Effective mass is not the same thing as the mass of the tonearm. It seems people are confusing these two terms. My SAE tonearm, for example has an effective mass at the headshell of 9.5g- according to my owners manual. The entire tonearm and counterweight certainly weighs more than 9.5g. The tonearm manufacturer has simplified a more complicated inertia calculation into an easy to apply value- effective mass. Now, I can add the mass of my cartridge to the effective mass of my tonearm and then apply the compliance of my cartridge to find the Resonance Frequency, Fn of my Tonearm/Cartridge system using: Fn=sqrt(k/m) where K=compliance (N/m) and m=mass (kg). Ideal Fn is around 10Hz. I recently lived this issue when I mounted my new Denon cartridge to my SME tonearm. The SME is a relatively low mass tonearm. The Denon cartridge has a mass of 8.5g and a compliance of 7.5X10-3N/m. This put my system Fn at about 16 Hz. (Insufficient mass) This was too high. I was fine until I tried to play a record that had a slight wave to it. The tonearm would dance across the record. I could see the cantilever move upward and kick the tonearm into the air. Searching AudiogoN, I found a place in England that sells a 4g mass (Aluminum) with threaded holes specifically made for the Denon cartridge. The added 4g mass lowers my Fn to just over 10Hz. I applied the mass to my cartridge and now it plays that same record perfectly. I also knew the added mass would work because my now dead Koetsu cartridge had a mass of 14g. I also found this 4g Al plate improved the sound of the Denon. The bass is better and imaging more focused. Not bad for a $19 tweak w/shipping. I have always had heavier (14g range) cartridges in the past and so never encountered this issue before. I could see how these kinds of problems could be frustrating to someone not trained in Engineering. |
Well Jlin, you will certainly find a lot of people agreeing with you. I for one like to look at all things a bit closer than most others. So please excuse me if I come to some different results. I am used to find the errors in other peoples thoughts. In fact - I earn part of my income by finding errors in concepts and setting them straight.
Just give it a thought .... maybe there is some truth in my point of view (just as a hypothesis...) and there are more physical details and interactions then meet the eye.
This is not 1st year college - this is still lower high school .......
But the model is still too simple as described earlier. |
Let me stick my oar into this old debate - Mark Kelly is exactly correct and Dertonarm is completely off base in his comment that " the inertia in a say 15 grams effective mass 12" tonearm with a given cartridge is always larger then in a 15 grams 9" tonearm".
The effective mass of a tonearm is in fact the inertia of the tonearm when it reacts to a deflecting force, which is what a warp is - that is what effective mass is BY DEFINITION. This is first year college physics. If the effective mass of a one tonearm is the same as the effective mass of another tonearm, it has EXACTLY the same inertia to a warp, regardless of its actual mass or physical dimensions. |
Syntax,
yet more room for continuous improvement?
"Watching Chinese TV can be very interesting", you say --- you are knowledgeable with this too?!
So how's your Mandarin, your Latin seems jolly good?
As to: I don't get "it".
That depends on your definition of "it".
Is "it" static or dynamic?
Greetings,
A. |
Axel, you don't get it.
How about a new hobby?
Watching chinese TV can be very interesting |
Hello sir,
I just purchased a Jelco SA-750D tonearm for $490 without cable. I will be installing it on a new plinth we are building. The cable cost me another $130 total and both appear to be real bargains. The Jelco arm is a real beauty and works and sounds very well from those who are using it. I will be installing a Pete Riggles VTAF "on-the-fly" adjuster. Once I get everything dialed in properly I will purchase a cartridge. It takes a little time but it's all worth it.
Bob |
"jacta alea est!" (The dice have been rolled)
Starting a war with Rome?
Crossed the Rubicon, no going back, hm.
What a crapshoot.
How about going back to tonearms then?
A. |
|
Bill,
Mrtennis?
...who the f*** is Allis...? (Clue "Living next door to Allis")
Someone you have a great time with, playing 'table-tennis'? You think Dertonarm is into this game?
Axel |
Dertonarm is Europe's mrtennis. |
"So now I also got it completely wrong, hm."
