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# Compression spring design confusion

## Compression spring design confusion

(OP)
I am designing a spring to be a replacement for existing springs. I have access to the existing springs and have tested them for load at height and measured key characteristics. I am working on a print to spec the springs to our vendor. It is a pretty simple/straightforward task, I'm just getting confused on specifics around the spring rate.

I am using the formula k=Gd^4/(8*N*D^3) to verify/validate what I am sending to the spring manufacturer. I have a couple options for how I can specify load. I can either specify loads at two heights, or specify required spring rate between two heights. I am confusing myself on what the above formula is determining, not sure if I am overthinking it. I am playing around with wire diameter, number of coils etc. so that I spec the right nominal values for our vendor accurately reproduce the spring.

I am not clear on whether the rate equation refers to the spring rate measured from deflection from free length, or deflection between two heights that are in the middle 60% of the spring.

I'll try to clarify my confusion with an example. I measured the springs at two heights, 1.39" and .98", and I measured the free height at 2.44" (1.042" avg coil OD .097 wire diameter for reference). The rate between the two heights is 32.3 lb/in. The rate at each height respectively is 30.3 lb/in and 30.9 lb/in when calculated from deflection from free height.

My confusion is whether that formula for rate, calculated the value to reflect the 32.3 value or the 30.3/30.9 values. Knowing that would help me to spec the correct# of coils and free length to our vendor.

### RE: Compression spring design confusion

Spring rate changes with geometry deformation. As the spring is compressed the pitch and diameter change slightly. The formula given is pretty good, but assumes neither change happens. It also doesn't account for the change in rate when the spring is collapsed solid.

What I don't know is why you think that duplicating the shaped of the spring with similar diameter wire would fail to produce an adequate replacement. Since you don't know what rate the spring was supposed to provide just providing the geometry description is as good as it gets.

### RE: Compression spring design confusion

(OP)
I did not know that diameter changes slightly with compression but that makes sense. Though would that still apply since I am comparing two ways of measuring rate at the same compressed heights? I guess my question would be from the example above, would you consider the rate between 1.39" and .98" to be 32.3 or ~30.5? Geometric deformations should be the same, I am just comparing two different ways of calculating rate, and wondering which way the formula for rate is calculating.

I could probably specify identical geometry, but for me it is hard to tell the difference in number of coils, especially on closed and ground ends, and where changing from 4.7 to 4.9 would have a noticeable effect on rate. Which is why I was using our design formulas to verify what I judged as the number of coils.

### RE: Compression spring design confusion

Generally speaking, you want to specify the spring at lengths within 15% and 85% of the compression. That is because the spring will be non-linear at the beginning and end of compression. Spring manufacturers are happiest with two basic lengths and a range of allowable loads at each length. In addition, you will want to specify the material and the heat treatment, the end condition (closed, ground, etc.) the wire size and either an ID or an OD depending on what it has to fit. There are a host of other things you may need to specify depending on your application. Just specifying geometry without specifying loads is not recommended as the stiffness will vary to the 3rd power of wire diameter. Any knowledgeable spring manufacturer can give you guidance and probably reverse engineer your spring for free.

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

### RE: Compression spring design confusion

(OP)
I have not reached out directly to our vendor, that would be a good idea. At this point, part of it is that I would like to have a better understanding of what is going on, not just for this project but future projects.

I've attached a picture to better show my current understanding/what I'm confused about (it is not to scale). dgallup, it sounds like what you're saying is that the design formula is closer to that 32.3 lb/in rate within the linear portion of the spring?

Which leads me to another questions. Is there a way to approximate that non-linear portion to be able to spec a more accurate free length. The free length is not important to spring function, but we usually spec springs to our vendor with free length toleranced using the SMI guidelines. We go backwards from our spring rate calculation and required load at heights, to determine free length. My current understanding (which could easily be wrong) is that because of that non linear portion, we are specifying free lengths shorter than what actual free lengths would need to be. I think it wouldn't matter much for most springs, as there wouldn't be too much of a difference, but we have some springs that require more precision.

Looking at the data for these particular springs the difference between the free length we'd normally spec (to achieve 32.3 lb/in rate and loads at 1.39" and .98") and the measured/actual free length is about .06"-.08". I don't mind just putting the free length as REF but I'd like to give them the right number to shoot for. In this specific case it would be easy since I have springs to measure that are exactly what I'd like to produce. But when I am not simply replicating a spring, I wouldn't be sure how to approach this issue.

### RE: Compression spring design confusion

It is the cube, but if the diameter is changed by as much as 1% then one needs a new wire supplier; the variation in torsion resistance would be 3%, which is smaller than other potential contributors. Since the OP doesn't know the function of the spring they also won't know whether the example is at the high side, low side, or right in the middle.

In a similar precision situation with +50%/-20% variation (disk springs) where we knew the load the springs were to apply we just measured each spring stack in QC and made an adjustment at assembly to match the QC compression measurement. The result was less than 1% variation.

If the acceptable variability of the required range was known then that should be on the drawing; it's not so there's no use in making a misleading paper trail.

If I was given the task to be really precise it would be with wire on the 0.1% wire diameter variation allowed and would integrate the deflection due to torsion around the helix including the pitch causing the section to appear elliptical and the compression causing the diameter to change.

I would not be surprised if there is commercial spring analysis software available that does this more neatly. I would expect major spring makers to have it and be able to supply any characteristics desired, such as free length based on two deflection/load points for the given spring OD and wire size.

### RE: Compression spring design confusion

(OP)
I like the idea of integrating around the helix for more precise calculations. I came up with an equation for D as a function of displacement, and plugged back into the original equation for rate. I could integrate that DF/dy to get an equation for force from displacement, but that would be kind of messy, so for now I just put it into excel to get the value at a several discrete values to check what I’d done against reality. I think I understand the logic behind it. However as the spring is compressed I get the mean coil diameter expanding, which results in the spring rate decreasing as the spring compresses more. As I’m looking at the real-life results the spring rate seems to slightly increase as the spring is compressed more. I also don’t see that non-linear behavior outside of the middle ~70% that occurs in real life springs. I only used the active coils in my calculations, and I think there may be something to do with the dynamics at the closed and ground ends that’s throwing it off (maybe those coils are actually partially active?). Or some other factor at work that I’m overlooking? I’m also not sure how to turn the closed and ground non-active coils into a workable equation in my model. It’s also very possible I misunderstood what you meant.
Thanks again for your guys help with this!

### RE: Compression spring design confusion

It is acceptable to specify free length and one gage length / load. I do that for a number of springs where free length is of primary importance but I know the spring makers I've dealt with prefer the free length to be reference and to specify 2 lengths / loads. But you're paying the bills so they will do what you want within physical limits. Expect to pay more the more demanding you get.

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

### RE: Compression spring design confusion

(OP)
I think I will have to leave free length as ref. I am still confused as to why the spring rate is increasing (slightly) with more deflection, if anything I'd think it should be the opposite.

### RE: Compression spring design confusion

Springs get more stiff as each coil touches its neighbor.
That's when the usual equations go to hell.

The touching can get stranger with different end treatments, which is why free length is not a good base for reference.

It will probably be instructive to get a serious spring tester and plot force vs. length from free to complete coilbind, every .001" of length or so. Plot a graph, and the middle will be straight-ish. The ends may have quite a variety of odd curls.

Mike Halloran
Stratford, CT, USA

### RE: Compression spring design confusion

(OP)
Ahhh I see, that makes a lot of sense. I think I will do that, sounds like it will help me visualize everything better.

Thank you all for your help!

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