Interference fit between helical coil spring and rod 4

[elogesh]

This is regarding to interference fit between coil spring and rod.

A rod is inserted into a helical coil spring inside diameter with an interference fit.
Is there any generalized formula to calculate the stress introduced in the spring due to this interference?

The stress should be evaluated after the insertion of rod and not during insertion of the rod.

I felt the change in curvature due to insertion of the rod should be accounted in the formula? whether am I right.

I referred formula from roark's formula for stress and strain from Warren young and found that,(page no 386)

Stress={(16PR)*{1+(5/8)*(d/R)+(7/32)*(d/R)^2}}/{pi*(d)^3)

Where P -load
R-mean diameter of coil
d-Wire diameter
pi=3.14....(22/7)

Can I apply this formula,

If there is any alternative formula,please provide the same.

Regards,
Logesh.E

 

[TheTick]

I have nothing specific. However, you might look into the relationship of stress, diameter, and deflection of a torsion spring.

 

[drawoh]

elogesh,

You are talking about a press fit. The rod is bigger than the ID of the coil spring, right?

I doubt there is a simple formula for this. The stress would be massively dependant on how you forced the rod down into the coils. The coil spring's movement would be restricted by friction with the rod. This force could be significant, and should be taken account of by your calculations.

Metal to metal press fits involve high forces. Are you sure the coil spring is going to move after all this?

JHG

 

[desertfox]

Hi elogesh

Normally springs have a clearence when being assembled over a rod. I think you may run into problems with an interference fit as the springs will have several thousands
of an inch tolerance on its internal diameter which will give you various intereferences/clearences. In addition springs are never straight along their length which will also cause varying stresses within the spring as it is assembled.Another major factor here is how will the spring function with excessive friction created by the intereference fit and how will you determine the load needed to compress or extend the spring due to the additional friction.
Can you give more details of your application and why you need an intereference fit? is the rod passing through the whole length of the spring? is it a compression or tension spring? with more information we may be able to help further.

regards desertfox

 

[elogesh]

Thanks for all your responses

I understood from desertfox that, few more additional input details are required.

"I think you may run into problems with an interference fit as the springs will have several thousands
of an inch tolerance on its internal diameter which will give you various intereferences/clearences"

I will pass this issue to the concerned person in our organisation


More details of your application and why you need an intereference fit?

I am collecting the details from the concerned; I will provide the same in a day or two.

is the rod passing through the whole length of the spring?

No. The rod is passing partially.

is it a compression or tension spring?

It is used as a torsion spring.

Rough spring details are as follows,

Outer coil diameter,Do =15.7 mm
Wire diameter,d =1.5 mm
Height of spring,L = 15.6 (approx)

No.of coils,N=10

Interference level , dl = 0.8 mm

Based on following formula, calculated contact pressure if rod is inserted in one coil.

Pull out load, F

F = m * pi *A
where
m = the coefficient of friction annular cylinder members
A = the contact area
pi = the pressure due to interference fit given by the following equation based on axi-symmetric analysis of thick cylinders

Pi = (E (dl) ((rb)^2 - (rt)^2)) /(2*(rt)(rb)^2)
where
E = the modulus of elasticity assuming both members are made of same material
d = the interference
rt = Outer radius of the inner member
rb = Outer radius of the outer member


Based on the above formula, contact pressure is found to be,

Pi =1.86 e9 Pascal

Therefore radial load per coil = 2*pi*Do*d*Pi

Radial load = 222054 N

From general torsional stress formula for the spring,

Stress =2.5 e12 Pascal

Allowable stress for the spring = 2e9 Pa

Stress created due to interference is higher than allowable stress.

From the above calculations, I understood that, probably I am going on the wrong route.

As I mentioned earlier, I will get the required input details and post within a day or two…


Once again thanks for all your responses...

Regards,
Logesh.E

 

[MikeHalloran]

What you're proposing is not a torsion spring, it's a 'wrap- spring' clutch.

If you try to press the rod into the spring axially, you'll have a hard time doing it. The rod will enter easily by hand if you just 'unscrew' the spring a half turn.

