# How to calculate the spring constant (stiffness) of a Spring Retaining Clip?

Hello
The Spring Retaining Clip is a component used in some pin&socket mechanisms. It is a spring ring made of a steel wire (let's say 1,5
loops) which fits over the female brass socket component - its function being to squeeze the socket tighter round the pin (with a higher elastic force than the socket would achieve by itself).
Where is it possible to find formulae to calculate the spring constant as a function of the Young modulus of the wire used to make it, the diameter of the wire and possibly the number of loops?
Is the force produced merely the product of this spring constant with the variation of the diameter?
Thanks for help.
Pierre LAURAT, PhD
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As I understand your question, the additional clip is analysed as a beam in bending. These clips do not wind around the socket otherwise friction would lock the mechanism preventing the socket from expanding and the pin from entering. Hope that helps
John

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Pierre LAURAT wrote:

Can you describe this spring clip more or post a link to an illustration? I'm not sure how it pushes radially on the socket.
Thanks.
Jeff out ...
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Hi Jeff
Here are the pictures:
http://www.ifrance.com/Tigerius/SpringRetaining1.jpg
http://www.ifrance.com/Tigerius/SpringRetaining2.jpg
Thanks. Pierre.

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Jeff-
Help me out here.....it not this situation just a "curved beam", a split ring
I think Roark might have a split ring but being a cheap SOB I never bought always borrowed :(
regards Bob
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Bob K 207 wrote: >

Since the loops are continuos (except for the first and last ones) I thought a loop could be treated as a ring. Since the spring retaining clip has a plane of symmetry, a half ring with the right boundary conditions should be enough.

There are arches and curved beam segments in Roark's.

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If you have more than one loop I do not think that it will behave as a spring, usually a retaining spring has less than oneloop. For example if you have two loops it will behave as two solid closed rings If you want to use let say a retaing ring with less than 360 degrees, then the formulation can be found in Design Handbook Engineering Guide to Spring Design 1987 edition from Associated Springs Page 68.

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One approach to estimating the force available.
Consider the wire clip straightened, and bodily fixed at one end, and uniformly loaded along its length. This deflection due to loading is increased until it represents the decreased curvature of the spring clip while free, versus its increased diameter when circling the socket. It is this increase in diameter that provides the closing force. The force to similarly deflect the straightened wire is a measure of the available spring force.
Brian Whatcott Altus OK
On 3 Nov 2003 08:37:26 -0800, snipped-for-privacy@legrand.fr (Pierre LAURAT) wrote:

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snip ...

It will be comparatively easier to use shear modulus (or the modulus of rigidity) for a spring instead of Young's modulus which is tension modulus of elasticity more relevant to axial stresses and strains. Spring is a case predominantly of torsional shear. (Refer to pp 27, Mech. of materials, 2nd Ed, Gere & Timoshenko).
For a spring with uniform radius = R, spring wire radius r = d/2, turns per unit length = N, modulus of rigidity =G, the spring constant = k may be given by
k = G*d^4/(64*R^3*N)
If this equation gives acceptable values for your purpose I can post the derivation otherwise I might have made some mistake in assumptions and/or calculations. In that case, consider aletrnative solution below. G can be substituted by Y as you need it but it brings in poisson ratio, an additional unknown. If your spring is not uniformly cylindrical but some other nice geometrical shape, another equation might be needed.
Aletrnative solution ------------------------ If a small experiment is possible, simply use f = kx and find two small extensions x1, x2 for two small loads f1, f2 respectively and solve for k the the two simultaneous equations f1=kx1 and f2=kx2.
Hope this helps.
--
Mohan Pawar
App. Engineering
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