Cartridge Compliance

the thin end of the wedge
Bebé Tonto

Post by Bebé Tonto » 28 Oct 2010 22:48

@Bebé Tonto, yes you've got the hang of entering what you know, and using it to work out what you don't. Damping factor is a key credibility check !
Excuse my ignorance... I thought "damping ratio" was a function of the moving mass, the rubber compliance and the frequency. Why is 0.05 a desired value?

Guest

Post by Guest » 28 Oct 2010 23:12

Bebé Tonto wrote:.....I thought "damping ratio" was a function of the moving mass, the rubber compliance and the frequency. Why is 0.05 a desired value?
c 0.05 just seems to be a common value ! But range 0.03 to 0.1+ is possible. It's a tradeoff between avoiding high mechanical impedance to signal frequency cantilever motion, and damping the tonearm/suspension resonance (and cantilever vibrations/self resonances) effectively. Affects trackability@VTF. Higher damping requires higher VTF.

It's not well specified, and no-one ever mentions it, but it's quite defining.

BigE
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Post by BigE » 29 Oct 2010 12:42

Hi BigE. Yes, by accounts the DL301II has 35cu@static and 13cu@100Hz compliance. Plugging these values in, i reckon trackability prediction equates to c 72um@300Hz for max spec VTF 1.6g. Which is not shabby.

Damping factor is 0.08, which is credible. Bit high perhaps.......are you certain of the 35cu@static figure (it suggests a double check IMO) ?
Yes, 35 checks out. I'll reset my vtf to 1.6 or 1.65. currently 1.7

Thanks for the dbl check!

BigE
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Post by BigE » 29 Oct 2010 13:55

Using my numbers, with 300 Hz and 0.14 lateral, 9 gm cart/fixings and 5 gm arm, the damping factor goes to 0.1 and the min VTF goes to 1.7. (arm is an SME IIIs).

I am thinking of nuding the DL103D cartridge, so that the weight of the cartridge should be less than 4 -- depending on the mass of the plate that will hold the nuded body to the arm. One option for mounting is two small tapped strips of brass to span the gap that is left when the cartridge is nuded.

That gives a much more reasonable resonance, almost 9 Hz. Biut the damping factor jumps to 0.12. What does this damping factor quantify? Is it sensible for it to change if the mass is changed or will it actually stay the same once calculated for the stock cartridge?

Guest

Post by Guest » 29 Oct 2010 14:40

BigE wrote:Using my numbers, with 300 Hz and 0.14 lateral, 9 gm cart/fixings and 5 gm arm, the damping factor goes to 0.1 and the min VTF goes to 1.7. (arm is an SME IIIs).
Hi BigE. Plugging in the numbers 35cu@static and 13cu@100Hz along with 5g arm, 9g cart/fixings I obtain min VTF = 1.56g, resonant f is 7.2Hz, and damping ratio = 0.09. So suggest recheck, because something is astray ! Perhaps you are reading from the yellow 'VTF box' rather than the blue 'min VTF required box .......?

The yellow box defaults to 1.7, it's an entry box, you can enter actual VTF there and it affects the graphic plots, but not the rest of the calcs.

Damping ratio is the ratio of actual damping to critical damping for the tonearm/suspension resonance, and it changes along with the resonant frequency. But the actual physical damping provided by the cartridge stays the same (is determined by physical suspension and calculated from difference between static and dynamic compliances). Your figures seem credible, because the static compliance and damping are relatively high one might expect a ratio close to 0.1, it looks about right and fine.

In a 5g arm without nuding the body, the resonance is about 7.2Hz, which still seems a bit low but perhaps quite tolerable. As you say, nuding might help, every g helps !

Now it makes me wonder if 9g for the cartridge is correct. I mean 9g for a 35cu@static cartridge seems like setting an arm challenge just for fun ! I see the DL301II and original DL301 have 4.7g mass in the database. The DL301C1 is listed in the database at 9.7g. Is there any chance the DL301 you have is not really 9g...........sorry to keep questioning your numbers, but this combination does seem unusual !

