Spring velocity
Spring velocity
(OP)
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.





RE: Spring velocity
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
RE: Spring velocity
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.
RE: Spring velocity
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
RE: Spring velocity
Cheers
Greg Locock
RE: Spring velocity
RE: Spring velocity
RE: Spring 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.
RE: Spring velocity
RE: Spring velocity
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