Eminent Technology ET-2 Tonearm Owners

Maths and Physics.

A few days back I wrote that the res freq of the arm was proportional to the square root of the inverse of the mass and stated that there was a discrepency in the ET2/2.5 comparitive figures that Chris had posted. This because the figures showed a halving of resonant frequency for the ET2.5. I speculated that this meant that the two sets of figures must have been taken under different circumstances. Chris followed up my post up with a question to BT where Bruce appeared to say that no, the measurement conditions were the same.
This did not make sense and was contrary to resonance theory. Since I did not know the actual question Chris asked Bruce, I decided to contact Bruce myself for clarification. Below is my question and Bruce's answer.
Note Bruce uses the phrase "everything else is the same". This could be where the confusion came from.



On 4/18/2013 10:22 PM, Richard Krebs wrote:
> Bruce.
> Good day to you..
>
> My question concerns the horizontal resonant frequencies of the ET2
> and ET2.5 Chris spoke to you about this some time ago and you gave him
> a range of frequencies 5-6 hz for the 2 and 2-3 hz for the 2.5. Chris posted your info on the ET2 audiogon thread. The range of frequencies for the ET2 was approx double the ET2.5 This is confusing if the same wand, cartridge weight and compliance was used for both arms, as it implies the the ET2.5 is around 4 times heavier in the horizontal plane.
>
>
> For a 8 gm cartridge of 30 cu I get horizontal resonance figures of around 4.7 hz and 4.2 hz for the ET2 and ET 2.5 respectively.
> Are my figures correct? If not where am I going wrong?
>
>
> Many thanks .
>
> Richard.
>
>

Richard,

Your figures are correct and closer to reality. The only difference in mass is in the spindle, everything else is the same. The spindle adds about 10 grams to the horizontal inertia figure and almost nothing to the vertical inertia. I hope this helps.

brucet

As you can see Bruce has confirmed my figures are correct and the resonant frequency of the ET2.5, for the same cartridge, is not half that of the ET2, but only slightly less, exactly as I calculated.
If any one wants to confirm this for themselves, they need only go to the horizontal frequency formula in the ET2 manual. Choose a total mass (Mc plus Ma) of say 40 gm.(simulating an ET2). Insert the compliance figure for your chosen cartridge and calculate the res freq. Now recalculate with Mc plus Ma equal to 160 gm. You will get 1/2 the original number. Recalculate again with Mc plus Ma equal to 50 gm (simulating an ET2.5) you will now get a figure only slightly lower than the original.

So what can we conclude from this.

Someone who understands the math and physics around the ET2/2.5 would know that......
a)....it would be obvious, from a mile away, that the resonant frequency of the ET2.5 with the same cartridge would not be 1/2 that of the ET2.
b)....a heavy arm, when and only when, connected to a low compliance cartridge is a high performance, viable alternative
c)....the air bearing employed on these arms is effectively rigid at audio frequencies. So they should look elsewhere when looking for the cause of compromised note leading edge performance.

Richard Krebs
For a 8 gm cartridge of 30 cu I get horizontal resonance figures of around 4.7 hz and 4.2 hz for the ET2 and ET 2.5 respectively.

Thanks for this info Richard. We have always discussed just the spindle HZ resonant numbers before (5-6hz for ET2), and (2-3 for ET 2.5). As you point out this is just part of the equation. Understanding how they interact with the other “parts” in coming to an overall horizontal 4.7 and 4.2 for ET 2 and 2.5 is interesting using a 30 cu cartridge.

But we need to remember even if we all use the same 30cu cartridge, the numbers will be slightly different for each of us. We use different cartridge screws, #’s of lead weights, different positioning of the counterweight cap; a little higher, middle or a little lower; and finally the single double and triple leaf spring. Each one of these changes the parameters a little. So like the saying goes trust your ears.

The big consideration here for me is how the I Beam is affected. Dover mentioned the 2 – 6 hz variance in the I Beam from Bruce.

As soon as you change any variables in the I Beam Hz changes.

I also use a larger bolt to hold the lead weights.

So for tuning the ET2, ET2.5
Based on my observations/hearing. The tonearm has been designed for the first time user to let the weights fall at their natural location on the I Beam. This is what the manual says. This is how it is setup with most users and those that don’t like to tinker with it; and the sound achieved is very good and musical when setup properly. All the past reviews of the arm are probably based on this setup. The manual does also say to get the lead out to the end of the I beam if possible. For those that like to tune it even more – that is the one of the objectives of this thread.

