That's another option. It would be interesting to get an idea about the price vs performance. "Factory tuned thus eliminating further adjustment" - a custom-factory-tuned device can't be cheap. Is there a provision for field tuning if we want? It would be very interesting and relevant to the current discussion if the manufacturer of those dynamic absorbers provided something resembling "application guidelines" for his product, but I don't see that on the website. Also I didn't see anything at the link to begin to judge performance (effective weight for purposes of separating those side resonances... and what range can they be applied without fear of damage to the absorber). Is there a way to use vibration meausrements to confirm that design stresses for the absorber itself are not exceeded in service? Is there a drawing? Does it look like that photo?

Back to the do-it-yourself-option.....

I had previously provided an analysis of absorber stresses using a simplistic assumption that the modeshape was the static deflection in my post 15 November 2009 02:52 PM here:
http://maintenanceforums.com/e...51089011/m/945109374

Now I have done a much more exact solution of the modeshape (and resulting stresses) than the previous static deflection approach. The results of the new analysis are attached to the present message. Assumptions are listed on the 1st page (Euler Bernoulli beam model, tuning weight acts like point mass, max shear and bending stresses occur at location of attachment of absorber to machine, mode shape during operation same as mode shape with traditional "fixed" boundary condition: displacement =0 and slope=0).

The resulting stresses show that max stresses are below endurance limit by more than a factor of 20 for this particular absorber and this particular measured vibration on the absorber tip. So I feel pretty good about the long-term performance as long as vib doesn't dramatically increase. An unfortunate aspect is that the resulting general analytical solution equation is ridiculously long (3 pages long), so would not be practical to plug it into an excel spreadsheet (even the expression for moment and shear at x=0 is still too cumbersome). However in this case the much simpler "static deflection" method yielded conservatively high prediction of stresses... I suspect that is the case in general but can't prove it yet (interested in any comments on that).

[EDITED TO ADD - There was a logical error in the statement "eq7:=simplify(eq6)" which removed the eq7 boundary condition from the problem, but I don't think it affects the validity of the results. While we lost one of 8 initial boundary conditions, we added yet another equation when we specified displacement ytop at the end of the absorber, which restores the total of 8 equations needed to completely define the 8 constants. And we can see from the plot that the continuity of moment at location of the tuning mass (the equation 7 that inadvertantly got ignored) is still satisfied].

An interesting thing is both a supervisor and a manager at our plant (from different departments and at different occasions) told me they thought a dynamic absorber was not a long-term solution in general, primarily due to concern about absorber failure. I am not sure what info these people used to form a basis for their opinions....will have to ask them about that.

I have a theory that if a lot of absorber failures have occurred, it's probably because people are not looking closely at the stresses. I think that vibration people in general are better at computing resonant frequencies than they are at calculating stresses (I certainly include myself within that generalization). So a vibration person is very capable of selecting an absorber to give the correct tuned resonant frequency... especially with the spreadsheet provided by Entek which specifically addresses resonant frequency but does not addresses stresses at all. Likewise I have not heard any thumbrules out there specifically geared toward limiting stresses (I'm interested in comments if there are some). I have never heard anyone else even mention the possibility of measuring vibration as a tool to calculate the absorber stresses, even though it seems a very logical approach to me. IF many people are simply sizing to match resonant frequency while not estimating stress, THEN it would not be surprising we have quite a few absorber failures. But more careful attention to stresses should eliminate that. (By the way this is definitely not meant as an insult against anyone that uses the Entek spreadsheet... we ourselves used that spreadsheet and made no explicit attempt to calculate stresses for our first absorber in another application: 75hp vertical pump motor.). Are there any thoughts on the above theory.... that the likely cause of most of absorber failures that are rumoured to have occured is that many absorbers were installed without a careful consideration of stresses during design and post-installation testing?

