# Critical frequency of a spring



## BrianC (Apr 2, 2010)

The problem is as follows...

In a cyclic operation, an A313 stainless steel wire helical spring has an outside diameter of 0.5 inch and a wire diameter of 0.08 inch with 30 active coils. The critical frequency is most nearly...?

The MERM gives a straight fwd equation (eq. 52.19) for the fundamental frequency of a steel spring with fixed ends. Since the problem states that the spring is under cyclic loading, I assumed the ends were fixed to a surface. In addition, Shigley gives an equations for a spring with one end free.

Now...the 6MS problem was solved by the author with the basic equation f = (1/2pi)*(k/m)^0.5. Where m is the mass of the active portion of the spring.

The 6MS solution solved for f = 63 Hz, while the MERM equation gave f = 212 Hz. The equation given by Shigley for a spring with one end fixed and the other free gives approximately the same answer as the MERM equation. Can anyone explain the application of these different spring critical frequency equations?


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## Oughtsix (Apr 3, 2010)

I have the same references you do so nothing else to make a comparison. I solved it with the MERM equation, looked at the SMS solution, shrugged my shoulders, and went to the next problem. Both solution methods make sense but I'm so frustrated with the SMS right now I don't believe a thing in it. I'm sticking with the MERM if a question comes up on the exam. Sorry that wasn't any help but I acknowledge the difference and would like to know.


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## gaidox (Apr 4, 2010)

i dont have sms md. if i were to solve this with the given you mentioned , i will used merm eqn 52.12 and 58.4 which will yield to same eqn that sms mentioned. its assuming free vibration . eqn 52.19 is approximate based on those eqns i mentioned above. you were given specific spring matl here so used it. hope i help.


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## Lily (Sep 15, 2010)

I may be wrong, but isn't gc missing from your equation? f=1/2Pi*(k.gc/m)[SIZE=8pt]0.5[/SIZE] in US units? that may be the reason behing this?


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## Relvinim (Sep 16, 2010)

That is about the 5th or 6th solution in the 6MS Machine Design that I did not agree with. Very frustrating to say the least. Good thing is it is forcing me to investigate further and understand the material better.


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## Lily (Sep 19, 2010)

I tried to solve the same problem this morning, and had the same frustration. then I looked into the shigley and it has this equation: f=1/2*(k*g/W)^0.5 ( 7th edition, equation 10.25). where W is the weight of the spring, there is Pi missing from the Shigley equation in comparison with sms solution 58. and if you take 63.63 Hz found in sms and multiply it by Pi, you find 200 Hz, which is similar to the solution using the MERM. So it looks like the Pi should not be part of the equation....


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## navyasw02 (Sep 19, 2010)

I havent tried it yet, but I'm not surprised that this question is wrong. So far, I think the 6MS MD is crap.


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