Vinyl Engines Cartridge Resonance Calculator

[Simon75]

I've not seen this resonance calculator, but presumably any calculations may go out of the window with fluid damped arms if the damping is applied and to what degree and with which viscosity of fluid?

Very good point. I think it should only be used as a rough estimate with certain tonearms.

[Simon75]

I should say that I misnamed it in my original post, it is evaluator not calculator.

[Barry]

This might be of help: https://theartofsound.net/forum/show...idge-resonance

[Simon75]

This might be of help: https://theartofsound.net/forum/show...idge-resonance

Thanks Barry that's really helpful, very clearly written.

[Stormin'Norman]

Shure did a test record some time ago that has been recorded with music and 4,5,6,8,10 & 12 Hz tones in the track so you can visually see the cartridge oscillating. Very much real world conditions. Mine oscillates at 8Hz.
Cost me a tenner at a record fair last Saturday. One to look out for, maybe !
Norman

[Fiddlefye]

I've been reading up a bit on cartridge compliance and came across Vinyl Engines cartridge resonance calculator. It seems like a useful tool but I've confused myself a bit with it.
When it asks for the effective mass of your tonearm I am assuming that does not include the weight of the cartridge. I am also assuming that the weight of the headshell is included in the effective mass of the tonearm. When reading the table you look at the weight of your cartridge(plus screws)against the cartridge compliance to get the result. Is this correct?

I really do wish that manufacturers include a figure for effective mass, but I've found that in general I've come close enough just giving a bit of thought and arriving at an impression. If one really wants to work things out one can do so. No, I have not attempted it myself.

"Principle: To measure actual tonearm effective mass, all one needs to do is determine the moment of inertia of the tonearm about the pivot, then calculate the equivalent mass required at the effective tonearm length to provide the same moment of inertia, and that mass is then the effective mass of the tonearm.

Step1 The tonearm is a lever balanced about the pivot. The vast majority of mass on one side of the lever is a lump mass in the form of the counterweight. So weigh the counterweight (mass m [kg]) measure the distance from the centre of the balanced counterweight to the pivot with a ruler (r [m]), and then calculate moment of inertia from I=m*r^2 [kgm^2]

Step2 To evaluate MOI of the cartridge side of the tonearm, remove the counterbalance and cartridge (inc mountings), then use a weighing scale to measure the weight W of the tonearm at the headshell end, with the tonearm parallel to the platter. W is half the weight of the cartridge side of the tonearam (less a small bit for the stub - ignore), so the mass Z of the cartridge side of the tonearm Z = 2*W (kgf), and since it is vertical Z is also the mass in kg. The effective length L can either be measured (between stylus tip and pivot) or looked up from published figures for the tonearm. Then calculate moment of inertia from I = Z*(L^2)/3 [kgm^2]

Step 3 Calculate the total moment of inertia I(tot)

I(tot) = [m*(r^2)] + [Z*(L^2)/3] kgm^2

Then effective mass M at effective length L is given by

M*L^2 = [m*(r^2)] + [Z*(L^2)/3] kgm^2

So M = ([m*(r^2)] + [Z*(L^2)/3])/(L^2) kg

which reduces to

M = [m*(r^2/L^2)] + [Z/3] kg

In itself, this is an interesting result. It shows the contribution to effective mass from each side of the tonearm, mostly it comes from the cartridge side. It shows what to vary if one seeks to increase/decrease effective mass, principally the mass of the cartridge side of the tonearm, Z. But some influence is also possible from a heavier counterweight, and in a non-intuitive direction perhaps (heavier = lower M because balancing distance r influences M as power of 2)."

[Barry]

The above is correct, and I agree with you that not all tonearm manufacturers quote the effective mass for their arms. But a large number do and the values can be found on vinylengines comprehensive tonearm data page.

As I said in my The Knowledge article ( https://theartofsound.net/forum/show...idge-resonance) the resonant frequencies are calculated values; the best and only way to be sure is to use a test record with either a sliding tone track, or descreet tone tracks covering the range of say 5 - 15Hz.

[Fiddlefye]

The above is correct, and I agree with you that not all tonearm manufacturers quote the effective mass for their arms. But a large number do and the values can be found on vinylengines comprehensive tonearm data page.

As I said in my The Knowledge article ( https://theartofsound.net/forum/show...idge-resonance) the resonant frequencies are calculated values; the best and only way to be sure is to use a test record with either a sliding tone track, or descreet tone tracks covering the range of say 5 - 15Hz.

Absolutely! Of the arm manufacturers who don't spill their secrets about effective mass a number of the most famous could be included in the list. In a way it reminds me of the old Rolls Royce comment that the horsepower rating of their engines was "adequate".

[tlscapital]

With the M55e at 6.7g plus the SME(non improved)tone arm mass at 12.5g and the dynamic compliance at 25×10-6cm it is giving the frequency at the less than ideal 7Hz. I don't know where vinyl engine got the dynamic compliance figure of 25 from as Shure don't provide it. The combination sounds right to my ears. I think the tool can be used as a rough guide rather than gospel.

Yes totally a rough guide rather than gospel. Yet your Shure M55 'E' is indeed of rather high compliance and if The combination sounds right to your ears I am positive that it could sound/perform even better on an SME3009 'Improved' S2 or even SII (always with steel knife edge !!!). Although I can't say so by experience, since I've only experienced it through my gradual SME 'Improved' effective mass enhancement for my Denon DL-102 whose manufacturer's compliance specs are never given but known of low compliance...

So it was a test/guessing game for me. And each mass enhancement benefitted the cartridge performance to new unexpected result. It worked that way for me and so believe it should the other way around also. And I only did that resonance calculation once at the end of this mass enhancement tweak long-long journey for the "fun" of it. Although I had to guess a compliant figure for this cartridge... Mhm and I did the calculation at the the different stages to only get the around '10' figure with my final effective mass enhancement. Funny.

[Barry]

With the M55e at 6.7g plus the SME(non improved)tone arm mass at 12.5g and the dynamic compliance at 25×10-6cm it is giving the frequency at the less than ideal 7Hz. I don't know where vinyl engine got the dynamic compliance figure of 25 from as Shure don't provide it. The combination sounds right to my ears. I think the tool can be used as a rough guide rather than gospel.

https://522bb370f5443d4fe5b9-f62de27...Phonograph.pdf Page 6. This quotes the compliance to be 25x10^-6 cm/dyne.

This quoted compliance is most likely the static compliance. The dynamic compliance at ~ 10Hz is half this value, so your calculated value needs to be increased by 1.4x to give a value of 10.2Hz.

I used to use a Shure M55E in an SME 3009/II arm years ago (actually 48 years!), with no problems at all.