Axel, join the club, I'm sure.
Makes me wish I could dump my table. Too darn complex. 1's and 0's are much easier to explain. Just 1's....and 0's???
But then what would I play all those great sounding records I've collected over the years with? It takes too long to convert them to loss less digital. |
So now what?
The monkey ran away before we closed the box.
So now I also got it completely wrong, hm.
Meanwhile I enjoy the easier VTF setting, even though I can't hear that extra benefit. (Be nice to just imagine it, and tell all about it :-) ha, ha.
A.
PS: Just changed some x-over components with my mid and sub RCs, and I can hear THAT! (at least :-) |
Well - no problem, you are most welcome.
I am still optimistic, that you will find out in due course.
Just look a little more precisely, a bit closer, what is actually happening while playing a record.
The model you are following is simply incomplete - thats all.
You'll find out.
Cheers,
D. |
Ahh, so all along you were putting us off the scent in our quest for understanding. Silly me, I thought it was because you had a completely inadequate grasp of the fundamental physics underlying the phenomena we were discussing.
Thank you so much for setting me right.
Mark Kelly
|
Nice to watch from outside things getting settled so comfortable.
Proving once again that all models and explanations are simply - you just have to narrow the horizon of survey and to exclude tiny details.
I'd rather take economical advantage from a more detailed model and instead going into a mission here.
Have fun - I am watching and musing.
Indeed Axel: Klappe zu - Affe tot.
But you got the wrong monkey.......
And you closed the trap too soon. |
Hi Mark,
y.s:
>> Not going to go there.<<< :-) SIR, yes Sir!
And one wise decision methinks...
Thanks for the 'dynamic' vs. 'static' input also.
I think it's just a convenience if you can set VTF with a correctly graded dial (save $$$ for a force gauge :-)
Though some say, that if you can't hear the difference it's due to your system's short comings.
Then so be it, and yet more room for continuous improvement.
Axel
PS: Klappe zu, Affe tot! |
Axelwahl
The only advantage I can quantify for spring applied VTF is one that seems to have have been ignored in this thread, namely immunity to movement in response to externally applied acceleration (read noise). As I see it, get rid of the noise and there's no point.
Perrew
Not going to go there.
Mark Kelly
|
Mark,
y.s.:
>>> ... your last point is where things get interesting.<<<
OK, that is where everything then would get 'relative' --due to a cart's compliance. (Never mind the carts particular damping 'scheme', MCs in particular)
B U T we still have not hammered this nail all the way in where 'dynamic' vs. 'static' balancing is concerned.
Would even THAT become a function of the cart's compliance and damping behaviour?
Could one cart sound better with dynamic and some other better with static balance?
Your comment on this might be interesting in deed.
Axel |
Mark, whats you favorite Tonearm of choice and why have you chosen it? |
FWIW, what Quiddity is saying makes sense to me.
IS it accurate to state that the combo of cartridge/compliance and tone arm together matters greatly? A great or expensive tonearm with mismatched cartridge/compliance still won't work well, right? |
Axelwahl your last point is where things get interesting.
Like everything else it is a matter of compromise. As you have noted, a low inertia arm reduces the maximal VTF variation. The compliance required to keep the resonant frequency in the right range changes at the same time, so the effect of a given warp in terms of displacement of the cantilever suspension depends on the resonant frequency: the higher the resonant frequency the smaller the effect.
Unfortunately we're not free to move here. As previously noted the product of inertia and (rotational) compliance forms a low pass filter. As the equation previously given shows, the attenuation and phase response of this filter depends on the ratio of f/f0, so as the resonant frequency moves towards the audio band the effects of these become more and more pronounced. That is why resonant frequency is optimised over such a narrow range.
Mark Kelly
|
Dertonarm
That is completely wrong (again). The resonant frequency changes because the moment of inertia changes. The effective mass is simply the moment of inertia divided by the square of the effective length.
The total mass is irrelevant to the argument.
As far as I can see my model is complete according to D'Alembert principle. If you can show me something I have left out and provide a reasonable basis for the claim I'm listening.
