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Recreating back-to-back bearing life calculation

Recreating back-to-back bearing life calculation

Recreating back-to-back bearing life calculation

(OP)
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)'  ?

RE: Recreating back-to-back bearing life calculation

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

RE: Recreating back-to-back bearing life calculation

(OP)
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)'  ?

RE: Recreating back-to-back bearing life calculation

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

RE: Recreating back-to-back bearing life calculation

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.

RE: Recreating back-to-back bearing life calculation

"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

RE: Recreating back-to-back bearing life calculation

(OP)
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)'  ?

RE: Recreating back-to-back bearing life calculation

(OP)

Quote:

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)'  ?

RE: Recreating back-to-back bearing life calculation

(OP)

Quote:

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)'  ?

RE: Recreating back-to-back bearing life calculation

(OP)
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)'  ?

RE: Recreating back-to-back bearing life calculation

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.
 

RE: Recreating back-to-back bearing life calculation

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

RE: Recreating back-to-back bearing life calculation

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.

RE: Recreating back-to-back bearing life calculation

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!


 

RE: Recreating back-to-back bearing life calculation

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

Thank you.

RE: Recreating back-to-back bearing life calculation

(OP)
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)'  ?

RE: Recreating back-to-back bearing life calculation

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

RE: Recreating back-to-back bearing life calculation

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

RE: Recreating back-to-back bearing life calculation

(OP)

Quote:

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.

Quote:

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)'  ?

RE: Recreating back-to-back bearing life calculation

(OP)
Fugeguy - I have been playing around with smath and it seems pretty handy.  I have a question:  is it possible to resize graphics that have been inserted into the worksheet?

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

RE: Recreating back-to-back bearing life calculation

electricpete,

I have only used SMATH a few times and there does not seem to a good way to re-size graphics.

I usually pre-size and take a screen shot with something that lets me choose the window size.

Also, it is not correct to split the load since the x and y values in the equations take that into account. That is why the y value for btb is .93 and it is .57 for tandem. Because in one arrangement (tandem) the bearings share the load and the other (BTB) they don't. The reason the tandem exponents are not half the btb exponents is governed by the equation for combined load rated i^.7* load rating where i = number of bearings sharing the load.

Here 2^.7 * .93 = .57.

- fuge

RE: Recreating back-to-back bearing life calculation

(OP)
Thanks. My last comments were off-base since I hadn't noticed that the Y values you selected were any different than the typical ones, these ones selected specifically for tandem application.  Good observation that the 2^0.7 is built into this tandem  Y value (2^.7 * .93 = .57), that helps tie it together.

I am hoping to tie it together a little more.  I would propose that the 2^0.7 representation of the rating of the combined tandem unit is an attempt to express the same thing as the life combination of individual bearings using L = 1/(1/L1+1/L2) under the assumption that identical tandem bearings will share the load equally... each sees half of the total load.

Attached is an attempt to explore this.  The two approaches differ by approx 7%... pretty close imo.

What do you think?

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

RE: Recreating back-to-back bearing life calculation

(OP)
Attached is the smath file if anyone wants it.

Note, if you try to use the life combination formula with exponent 1.1 instead of 1.0, results were more complicated.... that's why I stuck with 1.0.  

But we can qualitatively see that if we used 1.1, it is as if the inidividual lives increased by exponent 1.1, which pushes the combined life of part 1 higher, and the ratio of L10_Part1/L10_Part2 higher and closer to 1.0.

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

RE: Recreating back-to-back bearing life calculation

(OP)

Quote:

under the assumption that identical tandem bearings will share the load equally
This is an important assumption to talk about.  Even for identical bearings, they must be a matched set as stated above to share load equally.

The bearings of original post were not equal.  However if the bearings are supplied as a matched set of unequal bearings, I think as a first guess (in absence of OEM info), one would guess that the OEM would match them so that they shared load in proportion to their rating.... or if load sharing is non-linear (load-sharing fraction varies with load level) that they reached their rating load level at the same time.  This would be logical way for an OEM to optimize the combination, wouldn't it?

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

RE: Recreating back-to-back bearing life calculation

(OP)

Quote:

equation for combined load rated i^.7* load rating where i = number of bearings sharing the load.
Does anyone have a reference for this equation?  It is vaguely familiar to me, but I can't find it in any refernces.

