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25th August 2005, 02:38 AM  #1 
diyAudio Member
Join Date: Aug 2003
Location: Greece

An Excel spreadsheet for DIY Tonearm's Effective Mass Calculation.
Hi all,
I made an Excel page for the calculation of a Tonearm's Effective Mass and I would like to share it with you. The method is pretty simple. All you need is a cartrirdge of known compliance and the use of the HFNRR Test Record (Low frequency horizontal resonance test). Once the Cartidge is correctly setuped (VTF, VTA, Offset angle, Antiskating etc.) on the tonearm you let it ''read'' the low frequency horizontal resonance bands, and you find out the frequency at which the cantilever will become excited and vibrate out of control. Then you throw the results (cartridge's compliance, resonance frequency, weight of the cartridge and fasteners) into the Excel sheet and you have your Tonearm's effective mass. After experimenting a little with various tonearms and cartridges I have found the results pretty accurate. Regards Padel 
25th August 2005, 11:20 PM  #2 
diyAudio Member
Join Date: Aug 2003
Location: Greece

Some Improvements
Hello all,
I had a discussion with a friend yesterday about this Excel sheet and he mention that it will be useful to also add an option for calculating the Resonance Frequency and a cartridge's compliance. After some thought I made some improvements on the sheet, so it is now capable of calculating the resonance frequency of a given cartridgetonearm combination which I think is very useful if you want to know if a cartridge is a good match for a tonearm or viceversa. The optimum cartridgetonearm resonance frequency should be between 812Hz. The other improvement is the calculation of a cartridge's compliance which is useful if you own a vintage cartridge with unknown compliance. What I found very interesting is that with this sheet you can know what is happening to the resonance frequency if for instance use heavier screws or some short of a weight between the cartridge and the head shell. Many of you may remember some cartridge manufacturers that supplied a small weight for that reason. Regards Padel 
15th May 2006, 08:47 AM  #3 
diyAudio Member
Join Date: May 2006

Dear Sir,
As i need to know how to get the cartridge's compliance and resonance frequency, could you please let me know if there have any illustration to explain these two more simple for my easily understanding ? Thank you for your kind assistance. 
15th May 2006, 08:09 PM  #4  
diyAudio Member
Join Date: Aug 2003
Location: Greece

Quote:
Hello, There are four (4) parameters in a cartridgetonearm system, Cartridge's Compliance, Cartridge's Weight (+ screws, nuts etc.)Tonearm's Effective Mass and the systems resonance frequency. We want the system's resonance frequency to be anywhere between 812Hz. So if you need to calculate you cartridge's complince (if this parameter is NOT included in the manufacturers specification sheet sheet that came with your cartridge, or because you own a vintage cartridge) you must at least know the other three parameters. Check out your tonearm's specification sheet for the tonearms effective mass and use the HFNRR Test Record (Low frequency horizontal resonance test) to find the resonace frequency (See post #1). Put the results in the Excel Sheet (Version 2) and you'll get the results. Hope that helps. Regards P 

16th May 2006, 06:58 AM  #5 
diyAudio Member
Join Date: May 2006

Dear Padel,
Thank you so much for your quick reply. But I still have one question, as I do not have HFNRR test record(Low frequency horizontal resonance test) to find the resonance frequency. So I wonder if I can use another test record to get the answer, or I must have to buy one HFNRR test record ? Once I have one HFNRR test record, do I still need any other instruments to do the test to get the resonance frequency ? Thank you again for your help. 
16th May 2006, 02:54 PM  #6  
diyAudio Member
Join Date: Aug 2003
Location: Greece

Quote:
If I remember correct the only record that contained Low frequency horizontal resonance test tones was from Ortofon, but this is out of production long time ago. The only Test Record that I know with these tones in current production is the HFNRR. You do not need any kind of measuring instruments for these test. Regards P 

17th May 2006, 02:11 PM  #7 
diyAudio Member
Join Date: May 2006

Thanks for your reply.
Noted for Resonance frequency issue. But I checked with the Japan cartridge's manufacturer for cartridge's compliance who replied to me that they do not know what it is. Therefore, could you please kindly explain more details about cartridge's compliance ? Thank you so much. 
17th May 2006, 04:55 PM  #8  
diyAudio Member
Join Date: Aug 2003
Location: Greece

Quote:
Cartridge Compliance (Elasticity) : Let's take a look at a spring (any spring) designed to carry a given load. Place too much weight on this spring and it collapses. Place not enough weight on the spring and the spring won't compress at all and remains rigid. Think of the cantilever as a spring. In the case of a phono cartridge, the cantilever is a rigid arm connected to a springing medium mounted up within the body of the cartridge. This springing element may be as simple as a rubber donut that holds enough tension against the cantilever mounting to maintain relative position of the cantilever. Most importantly, the suspension must control the attitude of the stylus fitted at the cantilever's end. The amount of distance that a cantilever deflects under a given force load is referred to as cantilever compliance. Higher compliance cantilevers deflect a greater distance when a given amount of force is applied. Lower compliance cantilevers deflect lesser distances when the same force is applied. In other words, high compliance = softer suspension , low compliance = stiffer suspension. Tonearms Effective Mass: The amount of force felt at the stylus under dynamic conditions in any (xyz) arcing vector about the pivot. This differs from Verical Tracking Force which is set static and remains constant only under 'peaceful' conditions while the record is in play. Effective mass is influenced by the weight of the various appendages of the tonearm assembly in ratio to the distance from the pivot. Weight that is further from the pivot center will account for higher effective mass than the same weight if positioned closer to the pivot. Said slightly differently, the heavy bits on the tonearm need to be closer to the tonearm pivot or excessive effective mass will be the result. Phono cartridges have different weights from one product to the next, therefore tonearm makers rate their arms in terms of effective mass before a cartridge is mounted. Resonant Frequency (of the cantilever): The acoustic frequency at which the cantilever will become excited and vibrate out of control. This frequency is measured in cycles per second (Hz/sec). Resonant frequency of a cantilever is regarded as inescapable and the effect is controlled by manipulating this frequency to exist in a range below human hearing but not so low that it will become excited by external vibrations such as foot fall disturbance or that of a warped record. This ideal frequency range is 8 to 12 hz. The lowest of low organ notes rarely go below 20 hz. Footfall and record warps happen below 6 hz. Some Phono Preamplifier manufacturers for that reason placed a subsonic filter cutting everything below 25Hz but this ''technique'' introdused other problems. The effective mass of a tonearm in combination with the compliance of the cartridge cantilever serves to determine where the resonant frequency of a given tonearm/cartridge match up will be. In general terms, arms with high effective mass fitted with cartridges of high compliance result in resonant frequencies that fall below the ideal range. At the opposite end, arms with low effective mass mated to cartridges of low compliance result in resonant frequencies above the desired range. Both extremes are to be avoided. In other words, Resonant frequency of the cantilever is used as a guide to match cartridge's compliance to the tonearm's effective mass. Regards P 

18th May 2006, 12:46 PM  #9  
diyAudio Moderator

Hi Padel
Excellent writeup. Allow me to note a small (scemantics) error that sliped through: Quote:
I havn't open your spreadsheet yet, but I want to thank you for your positive and helpful attitude. Regards George 

18th May 2006, 01:41 PM  #10  
diyAudio Member
Join Date: Aug 2003
Location: Greece

Quote:
Regards P 

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