Mark Kelly
|
Axelwahl
Your suppositions are correct and the figures are reasonable.
If we model a 100 g counterweight positioned 50mm behind the pivot, its contribution to the effective mass of a 225mm arm is 4.94 g*. If this is the position for VTF of 20mN, it needs to be moved 4.6 mm to come into neutral balance. The new position will indeed make a higher contribution to effective mass, it becomes 5.89 g an increase of 0.95g.
This would increase the maximal tracking force deviation quoted above from 6.2 mN to about 6.4 mN, about a 3% increase.
* this ignores the moment of inertia of the counterwight about its own centre of mass but since this doesn't change with position it isn't important so I left it out.
Mark Kelly
|
Well - to get as plain as you: I think your model is incomplete.
The resonance frequency of a given cartridge/tonearm combination can be altered by moving a fairly heavy cylinder further away or closer towards the pivot.
The total mass of the moving body stays the same - of course.
But - I guess neither of us has any problems if we do not agree about the model at all. |
Dertonarm
That is completely wrong (again). The moment of inertia of a rigid body does not change with movement.
Yes we are talking differnt models. Mine is a model of what is happening, yours is a fiction. |
Well - since it is a dynamic model (or should be...) I still see excatly this dynamic aspect missing.
The down-swing and upswing of the pendulum (tonearm with cartridge at swinging end) is different in moment of inertia and force depending on the distance from the dead center of movement.
We are still talking different models. |
Hi,
excellent maths no doubt.
Let's look at some practical part of it all then.
1) Is the **effective** mass of an arm increased if the counter weight it moved further away from the pivot bearing?
(I think so, because the mass / moment is increased)
2) If a spring is used for VTF, the CW is further back from the fulcrum as the spring provides the down force and the CW only the arm balance.
What is the effect, if assumption of 1) is correct?
3) If static down force is used, the CW is closer to the pivot/fulcrum, the mass moment should therefore be reduced. What is the effect as compared to 2)?
Inertia has of course ONLY an effect if acceleration is present, and with any tonearm particularly riding a 'taco warp'.
Incidentally, I find the type of warp lifting a smaller area from the start-wax (~ 1" into the record) more common and more radical in vertical acceleration, plus the one that actually pushed in the (still soft?) start-wax for ~ 1/8" causing VERY nasty lateral acceleration.
This leads me to think that lower accelerated mass (effetive mass?), plus higher compliance be the better solution to this kind of problem.
But I still can not make the connection to the 'dynamic VTF' being of any advantage, since (given 1)'s assumption is right) the accelerated mass of the same arm with only using static VTF be somewhat lower.
Note: SME quotes, the V arm's effective mass 10 - 11 gr. (depending where the CW is positioned...)
Axel |
Kirkus
We are indeed "singing from sheet".
The point that seems to be lost on the other participants is that this is a dynamic analysis. This follows directly from D'Alemberts principle.
Mark Kelly
|
The point to note is that all this is dependent on the moment of inertia of the arm and the compliance of the cartridge. It has nothing to do with the method by which VTF is applied. Absolutely agreed - and we're on the same page as far as the proper electrical model for the cartridge resonance equations. If the moment of inertia of the arm and cartridge combination is 1.26 x 10^-3 kg.m^2 the maximal torque transmitted to the arm is 1.38 x mNm which is equivalent to a force of 6.2 mN acting at a distance of 225mm. Sure, absolutely - and calculating the rotational torque of the tonearm is necessary for evaluating the particulars of the downforce spring itself . . . but that's about all. I guess some of the assertions got jumbled around in various different posts . . . but my point is mainly that to calculate deviation of VTF across a warp . . . if you have an accurate figure for effective mass from the cartridge's point of view, then neither the rotational torque nor the length of the tonearm matters - the tonearm can be viewed simply as a pure mass that moves only on two axes. |
DIVIDED BY
Rotational compliance is linear compliance DIVIDED BY the square of the effective length. Sorry I wrote it the wrong way around.
|
Kirkus
I composed the above offline before you posted again, it is in response to your post from last night (my time).