I can see some advantage of having the mass lumped in the cartridge though !

BigE
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Post by BigE » 29 Oct 2010 16:07

Hi,

Thanks for asking. I can clear this up.

I actually have a 103D. It's compliance is 12, it's mass is 7.5 grams, but I have a shim in place until I mount the arm on a thinner arm board, so I used 9. Since all the denons with compliances around 13 have a static compliance of 35, that's what I used for the 103D.

I get 7.19 and 1.7.

using 13 instead of 12 gives the 1.56 vtf you got.

I made the assumption that it was more similar to the 30x series that others, and my flopping woofers when the stylus in in the lead in groove suggest that the 7.2 Hz resonance is quite believable..

At any rate, the calculator has convinced me to either nude the 103D or get a 301 mk II for my SME IIIS arm. IMO, getting a new cartridge would be the best alternative -- mine is VERY old, with VERY high mileage. I would not be surprised that the diamond is worn out. Good for nuding, and then retipping, but not much else given it's weight.

BigE
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Post by BigE » 02 Nov 2010 12:10

HI again!

LOVE THE CALCULATOR...

Does it double the effect of mass at the cartridge vs EM of the arm? According to my potentially flawed understanding, if EM is a measure of moment of inertia, then adding mass at the headshell should have double the impact, as the counterweight has to be screwed out....

Guest

Post by Guest » 02 Nov 2010 12:51

Hi BigE. Thanks !

Variation in location of the counterweight typically only has a small overall effect. It relates to 'moment of inertia', not 'moment'. All such variation is wrapped up in the 'effective tonearm mass' figure. Which does not break out contribution from headshell, arm tube and counterweight in spec figures. But counterweight moment of inertia contribution overall is generally surprisingly low, c 30% IIRC, and variation with balance location is small.

Contribution to effective tonearm mass Mcw from counterweight is :

Mcw = m * (r^2/L^2) [kg]

where :
m is mass of counterweight [kg]
r is distance from centre of counterweigt to pivot [m]
L is distance from pivot to stylus [m]

Here's a (long) thread on measuring/estimating your own tonearm effective mass : viewtopic.php?t=24136

The first method is wrong, the second one (about 8 posts in on the 1st page) is correct !

Hope this makes sense !

Guest

Post by Guest » 02 Nov 2010 14:29

Hmmm. On further thought, and some back of envelope calcs, for an example of a stock RB250, adding to a balanced cartridge mass by 2g necessitates moving the counterweight away from the pivot by c 3.6mm. In turn this adds c 0.6g to tonearm effective mass, just from the location of the counterweight, which is not insignificant. Inconveniently too big to ignore !

So for significant deviations from 'standard' cartridge/headshell mass (whatever that might be), standard figures for tonearm effective mass need adjusting. Also for significant variations in VTF ! Significant meaning perhaps >c 2g variation from 'norm'. Norm meaning perhaps 5g for cartridge plus fixings, 1.5gf for VTF.

I never knew that !

BigE
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Post by BigE » 02 Nov 2010 16:18

I just got back from a meeting, and finished this:

Here is an example:

Suppose my cartridge + fixings weighs 10 gms, and the cw weighs 50.

For the sake of simplicity, lets make the arm tube weigh nothing.

The arm tube from cw to headshell is 300 mm. Using the CW location as zero, 300 x 10 = 3000 gm-mm.

The balance point B would be at 3000 = B x 60 = 50mm from the counterweight.

Now if I increase the mass at the headshell by 10 grams, the moment of the cartridge side is 250 x 20 = 5000. The moment from the cw side has to be the same to balance it: 5000 = 50gm x 100mm -- so we moved the cw twice the distance away.

The distance between cw and headshell is now 350mm, so the total moment is now 350x20 = 7000 gm-mm

The contribution to the moment by moving the CW is immense.

