Spring velocity 1

[frayedknot]

I have a long rod that is coiled into a torsion spring at one end. I need to find the velocity at the tip when the rod is deflected X inches at the tip. I know I have a torsion spring and a flat spring. How do I model these together? Any help will be appreciated! I'm losing hair over this.

 

[GregLocock]

In the worst case that's a tricky one.

Are you looking for an analytical solution? or FEA?

Is the deflection due to the beam's bending significant compared with the contribution of the torsion spring?

Is this a large deflection problem? ie do you need to worry about the rotational inertia of the beam?

What you really need is to find someone who has analysed a Trebuchet. Not many trebuchet engineers around these days.


Cheers

Greg Locock

 

[EnglishMuffin]

"Not many trebuchet engineers around these days". You obviously haven't been watching the US history channel lately!
Blevins (Formulas for natural frequency and mode shapes Table 8-10) gives the natural frequecy of a distributed mass pinned free beam with a torsion spring at the pinned joint. It's in tabular form, so I don't feel much like reproducing it right now. But it might be OK for what is required here.

 

[GregLocock]

Good catch. Table 8-12

f=lambda^2/(2*pi*L^2)*(E*I/m)^.5

lambda is 1.2479 for kappa*L/(E*I) =1, rising to 1.8751 for infinity.

Cheers

Greg Locock

 

[GregLocock]

Although on thinking about it that may not help the original poster /very/ much

Cheers

Greg Locock

 

[EnglishMuffin]

Yes, well in my Blevins, 8-12 is the one with a mass on the end as well as a distributed mass. Anyway, one of those equations will probably do the trick. frayedknot may not need Rogaine for a while after all.

 

[EnglishMuffin]

Oh, I didn't see your last post, must have been posting at the same time. Well, I guess it depends on what he is trying to find out, which is not quite clear. If he wants to know what the relationship between velocity and displacement is at some time t after releasing the deflected rod, then one of those equations should be of some assistance. Perhaps he can enlighten us.

 

[frayedknot]

Thanks guys! Looks like the gibberish from a vibrations course I once took. I tried to model it as a 2-DOF system under simple harmonic motion (assume no damping) since I'm only interested in the maximum velocity.

Where might I find this Blevins dude, i.e. is it a common book at a local university's library? I'm working on a re-design of a current product...I want to increase the speed of this device. Ideally, I would solve for the velocity analytically to find the current design's speed AND understanding the relationship of the different variables so I know what to change to affect the velocity the most. The biggest bang for my buck...or for my boss's buck rather. Of course I plan to verify the speed calculations experimentally so it doesn't have to be exact...or even correct, as long as they show a relationship between the variables (i.e. change the material (E) some % and the velocity increases some %).

The rod actually tapers and it deflects a considerable amount.

FEA is out of the question...no software...no bucks to buy it.

This makes less and less sense the longer I think about it.

 

[EnglishMuffin]

Amazon should have a copy of Blevins - very well known text, and very useful. University libraries most certainly carry it. Of course, if the rod tapers, that equation won't be quite right. You could derive one from scratch using superposition of a tapered beam and a torsion spring. But it's a good start.

 

[GregLocock]

Amazon has it for 69 bucks

Formulas for Natural Frequency and Mode Shape
by Robert D. Blevins

You could do it with Rayleigh Ritz and a spreadsheet. William Thomson's book on vibrations explains that. Rao's book even includes a worked example on a tapered beam.

Once you know the resonant frequency then the rest is easy - max velocity=max displacement*f*2*pi



Cheers

Greg Locock