Calculating / Measuring Effective stylus mass

[dlaloum]

Hi Folks

Recently rereading the vintage 1967 article on measuring "pickups" (viewtopic.php?f=46&t=45930)

It occurred to me that it should be possible to use the methods mentioned to calculate effective tip mass at the very least to a degree that would be useful for comparison between cartridges if not perhaps absolutely correct.

The formula provided for effective tip mass is:


F=1/(2pi(SQRT(MC)))

Where F is the upper resonant frequency, M= effective tip mass and C=compliance

F can be measured (no problem there... although getting the right test record can be awkward!)

C on the other hand is more awkward - which version / measure of compliance is valid here !?

The article does discuss measuring compliance...
What is not clear is which measure of compliance would be relevant (and which units) to solve the above formula!

So for example the original V15V was claimed (based on Jean Hiraga period review) to have stylus mass of circa 0.1mg, and a Resonant frequency of 33kHz....

Not sure what units are required for that formula to work it does not seem to solve for that standard V15V (the values from the Jean Hiraga article may be wrong too...)

Is the method of measuring compliance provided in this article that different from the current "norms"?

Or am I missing something fundamental?

It would be interesting to be able to calculate a stylus mass....

bye for now

David

[Ldg]

Hi DL. The 'C' spring compliance meant is that of the vinyl groove wall indenting. Not the cartridge compliance. And in any event that compliance may not even exist, it's a construct, as follows :

Effective Tip Mass is 'measured' by looking at what VTF is required to just track a hf groove of set frequency and level. Thus determining mechanical impedance. And, at a set frequency, this impedance can be expressed as an equivalent mass. The Effective Tip Mass. It sort of hangs together IF trackability is acceleration limited (probably is at hf), and IF the cantilever is rigid (hmmmm, ooops I think it just fell over).

Anyways, so now the great and the good have devised an effective tip mass.

Then they see a top resonance. And, knowing the effective tip mass, deduce there must be a spring, and work backwards to find an effective compliance for vinyl-stylus groove indentation. But it's all a self-fulfilling construct, and falls apart if the cantilever flexes.

But, I venture, all mechanics (including the top resonance) can be explained by cantilever flex. Without requiring vinyl indentation spring. One needs to resolve whether the top resonance is due to self flex of the cantilever, or due to vinyl-stylus groove spring. Can't be both !

Anyways, that's how to measure Effective Tip Mass in the classic sense. Work backwards from VTF required to track a set hf frequency/level. But, I subscribe to flexible cantilever explanation, and don't find Effective Tip Mass figure too useful, other than as a figure of merit for hf trackability.

Just my 2p worth !

[dlaloum]

I prefer the cantilever flex explanation myself (just call me a disciple...).

I was sitting working through what key measurements would provide identifiers for cartridge performance...
There doesn't seem to be a good "spec" figure that would provide an indication of cantilever lightness/nimbleness/responsiveness - the ETM seemed an attempt to provide some form of relevant measure for this.

I just reread your thread where you developed the Transmission Line / Cantilever model concept...

Perhaps the right measure would be high frequency stylus impedance?

I do have the resonance frequencies as one measure ... which is of course related to cantilever length, stylus mass, density/rigidity etc... - and it is relatively simple - higher is better!

But things get more complicated as soon as you have a compound stylus structure like the Grado's, The Jico SAS or the Shure V15IV - where there tend to be multiple resonances...

In some ways the old ETM measure (flawed as it is) - is a good measure of HF tracking ability... perhaps what it needs is to be renamed?
But some assumptions / constants would be required to use that formula - and those were not published.... and differing methods of calculating ETM by differing manufacturers makes it difficult to try to work backwards from specs!
I'm not quite understanding the interaction / issue with cantilever flex... - presumably it invalidates that calculation method...

Still looking for a relatively easy to measure HF "trackability" unit....

bye for now

David

[dlaloum]

I just did a little interesting experiment...

Using several cartridges of known published ETM (Ortofon X5MC, 320u, Digitrac 300SE) - I measured the primary/first resonance, and used the formula from my first posting to revers engineer the vinyl/groove compliance constant - at least as it applies to the Denon Test record I use.

Base Data:

X5MC
ETM = 0.75mg
Res f = 17kHz

320u
ETM = 0.5mg
Res f = 21kHz

Digitrac 300SE (OM30)
ETM = 0.3mg
Res f = 27kHz

For all three the C constant calculates out to approximately 1.16 x 10^(-10)

To cross check I calculated the C constant for each of them then used it to cross check ETM for the others - they all achiever results pretty much spot on for their ETM spec.

So based on this an indicative ETM can be calculated using the following formula (assuming one has already measured the primary resonance)

ETM =((1/(ResF*2*3.14159)^2)/[1.16 x 10^(-10)])

Vice versa for cartridges where the ETM is advertised, this should provide a means for estimating the expected primary resonant frequency.

Calculating based on the Shure V15VMR 0.17mg gives resF=36k - very close to the published claim of 35kHz... the Shure constant was most likely slightly different. (different vinyl compound? Test record?)

Based on EPC100mk4 claimed resF of over 70kHz, gives ETM<0.04mg - seems about right there too...

Interesting?

bye for now

David

[Ldg]

Yes. On the face of it, you might have uncovered how spec ETM is derived, DL ! Would be great if you can confirm whether you are aware of any contradictory data, or examples which don't fit, DL.......?

I agree with those calculations, suggesting a common spring constant.

Then the acid question is whether ETM has been calculated based on a reference spring constant ? Or whether ETM has been independantly derived, and the spring constant really exists.......?

I have to say, given how round the ETM figures are (1 decimal place), and frequency (2 decimal places), the value of spring constant is within about 1% between all three examples. To me, that suggests obtained by calculation, FWIW.

If ETM is calculated this way, it's handy because one can derive the top resonance from spec ETM. But it does not make either ETM or the spring constant real, in this method they are restatements of the top resonance.

Very interesting DL. Be great if you can confirm you're not aware of contradictions.

[missan]

Seems very interesting, particularly if the same constant can be applied at styli from different suppliers.
missan

[Ldg]

Seems very interesting, particularly if the same constant can be applied at styli from different suppliers.
missan

Yes, it could be Ortofon's method, I suppose. The crux is whether the constant is real, in the sense that the resonance is due to vinyl-spring/ETM or not. Unfortunately, this method still doesn't reveal that, it assumes it is. The truth will out !

[dlaloum]

At this point I have a big ??? over the meaning of this ETM figure.

Clearly, given the calculation method, it is simply a restatement of the resonant frequency.

I do have another couple of Ortofon's to measure (530, OM20) - and that will complete the measurement of cartridges for which I have relevant specifications on which to base this calc.

The resonant frequency / ETM is potentially a valid indicator of cantilever/stylus quality and probably high frequency tracking ability.
It also provides a way of "ranking" a range of cartridges which are otherwise less well known (in a technical sense).

Given the ETM, an estimate of the res f can be made.

I measured three cartridges in a search of contradictions... so far it appears consistent.

Much to my chagrin, my X5MC appears to be a late 0.75mg version rather than the early 0.4mg version...

[Ldg]

Well, it could be worse. In this scheme of things, resonant f is inversely proportional to the square root of spec ETM. So about doubling ETM only results in about x1.4 reduction in resonant f. In this case though, it does appear to land the resonance in the audioband, which I've never really comes to terms with........