Wire form calculations and formula

[jamxb6]

I am trying to come up with a formula to tell me how and how much to preload a spring for a new product. The data that I'm starting with is as follows:

Imagine a spring in a the shape of an uppercase j, minus the flat on top, and instead of an arc on the bottom it has two right angle bends and a horizontal in between. The short leg is what holds the spring in position, and I'm assuming (not what actually happens but I think it will make things easier) that the spring only bends through the lower right bend under load.

Data I have is reaction load and horizontal deflection at two locations. Imagine the j spring as it is written, then position 1 is halfway up the length of the long side and the horizontal deflection is to the right. Position 2 is at the top of the j (end of long leg), and deflection again goes to the right. I've posted results of the raw data in the attached image.

I need to come up with a formula that makes load a function of angular deflection and moment arm (length from bottom to loading position), or a function of linear deflection and moment arm. I've tried beam caculations, but E is not constant but rather behaves inverse proportion to deflection. Once I have an idea of how to relate the things I need to, I can find out how much to over underbend the wireform to give me the required preload once it's installed. The new spring is also pretty simple, with a short leg, and a bend followed by a long leg.

Thanks

 

[chicopee]

".... but E is not constant..." I think that you meant "I" or "EI"

 

[Cockroach]

Handle it like a cantilever beam with shear, bending, rotation and deflection. You can correlate deflection to shear in the linear range of the material by calculating the bending stress at the support of the cantilever.

Regards,
Cockroach