Spring model 4

[Biggadike]

I've been modelling a fairly complex system, the heart of which is a spring.
The model allows the use of either conical or compression springs and when I first created it I used the text book equations which are normally pretty good.
What I have found is that for conical springs and wide coiled compression springs, the standard equations tend to predict stronger springs than measured. Putting a different modulus for the wire doesn't fit brilliantly.
I've made empirical changes to the standard equation with good results but I wondered if there is an established improvement to the standard equation.

 

[TVP]

The following is from Handbook of Spring Design that is published by SMI (Spring Manufacturers Institute:

Spring rate (R) for helical compression springs is defined as the change in load per unit deflection and is expressed as shown:

R = P/f
= Gd⁴ / 8D³N_a

This equation is valid when the pitch angle is less than 15 degrees or deflection per turn is less than D/4. For large deflections per turn, a deflection correction factor should be employed.

It appears as though this is one of the sections that was directly copied from the Design Handbook, Engineering Guide to Spring Design published by Associated Spring/Barnes Group in 1987. In this publication, they reference page 102 of the following book for the correction factor:

Wahl, A. M., Mechanical Springs, 2nd ed. New York: McGraw-Hill, 1963.

 

[Biggadike]

This is the imperial version of the formula I've been using. The correction factor you describe is obviously what I'm missing (and what I created empirically).

I'll try and track the proper equation down.

Having said that, I have seen discrepancies at pitches which should be OK by your information although they were probably fairly borderline.

 

[Speedy]

Biggadike,

How do you work out the actual profile of the conical spring? This would have a huge bearing on the load profile. I worked previuosly with large concave type conical springs. These had 4 spec load pts. What I did find was that if the wire touches when compressed the load is unpredictable. Also, the no of effective coils is hard to predict as there is no clear transition pt from torqued to untorqued wire at the coil ends.
Speedy

"Tell a man there are 300 billion stars in the universe and he'll believe you. Tell him a bench has wet paint on it and he'll have to touch to be sure."

 

[Biggadike]

There is a standard conical spring equation:

It is in the form of:

P=G(d^4)h/64((D/2)^3)Ac

Where D is the instantanious size of the largest coil given by another equation (this reduces with compression). When the max and min coil sizes are the same, the formula becomes the same as a standard compression spring. You have to calculate a spread of instantanious values, they produce a curved slope.

I found that the slope was too curved compared to real springs I measured. I changed this in a couple of places to match my data better - I won't publish the change as I haven't proved it in enough cases yet and anyway all it does is reduce the slope and degree of curve which isn't exactly rocket science.

 

[Speedy]

Like you mentioned, it is standard practice to calculate the load at the largest coil diameter of the 'unseated' portion of the coil.
Could it be that in reality,the wire is further torqued beyond this pt (into the 'seated' portion)? i.e the effective transition between the 'fully twisted' portion of the wire and 'still being twisted' portion is further into the coil and beyond the visible transition pt. This would have the effect of increasing slightly the D value in you equation and therefore reducing the slope.

As for relating the load to the deflection,I think I may have misunderstood when you said you were 'modelling'. I assumed you were dealing with actual springs, where there would be a question mark over the actual pitch profile.

Speedy

"Tell a man there are 300 billion stars in the universe and he'll believe you. Tell him a bench has wet paint on it and he'll have to touch to be sure."

 

[Biggadike]

By modelling I mean putting together a group of maths functions which predict (model) the net behaviour of the system.

The maths is simple in its approach. It assumes the part of the spring with the lowest resistance to movement is the only part which moves. Having moved, it grounds and becomes inactive and the next piece moves. I think in reality the coils never fully ground but contibute to the length of wire acting at any given spring rate. This length increases until the whole coil is acting at complete collapse. This would explain the lower real rate as more wire is taking the load in any given moment. Actually putting some maths to this effect is the tricky bit. I've fudged it at the moment, if my fudge looks inadequate then I might get a bit cleverer with it.
I was rather hoping someone would have tackled this already.

