Fatigue Analysis of a Preloaded Compression Spring

[mkenwort]

Hi all,

I'm having a tough time turning up any literature pertaining to the subject line problem. Perhaps this is predominantly due to my newness to the field of vibration analysis and the concurrent lack of keyword insight for searches.

Spring material: 302 SS, spring temper (AMS5688)
Temperature: 350F max

I did some spring analysis and determined the shear stress at the working height to be roughly 51 ksi with a nominal preload of 85 lbf. For this spring geometry, the first natural longitudinal frequency is 316 Hz and the vibration environment in this frequency range was measured as 20 g's. The weight of the component being supported by this spring is approx. 1.5 lbf. The weight of the spring itself is 0.16 lbf. I guess my assumption here is that the most severe loading of the spring will occur at it's first resonance even though the vibration environment from 100-300 Hz is at 40g's. I can probably change the spring to push the natural frequency out farther from the 300 Hz range if necessary anyway.

At this point, I'm not really sure how to proceed. What I'm thinking is that so long as the spring preload is not exceeded, then the vibration environment would set up a traveling wave in the spring. Not familiar with that sort of analysis either and google is being rather unhelpful. Ultimately, what I'd like to confirm is that my shear stress at working height + the alternating stress is sufficiently low that I can predict infinite life of the spring.

Keyword search is down right now so hopefully this hasn't been posted before. I browsed through 10 or so pages.

Thanks,
Mike

 

[desertfox]

Hi mkenwort

Can you provide details of your spring ie:- physical dimensions and stiffness, also what is the value of the alternating stress which is superimposed on the above static stress.
Is the 316Hz natural frequency for the spring mass system or just the spring.

regards

desertfox

 

[mkenwort]

Sure, no problem...

From the Mathcad sheet I worked up (phys. dims in inches):
d, wire dia. = .187
D, outside dia. = 1.460
Nt, total coils, squared and ground = 7.07
Fl, free length = 2.25
WH, workign height = 1.73

Combined with the G (11.2*10^6 psi), gives a spring rate of 164 lb/in.

For the alternating stress, I need to determine that based on the vibration environment. I guess that's really the trick of the whole problem here and I am making the initial assumption that my most severe loading occurs at the spring resonance. I guess if I were to take a stab at it, I'd say the alternating load would be 1.47 lbf * 20 (g's) (vibe environment at 316 Hz) and get the alternating spring deflection and subsequent shear stress based off of that???

316 Hz is the natural frequency of just the spring.

I talked to a colleague and he wasn't sure I should be designing for infinite life at the spring resonance anyway as I already designed the spring to place the resonance point outside of a fundamental frequency of the engine.

Again, thanks for any assistance. Upon reflection I am neglecting one of my boundary conditions. I have some pressure loading at the tip (the purpose of the preload in the first place) that is on the order of 8-10 lbf. I don't think this is a factor for the spring resonance, since it would have come up off of the contact plane as part of the assumption. Sorry I'm writing this on the run (meeting to get to), but hopefully that is coherent.

 

[CESSNA1]

MNKINWORT: The basic equation for the natural frequency of a spring-mass system is:

sqrt((k + w/3)/m)

k = spring constant
w = spring weight
m = applied mass (weight)

Why would you want to operate a spring at its resosnat frequency? You will have problems Suggest you not operate this system at greater than 1/3 the resonant frequency. if there is significant damping you maybe can go to 1/2 the resonant frequency.

There should be an S-N curve for this spring material. Some spring manufacturer's may be able to help you with criteria and specs.

Good Luck
Dave

 

[desertfox]

Hi mkenwort

Thanks for your response, firstly you need to calculate the natural frequency of the spring mass system not just your spring.

the formula for calculating this is:-

fn = (2*3.142)^-1*(k/(M+(1/3*m)))^0.5


where k=spring stiffness

M= mass of component

m = mass of spring

therefore converting 1.5 lbf to kg = 0.681

0.16 lbf to kg = 0.0727

164lb/in to N/m = 28970.98

substituting these numbers into the formula above yields a natural frequency of 32.257 Hz.
Not sure how you got 315 Hz for the spring alone, but according to my calculations its around 100Hz either way with 32.257 Hz your system frequency is at least three times this value, if you need to go further with your analysis then your looking at a forced vibration which should be covered in most mechanics text books, but feel free to ask for further help here.


regards desertfox

 

[GregLocock]

He's looking at the spring surge frequency, I think, which is the speed of axial compression waves in the spring itself. It is a significant design constraint in valve springs. I don't think you can really calculate a fatigue life at resonance unless you know the damping in the system.

Cheers

Greg Locock

 

[mkenwort]

Actually that is just the sort of key word I was looking for Greg. I think that is going to help alot from what I am seeing in the literature so far. Thanks, at least I can get started now.

 

[desertfox]

Hi mkenwort

I might be to late with this but have a look at this site it
provides information on spring resonance and also has a link to a free program you can download for calculating fatigue.


regards desertfox

 

[desertfox]

Hi mkenwort

The link is

http://www.mech.uwa.edu.au/DANotes/springs/design/design.html#fatigue

 

[mkenwort]

That's a great resource, thanks! I'd pretty much had it sorted out by this point, but that site would have saved some grief.