Recreating back-to-back bearing life calculation 1

[electricpete]

Attached is a calculation for a "back-to-back" arrangement of a SKF 7318 bearing (40 degree angle contact) and a SKF QJ318N2 (4-point contact / Gothic arch bearing).

I am interested in recreating the thought process of this particular author in this particular calculation. Everything seems straightforward, except one question written on 1st page and one on 2nd page.

1st question (1st page): Is there a way to estimate what fraction of axial load each bearing would carry based on the available info? (in absence of input from bearing OEM).

2nd question (2nd page): After calculating a life for each bearing (based on it's share of the load), this author combines the two lives using
Life = 1 / (1/Life1 + 1/Life2)
I'm trying to figure out the logic of this equation. I can imagine that the statistical life of the combination is slightly less than the shorter of the two lives (which is what this equation gives), but I'm not sure how to arrive at this exact equation. Has anyone seen it derived or stated in a reference?

=====================================
(2B)+(2B)' ?

 

[MikeHalloran]

I've made a decent living over the years, cleaning up after electrical types who got into trouble in the mechanical realm because they believed the math models were accurate and had some foundation in the core physics.


Mechanical things don't work that way.


All that the bearing manufacturers know about bearings, they found out by building and beating on a bunch of bearings, and then using mathematical repousse' on the collected data to build application equations.



Mike Halloran
Pembroke Pines, FL, USA

 

[electricpete]

In your eager rush to express your disapproval, you apparently didn't' even read the question: "is there a way to estimate", rather than "how do I calculate". That does not indicate that the person who wrote it believes there is an exact physics-based formula (note the word estimate rather than calculate) and also indicates uncertainty as to whether there is even a way to even estimate (hence the words "is there a way to estimate" rather than "how do you estimate").

I will record the answer to question 1 as no. I actually suspected as much since the loading is heavily dependent on fine geometric properties which are difficult to know.

How about quuestion 2?

It strikes me "back to back" is an odd description for these two bearings. Normally I picture back to back bearings are preloaded against each other, not sharing load. Let me check on that.



=====================================
(2B)+(2B)' ?

 

[Fugeguy]

electricpete,

I am not sure that I agree with how this was done.

Go to:

http://www.koyousa.com/brochures/pdfs/catb2001e_a.pdf

page 23.

In general whan ACBB's are back to back one carries thrust loading in one direction and one carries thrust loading in the opposite direction. There is no need to figure out how to split up the thrust loading based on percentages as one carries it completely solely based on the direction of the loading.

Take a look at the link and give it a try yourself.

If you want I can give you my 2 cents on how I would solve the problem.

- fuge

 

[Fugeguy]

Also the system life equation is in the link I sent above.

It is just a way to account for the fact that as system complexity increases (in this case more bearings) the liklihood of failure increases as well.

 

[MikeHalloran]

"Back to back" means the planar end faces of inner ring and outer ring of the bearings are in contact with each other. By itself, it doesn't tell you anything about the intended loading or purpose.

Similar bearings are sometimes preloaded against each other and/or paralleled for increased load capacity or controlled end play, and matchmarked as sets. The process gets expensive fast, and is normally found only in machine tools.

SKF probably had internal structural models of the bearings in question, and could evaluate how their clearances, tolerances and stiffnesses added up. I doubt that it's possible to find all the necessary information outside of SKF.



Mike Halloran
Pembroke Pines, FL, USA

 

[electricpete]

Thanks, good stuff. I think my question #2 is answered fairly well by Fugeguy's link. Section 5.2.5, on page 19/80 (labeled as page A27) states:
1/L^e=1/L1^e+1/L2^e+...
where e=9/8 for ball bearings. It is fairly close to the equation in my attachment, would be the same if you set e=1.

I still need to investigate the configuration closer. It seems to me that the description as "back to back" conflicts with a calculation that shows the applied load is split among the bearings (a certain percentage in each). So either the calc is wrong or the configuration is not back to back. I suspect configuration is not back to back, checking....

=====================================
(2B)+(2B)' ?

 

[electricpete]

If you want I can give you my 2 cents on how I would solve the problem.

ok, I want to know: what's your 2 cents to solve the problem?



=====================================
(2B)+(2B)' ?

 

[electricpete]

Also the system life equation is in the link I sent above.

It is just a way to account for the fact that as system complexity increases (in this case more bearings) the liklihood of failure increases as well.

Thank you.

=====================================
(2B)+(2B)' ?

 

[electricpete]

I have resolved my question about configuration. The configuration is back to back with the angle contact bearing on top and the 4-point contact on bottom as shown attached. That works for downward load sharing. And the 4-point contact handles any momentary thrust. For some reason I was picturing the angle contact on bottom, in which case back-to-back configuration would not provide sharing of downthrust (lower bearing would be situated to take upthrust)

=====================================
(2B)+(2B)' ?

