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Following few requests from Vinylphiles I would like to provide practical explanation of phenomenon : Cartridge/Arm Resonance Frequency. It comes from Compliance of cantilever suspension and Total Mass reduced to the stylus distance from Arm Pivot point.
The formula has been published many times and it looks like:
F(res)= 1/ ((2 x 3.142 x sq.root(Mtotal x Compliance))Where: Mtotal = Mass of cartritge + Arm Mass effective (in grams)
Compliance (dynamic) of Cartridge suspension (in cm/dyna)
It is difficult for me to type units and formulas, but dyna is a unit of force in cgs system , and 100,000 dyna = Newton.
Typical Compliance of Cartridges is 10 to 35 Compliance Units
Compliance Unit = 10 to minus 6 cm/dyna (must be used for above calculations)
Some manufacturers use : mm/Newton or micrometer/miliNewton
After simplification the formula looks like:
Fres = 1000/((6.28 x sq.root(Mt x CU ))
Examples:
1. Arm Eff.Mass = 8 grams
Cartr. Mass = 4 grams (Colibri)
Cartr. Compl. =35 CU
System Fres. = 7.8 Hz2. Arm Eff.Mass = 20 grams
Cartr. Mass = 13.5 grams
Cartr. Compl. = 5 CU
System Fres. = 12.3 HzNote: Formula is using Total Mass (by def. amount of matter)
VTF should not be used , becouse Force is interaction between
objects ( mass and force are two different phenomenons)
The good source of information is explanation inside of HiFi News Test Record Cover. As always feel free to call me at 763-478-6685.
Enjoy Vinyl Forever.
Wally Malewicz
Follow Ups:
Hello Wally,allow me to post again, what I've posted already a couple a times, but refreshing memory shouldn't do any harm :
Tone arm resonance is determined by the effective mass of the tone arm (incl. cartridge) and the dynamic compliance of the cartridge. Since tone arm resonance can not be eliminated, it must be positioned in a frequency region where it will least likely be excited by vibrations within the mechanical system [2].Vibration sources are [1] :
record eccentricities : 0.55 Hz
warp : 0.55 - 10 Hz
Turntable suspension : 3.5 - 10 Hz
music : 15 Hz (large pipe organ)Since music signals of 15 Hz are seldom, 20 Hz appears to be a more
practical value [1]. The desired resonance frequency of stylus/tone arm should therefore be above 5 but below 20 Hz.A statistical analysis of record warps gave as result that very few warps occurred above a frequency of 7-8 Hz [2].
The optimum resonance frequency is in the range between 8-15 Hz, where there is a minimum of groove modulation and warp to excite system resonance.
The resonance frequency of the tone arm is calculated according to the formula [1, 2, 5, 6, 7]
F = 1000 / 2 x Pi x sqrt ( MC)
Pi = 3.14159
sqrt = square root
C = stylus compliance in mm/N
M = effective mass of tone arm + cartridge in gr
The reason why the resonance frequence of the tone arm should be between 8 - 15 Hz is that otherwise the arm can be excited by warps or low frequent music signals such that mistracking or groove jumping or bottoming of the cartridge on the record surface can occur. Moderate tone arm movement will be audibly perceived as WOW, the stylus advancing and receding along the groove when the arm vibrates up and down. Thus wow is not induced by lateral vibrations such as coming from off-center records.
One has to distinguish between static and dynamic compliance. The compliance per se is determined by shape and material of the cantilever and by the type of damper on the cantilever [7].
The dynamic compliance can range between 10 and 40 % of the static
compliance [8].
It appears that the static compliance is sufficient for calculating
resonance frequency in the region of 0-20 Hz [1].A heavier weight placed closer to the arm pivot results in a decreased effective mass of the arm. resulting in an increase in natural frequency.
Adding weight to the present counterweight would thus increase the natural frequency. Adding weight to the cartridge or to the arm tube would decrease the natural frequency.
[1] Nakai : Dynamic damping of stylus compliance/tone arm resonance
JAES 1973 Sept., p.555[2] Happ, Karlov : Record warps and system playback performance
JAES 1976 Oct., p.630[3] Taylor : Measurement of spectral content of record warps
JAES 1980 Dec., p.859[4] Kogen et al. : Trackability 1973
Audio 1973 Aug., p.16[5] Kates : Tone arm outrigger damping devices
JAES 1983 Oct., p.714
[6] Rother : The aspects of low-inertia tone arm design
JAES 1977 sept., p.550[7] Obata et al.: A hi-fi moving magnet cartridge using recent technology
JAES 1984 March, p.123[8] Barlow : Notes on pickup design and response
JAES 1971 March, p.222
Klaus
Hi All,excuse me butting in with a few observations.
Has anyone tried running a Decca cartridge in a low to medium mass arm? It doesn't work! The Decca's *very* low compliance (high cantilever stiffness) ends up generating absurd levels of resonance (more like oscillation, in fact) in the arm/cartridge, at the slightest provocation.