 

[Lcubed]

The coils may ground completely with respect to axial movement, but still tend to rotate due to torsion. I haven't worked through the problem, but you may need to distinguish between the lengths which are effective in bending and in torsion, respectively.

HTH

 

[Biggadike]

Yeah Lcubed, I think you're right.
Also, the coils ground later than the standard equation predicts (I think). They resist grounding more and more as they deflect but do ground on lower coils as the grounding point is higher than the bed. If the conical spring is steep enough, the coils all need to ground on the bed and I'm not sure they would do that until the very end of travel.
I'm sure a good portion of the grounded wire is involved in the torsion if not all of it. Both of these effects spread the load across more wire than is allowed for in the standard equation.

 

[Speedy]

Have a look at this software;

http://www.hexagon.de/fed5_e.htm

It does seem to handle constant pitches only. Speedy

"Tell a man there are 300 billion stars in the universe and he'll believe you. Tell him a bench has wet paint on it and he'll have to touch to be sure."

 

[Biggadike]

The software looks interesting, thanks. The problem with that in this instance is that I need the maths to put into my model. The spring part is just one bit of the whole mathematical model so stand-alone solutions won't help.
That said, I liked the variety of stuff that package gives you - especially the stresses and harmonics.

 

[IRstuff]

One alternative is to use the standalong program to generate the curve and then fit the curve to an empirical formula for your simulation, rather than trying to find a closed-form equation.

TTFN

 

[GregLocock]

One thing that spring manufacturers often ignore is that the diameter of the coil increases as you compress the spring. I worked this out for a spring I designed, assuming that the volume of metal remained unchanged (ie effectively the total axial length of the wire remained constant), and the curve I produced was a much better fit than the simple equation.

The point about the grounded coils still remaining active torsionally is a very good one, I suspect, but I can't visualise how a coil that is unable to move vertically can really contribute to the vertical rate.

Cheers

Greg Locock

 

[Lcubed]

Greg,
Part of the overall axial stiffness of the spring is due to torsional stiffness. That stiffness may be less than expected, because the grounded coils can still squirm due to torsion.

 

[GregLocock]

Ah yes, the termination of the lowest free coil will be a torsional spring, not fixed. Ta Cheers

Greg Locock

 

[Biggadike]

Yes IRstuff, I could generate the curve with the stand alone programme but then you lose all the immediacy of the complete model where quick changes to the design can be seen as changes in the output.

So far we know the standard equation doesn't allow for torsion in the grounded coils, section change due to poissons ratio, reluctance to ground due to increased deflection in the coils.

I'd add to that list at least one other, change in effective coil diameter as the helix closes. And perhaps coil to coil friction in some designs.

Any other takers?

 

[macPT]

Good reference for spring design (free download!):
WINFSB4.0 in

http://www.gutekunst-co.com/D/Informationen/Informationen.htm.

You should note that this site is German and the design follows DIN standards (but you can choose the langage in the software). The error between design results and test results on some manufactured springs is negligible (not all the features were tested).

 

[MASSEY]

I like MATLAB's SIMULINK program for modeling systems like this. I would also try to model the system in Working Model software. Just some ideas if you had access to these.

 

[Biggadike]

Thanks chaps,
I use Mathcad for modelling, I know how to use it and the maths is nice and visible although I hear there are better similar systems on the market.
macPT's German spring software looks good - all of these bits of software have their own starting point which either suits your needs or doesn't. I like to put the spring details in and see what force deflection curve it gives me. That way I can get a measure of what factors effect what. This particular model predicts the pick-up pressure on a spring loaded pivoting paper hopper. It takes geometric factors into consideration, the weight and centre of gravity of the remaining paper stack, two forms of friction and of course the spring into account. So far it seems pretty accurate now that I've modified the spring equation to fit measured data.