 

[caoimhin1]

Just a comment on the arrangement. I've never seen a single row angular contact and a QJ type assembled together. Application should use either one QJ318 on its own, or two 7318B back-to-back or face-to-face as the application demands.
Configuration as drawing would not be approved by the bearing manufacturers.
Another question: have the two bearings been face adjusted and matched? If not, asking for trouble.

 

[electricpete]

The replacement bearings will be ordered as a set.

I haven't found this described in SKF literature. But I did find similar thing in MRC literature. See attached.

=====================================
(2B)+(2B)' ?

 

[Fugeguy]

electricpete,

My 2 cents is attached.

For normal operation I'd show a system life of 6,900 hours and in reverse the system life is 5,730 hours. You'd need some sort of duty cycle to blend those together but since they are so close I'd use the 5,730.

I didn't do much with the a23 because while it says that it is grease lube I could not find any mention of temperature or the specific grease.

Take a look closely since I just flew through this but it should give you the idea.

This is old school since now we would use contact stress to establish an adjusted life but this is still a good method for non-critical applications or to select bearings to start with.

Take care.

- fuge

 

[Fugeguy]

BTW, I just threw my calculation out there using 2x 7318's in a BTB because that is a more typical arrangement. If you have a sketch or something of the actual set-up I'd be happy to dial it in for what is actually going on.

It was just to give you an idea of the process because I thought there were some issues with what you posted originally.

 

[Fugeguy]

Look at the attached sketch.

Is this what is going on?

If so the calc you attached originally is using the tandem equivalent load equations but you cannot divide the load. The derating is due to the fact the load rating for two bearings in tandem is not 2 x but 2^0.7 x the load rating.

If this is what you have I'll look at it tomorrow. caoimhin1 is right that this is a little different beast!

 

[Fugeguy]

Didn't notice the attachment. It is clear now and I'll post something in the morning.

Thank you.

 

[electricpete]

Thanks Fugeguy. That’s a professional looking document... what software did you use to produce it?
At first glance it doesn’t look too much different, I’ll have to study it some mroe.

One point of peripheral interest on the original question - the MRC literature has an example calc for this configuration as shown attached. It does not require determining how the load splits... instead the combination of two bearings is given a single rating and the calc proceeds as a single-bearing calc.
.

=====================================
(2B)+(2B)' ?

 

[Skogsgurra]

This discussion may have some merits as a search for the 'inner truth' of bearing life in this special situation.

My long life with motors, drives and bearings has taught me that it isn't like that. Or rather - it is like that, but still not.

The life calculations are a good guide as to what bearing to chose. But more often than not, the shaft diameter alone says what bearing to buy. Extreme speeds and radial/axial loads are covered by the design equations. But when it comes to configurations where two or more bearings shall share load (hopefully equally) then tolerances, configuration and temperature coefficients play a much bigger role than the books say.

And, after all, what can one expect from an L10 number? A number that allows one tenth of the bearing population to fail *before* the calculated life and 90 percent to live an indeterminate time after the L10 number of hours.

Using five or six figures in life calculations may be good to maintain internal precision - but using them to predict a bearing's life should be avoided.

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[Fugeguy]

electripete,

thanks for posting this.

we don't do much with the x bearings and it was an interesting excercise.

attached is my thoughts on how to do the life calcs. as stated earlier this is old school since everything is contact stress related now but we'll still use L10 for quick checks. Skogsgurra is correct about what an L10 is but bearings are a lot better than when the original equations were developed (material, geometry, surface finish, etc) and now most bearings live many multiples of their L10 lives. if they don't you either have loads that were not accounted for, crappy maintenance practices or a severe environment.

Back to the original concerns-

there is no reason to "split" the load. the equivalent load equations and your mounting account for the load sharing, differences in contact angle, etc. Also, the original notes call this a back to back arrangement but the ACBB and x bearing really act in tandem.

anyway thanks again and the program I used was Smath and I got the tip here:

http://www.eng-tips.com/viewthread.cfm?qid=267391&page=3

- fuge

 

[electricpete]

This discussion may have some merits as a search for the 'inner truth' of bearing life in this special situation.

There is nothing to do with search for inner truth, and no misunderstanding as to what L10 represents. Regulations for this particular application require documented and reviewable L10 life calculations.

there is no reason to "split" the load.

The way I see it, we have 2 choices:

1 - if all we have is the individual load ratings for the 2 bearings, than we need to try to estimate the load split (*), calculate life on each bearing, and then combine the lives at the end.
2 - if we have combined load rating for the 2 bearings as in the MRC example, we can skip both the splitting of the load and the re-combination.

Sticking with the first case, if no combined rating is provided, I think splitting the load is required (* to the extent it can accurately be done and as stated above I agree bearing OEM is by far best equipped to that task). Looking at your calculation, I think you have assumed the total normal downthrust load of 20.9kN is applied individually to each bearing. But the actual load seen by each bearing is somewhere less than that (they loads sum to 20.9kN). Your caluculation would certainly be conservative, but overly-conservative compared to a calculation that splits the load among bearings (which would give lower load on each bearing and longer life).

=====================================
(2B)+(2B)' ?