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Hi all,I've searched the archives and still can't quite figure it out.
I'm building an arm from scratch, should I really shoot for 10Hz as ideal resonance, or is there some other value that sounds better (12+Hz)? Please don't answer in ranges, I'm looking for an exact value to shoot for, I know what cartridge I want to use and I can optimize the arm, not looking for a "good match" for pre-existing items.
Also how exactly do you calculate the resonance (plain english please), what is the difference between "effective" mass and plain old mass? Where does the counter-weight figure into all of this, is everything behind the pivot point irrelevant?
I'm comfortable with math but get confused with "definitions" and terms.
I'm working on an all carbon fiber linear air bearing low-mass arm for cartridge with 20 CU compliance.
Sorry for the tone of my post, I'm not a jerky grouch, just frustrated and confused and want to really define what I'm looking for as far as information so I don't get the same old "between 8 and 15Hz manufacturer recommended" type answers.
Thank you,
Erik
Follow Ups:
Hmmmm... "linear air bearing low-mass arm"-in a lateral sense this discussion about ten Hz. will not be valid. Complex matter. Arm is not rotating in a lateral sense but all parts have the same movement. All mass is moved in a linear direction by the tip itself. The compliance of the cantilever- suspension is not loaded in a normal way.
This means a very low rf, even with a low effective mass. The tip feels the total mass in a lateral sense. Freedom of movement depends on complex slip- stick- processes. My cantilever will bend and stretch sometimes, causing stretching- effects in both lateral and vertical directions. This means riks of dynamic wow and fluctuations in tip- groove contact pressure.
IMHO the engineering offers for such an arm are not in realistic proportions related to the few merits and the mentioned risks.
Hi headshell,I tried to email you but it came back. Oh well! I'm looking at mostly resonance and the verticle plane, I know the roll off will be steep but I want it to begin in a good place. This is my second "DIY low mass air bearing arm" and I'm just trying to improve apon the first which worked REALLY well but unfortunatly was broken in my last move. I didn't have any of the stick-slip problems you mention(could have been lucky). My old arm had no problem tracking one of those defective runouts that goes back and forth without jumping the groove, so it's worth a shot.
For me, tracking the groove in the same many as it was cut makes too much sense to want to try another type of tone arm, all of which have their own set of drawbacks to overcome, though in my mind fewer merits if I can do this one right.
Even if it totaly sucks (sounds bad)and breaks a stylus and ruins a record, I still would like to undertake the journey and learn a little more. I have'nt spent any money yet and it will probably cost me less than $50 bucks to get it done, so why not? If it's not an improvement I can just re-build my old arm!
Also, what is you opinion of using a headshell? (I figured you would be the one to ask!) I have the option of running the wiring straight through from cart to phono section with out any contacts etc., would this sound that much better? If I wanted to use a different cartridge, I could just build a separate carrier and arm optimized for that cart, just as easy to change as a headshell and better sounding?
Thanks, Erik
> how exactly do you calculate the resonance (plain english please)If you know the cartridge's compliance at resonance and the tonearm's effective mass you may apply the following formula:
Resonance Frequency = 1000 / {2 x (pi) x Sqrt[C x (MC + EMA)]}
Where:
(pi) = 3.14159
C = Cartridge Compliance in mm/N
MC = Mass of Cartridge including mounting bolts in grams.
EMA = Effective Mass of Tonearm in grams
Sqrt[ ] = Square Root of everything inside brackets.> what is the difference between "effective" mass and plain old mass?
There is significant difference, which is exactly as Mark Kelly explained.
Another way of looking at effective mass is from the spring mass model. The cantilever has a spring suspension and the cartridge and tonearm have mass. The spring suspension in conjunction with the mass interact to produce a resonance frequency. The effective mass of the system is the same as a point-mass that if placed directly at the spring would produce the same resonant frequency.
