Tuned Mass Damper - quick guide to tuning them 2

[GregLocock]

Just a quick look at TMDs, which came up elsewhere. In this case I am looking at the normal automotive case, where a large body is excited directly by a force, and we then bolt on a TMD. Typical example is the harmonic damper on the crankshaft, used to suppress torsional vibrations, and bending in some cases, or the extension housing damper on rear wheel drive cars to suppress powertrain bending. Some cars have 6 or more.

Here's the system



M1 is the engine or other large object, m2 is the TMD.

I'll start with the classic approach where the TMD is tuned to the problem frequency of the main system, with no damping for the TMD. Great response at 5Hz, pretty lousy at the 2 resonances.



Now add some damping to c2

So there's some residual response at 5 Hz, but the 2 split resonances are down.

Now change m2 to 0.3, this should reduce the frequency range between the two red peaks.


OK, that worked. go back to 1.0 kg for m2, and try under tuning it, so instead of 5 Hz, make it 4 hz



That's good, we've now got suppression across quite a broad range. Or try overtuning it, to say 6 Hz

and increase c2 to 3, to try and get the red peaks down


Incidentally a mass ratio of 0.1 is quite high, that's why you need to mount the TMD at an antinode.

 

[GregLocock]

Oh, and here is the last one but with the TMD tuned to 7 Hz


So you get less attenuation, but over a bigger frequency range.

Units used throughout are any self consistent set, so N/m, N/m/s and kg in SI

 

[GregLocock]

After a bit more thought I realised that in many cases we are more interested in the force that is going into the 'foundation' via k1 and c1, rather than the vibration of the mass m1 itself. Also I wondered whether a TMD could be used on a typical engine mounted on rubber engine mounts. A rule of thumb is that 80 Shure rubber gives you a c values of about 0.3% of the spring rate, so here's the best solution with 80 Shure engine mounts and TMD. even with a 10% mass ratio, struggling to get 6 dB. This is why we switched to hydromounts.

 

[XR250]

Apparently, some downhill teams are experimenting with TMD's on the front of the mountain bikes. Supposedly makes a noticeable difference.

 

[GregLocock]

Not very surprised, Renault used one in F1 until it got banned on very dubious grounds.

 

[Denial]

Thanks, Greg. Dramatically informative material.
[My website (https:/rmniall.com) has a spreadsheet for two-degree-of-freedom dynamic systems, which includes a facility for sensitivity analysis. But nothing comparable to what you have presented.]