Since the issue of efective mass is causing confusion, I can take it out of the argument by reverting to rotational units. If we assume the arm is 225mm long then we have an angular deviation of 4.4 mrad per mm of warp so a 5mm warp will be 22mrad. At the frequency given this is a maximal acceleration of 1.1 rad.s^-2. If the moment of inertia of the arm and cartridge combination is 1.26 x 10^-3 kg.m^2 the maximal torque transmitted to the arm is 1.38 x mNm which is equivalent to a force of 6.2 mN acting at a distance of 225mm. This is exactly equivalent to the previous calculation.
Mark Kelly
BTW I meant to write "the phase and amplitude of the response becomes important" in the post above.
|
Kirkus
You make a good point so I'll answer that first. The answer should make it plain that everything Dertonarm has said in response is wrong.
I chose the example I used because the frequency was far enough away from practical cart/arm resonances for that factor to be safely ignored. As the frequency of the warp increases two things happen. The first is that the maximal acceleration (per mm of warp) increases with the square of frequency so the effect becomes more and more pronounced.
The second is that the phase of the arm's response to the warp becomes important. The easiest way to analyse this is to convert to electrical analogy. We can use either a force current or a force voltage analogy, the first is more elegant mathematically so I'll use that. In this analogy the moment of inertia of the arm (with the cartridge attached) becomes an inductance. The rotational compliance of the cartridge (which is the actual compliance times the square of the effective length) becomes a capacitance.
These two form an LC low pass filter and it is obvious by inspection that the product is identical to the usual product used in resonance calculations (effective mass x compliance) so the f0 of the filter is the same as the resonant frequency.
The other thing we need is to know the Q of this filter, which is determined by the hysteresis loss in the cartridge suspension. Since this will also affect the high frequency response of the cartridge way may assume that it is low enough that the Q of the filter is quite high. Perhaps JCarr can chime in here with some accurate values, if not weÂ’ll just assume a range of values greater than 5.
The phase angle of the response is given by :
Tan^-1(Q(2.f/f0 + SQRT(4-1/Q^2)) - Tan^-1(Q(2.f/f0 + SQRT(4+1/Q^2))
From which is may be seen that if Q is greater 5 and f/f0 is less than 0.5 then the phase error is less than 7.5 degrees.
Similarly the amplitude response may be calculated from the formula
1/(1 – (f/f0)^2 +j.f/Q.f0)
From which it can be seen that there is some amplitude peaking: about 30% for Q = 5 and f/f0 = 0.5, reducing to a few percent when f/f0 is less than 0.2. If we take 10% as an acceptable error then as long as the warp frequency is less than 0.3 times the resonant frequency of the arm / cart combination the calculation I gave in my post above is “good enough for Jazz”. Using your range of warp frequencies this is equivalent to arm cart resonance being around 10.
The point to note is that all this is dependent on the moment of inertia of the arm and the compliance of the cartridge. It has nothing to do with the method by which VTF is applied. |
I don't get your last comment (unless Mark's comment that effective mass = moment of inertia divided by square of effective length is wrong). If Mark's equation is right, the two could be different and still result in an identical third (effective mass) value. No, the equation isn't wrong; I believe that Mark was using it to make a point about how little variation there is in the deflection of a dynamic VTF spring, and thus a correspondingly extremely small change in the VTF at the end of the tonearm as a result of this change in spring deflection. For this calculation, the tonearm length is of course relevant. The misconception that I understood from Dertonarm's comments is that given two tonearms of different effective length, but identical effective mass . . . that they will somehow present different forces against the cartridge when tracking vertical undulations and warps: Only if the moving mass is homogenous distributed in the whole moving corpus - which is not the case in a tonearm with mounted cartridge.
