Suspension Sag Equation

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hooha

Hi guys,

Can someone please post up the equation used to calculate suspension sag of a driver?

Thanks a bunch.
Mark

Thanks a lot.

GM

AndrewT said:

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

kstrain

AndrewT said:
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

AndrewT

GM said:

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

kstrain said:

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

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.

GM

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

AKN

Paid Member
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,

AndrewT

4fun said:
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?

AKN

Paid Member
AndrewT said:

Does the air load depend on cone velocity or cone displacement?

I'm not certain but I think we should talk about air that moves along with the moving system, i.e. air in close to cone. How that additional mass change with frequency I do not know. But we are talking about sag so no frequency.

What proportion of the total dynamic mass comes solely from the actual mass of the moving components?

Good question, I can only take an example:
15" woofer
Mms 155g
Mmd 140g
Actually LspCad calculates the factor between Mmd and Mms, how, an approximation? I'd like to know this.

How high would Fs' rise above Fs?

Fs=1/(2PI*sqrt(Cms*Mms))
I think we should insert Mmd instead to get Fs', i.e. driver operating in vacuum.

Regarding sag, why not just write:
sag~=Cms*Mmd*g
And include a reservation for Cms nonlinearities.

hooha

4fun said:

Regarding sag, why not just write:
sag~=Cms*Mmd*g
And include a reservation for Cms nonlinearities.

I was thinking the same thing when I looked over the equation yesterday. Using Mmd instead of Mms would produce a more accurate result.

What actually spawned this request was a "chat" I had with someone regarding what alignment tolerances were available when using a motor equipped with XBL2. It was explained to me that alignment of the voice coil in the gap was very critical and that the tolerances were very tight in order to be fully effective.

That made me think of the potential sag issue when mounting an XBL2 sub horizontally. Would the technology be less "effective" due to suspension sag? Even less after suspension break-in?

AKN

Paid Member
Hi hooha,

If I got the xbl^2 motor right there is always a total of one gap height in use. In resting position VC is exposed to two half gaps. With enough excursion the VC will be fully exposed by one of the two gaps. So by “throwing away” half of the available flux we get approx double linear excursion.

Why should xbl^2 be more sensitive than a standard motor for VC offset? If that would be the case xbl^2 would not have such good BL linearity as it obviously have.

Personally I don’t like horizontal mounting. I’m too worried about increasing long time creep.

hooha

4fun said:

Why should xbl^2 be more sensitive than a standard motor for VC offset? If that would be the case xbl^2 would not have such good BL linearity as it obviously have.

I don't know, that's why I was asking. It seemed odd to me that if the alignment had to be so precise, any deviation would result in the technology not being utilized to its full potential.

Thanks for the response.
Mark

AndrewT

Hi,
use that 5% rule and see what you get.

Xmax >= 4970/Fs^2.

It's probably close enough even though it includes air load in the Fs measurement.

iand

hooha said:

I was thinking the same thing when I looked over the equation yesterday. Using Mmd instead of Mms would produce a more accurate result.

What actually spawned this request was a "chat" I had with someone regarding what alignment tolerances were available when using a motor equipped with XBL2. It was explained to me that alignment of the voice coil in the gap was very critical and that the tolerances were very tight in order to be fully effective.

That made me think of the potential sag issue when mounting an XBL2 sub horizontally. Would the technology be less "effective" due to suspension sag? Even less after suspension break-in?

With XBL2 the accuracy of centering of coil relative to the gap(s) is no different to a conventional driver, and it's this that cone sag would affect.

The length of the coil relative to the top plate widths and spacing *is* critical, if this is even slightly wrong there'll be a dip or a hump in the middle of the BL curve which will give bad distortion even with displacements much smaller than Xmax.

This is probably what was meant -- if you look at the XBL2 paper you'll see a bit of a wiggle in the middle of the BL curve as the coils move in and out of the split gaps.

Ian

hooha

iand said:

The length of the coil relative to the top plate widths and spacing *is* critical, if this is even slightly wrong there'll be a dip or a hump in the middle of the BL curve which will give bad distortion even with displacements much smaller than Xmax.

Ian

This is what I was thinking about.

I doubt this would actually translate into anything audible anyway. I have yet to come across someone who can actually pick an XBL2 driver out of a blind A/B listening test, let alone identifying the changes in tolerances...

AKN

Paid Member
Hi,

I thought that mfg using XBL^2 motor had figured out the VC length - gap spacing - winding technique so there should be no wiggle in BL but maybe not.
Sag with this motor (if non optimal) would offset the eventual wiggle point out of the zero crossing and therefore distortion would be more audible.

iand

hooha said:

This is what I was thinking about.

I doubt this would actually translate into anything audible anyway. I have yet to come across someone who can actually pick an XBL2 driver out of a blind A/B listening test, let alone identifying the changes in tolerances...

Which just hows how much distortion the ear can tolerate before it gets upset

Ian

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