# Converting energy into torsional spring displacement

1. Feb 22, 2016

### Infinitybyzero

Hello, I'm trying to figure out a general physics problem here and I'm trying to relate energy held in a rotating shaft to be dissipated by a torsional spring. Let's say I have energy E (Joules), shaft outer diameter D, and torsional spring capacity T.

T is what I'm designing for with all properties relatively open, subject only to the constraint of the spring's ID (fully loaded) never less than D and it's OD (unloaded) never greater than 4D. Wire thickness, leg length, and number of active legs are all "change as needed." Assume that the shaft dissipates the energy directly in torsion through a 100% efficient clutch.

I'm looking for guidance on how to design the spring for this layout. I would like to be able to design it in terms of rotational deflection of the spring.

2. Feb 23, 2016

### Nidum

Are you describing a shaft with a spring wound around it in such a way that the rubbing action between shaft and spring (a) partially winds up the spring (b) dissipates energy by friction ?

3. Feb 23, 2016

### CWatters

The equation for the potential energy stored in a torsion spring is similar to that for a linear spring... PE = 0.5kθ2 where k has the units NmRad-1 and θ is in the displacement in Radians.

Unfortunately I can't help design the spring. I think you may need a book on torsion spring design. Google can find spring manufacturers that have some info and calculators that might do the job...

http://www.springsandthings.com/pdf/torsion-springs.pdf
and
http://www.acxesspring.com/torsion-spring-calculator-instructions.html

4. Feb 23, 2016

### Infinitybyzero

Assume that when the energy-filled shaft engages the spring, energy transfer is 100% and the spring has enough capacity to safely take that energy.

I understand I need to design for k, but I'm looking for a way to basically get k in terms of D and E, if that's even possible (or useful). I've used the acxess spring calculator and played around with the variables but it's really tough to get the displacement I need without doing weird variables. Basically too many dials to turn with no reasonable first guesses at parameters.

5. Feb 23, 2016

### Nidum

Sorry but question does not make any sense .

6. Feb 23, 2016

### Infinitybyzero

I have kinetic energy that has been put into the shaft, say 1000 n*m worth. It spins freely with this energy until a clutch engages it with the spring (and it's shaft). The transfer mechanism isn't important for this conversation. When the spring is engaged, it has characteristic k and deflects θ. Theta is my most important variable and I would like to know how to maybe set up a spreadsheet that calculates theta in terms of k(and its variables), as well as E.

7. Feb 25, 2016

### CWatters

I gave you the equation that relates energy, k and theta. You will have to pick a value for either k or theta. Perhaps try picking a small value for theta like 1 rad?