Brings up again the picture of the Micro Seiki and other turntables which increased their moment of inertia by moving most of the mass towards the outer rim. You are correct in that the effective mass at one end of a tonearm is the result of its static mass, length, and distribution of mass along the length. But the 'effective mass' specification takes all that into account, and if you change two of these factors (i.e. length and static mass) to acheive the same effective mass at the cartridge . . . the cartridge doesn't care one iota. To use the platter analogy . . . you can either increase the rotational mass by adding a BUNCH of weight close to the center, or a whole lot less weight at the edge. But which ever way you do it (practical considerations aside), the platter can have the EXACT same rotational mass either way. As long as the "effective mass" at the circumference of the platter is the same, they will exhibit the same inertial characteristics. |
Well it comes down in several aspects to the static vs dynamic model....
Aber es hat weder mit dem Hammer zu tun, noch damit, wo er hängt (im Zweifel immer an der Wand...). |
"Quod erat demonstrandum in realitas mobilis versus modelus in spiritus ?"
Which was to be demonstrated in actual motion (real life), compared to a mental model (i.e. theoretical only))?
Latin can be handy, but mostly in legalistic situations --these days...
Are we now getting ready to go in the dock over: moment, and mass of inertia (effective mass)?
It makes for a degree of interesting and slightly confusing reading, yet we seem no iota closer to the 'true' sonic effects of gravitational vs. spring force VTF...
Wo hängt denn jetzt der Hammer?
A.
PS: AND cart compliance must be part of the equation, I say. |
*** Yes, we are indeed talking about the same thing. The "effective mass" of a tonearm is the inertial mass of the end where the cartridge bolts on. The interchangability of inertial mass and gravitational mass is fundamental to classical physics . . . as P=mv and F=ma . . . mass = inertia. ***
We are not yet talking about the same thing.
Small derivations, but our models are different.
And I seem to be unable to illustrate what I mean.
We have a force of inertia and we have a moment of inertia.
If we do not set up a model which takes speed into calculation we do not reach the point.
I do not mean audio modulations in the vertical mode - the tonearm is moving vertically - not just the cantilever.
Or better. it should, but due to its moment of inertia it can't follow the counter-movement in zero time but changes the VTF and compresses (and other way around milliseconds later again) the cantilevers suspension and thus moving the attached coil out of the optimal position due to constant increase and decrease in VTF.
**** The angular force vector around the vertical bearing will of course change with all different manner of tonearm-design factors (including effective length) but is irrevelant to the cartridge between two tonearms that have the same effective mass. ****
So the moment of inertia is independent from the distance of the majority of the moving mass to the center of movement ?
Only if the moving mass is homogenous distributed in the whole moving corpus - which is not the case in a tonearm with mounted cartridge.
Brings up again the picture of the Micro Seiki and other turntables which increased their moment of inertia by moving most of the mass towards the outer rim.
We already have different calculations for the force inertia of cylinders, balls and sticks - to name but a few.
I am not questioning your thoughts, I just think we didn't have set up the correct model yet.
**** Oder . . . herrum sitzen und daumen drücken? ****
Well - wer sitz herum und drückt die Daumen wem ? |
I think this is a similar issue that the motorcycle industry had to solve! In the case of shaft drive motorbikes, if they have a simple swingarm for the rear wheel, when power is applied there is what is called "drive shaft jacking" where the rear of the bike will rise up as power is applied. It takes some getting used to.
The solution was a parallelogram swingarm.
Seems to me that the spring that applies the tracking force could be mounted on a parallelogram device (independant of the arm gymbals) that articulated as the arm rides inconstancies in the LP surface. Then the variations in the spring tension could be substantially reduced (not eliminated).
