FEA of roller bearing assembly 1

[gio1]

Hello

I'm about to start a FEA on an assembly consisting of a flange mounted around a rotating shaft through a roller bearing and loaded radially. I would be interested in hearing your thoughts about a possible analysis approach (contact modelling for all the rollers? How to model the cage? And also what maximum surface stress is allowable to prevent premature surface wear (steel on steel on steel)?

Thanks

Gio1

 

[Stringmaker]

I've never done an analysis like this but here are a few things I would take into consideration to start with:

1) Symmetry...can any sort of cyclic symmetry be used or could this even be done in 2-D?
2) Static or Transient Analysis...if transient you may want to use an explicit solver if you have access to that type of software


Just a few thoughts/suggestions...take them with a grain of salt.

Good luck,
-Brian

 

[GregLocock]

We use compression only springs aligned with the pressure angle of the rollers. Your bearing manufacturer should be able to tell you what value to use as the spring, it is not an easy number to calculate. In my opinion it should be a non linear spring, according to the Hertzian model.

I wouldn't worry about the cage, in general.

You can't usually use symmetry.





Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[gio1]

I am indeed planning to use an explicit solver, the only problem seems to be the small integration step involved (due to the tiny elements needed for modelling the rollers smoothly)

Greg, it seems to me your approach will get the force distribution right among the rollers, but how do you go about assessing the contact stress on the shaft or the flange? (I'm interested in this to predict possible surface wear). May be with standard Hertzian formulae?
I agree with you that the cage is not important, I was referring to a way of keeping the rollers straight during the analysis (that is, if I will have to model each one of them).

The assembly is symmetrical about two planes but as Greg's points out I can't use this conveniently, especially in case of a transient analysis

Cheers

Gio1

 

[GregLocock]

I don't know. We've got these springs terminated to the races of the ball bearing, which averages out the peaks sufficently to give smooth stresses at the shaft/inner race interface, which is what I'm after.

If you are interested in the contact stresses for the roller against its race, I think you are pushing the boundaries of what is commonly done.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

If I'm understanding your question correctly, the analysis is a lot simpler than what you're suggesting.

L10 = 1E6 revolutions * (C/P)^3

where L10 is point where 10% of bearings will fail, C is bearing radial load rating, P is actual radial loading.

There are a lot of other correction factors that can be put in for lubrication conditions, environmental conditions etc. See the bearing manufacturer's websites.

You would be reinventing a wheel to try to develop anything from scratch since there has been so much analysis,testing, research and literature published on this application.


=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

I didn't mean "this application"... I meant rolling bearing applications. Is there something about your application that makes it different than most?

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[gio1]

Electricpete

I forgot to mention that the rollers run in direct contact with the shaft and the cage; it is a bespoke bearing being developed specifically for this application.

My concern is the sensitivity of the assembly life to:

- Deformation of the housing (flange)
- Fluctuating loads on the shaft
- Surface wear of shaft and flange at rollers contact interface (the rollers are made of ceramics)

I was considering FEA to account for the deformation (ovalisation) of the housing under radial loads. The rollers are tiny (3mm diam.) and could be modelled as rigid bodies, but mesh density on the flange would have to be extremely high to correctly capture the hertzian stress. Given that a dynamic explicit analysis is required (for shock loads) element size has a direct impact on analysis runtime, and it is also not possible to exploit symmetries...

regards

gio1

 

[electricpete]

If I understand right, your shaft plays the role of the inner race and your housing plays the role of an outer race.

So, it’s still a rolling bearing, just that the inner and outer rolling surfaces were not provided by a bearing manufacturer.

I trust you will not be surprised to learn that the wear will depend heavily on the lubrication conditions.

I suspect most would be suprised to learn that the fatigue life of balls and races in a rolling element bearing also depends heavily on lubrication conditions.

“Engineering Tribology” by Stachowiak and Batchelor states as follows: “The thickness of the lubricant film in relation to surface roughness plays important roles in the determination of frictional torque, heat generation, wear, and fatigue failure.”

Beyond surface roughness effects, it is evident that small level of particulate contimination within the lubricant can greatly accelerate fatigue as well.

I have serious doubts that you can get any good life predictions from FEA. I would think you can do better by comparing your installation to standard rolling bearings and adjusting their life predictions. Just my opinion.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

Maybe I have jumped the gun. Is there any lubricant in your bearing?