As a side note – would absorber failure be a violent event that would likely endanger people or equipment? I tend to think the hazard is limited to the weight of the absorber accelerated by gravity falling on top some person (or their foot) or some equipment (*).... and any energy imparted by the initial vibration is small in comparison to the energy due to gravitational acceleration during the fall.
a=g
v = g*t
x=0.5*g*t^2
To fall a distance d, the time tfall satsifies
d=0.5*g*tfall^2
tfall = sqrt(2*d/g)
vfinal = g*tfall = g*sqrt(2*d/g) = sqrt(2*d*g)
Assume a fall distance d=10". The final velocity is
vfinal =sqrt(2*10*inch*32*12*inch/sec^2)) ~87ips
Even with that small fall distance, the final velocity is much larger than the initial peak velocity measured 5 ips.
*- By the way I'm not saying the hazard from gravitational acceleration is small, only that there seems no significant additional hazard associated with some kind of "whip" of a vibrating piece breaking loose that we might imagine.

This message has been edited. Last edited by: electricpete,

DA_ModeshapeAnalyticalR2.pdf (58 KB, 16 downloads)

quote:

Originally posted by Robert U.:
IRD used to have a file called ABSORBER they used to hand out. As soon as I fine a 3.5" floppy drive I will take a look at it.

I have this ABSORBER file and am willing to post it but I do not want to infringe on copyright as it states the following

This program is the exclusive property of IRD MECHANALYSIS, INC.



THIS PROGRAM IS DISTRIBUTED SOLELY AS A COURTESY TO OUR CUSTOMERS.



COMPILER COPYRIGHT BY MICROSOFT (C) 1985, 1986


IN NO EVENT SHALL IRD MECHANALYSIS, INC. BE LIABLE FOR ANY DAMAGES WHATSOEVER
(INCLUDING WITH-OUT LIMITATION DAMAGES FOR LOSS OF BUSINESS PROFITS, BUSINESS
INTERRUPTION, LOSS OF BUSINESS INFORMATION, AND THE LIKE) ARISING OUT OF THE
USE OF OR INABILITY TO USE THIS PROGRAM.


Terry O what do you think

I would not recommend posting a copyrighted spreadsheet. There have been some previouis discussions about these spreadsheets...

I believe my spreadsheet (attached) does what the Entek spreadsheet is supposed to do, only better (more exact). See the tab “Compare Dunkerly vs Fox”:

• “Dunkerley” is the method used by my spreadsheet.
  
• “Fox” is the method used in Randy Fox's spreadsheet and Fox's paper which I assume is same as Entek spreadsheet since Fox was an instructor for Entek (and a good one, by the way!). This method is imo a misapplication of Dunkerly's method(*).
• You can see on the right side of the chart, the resonant frequency of the correct Dunkerley method comes closer to the target than the Fox / Entek method.

(*)This subject was well discussed in the followiong thread, including the manner in which Dunkerley was (imo) misapplied by Fox / Entek:
http://maintenanceforums.com/e...741082733#2741082733

Many have said the Fox/Entek is close enough, given the ability for adjustement, and I don’t disagree at all. However, why not use my spreadsheet and get closer? And by the way, my spreadsheet also includes provision for either rectangular cross section or circular cross section (all-thread). And my spreadsheet includes a clear explanation of how the results are calculated with derivation... something sorely missing in the others imo. The only thing that Entek has which is missing from mine is a menu of material types – I assume people are sticking with steel.

In either case, these spreadsheets so far only help you get the correct resonant frequency. That’s the easy part imo since the formula is straightforward and in fact the adjustment is forgiving of errors such as made by Entek. The challenging part imo is estimating the stresses and durability, which is the main theme of this thread.

This message has been edited. Last edited by: electricpete,

75210575_DynamicAbsorberDunkerleyR1.xls (78 KB, 23 downloads)

I think there are multiple stress concentrating/raising factors that could conspire to make a cantilevered bean made from threaded rod susceptible to fatigue failure.

The Notch effect is likely even greater than obvious thread geometry, because of the scratches and tears inherent in cut ( not rolled) threads.