I imagine such a device would raise the cost of the arm :) |
Furthermore I was referring to the inertia and you are referring to the effective mass. Yes, we are indeed talking about the same thing. The "effective mass" of a tonearm is the inertial mass of the end where the cartridge bolts on. The interchangability of inertial mass and gravitational mass is fundamental to classical physics . . . as P=mv and F=ma . . . mass = inertia. I believe (think, know, have had it checked at the technical university Munich in 1995 with precise laser graphics - choose one), - and this is backed by technical papers of the record industry too - that there is a (although tiny in distance) constant vertical movement while playing a record. Well, yeah . . . any simple analysis of the tonearm/cartridge resonance envelope shows that in the audioband, if there is vertical modulation, there must be vertical movement of the headshell. But that's not what we're talking about here . . . . we're talking about the reflexion of VTF as it varies with vertical headshell position, which is why Mark is analysing this in terms of record warps. And here the question is exactly about record imperfections, NOT audio-related vertical modulation. So I think we do see a vertical angular movement - not constant, but even worse alternating in direction - even if not always apparent to the eye. Yes, angular movement . . . but the force we're talking about is being applied to the end of the tonearm, which is where the effective mass is measured. The angular force vector around the vertical bearing will of course change with all different manner of tonearm-design factors (including effective length) but is irrevelant to the cartridge between two tonearms that have the same effective mass. Quod erat demonstrandum in realitas mobilis versus modelus in spiritus ? Oder . . . herrum sitzen und daumen drücken? |
Kirkus,
I don't get your last comment (unless Mark's comment that effective mass = moment of inertia divided by square of effective length is wrong). If Mark's equation is right, the two could be different and still result in an identical third (effective mass) value.
Mark,
The reason I asked my question above was that I thought, as Kirkus later suggested, that the compliance is in series with the moment of inertia on any change in aspect of the record (which we know has a VTF delta, but also has a VTA delta). I have forgotten much of my physics (and probably never knew as much as you have forgotten, even though it seems you haven't forgotten anything) but I would have thought the compliance was a significant 'external force' with regard to the d"Alembert principle.
In any case, leaving aside compliance effects, I would have thought that for a given mass of cartridge at the end of a given tonearm length, a spring-loaded system would reduce the effective length of a tonearm vs a gravity-loaded system. Would this not mean, assuming identical mass and tonearm length, that a spring-loaded system had a lower moment of inertia? Hmmm... Am I taking the number out of one side and not both?
I should go read a textbook again... |
Dear Kirkus,
*****thus the inertia in a say 15 grams effective mass 12" tonearm with a given cartridge is always larger then in a 15 grams 9" tonearm with the very same cartridge.
No. This is the classic "which is heavier, a pound of lead or a pound of feathers?" axiom. It's just that 12" tonearms tend to have higher effective masses than their 9" counterparts of the same make and "model", because they're bigger. *****
well.... I am kind of familiar with the feather/lead picture which I used (guess like many fathers..) to illustrate the point of gravity to my son once.
Furthermore I was referring to the inertia and you are referring to the effective mass.
Common knowledge assumes, that we do not see a vertical movement in the tonearm, but we do - and do so constantly during play.
I believe (think, know, have had it checked at the technical university Munich in 1995 with precise laser graphics - choose one), - and this is backed by technical papers of the record industry too - that there is a (although tiny in distance) constant vertical movement while playing a record.
The surface of a vinyl record is anything but dead mirror flat.
It does consists of hundreds hills and valleys (not warps) due to fluctuations in thickness as result of the molding process.
These are minor, but so is the contact area of the stylus.
So I think we do see a vertical angular movement - not constant, but even worse alternating in direction - even if not always apparent to the eye.
Based on this model my assumptions aren't that far fetched anymore.
Quod erat demonstrandum in realitas mobilis versus modelus in spiritus ?
Yet ? |
thus the inertia in a say 15 grams effective mass 12" tonearm with a given cartridge is always larger then in a 15 grams 9" tonearm with the very same cartridge. No. This is the classic "which is heavier, a pound of lead or a pound of feathers?" axiom. It's just that 12" tonearms tend to have higher effective masses than their 9" counterparts of the same make and "model", because they're bigger. Inertia is increasing with the distance to the center of movement. This would be true if we were assuming a constant angular acceleration about the vertical tonearm pivot, but we're not. We're assuming a constant linear (okay, circumferential) acceleration at the end of the tonearm. Again . . . if the moment of inertia, applied (circumferentially about the tonearms' pivots) to the end of two different tonearms is different . . . then their effective mass is NOT the same. QED. |
Just a short note from the office between two meetings....
I don't think I was completely wrong.
