Torsion Spring Number of Active Coils

[DownHillHero]

I am trying to come up with a torsion spring, but not knowing much about torsion springs I do not know if my results are very valid. I am trying to figure what diameter of wire is needed as well as how many turns are needed.

Design parameters:
k = 9314 in*lb/turn
D_m = maximum of 3 in.
The spring will turn 1/4 of a turn therefore M = 2328.5 in*lb

so far I have been using two equations to try and design the torsion spring.

1. k = (E*d^4)/(10.8*D_m*N_a)
2. S = (32*M)/(pi*d^3)

where
k = spring rate (in*lb/turn)
E = Modulus of Elasticity (psi)
d = wire diameter (in.)
D_m = mean diameter coils (in.)
N_a = number of active coils
S = stress (psi)
M = Torque (in*lb)

To begin my calculation I selected ASTM A228 as my material.
E = 30500 ksi
Yield strength = 231000 psi

Using equation 2 I solved for the diameter of wire I would need to use which worked out to be 0.4682 inches

Then using equation 1 with the parameters stated above solving for N_a I am getting around 4.9 coils.

Do these value seem valid?
I am wondering if there are any restrictions on the equations that I have used which may give invalid results.
Lastly is there any material that would be more suitable for a torsion spring such as the one I have described?

 

[israelkk]

As far as I know ASTM A 228 (Music wire) maximum diameter is 0.25".

 

[DownHillHero]

Thanks israelkk,
I knew music wire generally had a smaller radius I just didn't know how small, looks like I will have to use a different material and rework the calculations.

Any suggestions on a material generally used for springs that has a maximum wire diameter of about 0.5" ???

 

[israelkk]

Is this an academic problem or a real problem?
It is not clear from your post how many cycles the spring has to live the 1/4 turn and if it always to one direction or both directions? From a quick check, for cyclic operation you may not be able to find simple solution without some secondary operations on the spring that will make it much more expensive and will be only a proper for a spring that deflects to one direction only.

 

[DownHillHero]

This is a real problem.

The spring has to be able to have a 1/4 turn in both directions. The spring should live for around 10000 cycles.

Do you know of any sources that can help me determine how this spring should be designed?

 

[israelkk]

This is not a simple case, you are asking for a large torque from a 3" outside diameter spring. You didn't mention the maximum length of the spring that you can allow. There is also missing information regarding environment conditions, is it needed to be plated, etc. You need an expert to design such a spring if it can be done at all. Where are you located?

https://sites.google.com/site/israelkk/home

 

[DownHillHero]

The maximum length of the spring would be 5" so if your wire diameter is 0.5" you should be able to get about 10 active coils (I realize it will be less because we are placing the torsion spring in compression and tension so some spacing between the coils will be required to account for the decreasing in length)

As far as weather conditions go it would be mounted on the outside of a car, it would have some type of covering to protect it from things such as rain.

From reading a rather lengthy article about torsion springs it appears that the all the conditions are accounted for by safety factors and the equations I stated above are still valid..???

I think if we decide to go this route with the project it would be a great idea to have an expert design such a hinge, however I was hoping to do some preliminary calculations to see if this would even be possible before hiring and paying an expert to tell me that it is not.

 

[israelkk]

I think paying an expert that will tell you that it is not going to work worth any penny of it. Otherwise, you may continue with your project which I believe the spring is only a part of it, spend time and money just to find at the end that you will not be able to find such a spring. I have seen projects of millions of dollars go to the drain just because same logic used at the preliminary stages of the project. As I told you, from a quick check it is not a spring that the occasional designer can design just from the SAE or SPEC spring handbook formulas.

I have noticed from your last post that this is not just a torsion spring but you also use it as a compression and/or tension spring which is a whole new game am I correct?

Usually torsion spring coils are touching each other and the spring's length changes as a result of the torsional deflection, at the same time the outside diameter decreases or increases too.

 

[DownHillHero]

Yes the spring is only a part of the project and of coarse it would be best to have an expert design the spring however several other designs are being taken into consideration perhaps after a full on discussion about the direction we cant to go an expert can be hired if we decide a torsion spring is the best option.

Sorry for the confusion but I was talk about putting the torsion spring in tension or compression, not sure if those are the correct terms but basically the different directions you can go with a torsion spring.

From reading some posts it seems as though torsional spring are much better for only one direction, if you are going both it complicates the spring quite a bit?

 

[DownHillHero]

Would a spring that requires 1630 in*lb still be a very large torque for a 3" outer diameter?