In operation, if torsion is applied in a direction that loosens the spring, it will behave like a torsion spring, i.e. the wire will be stressed in bending as the spring unwinds.

If torsion is applied in a direction that tightens the spring, the wire will be stressed in tension, and unless the wire is square in cross section and lubricated with moly grease so its surface can slide on the rod, only the end turn will be seriously stressed.

It will be _seriously_ stressed, because it's not acting like a torsion spring, it's acting like a cable wound on a drum.

Torsion spring formulae will give wildly inaccurate results; the torsional spring constant in the tightening direction will be _huge_. In a real wrap-spring clutch, the clutch locks up in a fraction of a degree of rotation, and torsion applied to the tang on the end turn of the spring is transferred to the clutch hub, in this case the rod.




Mike Halloran
NOT speaking for
DeAngelo Marine Exhaust Inc.
Ft. Lauderdale, FL, USA

 

[desertfox]

Hi elogesh

The I.D. of a torsion spring tends to get smaller as the spring is wound up so the stresses you will get in the wire
will be considerably high if you combined it with an interference fit. Again these springs are designed with a clearance normally when fitting over a shaft.
Also if you only partially fit the rod into the spring then you will lose some of the active turns of the spring and all your design calculations for the spring in terms of allowable stresses and stiffness are no longer valid.
I notice also in your last post the allowable stress seems very high is this an error because the value quoted is comparable with the Modulus of Elasticity of steel.

regards desertfox

 

[vonlueke]

>> Is there a formula for calculating the stress in the spring after insertion of the rod? <<

elogesh: As MikeHalloran said, you apply torsion to unwind the spring, insert the rod, then release the spring. I'll try deriving an answer to your above sentence, except using my own notation. In your given question, there's no axial compression nor elongation of the spring stated, implying the spring is at its original axial length in the final assembly. And I'll conservatively assume the rod is a rigid body, thus maximizing expansion of the spring. I'll also assume longitudinal strain in the spring wire is uniform from the inside to outside diameter of the spring wire (probably a reasonable assumption). Therefore, strain of the spring in the hoop-wise direction would be, eps_hoop = (D-d+t)/(d-t), where D = rod diameter, d = mean coil diameter (prior to assembly), and t = wire diameter.

Slope of the spring helix is, p/(pi*d), where p = coil pitch (axial length per coil), and pi = 3.14159. Thus, helix inclination angle, theta = atan[p/(pi*d)]. Therefore, strain of the spring in the inclined, helix direction would be, eps_wire = eps_hoop/cos(theta). Substituting the above into Hooke's law (sigma = E*eps_wire) gives the following equation for uniform tensile stress in the spring wire.

sigma = (E)(D-d+t)/[(d-t)cos{atan[p/(pi*d)]}], but not less than zero.

As an example, let rod diameter D = 13.5 mm, mean coil diameter d = 14.2, wire diameter t = 1.5, coil pitch p = L/N = 15.6/10 = 1.560 mm, and E = tensile modulus of elasticity = 200000 MPa. Hence, sigma = (200000)(13.5-14.2+1.5)/[(14.2-1.5)cos{atan[1.560/(3.14159*14.2)]}] = 12606 MPa.

 

[elogesh]

hai,

Thanks for all your responses.


Desertfox:
I notice also in your last post the allowable stress seems very high is this an error because the value quoted is comparable with the Modulus of Elasticity of steel.

It is a chormium,nickel alloy stell and hence has high strength.


Second observation was that the rod can be incerted manually into the spring. hence push in load should be very low order.


Mike Halloran:

In operation, if torsion is applied in a direction that loosens the spring, it will behave like a torsion spring, i.e. the wire will be stressed in bending as the spring unwinds.

I think, i should work on the bending stress induced during unwinding. But I know the interference levels only.I don't know the force, how to calculate it.

Vonlueke:
Thanks. I am going through your formulation. i will respond soon.

Regards,
Logesh.E

 

[israelkk]

Look at the book "Mechanical Analysis and Design" , Arthur H. Burr 1982 ,Elsevier Science Publishing Co. Inc. In page 100 it has the best explanation about coil spring clutches including stresses.