What one is effectively (sic) doing with a 'heavy' arm is creating a simple 'mass-damping' mechanism.
Damping! well, maybe the answer has already been supplied by Well Tempered Labs and Max Townshend! A light, stiff arm with near-frictionless bearings and loads of hydraulic damping. My Townshend Rock is in the process of having it's paltter bearing overhauled in preparation for having a Garrott Micro-Scannered Decca FFSS C4-E bolted into it. Should provise some intersting illustrations of dynamics and 'speed', I reckon!
regards,
Rainer.
I ask because in several tech. papers I have read, one by R. Graham included, it is stated that the ideal tonearm would be one with the least amount of effective mass. And since the effective mass counters the spingness of the cartridge ( as in "inertia"). My understanding is that the lower mass the better to avoid the effects of the inertia, but, adequate damping would be desirable to avoid the cartridge from just moving along w/ the stylus within the groove pattern and not generating the output. The question is, does this have any effect ( lower mass and proper damping)in the resonant freq. of the cart-tonearm system?Yoyo
I can easily why a very low-mass arm would be ideal in terms of tracking warps and off-center grooves. However, in terms of resonance (which we seriously want to avoid), we have to get the resonant frequecy above the frequency of the warps and off-center grooves, but below the lowest recorded frequencies. I guess that an infinitely light arm/cartridge would work because the resonant frequency would actually be _above_ the highest recorded frequency, but in the real world we can make an arm and cartridge that light (we'd probably be talking about micrograms!).
HiThe people in this discussion might be interested in some turntables and an arm made by David Gammon in the seventies.
I remember these very well in fact and have set them up with V15 III cartridge (if I recall correctly) to work beautifully.
David Gammon designed an arm which was "vestigial" in nature, this has the axis for the vertical pivot just behind the cartridge and gives an eexceptionally low effective mass in that plane. In fact the effective mass in the horizontal plane was very low indeed as well owing to ingenious design.
The tracking weight for the cartridge was then set very very light, less than 0.1 gram in fact would work very well indeed.
This arm would track exceptionally well.
As for the sound quality? To be honest I can't remember all those years ago :(
After creating the vestigial arm David Gammon designed the "Transcriptor Transcriber" turntable. This is a forgotten design now but was IMHO a masterpiece :) This was a tangential tracking turntable in which the platter moved, but the "arm" remained still. The arm was called the "micro-tracer" and attached to the glass lid. When you lifted the lid the the arm is then lifted off the record. The "micro-tracer" arm was in fact a tiny unipivot arm of only an inch or less from the stylus to the uni-pivot. This could be set to an extremely low tracking weight indeed, much less than 0.1 grams, but I can't remember the weights because there was no need to measure, all you needed to do was set the arm to zero, and then increase the weight on the cartridge by a tiny amount and that was it set.
The "micro-tracer" arm of the Transcriber turntable "broke" a tiny laser light to instruct the platter to moved either right or left. The platter was positioned laterally using a "worm drive" driven by a motor. The actually platter itself was belt driven by two motors and these two motors moved laterally with the platter as the needle made its way across the record.
To describe it sounds like it is a crazy mess, but in reality the Transcriptor Transcriber was extremely compact indeed and the easiest turntable to use ever IMHO.
There is a web site now to illustrate the Transcriptor turntables and people interested in innovative design may want to have a look and so I've put the link below.
As described above I feel the "Transcriptor Transcriber" is the most interesting design of these, but they are all worth investigation.
The lower Effective Mass of Arm will increase the Frequency of system resonance (acc. to formula). The reasonable damping will decrease the Amplitude of System Resonance (analogy to cars shock absorbers)
The acceptable System Resonance Range is 8 to 12 Hz.
There is a problem with data for Cartridges and Arms. Most of manufacturers do not publish Dynamic Compliance of Cartridges and Effective Mass of Tonearms. No comment WHY.Wally M.
The problem I see with this is that in practice I see arms that are substantial and made with metal still resonate at the 8 to 12 Hz region and others made of wood, carbon fibre, or other lightweight materials also resonate at the prescribes freq.I know its effective mass and not total mass! but I don't see how a lighter weight arm (total mass) that requires a lighter weight counterweight can have the same effective mass as one that has a higher total mass and thus requires a heavier counterweight. Since the cartridge is mounted at the long end of the tonearm the effect of the arm's mass is substantial due to the length, and thus the total mass of the tonearm has an effect on the effective mass, inertia, etc.
I think!Yoyo
Let's assume that the arm had no mass at all and the cartridge's mass was some fixed amount. One could balance that mass with a light counterweight all the way back or with a heavy counterweight close to the pivot. However, the small, distant weight would contribute more to the effective mass than the heavy, close one.
Well, a lighter weight arm could possibly use a heavier cartridge if it could compensate with the counterweight, and therefore it would act like a heavier arm with lighter cartridge. Remember, effective mass _includes_ the mass of the cartridge, and different cartridges seem to vary quite bit in their mass.Probably more pertinent is the cartridge compliance. A low-mass arm will usually be paired with a highly compliant cartridge. This will give the same resonant frequency as a high-mass arm with a lower compliance (i.e., stiffer) cartridge.