 

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

RE: Recreating back-to-back bearing life calculation

(OP)
I found that reference:

Quote (ANSI AFBMA Std 9-1990 = LOAD RATINGS AND FATIGUE LIFE FOR BALL BEARINGS):


5.1.1.3 The basic radial load rating for two or more similar single row angular contact ball bearings mounted side-by-side on
the same shaft such that they operate as a unit (paired or stack mounting) in "tandem" arrangement, properly manufactured and
mounted for equal load distribution, is the number of bearings to the power of 0.7, times the rating of one single row bearing.

 

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

RE: Recreating back-to-back bearing life calculation

(OP)
Interesting that the references which include the statistical life combination equation L = 1/(1/L1+1/L2)  (such as Koyo and NTN) do not include the revised rating equation C=C1*n^0.7 for n identical bearings, and the reference that includes the rating equation C=C1*n^0.7 (AFBMA) does not include the statistical life combination equaion L = 1/(1/L1+1/L2). So each of these references lists one or the other but not both. I think the reason is that they represent the same thing, so you can only use one or the other in your calc.   If unequal bearings, you are forced to use the life combination equation.

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

RE: Recreating back-to-back bearing life calculation

(OP)
In my smath file, I left out the factor Y.  In my analysis it is assumed constant, so does not affect the conclusion regarding the ratio.

As an interesting side note, the factor Y is used to capture the statistical life combination in the catalogue that Fugeguy used (which bearing oem was that?).

So in summary, there are actually three different ways  that exact the same effect (statistical combination of identical bearings sharing load equally) can be captured:
1 – By combining L10 lives of individual beairngs using L=1/(1/L1+1/L2) as suggested in Koyo and NTN catalogues
2 – By using a revised rating of the combined unit Ccomb = Cindividual * n^0.7 as suggested in AFBMA standard above.
3 – By adjustment of the Y factor as in the bearing catalogue referenced by Fugeguy

With three different possible ways to capture the same effect,  it is important that we use one and only one.   If you mixed and matched coefficients or equations from different sources you could get in trouble.  The value of Y needs to be coordinated with the value of C and also with the treatment as single unit or multiple units whose life is combined at the end.

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

RE: Recreating back-to-back bearing life calculation

If the bearings are a matched set and you knew the approximate life calcs, would it not make sense to interchange the two bearings at half life to get longer life from them?

RE: Recreating back-to-back bearing life calculation

(OP)
The angle contact 7318 has to always be on bottom and so there nothing you can swap to extend it's life.

The split inner race 4-point contact QJ318 is bi-directional, so assuming (*) it is ground exactly the same in both direction, you could flip it around to swap the intermittent up-thrust surfaces into the continuous downthrust duty, which might almost double the L10 life of the bearing.  (* Not a good assumption. The MRC pairs come with arrows on both the angle-contact and the split inner inner inner ring bearing which are supposed to be installed in directino of continuous thrust, so they have a preferred direction and swapping would be outside OEM's recommendation).

In this particular case, according to the original calc attached at beginning, the 7318 has lower life and is limiting, so flipping the QJ318 wouldn't buy you much even if it was ground identically.

More importantly, it is our general practice to replace a bearing every time it is removed.  This is based on
1 - concern about the same bearing being originally installed then removed/reinstalled onto inner race, which brings some trauma to the bearing.
2 - a lot of the cost is manpower anyway. So if you're spending the manpower to disassemble and swap, you might as well use a new bearing.

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

RE: Recreating back-to-back bearing life calculation

(OP)
Correction in bold:

The angle contact 7318 has to always be on bottom and so there nothing you can swap to extend it's life.

should have been:

The angle contact 7318 has to always be on top and so there nothing you can swap to extend it's life.

 

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

RE: Recreating back-to-back bearing life calculation

(OP)

Quote (electricpete):

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?
I did figure out this appears to be a very basic textbook statistics principle, sometimes referred to as "series" combination of components.

It is discussed a little here.
http://www.theriac.org/DeskReference/viewDocument.php?id=219#section3

I have also attached some basic proofs.  If the probability of surviving to time t for bearing 1 is exp(-lambda1*t) and for bearing 2 is exp(-lambda2*t), then I proved the MTTF for bearing 1 alone is MTTF1 = 1/lambda1 and for bearing 2 is MTTF2 = 1/lambda2 and for the series combination has MTTFtot =  1/(lambda1+lambda2) = 1/(1/MTTF1 + 1/MTTF2).  If we substitute L10 life for MTTF, we see this is identical to the equation posted in original post.  I'll have to think a little bit about whether there is basis for this substitution, but it looks pretty close to me.
 

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

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