For some environments and materials the potential for stress corrosion should be thrown in, too.
http://www.npl.co.uk/upload/pdf/stress.pdf

quote:

It would be interesting to get an idea about the price vs performance. "Factory tuned thus eliminating further adjustment" - a custom-factory-tuned device can't be cheap.

Did you find out? You have to consider your company's engineering time and other resources when comparing the price.

I saw them used on aircraft. A company making the planes certainly had both the engineering capability and the manufacturing ability to make absorbers but choose to buy them.

EPete,

When I open your spreadsheet (DynamicAbsorberDunkerleyR1.xls), the only thing I see is the instructions. I don't see any cells to insert numbers. What am I missing?

Regards,
John J

John – there are several tabs. You can select a different tab by clicking the tab name at the bottom of the screen. The tab labeled “Calculate” is the one to input the data. Some other tabs “Figure” shows the basic layout (nothing new), “Derivation” shows the derivation of the equation, “CompareDunkerlyVsFox” shows comparison of results discussed above.

Bill – No, I have no further info on the device that you mentioned.

For my part I think an undamped dynamic absorber is a fairly easy low-tech thing to design except for the stress analysis. I have spent some time trying to find way to estimate the stress on the base and I think I might be able to develop a reasonable approach. Once I have a handle on the calc method, it shouldn’t be hard to repeat the calculation when needed.

The method that I attached 06 December 2009 01:01 PM to calculate bending stress at the base of the absorber worked, but the alebraic solution is so ridiculously long that it’s not suitable for spreadsheet, not easy to share, also not easy for someone else to “double check”. I might try redefining my variable xt so that xt=0 at the top of the absorber... should simplify the solution since two unknown constants drop out immediately based on the boundary condition at the free end of the absorber. Otherwise, I might try using Raleigh Ritz to develop an approximation of the modeshape (which would be algebraically simpler in form), then solve the magnitude (from either applied force or measured vibration), then use that to estimate the bending stress at the base of the absorber.

This message has been edited. Last edited by: electricpete,

I'd presume and calculate for first bending mode resonance, then use These formulae plus a little algebraic manipulation to be pretty close on the stress

.http://www.engineersedge.com/beam_bending/beam_bending9.htm

I'd machine a nicely radiused diameter maybe 10% smaller than the thread minor diameter for a few inches near the fixed end.

http://www.boltman.com/images/...urbineB16Nitride.jpg

and install it so the reduced diameter started within the jam nut. the purpose would be to enforce a relatively known geometry, free of geometric stress concentrations to fall at the point of max stress. If I really wanted it to last forever I'd shoot for a calculated stress at maximum displacement of less than 30,000 psi, then I'd shot peen the reduced area to MIL spec MIL-S-13165 and spray a few coats of LPS 3 or CRC SP-350.

I'd glue a few heat sinks and other gizmos on the moveable tuning weight to add an air of mystery and, depending on the customer, some sales appeal ( just kidding about this part ).

Hi Dan

Thanks for the suggestions.

Fantastic idea to try to machine the all-thread geometry to reduce stress concentrations like is sometimes done for bolts. I have to think about that a little. The shot peen and coating I assume will help prevent fatigue cracks forming at the surface (?)

As far as the link – it shows beams with lumped attached mass, no distributed mass. However I am also modeling the distributed mass of the bar. Including both distributed and lumped mass at the same time makes it a little bit more challenge since there is no textbook modeshape solution (other than the one above with cos, cosh, sin, sinh that gets very ugly). I just mentioned Raleigh Ritz – the simplest version of that would probably combine the two modeshapes: 1 -cantilevered massless beam with lumped tuning weight near end, 2 - cantilevered distributed mass beam without attached tuning weight))

For the absorber that we just installed (see D.A. on motor generator thread), the rectangular bar is more massive than the tunable weight, so distributed mass can’t be ignored. The bar was 1” x 12” with 29” free length (about 100 pounds bar weight) with a discrete 40 pound mass attached 21” out.