Does anyone know the effective mass of the Wilson Benesch Act 0.5? For whatever reason, I could not determine the resonance frequency of this are with a Clearaudio Aurum Beta cart. using the HiFi News test record. The combo seems to otherwise work fine, though.JB
Jonathan,
Your Arm has unique pivot based on Kinetic Damping (3 Balls and Pivot Cone). Be happy that you cannot determine Frequency of Resonance.
Your WB 0.5 Arm has Eff.Mass between 10 and 15 grams.
Wally M.
Hi Wally,I don't think that you should be happy that he can't determine the res. freq. of your arm/cart combo. Plug on, Jonathan. Nirvana might be just around the corner. You are obviously asking this question because you're curious and want to make sure you're milking the most out of your rig. You can try to lower the res. freq. experimentally by adding some mass at the headshell (say a bit of Blu Tack and a dime). Be sure to readjust the tracking force of course. I'm not sure how you can experimentally raise the res. freq. (i.e. lower the total mass of the arm/cart combo) ... drill holes in the arm wand (just kidding)?
The HFN RR test record sweeps lateral resonance from 5 to 25 Hz and vertical from 6 to 16 Hz. If your arm isn't "singing" in these frequency ranges then you're in no man's land, resonating ouside the desired 10-12 Hz sweet spot.
I don't think that Wally is saying that yourarm defies the laws of physics (are you Wally? ... very big grin)?
Cheers,
Thom
Hi Thom> > I don't think that you should be happy that he can't determine the res. freq. of your arm/cart combo.
Damping reduces both the amplitude and the frequency of resonance. In fact, when the damping factor becomes equal to or greater than [2·sqrt(m/c)], the resonance frequency disappears. The point at which the resonance frequency disappears is called critical damping. Any further damping is called super critical damping.
> > The HFN RR test record sweeps lateral resonance from 5 to 25 Hz and vertical from 6 to 16 Hz. If your arm isn't "singing"
> > in these frequency ranges then you're in no man's land, resonating outside the desired 10-12 Hz sweet spot.This is not necessarily true. Damping reduces the effects of resonance and makes it very difficult to measure with the HFN&RR test record. A tonearm need not be critically damped or even have its resonance frequency reduced below the 5Hz test record minimum to be immeasurable while damping is engaged.
IMO, damping is a good thing. A tonearm without damping is like an automobile without shock absorbers.
Best regards,
John Elison
If this is correct. (indeed is not incomppatible w/ what Wally said)You can have a very low mass arm and if its adequately damped the resonance can be controlled to be within the 8-10 Hz region w/o having to use large mass to lower it. Result,Low inertia and correct resonance.
Another factor that has to be considered on this is that every materia has a diff. inherent resonant characteristic. So, the eff. mass to resonance formula is effective when the other factors including the resonance characteristics of the material are the same ( as in apples to apples).
I think!
Yoyo
Yup Wally,John stated it nicely, and after having a moment to return to this topic, I can't find fault with his analysis. I suppose this was what you were trying to say in your inital reply to the poster. I am in no way against an appropriate amount of damping (the key word here is appropriate). I have long ago come to the conclusion that one can overdamp something, but that's a topic for another thread.
Having said that, and knowing that we live in a physical universe, I think it more correct to state that damping has the potential of reducing resonance to insignificance but not to completely eliminate it.
Cheers,
Thom
Hi Yoyo,> > You can have a very low mass arm and if its adequately damped the resonance can be controlled to be within the 8-10 Hz region
> > w/o having to use large mass to lower it. Result,Low inertia and correct resonance.What you say may be true, but it is impossible to reduce a tonearm system’s effective mass below the actual mass of the cartridge, and most cartridges weight between 6 and 10-grams. Furthermore, in order to achieve the desired strength and stability required for optimal performance, a tonearm must contain sufficient mass. Consequently, the better performing tonearms today tend to be of medium to medium-high mass.
> > Another factor that has to be considered on this is that every materia has a diff. inherent resonant characteristic.
> > So, the eff. mass to resonance formula is effective when the other factors including the resonance characteristics of the
> > material are the same ( as in apples to apples).The arm/cartridge system resonance is exclusively a result of the effective mass of the system reacting with the cantilever spring suspension. The inherent structural resonant characteristics of the materials used in the construction of the system do not play a role in the arm/cartridge system resonance. However, they certainly play an important role in the overall sound quality that is ultimately achievable by the system. Generally speaking, low mass tonearms have higher levels of unwanted internal resonances than medium and high mass arms.
Best regards,
John Elison
Thanks John for Closing the Case.
My Measuring Setup and Test Records are capable to determine existance of Resonance Frequency for Arm Mass/Cartridge Compliance, even in cases when Resonance is not detactable by Ear.
Vinylphiles - Use your Ears to enjoy Music.
Wally M.
nt
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