In other words, the total mass of a tonearm might be several hundred grams, but its effective mass might be only 12-grams. Take the following example of a tonearm:
Click on the link below for a thread that describes in detail how to calculate the effective mass of this tonearm.> Where does the counter-weight figure into all of this, is everything behind the pivot point irrelevant?
No, everything behind the pivot is relevant and adds to the tonearm's effective mass. When you go through the calculations in the link below you will understand how everything figures in.
There is a lot involved in the questions you ask. Mark Kelly is an expert who knows the answers to your questions. However, it requires significant information and technical knowledge to answer your questions completely, which can be obtained from a thorough study of mechanics and dynamics.
Best regards,
John Elison
IF you know what a moment of inertia is, the effective mass is the moment of inertia of the arm about its pivot point divided by the square of the pivot to stylus distance. Anything which pivots with the arm is included in the moment of inertia.
Mark Kelly
Hi Mark, I've been boning up...So for unknown or "scalar" moment of inertia I would use I=sum of MiRi^2 using the cartridge weight and center of counter weight with the center point of the bearing tube as the axis? Where does arm weight factor since it's mass will not have a center other than perpendicular to the axis?
This stuff is interesting, I have a mountain bike with 29" wheels, as opposed to the standard 26". That whole moment of inertia thing works well off road.
The more I learn the more I don't know, never truer.
Thanks,
Erik
For a first cut the small or at least short items can be considered as point masses and the classic M.R^2 formula applied. Long thin parts such as the arm tube need a further elaboration: use the point pass formula taking the geometric centre as the centre of mass but then add the moment of inertia about the centre of mass. For a long thin object the moment of inertia around the centre of mass is M.L^2/12 where L is the total length.The most difficult part to determine will be the "rider" which interfaces with the bearing tube. Fortunately it will also have a small impact on the total effective mass because it is, perforce, so close to the pivot. If you post a drawing of your proposed rider I can work it out for you and run you through the calculation.
Mark Kelly
Thanks Mark,
The "rider" will be round carbon fiber tubing also, it's distance from the pivot axis will be ~15.375 mm (= r at tubing wall center). The carier or rider tube can be any length, though 4-8 inches would probably work best, with a mass of 5.4 grams per inch.Tone arm material will be round carbon, 1.4125g per inch again can be any length to get things right.
Headshell, cartrige, and mount, 21.6g (cartridge alone 5.5g)
counter weight and mount, 82.1g adjustable over 3/4 of an inch or so.Please forgive my significant digits,
Erik
The carrier will have an Icm of 3.3 x 10^-8 kgm^2 per inch of length as is but this is useless because it will obviously have some fixings for the arm tube and the counterweight carrier. For a thin walled tubethe error between using the method of subtraction of concentric cylinders and the wall centre is very small.The rest of the items you can figure out using the formulae you already have.
Mark Kelly
Thanks a lot Mark!There will be very few fixings other than some epoxy, the counter weight will be very close to the carrier. I included the mount and hardware weights in my measurements.
It's amazing how fast this thread got burried, busy board!
I'll be sure and post the results when I get it all together.Thanks again!
Erik
Thanks mark,I'm a little fuzzy on moment of inertia, I'll have to study that one a bit, is that like having a heavy rim on your platter or along those lines? How would estimate that?
I'm sure I could measure it once the thing was built but, that would be putting the cart before the horse, I'm still in design phase though I will soon know what all the components weigh, along with a weight per inch on the tone arm material to optimize mass vs. length.
Another quesetion, is it worth doing away with a removable headshell, it would be convineient but what about sound? It would almost be as easy to build a seperate arm and carrier optimized for each cartridge other than changing out the head shell and adjusting down force.
With what I want to do the "carrier" tube will be ~1 1/4" carbon fiber tubing, it's round so will the pivot point be a virtual pivot at the center point of the stationary air bearing tube?
If I vary the length of the tube to try and compensate for mass to reach a set resonance I guess I'll have to try and sneak up on it til lenght and mass are where I need them.
Thanks,
Erik
Send me an email. Much better. Need time for this.
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