Single, double and triple leaf springs that are not discussed in the manual but Bruce supports as we are still using a decoupled counterweight system.

Chris,

The thicker spring results in a higher resonance frequency. Thanks
Brucet

The thicker spring works better for lower compliance cartridges for me. But it raised the resonance frequency – not good. This is countered by getting the lead to the end.

Chris,

You always want the horizontal natural frequency of the counterweight to be less than the cartridge/arm resonance, this is the case 98% of the time.
The natural frequency of the I-beam/leaf spring depends on the thickness of the spring, the amount of weight, and where the weight is on the beam. The natural frequency goes down as the weight moves further out on the beam which is where we want it to be.
Brucet

If the sound is still not right with a double spring in your setup – drop down to the single leaf spring.

Aluminum Gooseneck on the ET 2.5.

A much tighter coupling at the arm tube and at the air bearing spindle inserts.

Tight enough that it requires effort to set Azimuth.

Eliminates the bolt that joins the carbon fibre armtube insert to the actual carbon fibre joint (Gooseneck).

A really good thing not only because of the eliminating a bolt, but because some over tighten it and others not enough. The 3 holes for leveling are gone. Not an issue with me as I always used the middle one. Much tighter overall. I like it !

Going through the cartridges with it.

A clearaudio virtuoso SS retip is on there now.
Cheers

Maths and Physics.

Stiffness
Many years ago I remember reading an audio magazine which tested the rigidity of the ET2 bearing. It may have been Martin Colloms, but I can't be sure. This was done, again from memory, where accelerometrs were used and a sweep frequency was applied to the spindle. The result showed a bearing that was stiff at audio frequencies.
This is explained by the design of the bearing (it's self centering characteristics) and its extremely high resonant frequency. Many times higher than the audio spectrum. Although the bearing uses air which we know to be compliant, at the frequencies of interest, the bearing medium is stiff.
I also show here a quote from an industrial air bearing manufacturer. While these a big load bearing devices, their design is virtually identical to the ET2

"Outstanding stiffness for small deflections Most engineers visualize an air bearing as being like a hovercraft, and they erroneously conclude that a bearing which floats on air cannot be very stiff. Actually these gas bearings are many times stiffer than a ball or roller bearing. Sapphire orifices within the bearing gap control the pressure in a film of air which is only 0.0003 inches thick. As a load is applied to displace the bearing rotor or slider, the gap decreases very slightly on one side, reducing the flow of air through the adjacent sapphire orifice. This results in a pressure increase in the gap on this side which pushes the rotor back to its original position. In essence, the air bearing is a servomechanism with closed loop control, and maintains a uniform gap in spite of external forces that may be applied. This results in bearing stiffness of millions of pounds per inch for small deflections. Stiffness is linear and does not change with temperature. In contrast, ball or roller bearings have almost no stiffness unless heavily preloaded. The stiffness of a ball bearing is not linear, and varies considerably with temperature."

Amplitude
A few weeks back I posted a transmissibility graph showing the effect of excitation frequencies at various multiples of the resonant frequency. This graph can be used to show relative resultant amplitudes for known resonant and excitation frequencies.
For a standard ET2 using in my case a Shelter Harmony, we get a resonant frequency of 8.4 hz. On my heavy arm, this frequency drops to 5.3 hz. If we take the lowest frequency of interest to be 20hz we get multipliers of res freq of 2.4 and 3.8 respectively.
By applying these multipliers to the graph we can see that the system which resonates at 8.4 hz shows a small rise in amplitude about 15%. If we now compare this with the 5.3 hz example we see a much smaller rise around 5%. We have to extrapolate this answer, since it is off the scale of the graph. In other words at audio frequencies the heavy arm produces less bass boost.
You can also see that the damping applied has very little effect on the resultant gain as the lines are trending together. This means that even if we factor in a higher resonant amplitude for the heavy arm, we can see that while it alters things slightly, it has minimal effect.

There is some merit in a discussion of what happens at sub sonic frequencies but the arm with the lower multiplier (lighter arm) will face problems sooner as we decend below audible frequencies.

As before these are all first principle discussions. It is what it sounds like that matters.

Chris.
Glad that you like the aluminium goose neck. I designed it to be as stiff as possible. The tighter fit into the wand and spindle is deliberate. Also it is made from the same grade of aluminium as the spindle, 6061 T6. This to minimise the different material count in the arm loop.