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Vintage Audio (record players, hi-fi etc) Amplifiers, speakers, gramophones and other audio equipment.

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Old 4th Jan 2017, 9:38 pm   #1
mark_in_manc
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Default Arm mass (not tracking weight!)

Hi folks

I've been reading around a bit on hi-fi sites about ideas on arm mass, and how a small number is apparently a Good Thing (TM).

I'm open to this as a possibility - but also, I used to work as a noise- and vibration- control engineer, and I thought the system might lend itself to analysis with a simple lumped-element equivalent circuit model.

I did this (and if anyone really wants to see it, I'll post a pic of the filter circuit and maths). The result gave an open-circuit voltage output for a dynamic cartridge as a 2nd order hi-pass filter, with Q set by damping of the stylus-cartridge interaction and resonance set by the arm mass M and the stiffness K (or compliance 1/K, if you prefer) of the stylus mounted in the cartridge (in the normal f_res = 1/(2 pi) * sqrt (K/M) style).

If this is right, then a higher arm mass means a lower resonant frequency, and hence a flatter response through the bottom end of the band of interest / more bass extension. So why go for a lighter arm?
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Old 4th Jan 2017, 9:48 pm   #2
PJL
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Default Re: Arm mass (not tracking weight!)

Records are not perfectly flat and you actually want a constant distance between the cartridge and the record. Some of my records are far from flat . It would be interesting to work out what the roll-off frequency is for a very low mass arm.
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Old 4th Jan 2017, 9:59 pm   #3
Ted Kendall
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Default Re: Arm mass (not tracking weight!)

The effective arm mass interacts with the cartridge compliance much as a weight on a spring, and this system has a resonant frequency. The trick is to place that resonance above the warp region and below the lowest frequency of interest recorded on the disc - somewhere between 7 and 10 Hz is about right. Thus, heavy-tracking moving coils of low compliance (eg Fidelity Research) work best in high-mass arms, and exotic beasts such as the ADC 26 ideally need an arm of negative effective mass to place the resonance, although an SME III (effective mass about 5g) works very well in practice.
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Old 4th Jan 2017, 10:18 pm   #4
mark_in_manc
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Default Re: Arm mass (not tracking weight!)

That's interesting - but what is 'negative effective mass' - it suggests an 'inertia' which acts in the same direction as an acceleration? The compliance, however large, I would think will be a positive real number (or even a positive complex number, if you want to lump damping in with stiffness) so mass comes out to be reassuringly real and positive!

7-10 Hz is useful info. I should think the force-displacement characteristic for a cart-stylus combo is not a straight line, so the stiffness (and hence resonant freq) will be a function of tracking weight too.
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Old 4th Jan 2017, 11:20 pm   #5
Ted Kendall
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Default Re: Arm mass (not tracking weight!)

The mass of the cartridge itself also has to be taken into account. The 26 was a worst-case example, weighing about 8g and having a compliance in the 50cu region. As the cartridge was already too heavy for an optimum resonant frequency, the arm had ipso facto to be of negative mass if that figure was to be achieved. Sony made a servo-controlled arm, the Biotracer, which could indeed behave as if of negative effective mass.
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Old 5th Jan 2017, 12:06 pm   #6
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Default Re: Arm mass (not tracking weight!)

Interesting discussion - I am a hopeless Decca moving iron fan - over the years I have found that:- an SME 12" tracks them quite well, but a 9" doesn't (without damping). Decca's own International needs damping to track its own cartridge - remember the little capsule you had to upend for 48 hrs into the unipivot housing?! I now have a Helius unipivot copy (I know it's a copy because Helius told me when they mended it for me). In tonearm terms it feels like a weighs a ton....but it tracks the Decca London SG perfectly. I always thought these carts needed a high mass arm because they were exceptionally active and 'shook' low mass arms - is that about right?
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Old 5th Jan 2017, 9:29 pm   #7
Ted Kendall
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Default Re: Arm mass (not tracking weight!)

That's part of the story - the less compliant the pickup, the more energy it extracts from the groove in having its suspension deflected, and it all has to go somewhere. Deccas are prone to instability in unsuitable arms - SME used to recommend damping of the pivots on the Series II - and having the resonance in the warp region could result in some astonishng gymnastics!
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