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

Regardless of whether there is a lubricant involved, these questions of wear rate and fatigue lifetime are at the center of the field of tribology. (I’m not sure about shock).

You might get some additional responses and possibly good links if you post this question in the tribology forum.

It would be helpful to identify to identify the temperature, speed, bearing man diameter, (we already know roller diameter), any lubricant or fluid present – those would give an idea of what lubrication regime you are operating in (elastohydrodynamic?). Also the shaft, housing and roller materials along with total load could be useful.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

Just one more piece of info along the same lines as before.

ABMA Standard 11 gives “Load Ratings and Fatigue Life for Roller Bearings”.

There is quite a bit of information in there including how to calculate bearing rating from bearing geometry and materials, and how to get statistical estimates of fatigue life from bearing rating and bearing loading and operating conditions.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[gio1]

Electricpete

Thank you for your valuable posts.

I am aware that lubrication condition are going to be critical for this application. In fact this is only the development of a test rig for the final objective of the project: a connecting rod running on ceramic rollers (the bearing is made in two halves) at high speed/loads. As such oil lubrication will be present and proper filtering (especially during engine run-in) is crucial for durability. Also EHD lubrication conditions are clearly to be avoided with rollers (correct me if I am wrong)

I see FEA not so much useful in helping predict wear as much as in helping define the optimal number/diameter of the rollers in relation to the deformation of the outer race under load and the hertz stresses (I don't think classic theory can consider ovalisation of races when predicting hertz stress). Fatigue failure could also be predicted if contact stresses are reasonably accurate.
The bearing runs at an average 18000rpm with peak linear speeds on the inner race of 80m/s.

Thanks again for the useful references

Gio1

 

[electricpete]

EHDL is a preferred lubrication regime for rolling element bearings. The alternative would be boundary lubrication where more wear and stress occurs.

I reviewed one of my tribology handbooks and saw an interesting historical development of EHDL theory. In the old days using only Hertzian contact (the elasto part of EHDL) they predicted lives much shorter than in practice. Even when adding hydrodynamic film effects (the HDL part of EHDL), the large force/area pressure loads caused prediction of films much smaller than roughness and hence boundary lubrication with prediction of very short life. It remained a mystery for awhile. Only when they added in the dramatic variation of viscosity with pressure did they get good results. So EHDL has 3 elements: 1- hertzian contact deformation, 2 - hydrodynamic theory, 3 - pressure-viscosity coefficient. That was a long story but I wanted to make the point based on the above, it appears your FEA with hertz theory in absence of other factors probably would likely predict much too low of a life. (maybe it would be some value to have a lower bound on the life?)

To stay in the EHDL regime and avoid boundary lubricaiton, you would need to exceed the minimimum viscosity at operating temperature as shown on Figure 1 of page 4 here:

http://www.mrcbearingservices.com/docs/lubrication.pdf

The chart is based on mineral oil. If using synthetic you also need to look at p/v coefficient (varies widely for synth but not for petro).

Also the chart would be based on typically smooth bearing surfaces. If your shaft or housing are rough you'll need to boost the viscosity for that. Not sure how to easily quantify that.

In general it is not difficult to meet the viscosity requirement unless you expect to have a temperature problem. Higher temperature causes lower viscosity. Increased base oil viscosity causes lower operating-temperature viscosity. Bottom line is for high linear speed application you may not be able to find any suitable lubrication that will give a reasonable temperature within the safe range of the lubricant (as a conservative rule - less then 210F).

18000rpm
divide by 60
300 rotations/second
multiply by 2Pi
1885 Radians/second = w
Linear speed = w*R = 80 m/sec
R = w*R/w = 0.04m = 40mm
D = 80mm
From the chart that looks like just over 3 cSt at operating temperature.

From figure 2 it looks like VG22 or even lower would work. As long as that is low enough to keep you from heating above 100C or so.

NO. I did that wrong. I'll leave it there as an example to myself what not to do. You need to determine your minimum speed and figure your viscosity from there.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

"Increased base oil viscosity causes lower operating-temperature viscosity"
should have been
"Increased base oil viscosity causes higher operating-temperature viscosity"

That wasn't a very good paragraph except for the bottom line - there may be no base oil viscosity you can pick which is low enought to prevent overheating at max speed and high enough to meet minimum viscosity at operating temperature at minimum speed.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.