I tried to make the tunable weight relatively smaller to make tuning easier. (If it’s large, then it’s more difficult to handle, and small movements cause larger change in frequency). Also I went for high ratio of bar width b to thickness h (12”/1”). For a given value of area moment of inertia I, we tend to get lower bending stresses with high ratio b/h (since max bending stress per moment is proportional to h), but the bar also tends to weigh more with high b/h (because I=b*h^/3 = Area * h^2..... lower h means higher A to achieve same I).

The result of the above considerations is we have a more massive bar and we can’t ignore the mass of that bar.

I think those heat sinks should probably have a small breadboard with a few resistors and capacitors as well ;-)

This message has been edited. Last edited by: electricpete,

I believe the stress at the fixed end of a uniform beam would only know about the displacement/deflection at the free end. I was thinking you already had built a successful prototype, so had an idea of the tip deflection/vibration.

A decent first mode solution for eigenfrequency would only require a few beam elements and single mass element. That's well within range for the demo version of 'most any FEA program.

Hi Dan,
I do have an installed absorber. I have in fact done a finite element solution in Matlab. I have also solved the stresses analytically as attached above. But I am still working on putting together something simple enough to put into a spreadsheet. It would calculate stress not only based on deflection, but alternatively based on a specified force transmitted from the machine so that we can compare designs in advance. Give me a couple of weeks to figure out how to do it and hopefully you can see what I mean (I anticipate it will be a pretty good tool, but maybe I'm counting my chickens too early... time will tell).

The beam stress is completely characterized by the deflection at the tip IF we know the deflection shape (in this case since the absorber is exctied at its resonant frequency, the mode shape). Mode shape depends in part upon the mass distribution. The link above has a deflection shape corresponding to point-load on the end, which would be the mode shape of an absorber that had all its mass at the tip of the absorber. That might be a good approximation if the bar mass was less than tuning weight mass, but it wouldn't reflect the type of absorber that we built very well.

quote:

As far as the link – it shows beams with lumped attached mass, no distributed mass.

In Hartog's "Mechanical Vibrations" appendices section III (natural frequencies of simple systems) there is a cantilever with end mass that just chunks in 23% of the (uniformly distributed) beam mass.
I'd think that might get me in the ball park pretty quick.

Thanks Dan

The formula that you referenced allows us to compute a resonant frequency.

I already know the resonant frequency (it is calculated in my spreadsheet linked above in a simple manner based on Dunkerely.... which is a little more general that the Den Hartog formula because it allows for the possibility that the distributed beam mass extends beyond the lumped mass as typically we leave room for adjustment and the lump is not all the way at the end).

I already have the frequency...what I need in order to convert displacement into stress is the mode shape.

EPete,

I was looking at your spreadsheet DunkerlyR1 and comparing the weights for Fox and Dunkerly. Impressive how fast you come up with spreadsheets and I appreciate them. I have some concern with the Dunkerly calculations. In your comparison section, the weight for the 16-inch “a” dimension is more than double for Dunkerly than Fox. Using Dunkerly, the “a” dimension for a 12-lb. weight would be set at about 21 inches, where it is about 16 inches for Fox. Have you constructed a dynamic absorber using Dunkerly yet? I have built several using Fox and have never had to move the weight more than a fraction of an inch from the calculated “a” dimension to get it to work (tuned). I programmed one dynamic absorber that I built with the Fox method and used those numbers for Dunkerly and it provided a negative weight. The Fox method is one that IRD provided a Sharp Basic program many years ago (in the early 80’s I believe). I programmed it into a Sharp 5500III and have used is several times with great success. I like to use round stock to make dynamic absorbers now, so I just calculate the MI for the round stock I want to use and convert it to square stock and put the square stock dimension into the computer and it gets close enough that very little adjustment is required.

