface, it can be described as a "bed of nails" approach. Only a correctly applied pressure (which honours element formulations) using cosine/gencoz can apply a smooth continuous pressure (a "water bed" approach). The "spoke" method will give rise to stress singularities.

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[crisb]

The following publication may be of interest. The Hertzian stiffness is shown on page 31.

http://doc.utwente.nl/32063/1/t000000d.pdf

 

[flash3780]

johnhors,
Good points, all. I'd add that the methods that I described are best used for representing the loads on a bearing raceway when the area of interest is not the bearing, itself. In that situation, the stress concentrations created by the CONTAC52 elements are localized and acceptable. The aerospace company that I worked with liked the spoke method because it prevented "unrealistic ovalization" of the bearing raceway.

If you're interested in the bearing, itself, you'll probably ignore most of the external parts in order to focus on the areas of interest. I'd argue that a bearing assembly is best represented by a 3D FE model. Modeling contact stresses within a bearing requires very fine mesh controls at the contact interface. You'll want to pay close attention to your contact formulation and consider matching nodes across the contact surfaces to provide the most accurate representation. A full Lagrangian contact formulation is likely the most appropriate for this sort of analysis.

Bearing manufacturers often offer load ratings, and coupled with analytical bearing calculations (Hertzian contact stress, bearing life calculations, heat generation, etc.) the ratings provide sufficient information for most design situations. Analytical calculations for designs requiring roller bearings are quite mature. I'd recommend checking out Tedric Harris's books on roller bearing analysis.

In recent years, finite element modeling has been used to model bearings in more detail, investigating things like spall initiation and crack growth. These investigations are quite rigorous and probably require more forethought than you'll get from this forum. Good luck.

//signed//
Christopher K. Hubley
Mechanical Engineer
Sunpower Incorporated
Athens, Ohio