As per theory tuned vibration absorbers are very effective but how well do they work in real life. In the theory, the derivation is based on undamped system while in real life, the applications always have some amount of damping. How well do the tuned vibration absorbers work in presence of damping? The simulations I have performed using Ansys show that they reduce the amplitude of vibration of the main body by only marginally in presence of damping. Can some one throw some light on this? Thank in advance.
my real life engineering experience is telling me that vibration absorbers (to be precisely, i'm talking of tuned mass dampers - TMDs) work very effective - as long as they are properly matched to the relevant structural mode and frequency of vibration which has to be damped. think e.g.of slender, usually lightly damped, lightweight footbridges: TMDs are meanwhile commonly used to reduce vibrations induced by pedestrians (and they work: you can google e.g. for "millenium bridge, London").
In regard to your question, for that example, we are talking of low damped structures of typically 0.5%~1% overall damping, which will be increased maybe to 3..5% (or even a bit more) damping for the system with a properly placed TMD, without excessive need of additional mass. In terms of reducing vibration amplitudes this increase of damping is really a word.
If you don't experience significant effects of a TMD in your simulations, i'd suppose a mistake of your TMD-design, wrong placement (perhaps in a nodal point?) or some other systematic error in your simulation... real life shows they work, and that pretty good.
I concur with Andreas. TMDs are very effective in solving real world problems as evidenced by the Millenium Bridge example. Modern fully welded structures are typically very lightly damped (< 1% of critical). TMDs have also been used to reduce first mode vibration in tall slender buildings. However, I advise against attempting to design a TMD without actual measurement data.
http://en.wikipedia.org/wiki/Tuned_mass_damper
https://www.physicsforums.com/threads/vibration-absorbtion-problem.575605/
The amplitude of vibration of the primary mass (your machine) can be derived to be the following. (assuming lumped 1DOF primary system and lumped 1DOF absorber)
Xk/F0=1−ω^2/ωa^2(1+μ(ωa/ωp)^2−(ω/ωp)^2)(1−(ω/ωa)^2)−μ(ωa/ωp)^2)
To attempt to eliminate the vibration of the primary mass by means of this secondary mass we can design the natural frequency of the absorber to match ω. From the equation we can see that in theory this makes the numerator zero. So what you can do is design the absorber to meet some specs.
1) specify a max deflection you would like the absorber to operate at (say 0.2cm)
2) design the linear stiffness of the absorber by ka=F0/Xa where, F_0 is an estimated force your unbalanced machine creates (you can try to measure this)
3) the last parameter of the absorber is mass, this can be obtained through ma=ka/ω2. where omega is the operating speed of the unbalance vibration.
I do agree with the previous responses. These kind of passive vibration absorbers work quite well in a number of practical applications, such as bridges (example is the Millennial Bridge in London) and tall buildings (example is the Taipei 101 skyscraper). Other example of tuned mass damper is the Stockbridge damper that works under the same principle. This is used to suppress wind-induced vibrations on slender structures (examples are overhead power lines and long cantilevered posts). Obviously, they will work correctly if and only if their proper design is made considering all the structural details.
I also agree with above findings - TMDs when designed based on the actual behaviour of the system can achieve very impressive vibration reduction even for low mass ratios. I've published some examples here:
Conference Paper Vibration Control of Piping Systems and Structures Using Tun...
Hi
The efficiency of a TMD depends on how it is tuned. The TMD can be tuned to provide damping (conversion of vibration energy into heat) or to provide 'stiffness' by acting in reverse phase. The former would rely on losses in the TMD, where the latter could be loss free.
Simply put, for a well tuned TMD, the larger its mass, the more robust the TMD performance.
The theoretical limit for the smallest TMD size depends on the theoretically smallest Q-factor [Q = 1/eta = 1/(2*C/Ccrit) ]. The acoustic Helmholtz resonator is a version of the TMD. It was derived a long time ago that the highest Q-factor one can attain is ~Q = 28 (if memory serves me correctly). Even for a perfectly internally lossless resonator, there will be damping, as seen from the resonator, as energy is radiated into the system the resonator connects to.
This implies that the smallest size lands in the ballpark of (1/28 = ) ~4% of the modal mass. Tuning would then be very sensitive.
A TMD does not work for transient problems. It can affect only slowly varying sources and steady state vibration.
Perhaps your TMD is too small to make a difference?
Sincerely
Claes
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