coil spring FEA

[gio1]

Hello

I am planning a FEA of a dynamic system which includes some steel coil springs, using an explicit solver.

Before starting the dynamic analysis I have done some static and free modal analyses on the spring FE models, to ensure that their stiffness and first natural frequency is similar to that quoted by the manufacturer. The springs have linear behaviour.

Surprisingly neither the stiffness or the frequency are close to the values in the specification sheet.

A quick check with classical calculations gives a stiffness which matches that quoted by the manufacturer. Measuraments also confirm this value and show a very linear behaviour throughout the stroke. FE static analyses give a value about 25% lower for all springs.
In the analysis one end of the coil is restrained and a displacement load is applied to the other end. The reaction force is then calculated.
The elastic modulus used is correct (steel - 208 GPa). The analysis is a linear one, solved in Nastran. As the actual spring behaviour is linear I think a linear static analysis is applicable.
I have repeated this analysis with 2 different FE models: one made of hexaedral elements, another made of second order tetrahedral elements, with adequate density in both cases, but the results are similar.

As for the first natural frequency, the free modal analysis (again, in Nastran) gives a value which is approximately 36% lower than that in the specification sheet. The density of the FE model was calculated to achieve the same mass of the actual spring (as measured).
In this case classical calculations do not agree with the spec sheet either, but give a value about 26% higher than the FEA (the same value is also confirmed by the EFUNDA spring calculator, based on classical analysis:

http://www.efunda.com/designstandards/springs/calc_comp_designer.cfm#calc)

I don't understand this big discrepancy. Is there any big non-linear effect which I am neglecting and is compromising the analysis?

Thank you in advance for your help

 

[GBor]

You say that the mesh density is "adequate", but did you run a mesh sensitivity analysis to prove that it is "adequate"?

 

[gio1]

With "adequate mesh" I mean that its density could be good for stress analysis. In this case I am only interested in displacements (stiffness analysis) and natural frequency (modal analysis).

 

[gwolf]

Tricky situation, been here before in other guises. My gut feeling is that you know what you are doing but have made a simple typo-like mistake somewhere. When using NASTRAN pay particular attention to some of the more obscure fields on the data cards if you used a pre-processor to fill in the blanks - you may have an unforseen option switched on. I would start by running a simple nonlinear static case to satisfy yourself that there is little difference and then be very methodical about checking your input data to the problem, line by line. If you go about it very methodically you should crack it quite quickly. I was tempted to suggest that you check the boundary conditions but this is more likely to stiffen the structure than anything else in this case.

Try looking at animated mode shapes - they are often very revealing.

 

[israelkk]

I do not understand why someone will want to model a helical compression/extension/torsion spring using FEA where the subject is well known and proven for decades.

First of all helical spring were analysed analytically to an extensive depth by Wahl and others. The design equations are well proven beyond any doubt including surge etc.

Secondly, what is the point in calculating the natural frequency of a spring by itself? In practice a spring is never operates by itself alone. There is always some added mass or inertia in the system. When the spring mass is large compared to the external mass it is practical to take 1/3 if the spring mass into account.

A manufactured spring can be practically accurate within +/-10% for load per deflection except where screening can result in +/-5% accuracy at a higher cost. So, whats the point to try using FEA to achieve higher accuracy.

All spring formulations intended to make a first approximate starting point for the spring manufacturer to start with until he reaches the desired properties. To get the force at a desired compressed height or to get the spring constant (measured between to loaded heights) the manufacturer slightly changes the number of active coils, outside/inside diameter, free height etc, (except wire diameter).

When you put dummy springs in the boundaries of your modeled parts to simulate flexible boundaries, do you also analyse those "spring" too.

http://www.webspawner.com/users/israelkk/

 

[gio1]

israelkk,

I might follow your suggestion and avoid using FEA for modelling a coil spring. But this does not explain why FEA results are not even close to classical calcs.

In this specific case FEA modelling is required for a dynamic simulation of a complex system. A dummy spring is probably good for static/lightly dynamics cases, but missing the high order modes it does not provide the correct response to a variable excitation with high frequency content. The accuracy needed for dynamic stress prediction requires FEA.

 

[johnhors]

Please excuse me for asking the dumb obvious, but as you are not using SI units (i.e. GPa for E), are your units dimensionally correct?

 

[GregLocock]

There are several gotchas with spring calcs.

As you compress the spring the coil diameter increases and the rate drops. This effect will not show up in a geometrically linear analysis. The correction to the simple hand calculation is easy enough to do, but rarely done.

The behaviour of the ends is non linear, in many cases. The coil in contact with the seat gently shorts itself out, as load is applied, so increasing the rate, but the way the bending/shear stress in the final coil is transformed into torsional stress in the main part of the wire is a bit tricky.

Does your model let the spring seat rotate axially?

It's interesting that your error in the surge frequency calculation was even worse than the rate calculation, since that is a square root relationship, it should be better.


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[desertfox]

gio1

Hi I am no expert in FEA but I agree with israelkk on this subject of springs and would much prefer to use classical
calculations.
As to why the FEA results may differ I can only think of one or two possiblities:-

1/ Springs are designed to give a load at a given length or
they are designed to give a particular spring rate.
However if you choose the first critera then the spring
manufacturer will adjust the spring slightly to achieve
that particular load. This means the rate may be
slightly higher or lower than that calculated and in
addition a compression spring does not have linear
behaviour over the first and last 15% of the full
deflection range, which may account for some of your
differences.

2/ Errors can occur using standard spring formula if the
pitch angle is greater than 10 degrees, if this is the
case then the standard formula can be used but the
pitch angle as to be taken into account.

The book called "Mechanical Springs" by A.M.Wahl explains it in much more detail than I can here.

best regards

desertfox

 

[crisb]

Isn't spring stiffness related to the torsional stiffness of the wire?

Why not go back a step, do a simple model of a round bar under torsion using the same method, and see if you get the right torsional stiffness, it wont take long, and might help you find the error.

Are you sure you have used the correct Poisson's ratio/shear modulus and that the element type and density are adequate to model the torsion effects in the wire?

Frequency is dependant on stiffness so if stiffness is wrong so will the frequency.

 

[gio1]

Thank you all for your suggestions, I will try crisb's for the moment and check the torsional stiffness

 

[gio1]

The torsional stiffness calculated by FEA was correct

The problem is the following

The stiffness and frequency quoted by the manufacturer are those in assembled condition (preloaded spring) although this was not clear from the spec sheet.
Although the spring is linear the preload causes the end coils to gently touch each other thus effectively stiffening the spring by reducing the number of active coils. From then onward the spring is linear again.
Measuraments were conducted at loads higher than the specified preload, so showing no change in stiffness!

The FE analysis did not include a model for the self-contact of the coils so I was effectively calculating the initial stiffness, lower than the operating one. The same applies to the natural frequency.

A FEA with self contact model has given the correct stiffness.

Thank you for your help