Suspension Sag Equation
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 19th February 2008, 04:44 PM #1 hooha   diyAudio Member     Join Date: Apr 2005 Location: Winnipeg, Manitoba Suspension Sag Equation Hi guys, Can someone please post up the equation used to calculate suspension sag of a driver? Thanks a bunch. Mark __________________ Breaking speed records - http://www.mach5audio.com
 19th February 2008, 05:03 PM #2 AndrewT   R.I.P.   Join Date: Jul 2004 Location: Scottish Borders http://www.diyaudio.com/forums/showt...377#post965377 This may help. But note I am challenging that respected source. __________________ regards Andrew T.
 19th February 2008, 05:10 PM #3 hooha   diyAudio Member     Join Date: Apr 2005 Location: Winnipeg, Manitoba Thanks a lot. __________________ Breaking speed records - http://www.mach5audio.com
GM
diyAudio Member

Join Date: Jun 2003
Location: Chamblee, Ga.
Quote:
 Originally posted by AndrewT But note I am challenging that respected source.
Hmm, there's a suspended mass (Cms, Mms) and the gravitational force applying a constant force on it, so what's missing to make it more complex?

GM
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kstrain
diyAudio Member

Join Date: Apr 2006
Location: Glasgow
Quote:
 Originally posted by AndrewT http://www.diyaudio.com/forums/showt...377#post965377 This may help. But note I am challenging that respected source.
I'm not sure which aspect you are challenging, but it all looks OK to me (not going to the source, just what you wrote):

"Mms =1 / [(2*Pi*Fs)^2*Cms]"

The spring constant can be written k=1/Cms. Then writing the angular frequency ws = 2*Pi*Fs makes the equation match the standard form of the result for the resonant frequency of a "simple harmonic oscillator" - aka a mass on a spring - that looks like "w^2 = k/m".

"sag=Cms*Mms*g = g / [2*Pi*Fs]^2"

Again the spring constant is 1/Cms and the force stretching the spring is indeed the weight Mms*g so multiplying them gives the sag is as written.

"so sag depends of Fs squared, as I said it sounds too simple."

The result follows and - in case anyone is interested - is normal for systems of a mass on a spring under gravity (because the same "mass" is involved in calculating the gravitational and inertial effect - a deep, but mysterious, principle of physics). At which point I'd better stop or this is too much like the day job

Hope I did not misunderstand your challenge.

Ken

ps. posted here because here is where we are

pps. (edit) I'm always posting too slowly - already answered...

 20th February 2008, 05:39 AM #6 aznboi3644   diyAudio Member   Join Date: Dec 2007
AndrewT
R.I.P.

Join Date: Jul 2004
Location: Scottish Borders
Quote:
 Originally posted by GM Hmm, there's a suspended mass (Cms, Mms) and the gravitational force applying a constant force on it, so what's missing to make it more complex? GM

Quote:
 Originally posted by kstrain I'm not sure which aspect you are challenging, but it all looks OK to me (not going to the source, just what you wrote): "Mms =1 / [(2*Pi*Fs)^2*Cms]" The spring constant can be written k=1/Cms. Then writing the angular frequency ws = 2*Pi*Fs makes the equation match the standard form of the result for the resonant frequency of a "simple harmonic oscillator" - aka a mass on a spring - that looks like "w^2 = k/m". "sag=Cms*Mms*g = g / [2*Pi*Fs]^2" Again the spring constant is 1/Cms and the force stretching the spring is indeed the weight Mms*g so multiplying them gives the sag is as written. "so sag depends of Fs squared, as I said it sounds too simple." The result follows and - in case anyone is interested - is normal for systems of a mass on a spring under gravity (because the same "mass" is involved in calculating the gravitational and inertial effect - a deep, but mysterious, principle of physics). At which point I'd better stop or this is too much like the day job Hope I did not misunderstand your challenge. Ken ps. posted here because here is where we are pps. (edit) I'm always posting too slowly - already answered...
Hi,
are you two guys saying that my interpretation is correct:- that sag depends ONLY on Fs^2 and has no place for stiffnesses in the simplified equation?
If the simplified equation is correct then that result comes directly from the source equations and then I agree completely with the originally quoted equations.
__________________
regards Andrew T.

 20th February 2008, 04:03 PM #8 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. Well, these formulas are literally Greek to me, so all I'm saying is that a driver's Fs is a function of mass and compliance (stiffness), so down firing just adds the gravitational force component to my way of thinking: Fs = [(1/Pi)/2]*{[1000/(Mms*Cms)]^0.5} where: Mms is in grams and Cms is in mm/N GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.
 20th February 2008, 04:09 PM #9 AKN   No snake oil diyAudio Member     Join Date: Aug 2005 Location: In the middle of Sweden Hi, Getting sag out of Mms or Fs should give slightly exaggerated numbers. Mms includes the mass of the air loading the driver. Air will not act as a weight contributing to sag. I believe Mmd should give a more accurate sag value. Any Cms nonlinearities will possibly slightly decrease sag. That said, I think that we will only get an approximation of sag. Long time creep du to plastic properties of the suspension materials may eventually come into play as time goes by, __________________ / Anders
AndrewT
R.I.P.

Join Date: Jul 2004
Location: Scottish Borders
Quote:
 Originally posted by 4fun Long time creep due to plastic properties of the suspension materials may eventually come into play as time goes by,
good point, I've not noticed before.
4fun,
if the simplified equation is true then Fs controls the amount of sag, That uses Mms. That would seem to indicate that Fs is the wrong value to use. Presumably on that basis, Fs' excluding the air load, would give a better estimate of sag.
Does the air load depend on cone velocity or cone displacement?
What proportion of the total dynamic mass comes solely from the actual mass of the moving components?
How high would Fs' rise above Fs?
__________________
regards Andrew T.

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