The inertia in a tonearm/cartridge combination does depend on the effective length, as this is not a homogenous corpus, but the majority of the mass is situated at the very end of the moving corpus - thus the inertia in a say 15 grams effective mass 12" tonearm with a given cartridge is always larger then in a 15 grams 9" tonearm with the very same cartridge.
Inertia is increasing with the distance to the center of movement.
The more so, the further away the majority of the mass from the dead center of movement.
Now we get closer to the model of a tonearm w/cartridge mounted far away from the pivot.
With the model of a pivot tonearm we are looking at the simplified calculation (taking the tonearm as a mass homogenous corpus) of (following Steiner AND WITHOUT including the cartridge mass at the moving tip of the lever !): J = 1/3 m x (2R) sq
J = inertia
m = mass
R = radius
sq = square
More to follow tonight. |
Assume a standard "taco warp" so the warp frequency is 7 rad.s^-1. Hi Mark - please, what's a "taco warp"? I'm assuming it's not related to female tonearm connectors :) . . . but seriously, while I can't really conceive of a standard shape to the minor warps on my records (for those that actually get played, not the obviously 'defective' sort) . . . just going by the tempo of the excursions, I'm guessing that 1-3 Hz is about the frequency range of most of them. So your 7 rad/sec (a little over 1 Hz) is a good figure, but probably a little far away from resonance for calculating good maximum/minimum changes in VTF. If the inertial mass were 25 g (say 15g arm plus 10g cartridge) and the warp were 5mm high, the maximal variation would be around 6.2 mN. A similar calculation allows a maximal warp tolerance to be derived for any arm / cart combination as a function of VTF. But the record doesn't act directly on the effective mass of the arm/cartridge - the compliance of the cartridge is in series. So for the actual change in VTF, you'd need to add a scaling factor based on the cartridge/arm resonance, no? Also, the point of maximum/minimum force in the warp cycle will change with warp frequency, as will the phase relationship between the force exerted by the record on the stylus and the force exerted by the cartridge on the tonearm will change as the warp frequency approaches the primary resonant frequency. Which makes me think that in most cases, the minimum/maximum cases of effective stylus VTF are unlikely to occur very near the tops/bottoms of the warp excursion, meaning that we're also going to see these extremes as occuring at a slightly altered VTA, the extent of which depends on the slope of the warp, hence its amplitude and frequency. Now my head's starting to spin . . . The important point is that it has nothing to do with the balance of the arm but is stictly related to the moment of inertia (and the mass of the cart). Yes, this is indeed the important point . . . but I would clarify that it's the moment of inertia from the effective mass of the arm/cartridge combination, coupled with the resonant behavior of the cartridge compliance interacting with this effective mass. But the big point with static vs. dynamic-balance is . . . what exactly is issue that the dynamic-balance system is trying to solve? Is it always used as an attempt to improve the constancy of VTA with tonearm position? In the tonearms I've set up, it seems that many are position-sensitive (remove the mat from under the force gauge and get a different reading, etc.), and many are not . . . and this doesn't necessarily correlate with whether or not the particular tonearm has a dynamic-balance system. So it seems to me that it's more in the overall execution than anything else. |
T-Bone
Yes, that is what I am saying.
It follows from a simple torque balance on the arm according to D'Alembert's principle. Rather than boring everyone by converting forces to torques and computing moments of inertia, I used the concept of equivalent mass.
BTW the figure given only applies to the example given, obviously different constraints will result in different figures.
Note that this is a force variation, the way the cart responds to the force variation will depend on the compliance. Also note the assumption of equal inertia is not equivalent to an assumption of equal structure but the differences are so small as to be immaterial to the argument.
Mark Kelly
|
Mark,
Are you implying that in all situations where the effective mass or "inertial mass" (not sure which one you mean, or if you mean to say they are the same) is 25g, and the effective length is identical (let's just say that the combination of total mass at the effective length is identical and the effective length is identical), that the maximal variation due to warp riding (which you put at 6.2nM) will be identical, regardless of compliance of cart, and regardless of what force mechanism is keeping the stylus on the record? |
Completely wrong.