Regards,
John J

This message has been edited. Last edited by: John J,

Yes, we used the Dunkerely spreadsheet to design the absorber on our Motor Generator. The target was going to fall somewhere in the middle of the slot, and that's roughly where it ended up although I never took any measurements.

The Fox spreadsheet is not a yardstick that should be used to measure other calculations. As was discussed in the other thread it is an incorrect implemeentation of Dunkerely's method. In contrast you can see in my derivation it is a correct implementation of Dunkereley's method.

Here is how I developed the table for comparing Fox to Dunkerely. I have a general spreadsheet called RotoSolve linked here:
http://home.comcast.net/~electricpete/rotosolve/
(note the versions of the spreadsheet at that link are older... I have to update them).
I took that RotorSolve and customized in into the attachment by adding a "front-end" tab labeled "DA_Compare". Put your inputs into the green cells in DA_Compare, then press "run" button in the "main" tab, and your results (frequencies) will appear in the "outsheet" tab.

You can verify any of the items listed in my comparison table using this spreadsheet by filling in those green cells in DA_Compare. As you can see from the table, the Dunkerley method does very well at creating the target frequency (30hz in this case), while the Fox method does worse and worse as a/L decreases.

An very important point to note, this RotoSolve spreadsheet uses an algorithm which is completely independent and different from the Dunkerley calculation. It is a "transfer matrix" algorithm and it has been verified against test cases 6 ways from Sunday as you can see in the above link.

This message has been edited. Last edited by: electricpete,

CompareWithRotoSolve2.xls (498 KB, 16 downloads)

Based on the table, Fox is close to Dunkerly when a/L=1, but gets worse as a/L decreases. That is somewhat expected from the nature of the "error" that I discussed in the other thread. The direction of the error is such that the predicted frequency using the Fox approach is higher than the target.

ALL three of the methods discussed here paragraph (Dunkerely, Fox, and the transfer matrix spreadsheet in the form that I attached here for validation of results) share a common set of assumptions / limitations which will tend to make the actual resonant frequency be lower than the calculated/target resonant frequency:

• 1 – All three assume a perfectly rigid mounting of the absorber, but it may not be the case in real life.
  
• 2 – All three neglect beam "rotary" (*) inertia and shear deformation. This has negligible effect if absorber is long and thin (large L/h), but can cause an error if absorber is short and fat
  
• 3 – All three treat the attached tuning weight as a point mass, which does not account for the rotary (*) inertia of the tuning weight, which is a small error if the tuning weight has small dimensions, but becomes a larger error if the tuning weight extends outward far from the center of the beam (in the direction of motion).

All 3 of above effects tend to push actual resonant frequency below predicted, which tends to reduce the magnitude of the "error" that I associate with the Fox equation. If you're very lucky, the 3 errors above might exactly cancel the error of the Fox equation so the result is right on target. Tough to talk specifics without knowing specific design. Item 3 could be easily and accurately evaluated for a specific design using a slightly different setup of the same transfer matrix program. The error in item 2 might be guesstimated based on standard published charts covering error associated with neglecting shear deformation and rotary inertia for cantilever beam (there is a chart like that in Harris' Shock and Vib Handbook). Item 1 – who knows.

I guess there could also be a small stiffening effect if a flat tuning weight is fastened against the bar, like we did for our motor generator dynamic absorber.... this could create an error in the other direction (actual resonant frequency higher than calculated or target).

Experience suggests Fox is close enough with a modest adjustment range as you say. I suspect the same will hold for my Dunkerly spreadsheet also.

* "Rotary" inertia doesn't mean anything is rotating in the sense we normally use the term.

This message has been edited. Last edited by: electricpete,

EPete,
Thanks for all the time you have spent on this. It is very interesting. Wish I had the engineering background to understand more of it, but you have helped a lot. Since I have had good results with the IRD (Fox) method and have it in my pocket computer, I will continue to use it, at least until the computer fails. I will keep your spreadsheet in my laptop for backup if I have any problems. Again, Thanks.

John J