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Spring theory Design Question?

Spring theory Design Question?

Spring theory Design Question?

Hello All-

I have a question regarding spring design theory and was wondering if you all could help.

I am reasearching spring design for a project and came across an article which can befound here...


The article pertains to making a composite spring.  My question is can the eqautions and principles shown in the article be used in designing a hollow core metal spring with an exotic metal such as Titanium?; or are there a different set of formulas and factors that need to be used?

I have looked everywhere i can think to but have not been able to find info that is valid.

If anyone could point me in the rite direction it would be greatly appreciated.

Thank you for your time

RE: Spring theory Design Question?

The short answer is "Yes."  The equations assume that the coils are "close wound"(helix angle is small) and that the ratio of the spring diameter to the "wire" diameter is large (10:1 or greater).

RE: Spring theory Design Question?


Thank you very much

RE: Spring theory Design Question?

I do not agree with sreid's statement that the "..."wire" diameter is large (10:1 or greater)..". Many springs are normally go upto 3:1 (see "Wahl constant" definition). I have designed and used many springs with such 3:1 ratio.

You indeed can use the same formulas however, remember that the wire section moment of inertia is smaller due to the hollow core. You have to update the formula to take into account the core hole diamter inside the wire. Since the spring force and rate formulas are already "cooked" formulas based on solid wire you will need to know how those formulas developed to be able to update them for the hollow core wire.

RE: Spring theory Design Question?

The formulas in the referenced website do not contain a stress multiplier factor for the D/d ratio.  And the formulas are stated to include the J for tubes.  And although the formulas include shear stress for both direct and torsional shear they point out that the torsional shear dominates for small helix angles.

RE: Spring theory Design Question?


I looked again in the artcle and you are right, it gives the formulation for hollow core wire with the correct J. However, for Strong1 to use it properly he needs to apply Wahl factor to account for stress concentration due to wire curvature.

As you said these formulas neglect Wahl factor therefore they will fit for springs with a ratio of the spring diameter to the "wire" diameter (10:1 or greater). Sorry for missunderstanding your first post.

RE: Spring theory Design Question?

Thank you gentlemen...I appreciate your answers greatly


RE: Spring theory Design Question?


I have one more question and then i will leave you alone :)

Would the same principles and eqautions as well as wahl factor be used to design a hollow core RECTANGULAR SPRING?...I.E. the inner spring of a valve spring on some engines valve train.

I apologize for all the question but really appreciate your help.

If they are different eqautions would you be so kind as to say what they are?  I really havent had any luck finding pertanent information.

Thank you

RE: Spring theory Design Question?

Basically, yes, you just have a square torsion bar vs. a round one.  There are some additional stress concentration factors, however, due to the square shape.

RE: Spring theory Design Question?

Sreid answer is correct again. Just want to add that the Wahl factor for rectangular wire is different from the round wire and as Sreid mentioned the stress intensifier on the sides of the rectangular section are not the same and they change with the ratio between the sides. The stress intensifier on the long side of the rectangular section is larger. I am pretty sure that any good mechanical design book such as from Shigley or Norton are dealing with this type of spring. The best is to find a copy of a spring handbook from SPEC or the SMI or Wahl's book Mechanical Springs.


RE: Spring theory Design Question?

I was interested in the Spring thread. Do you guys beleive ther e is potnetial in hollow springs from (or even hollow with internal structures like spirals) performance materials like titanium?

It is possible to make such designs with advanced manufacturing techniques.

RE: Spring theory Design Question?

Certainly in applications where weight is more important than cost, hollow coil springs make sense.

RE: Spring theory Design Question?


The only eqaution i have been able to find regarding Wahl factor is as follows...

W=4C-1  0.615
  4C-4  C

Is this correct?

My reference material has not arrived as of yet.

Thank you

RE: Spring theory Design Question?

Hollow wire compression springs have been done occasionally in the past. Ford experimented with them in the 70's. I tinkered with them in the late 90's for mountain bike suspension (that was when mountain bikes cost a lot more). I recall hearing of some high temperature applications where coolant was run through the ID of the spring wire.

The design equations can be adapted from those for hollow torsion bars, which SAE publishes.

I eventually concluded that the space efficiency for a shock spring declined enough to negate the weight advantage. Getting seamless tubing of sufficient strength is another problem. I finally just went back to titanium and super-high strength steels for the tough applications.

Titanium is a fun spring material, but it requires a superbly clean surface before it goes into the vacuum furnace, and that may tough on a piece of tubing.

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