WRT to the moment of inertia,

Before addition mr^2 = 10*250^2 = 625,000 on cartridge side and ml^2 = 50*50^2 -125,000 on cw side.

After addition, mR^2 = 20*250^2 = 1,250,000 on cartridge side and
mL^2 = 50*100^2 = 500,000.

The cartridge side only doubled, as the distance stayed the same, but the
cw side quadrupled as the distance was doubled.

The change in distance of the cw side is important.

Guest

Post by Guest » 02 Nov 2010 18:27

Good stuff BigE.

More generally then, variation in effective tonearm mass M due to moving a counterweight of mass m between distances r1 and r2 from the pivot, on a tonearm of effective length L is given by :

15513

where units are SI.

Results vary significantly with specific arm numbers. Your example, BigE, though credible for an ultra light armtube, heavy cartridge and light CW, is perhaps not typical, and one gets a very different result for a common arm such as an RB250. An RB250 has a counterweight of mass c 130g, typically located 3.6cm from pivot, and the armtube countributes the majority of inertia (mass) that determines effective mass. Hence my example yields quite different result and conclusions. In that case, variation is far smaller.

Horses and courses then ! The extent to which tonearm effective mass varies with CW location, due to balancing cartridge mass or setting VTF, depends on construction of the arm. In some arms/setups it can be significant, in others far less so.

Interesting !

BigE
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Post by BigE » 02 Nov 2010 18:55

So, how much do you thing that including this notion -- changing the cartridge weight => changing CW to balance and therefore changing EM will affect the results of your resonance calculator?

It looks like including this will lower resonance sooner. Which may be of some merit for those adding mass for fitting DL103's to medium weight arms... they would not have to add as much to decrease the resonance.

IMO, it's promising, as many report decent results with less than gargantuan EM.

Guest

Post by Guest » 02 Nov 2010 21:10

For an RB250, a 2g variation in cartridge mass/VTF might result in effective tonearm mass variation of 0.6g due to relocation of CW. For an 11g arm, that amounts to c 5% variation in effective tonearm mass. Which amounts to c 3.75% of total effective mass. Which suggests only c 2% variation in resonant frequency, and that is small enough to ignore.

For a light armtube, light CW arm where the CW largely determines effective mass, 2g variation in cartridge mass/VTF might result in effective tonearm mass variation of 1.4g due to relocation of CW. For a 6g arm, that amounts to c 23% variation in effective tonearm mass. Which amounts to c 11% of total effective mass. Which suggests c 5% variation in resonant frequency, and that amounts to overestimating resonant f by c 0.5 Hz. Or about 0.25Hz error per gram of extra cartridge mass. At 5g extra, it starts to become notable.

I've never seen mention of this effect, nor any resonance calculator that takes note of it. I'm inclined to add a feature to my calculator that at least flags the circumstance of light arm + heavy cartridge, and advises to subtract c 0.25Hz per g excess over cartridge mass of 5g, from predicted resonant frequency. And 0.25Hz per g extra VTF over, say, 1.5g. Or I may do it automatically, but that seems a bit guessy ! Without going into intracate detail of tonearm construction, it's impossible to know the correct factor.

The majority of common arm/cartridge combinations, this does not apply to, of course.

Thx for the spot, BigE ! It's new to me.

BigE
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Post by BigE » 03 Nov 2010 03:11

Glad to have stumbled into it.... literally.

sreten triggered this by suggesting that there is a "dramatic" difference in moving the counterweight, I just wanted to understand how that could be.... with you posts and the calculator leading the way.... even the numbers I picked were a total fluke.

Sometimes we just get lucky! :lol:

Guest

Post by Guest » 03 Nov 2010 09:05

It was useful to put some numbers on it too. On that basis, I wouldn't describe the effect as necessarily 'dramatic', but notable under certain circumstances. In fact, for some common arms it seems small enough to ignore. Which in itself is useful to know ! All good stuff.