Your first paragraph makes no sense: the effective mass of an arm is simply the moment of inertia divided by the square of the effective length.
In the second para you present a supposition which I have already shown to be wrong but you do not support it with evidence.
Mark Kelly
|
If it were as you stated, in consequence the derivation in VTF would be worse with increased effective length (= increased inertia) and increased effective mass (= increased inertia). Thus a super lightweight short (9") tonearm would be best in conjunction with a low mass body cartridge.
What brings up the Black Widow w/MM again.
However the sonic results do show us a different picture.
The derivation in VTF with a dynamically balanced tonearm is less than with the same tonearm in static balanced mode.
As all dynamic balanced tonearms can be used in static balanced mode too, this is easy to illustrate in demo. The static balanced mode to some does sound more "livelike" due to more alternations in VTF. The dynamically balanced mode often is mistaken for being too "remote - less lively".
But it is due to more constant VTF.
So same -static- inertia, same effective mass, same effective length.
The whole static spring-mass-system is the same in both modes - but we face different behavior.
I do not think we have yet reached the verdict with the model as described by Quiddity.
Some dynamic aspects has to be taken into consideration too - aside from the pure static model. |
Next a look at the effect of "warp riding". Assume a standard "taco warp" so the warp frequency is 7 rad.s^-1. This gives a maximal velocity of .007 m.s^-1 in the vertical plane for each mm of vertical warp and a maximal acceleration of .049 m.s^-2 (again for each mm of vertical warp).
The product of this acceleration and the effective inertial mass of the arm / cart combination gives a maximal VTF variation when riding the warp. If the inertial mass were 25 g (say 15g arm plus 10g cartridge) and the warp were 5mm high, the maximal variation would be around 6.2 mN. A similar calculation allows a maximal warp tolerance to be derived for any arm / cart combination as a function of VTF.
The important point is that it has nothing to do with the balance of the arm but is stictly related to the moment of inertia (and the mass of the cart).
Mark Kelly
|
D (and others),
I can envisage the practical difficulties of applying dynamic balancing force onto a unipivot bearing. I can see similar problems if a magnetic bearing is not otherwise stabilized. However, if the thread/magnetic/hydraulic/whatever bearing has more than one support point, doesn't give the same stability as, at a minimum, a double knife-edge? |
Dear T_bone, how to dampen a spring to be used in a dynamically balanced tonearm has been nicely demonstrated by Isamu Ikeda in his (...here we go again...) FR-60 series.
A new or in stock condition FR-60 tonearm will feature a long spiral spring which is embedded in a lot of white and creamy grease.
Much more than you can see on any of the pictures of dismantled FR-64/66 on the web.
If a spring is fairly large, fairly wide in diameter and quite solid (stainless-steel) it is - due to its location at the very center of gravity and inertia and to its position in conjunction with the surrounding grease and the fact that its edge is in contact with another surface on the whole length - most unlikely to resonate at all.
There are many more light-weight parts much less dampened in many more high-ticket tonearms past and present who are much more likely to resonate and add colorations to the sonic picture than a hefty and highly damped by several different measures spring.
Furthermore we do see dynamically balanced - i.e. spring loaded VTF - in very different tonearms ranging from high effective mass (FR, Exculsive, MAX (depending on armwand and headshell)) to medium and low like MA-505, SME V et al.
So it is neitehr a measure taken to deal with warp or high compliance (most unlikely to go with a high effective mass tonearm anyway...).
Interesting enough we see dynamically balanced design in the most expensive stock toonearms of the early 1980ies:
The Exclusive EA-10, Micro Seiki MAX-282, FR-66s/fx and SME V - all dynamically balanced.
All made by fairly large companies and/or specialized tonearm-manufactures which tried to set the benchmark for the component.
Constant VTF independed from the static balance mode of the tonearm does have several virtues and no disadvantage.
It can however - not be incorporated in every tonearm. It depends on the bearing you choose.
Consequently there must be disagreement about the dynamically vs static balanced mode - depending what "school's" scholar you are..... |