 

[vonlueke]

elogesh: My above formulation assumes the ends of the spring cannot move, and that somehow the spring is expanded to the rod diameter. (And obviously, if the stress exceeds the yield strength, the spring yields -- and the stress could reach a maximum of the spring ultimate tensile strength, after which the spring would break.)

However, my formulation doesn't seem to apply in your problem, because the ends of your spring can obviously move. As mentioned, you unwind it to insert the rod, and upon releasing the spring, it of course remains in a partially unwound position, in which case the spring stress will be far lower than in the scenario I formulated in my previous post.

 

[alpharam]

I would refer to each coil as a separate beam and (as soon as we know the deflection, which is roughly ODrod.max-IDspring.min), it is possible to calculate the stress.
Imagine each coil straightened and represented as a separate beam with round section and 1.5mm diameter and the length of 15.7*3.14 (roughly). This makes sense if the spring was lubricated before the assembly, of cause.

 

[vonlueke]

alpharam: The approach you're describing is already worked out, with a solution, in my first post. Note that D-d+t in my first post is exactly the same quantity as ODrod-IDspring in your post.

But, as I attempted to explain in my second post, this concept applies only if you assume the ends of the spring are fixed, such that the spring cannot unwind when you insert the rod. (And this would presumably require either a rod whose end is tapered, to facilitate insertion, or else a relatively very flexible spring).

However, MikeHalloran, above, describes a different scenario in which you unwind the spring, insert the rod, then release the spring, in which case the spring will not return to its original position but instead will remain partially unwound when it contacts the rod. As I attempted to explain in my second post, this is a completely different scenario than the one alpharam describes (and the one I solved in my first post).

In his second post, elogesh implies that the spring can unwind, because he says "it is used as a torsion spring."

elogesh: If the ends of the spring are fixed, such that the spring cannot unwind at all when you insert the rod, then the stress in the spring is as derived in my first post. If, on the other hand, you have a different situation, or an applied external load on the assembly (such as torsion), or want something other than stress in the spring, please let us know.

 

[elogesh]

Hai,

Thanks to Mike Halloran,Desert fox,vonlueke for your replies.

I got fewmore information about the spring.

I want to share little bit background information about the problem.

One of our colleague asked to calculate the stress developed in coil of spring after the insertion of the rod.He also hinted me use curved beams in flexure.I was little bit surprised, because I felt calculation for stress in spring involves torsion and tension effect.
Then I developed formula as mentioned in the earlier thread.
Then deserfox raised immediately whether it is tension spring or compression spring.I seen the application and referred it as torsion spring.

I enquired with the colleague and came to know that it is wrap spring clutch.Even before that Mike judged it perfectly.

Now, I will share few of experimental details carried out by my colleague.

The baseline design of wrap spring clutch cross-section is usually square or rectangular. On the spring coil outer diameter a gear is fitted with interference and on inside a rod is inserted with interference.Then the gear is rotated in both direction. In one direction, it carries good amount of torque and in other direction it slips.

Then they changed the cross-section of spring from square to circular.When the gear was rotated it sliped in one direction but in the other direction, spring was broken in some samples and few other samples the spring was permanently deformed.

He is interested to change square cross-section into circular cross-section of the spring clutch.

This was the background of the problem.

So when colleague asked to calculate the stresses, with the following idea,

After the insertion of the rod, circular spring has high elastic stress compared to square spring. When futher torque is applied while rotating the spring it goes to plastic zone.

We are also evaluating the effect of change in contact area due to change of cross-section.

Israelkk:
Our orgnisation doesn't have the book currently,
"Mechanical Analysis and Design" , Arthur H. Burr 1982 ,Elsevier Science Publishing Co. Inc. In page 100 it has the best explanation about coil spring clutches including stresses.

We are planning to purchase the book.

Thanks.


Regards,
Logesh.E

 

[israelkk]

elogesh

There is newer edition for "Mechanical Analysis and Design" , Arthur H. Burr from 1995 but to my opinion the older one is a better concerning wrap spring clutches.

Try here for the book

http://dogbert.abebooks.com/servlet...=0&tn=Mechanical+Analysis+and+Design&sortby=2