# Vibration Absorbtion Problem

1. Feb 8, 2012

Hi,

So I'm on a work term during a semester off at school (Mechatronics), and have been asked to see if it is feasible to replare some concrete plynths with steel. These are used to support a motor and, possibly, some excentrically rotating masses.

My problem is that I don't really know where to begin. I took a vibrations course back in 2nd year but I don't recall going in depth with vibration absorbers. Is there any material you guys can point to that would be useful in this application? Any advice is welcome.

Cheers

2. Feb 8, 2012

### Bobbywhy

3. Feb 14, 2012

### FeX32

If you give some more details I can help you. There are many types of vibration absorption. Active mass dampers, passive vibration isolators, semi-active isolators, etc.

4. Feb 14, 2012

### OldEngr63

Does the machine run at constant speed, or does the speed vary?

5. Feb 15, 2012

Machine runs at constant speed (well, minus for the start-up/shut-down which is not frequent)

For vibration isolators, the simpler the better. I don't think active damping would be considered.

I was looking into designing the supports for the machine to be Tuned Mass Absorbers. I cannot find much literature on them, though. I basically just know that you want to design the natural frequency of the absorber to equal the forcing frequency. Currently it sits on large and tall (meters high) concrete plynths to ensure that no vibration problems will ever present themselves.

Not sure how much info I can give out, but what would make it easier for you to help, Fe? This is more of a little side project I picked up 'cause it's interesting (and most likely not see frution), but I don't want to mess with IP.

6. Feb 15, 2012

### OldEngr63

Look up a study done by Brewer Engineering and Prof. Stephen Crandall at MIT a number of years ago to see a case study on tuned vibration absorbers for a power plant fan (I forget whether it was FD or ID fan). The absorber were installed at the Newington Station and proved to be very effective there. I think this sounds like just what you want.

7. Feb 15, 2012

### Bobbywhy

8. Feb 15, 2012

### FeX32

For a sinus vibratory force as you have a tuned mass damper, a.k.a a vibration absorber in the form of an added "sping" and mass is usually the best choice.
Here is some basic info:http://en.wikipedia.org/wiki/Tuned_mass_damper

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)

\frac{Xk}{F_0}=\frac{1-\omega^2/\omega_a^2}{\left(1+\mu(\omega_a/\omega_p)^2-(\omega/\omega_p)^2\right)\left(1-(\omega/\omega_a)^2\right)-\mu(\omega_a/\omega_p)^2}

Consequently, to attempt to eliminate the vibration of the promary mass by means of this secondary mass we can design the natural frequency of the absorber to match $\omega$. 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 $k_a=\frac{F_0}{X_a}$
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 $m_a=k_a/\omega^2$. where omega is the operating speed of the unbalance vibration.

You now have a vibration absorber which can be further detailed and experimented with on the equipment and possibly further improved.

Cheers,

9. Feb 16, 2012

### FeX32

If you must repair the support beams than the best solution to your problem is to design the beams such that they suppress the vibration absolutely. The second best option is the above TMD (tuned mass damper). Basically what you need is the vibration spectrum of the equipment. Some force vs. frequency data. Then you can design the supports such that none of the vibration "gets through" them..

10. Feb 16, 2012

What do you mean by them suppressing vibration absolutely?

11. Feb 16, 2012

### FeX32

I mean the supports can be designed to let no vibratory force through without using a TMD. The literature on both of these topics is not scarce. The methodologies are also well developed.

12. Feb 23, 2012

Got to do a bit more work on the problem between actual work. I calculated all of the loads and determined where the vibration is coming from. There's one thing that I can't understand for the life of me... and it's making me feel like I'm missing something very basic.

I'm trying to prove to myself analytically that the concrete supports work (they obviously do in real life). I'm assuming that the theory behind their construction is that the natural frequency of the foundation should be larger than the forcing frequency (I read about 2x or more). Using this equation I was able to calculate the amplitude ratio of the concrete design:

Amplitude ratio = actual amplitude/free amplitude = (w^2/w_n^2)/ sqrt((1-(w^2/w_n^2))^2+(2cw/w_n)^2)

Now I estimated the plynths as blocks and estimated their spring constants as EA/l (combining F=k*dL and E= F/A/dL/L). Calculated their mass as A*l*rho. Thus, the natural frequency is sqrt(E/(l^2*rho).

This is all good for concrete as I get a very small amplitude ratio of around 0.008.

However, I get an even smaller amplitude ratio when using steel and the same method of finding spring constant. I doubt this is the case in real life as I read in studies that introducing steel reduces stiffness and lowers natural frequency to the forcing frequency.

I know I'm making a bunch of big assumptions (concrete is elastic at this point, spring constant calculation, damping is very small, solid block supports for steel & concrete, etc) but what am I missing/messing up?

Edit: Thinking about it, this result might actually be okay (but useless). I am assuming that the steel was just a solid block. Obviously, this isn't how it'll be constructed. I need to learn about supports now, and how to determine equivalnet mass & spring constant.

Last edited: Feb 23, 2012
13. Feb 24, 2012

### FeX32

Are you assuming a huge solid piece of steel? If so this would cause huge error. One huge block of steel, wow.

There is likely to be a couple c-channels or I beams that make up the structure. Their elasticity is going to be made up of their components.

Also, concrete doesn't abide by the same modulus rules as steel (or any metal). If you want something accurate you need to look up concrete design.

Why are you doing this if the concrete works fine.

14. Feb 24, 2012

### FeX32

And don't forget about the steel within the concrete..