Trouble with torsion spring calculations

[Carburize]

Ladies and Gentlemen,

I’m trying to calculate the elastic potential energy stored in a double torsion spring, as well as the stress at peak torsion. I am obviously screwing up some calculation, because the stress level I am getting when the spring is “cocked” is 386,000psi. This is obviously not correct since the spring is not broken or permanently deformed, and it lasts a long time in service. I also suspect that I got the spring rate wrong as well, since some figures that use the spring rate in their calculation seem “goofy” for lack of a better word. Can someone kindly point out where I am going wrong? The spring dimensions and attributes are:

Material: Music Wire (assumption), minimum ultimate tensile strength 309,000psi for this particular wire size.
Wire diameter, d: .045”
Mean diameter of coil, D: .360”
Spring Index, C: 8.00
Wahl Factor, K: 1.1
Angle between free state and assembled (position 1) state: 96 degrees
Angle between free state and “cocked” (position 2) state: 161 degrees
Lever length 1: .628”
Lever Length 2: .855”
Number of body turns: 4.07 per side (8.14 total)
Number of active turns (taking the ends into account as partial turns): 4.51 per side (9.02 total)


Based on the above information, I am calculating:

Spring rate: 7.02lb in/per revolution (one coil only) (this seems low according to my calibrated fingertips – am I screwing something up here?)
Assembled Torque (position 1), M₁: 1.87lb in (one coil only)
Potential Energy (position 1), U₁: 0.25in lbs (one coil only)
“Cocked” Torque (position 2), M₂: 3.13lb in (one coil only)
Potential Energy (position 2), U₂: 0.70in lbs (one coil only)
Total stored potential energy between the 2 positions: 14.4 inch ounces, taking into account that it is a double torsion spring and there are 2 coils
Stress at position 2: 386,000psi (bogus number) using the formula S=[ (32M₂)/(3.1415*d^3) ] x K

Can anyone tell me, for starters, why my calculated stress is so high? I am aware that there is a residual stress induced during the coiling operation that serves to increase the elastic range, but my stress figure seems absurdly high.

Thank you for your help in advance.

[JAlberts]

Carburize,

I have run the stress calculation for your specified design and have confirmed that your calculated stress result is, in fact, correct; and, that for ASTM A228 wire of your specified diameter your indicated minimum tensile value is also correct.

Beyond that, I have no explanation for the lack of wire failure other than to say that the published values are "minimums" and the wire, or spring, material that you have may simply exceed those values.

At the same time, this level of stress obviously well exceeds the recommended % min tensile strength for working springs with a good life expectancy.

[Carburize]

JAlberts,

Thank you for taking the time to confirm my calculations. The spring in question is an AR-15 hammer spring, and it has a strong track record of providing reliable ignition for thousands and thousands of rounds. It appears to be durable and to have a long fatigue life in service.

Is there a way to calculate the residual stress from the coiling operation? Is it possible that a spring made from music wire near the upper limit of the ultimate strength range (342,000psi) in conjunction with the residual stress would allow the spring to see that kind of calculated stress level and not yield?

[JAlberts]

I’m afraid that my background with spring design is too limited to address the above questions; but, contacting a custom spring manufacturer might offer some light on the subject.

Just as a thought, have you tested the deflection force on any well cycled springs to see if there is any reduction in the springs' torque force at their "fully cocked" position to see if they might have experienced any plastic yielding that would relieve some of the calculated initial extreme tensile stress?

[Carburize]

I don't have the equipment to perform any reliable testing. I can't imagine that the spring would be that poorly designed so as to yield in service. The other compression springs in the gun are quite well-designed.

There are also "extra-power" hammer springs on the market that are used for firing ammunition having notoriously hard primers. I do not know how these springs are able to deliver more kinetic energy to the hammer, since apparently the standard hammer spring is very highly stressed. I have an application that may require more hammer energy.

Thank you again for your help JAlberts.

[JAlberts]

In some designs, specifically belleville type springs, and in some compression spring, the springs are intentionally designed beyond yield and then exercised (ie, preset) the their final state to insure that the maximum available performance for the spring material will be achieved.

Depending upon your design requirements and cost limits Ni Alloy 718 has an incredibly high tensile stress but definitely at a proportionally higher cost than other more standard materials; but, I used it in a specialty "flexing disc" design when no other material would work and the performance capability it provided warrented the extra cost.

[Carburize]

Is it possible to "prestress" or "scrag" a torsion spring? I posted my basic original post on another forum, and the poster who responded said there is a little-known process for torsion springs. I was under the impression that a torsion spring, unless thermally stress-relieved, was prestressed by default, meaning that there exists a beneficial residual stress that increases the elastic limit of the spring. Is anyone aware of a secondary prestressing process for torsion springs?