[sdiy] Programmable Logic?

[Tim Ressel]

Yo,


Ah, gearboxes. As it happens I have a bit of
experience with this kind of thing. I worked at a
place that was doing spectrums of gearbox vibrations
to determine driveline health. Basically what you'll
see in a gear train like the Hammond tomewheel setup
is frequency (or phase) modulations from various
sources. Any gear has a 'pitch circle' which
more-or-less the middle of the gear teeth. Nothing to
do with musical pitch; but an amusing coincidence. 

See:
http://shopswarf.orcon.net.nz/spur.html

When two gears mesh, their pitch circles want to
touch. This is how one determines gear positioning at
design time. Now if for example a shaft has a slight
bend, the pitch circles move towards and away from
each other at a once-per-revolution rate. Due to the
gear teeth being angled, this results in a phase
modulation. Note that the modulation rate is equal to
the number of teeth i.e. a 100t gear will have phase
wobble every 100 cycles. Now if both shafts are bent,
each gear will have this modulation. And if the gears
are of different sizes, then a complex modulation
ensues.

Gear imperfections will also lead to 'noise'. This
will be more of a single butst of phase (and possibly
amplitude) modulation. Also the mesh frequency, or how
often gear teeth touch each other, will show up but at
a high enough frequency as to not be applicable.

A much smaller effect that can probably be ignored is
the bearings. If ball bearings are used, then a small
amount of noise is being sent down the shaft in the
bearing. There is a complex set of formulas to
determine the frequencies using the bearing speed,
number of balls, relative sizes, etc. I can dig up the
info if anyone wants it, but I think the effect can be
safely ignored. 

I find this very interesting. Simulating the complex
phase modulation of multiple gear trains will not be
easy. I think the way I would approach it would be to
use a DDS oscillator and do all of the modulation at
the input. Or something.

PS: Does anyone have info on the gears in a Hammond? I
tried a few times to find out with no luck.

--TimR


--- Magnus Danielson <cfmd at bredband.net> wrote:
> From: James Patchell <patchell at cox.net>
> Subject: Re: [sdiy] Programmable Logic?
> Date: Mon, 19 Jul 2004 17:55:26 -0700
> Message-ID:
> <5.2.1.1.2.20040719175140.00b718b8 at pop.west.cox.net>
> 
> > Actually, this is a subject that kind of
> fascinates me....although, I have 
> > not done much research....
> > 
> > Doing an ideal tone wheel simulator is easy, in
> fact, in a spartan 3 it 
> > would barely be a hiccup...
> 
> I agree, the Spartan 3 is powerfull.
> 
> > The problem is the phase jitter...after all, the
> tone wheel generator is a 
> > collection of cogs that do the frequency divisions
> to get all of the 
> > pitches you need, and the gears do not really do a
> very good job of that, 
> > really, however, most people seem to feel (me
> included), that this is what 
> > makes a Hammond organ sound the way it does.  So,
> the big question is, how 
> > do you simulate the non- ideal nature of the tone
> generator?
> 
> If you only want the pitches, then you should be
> looking at the integer 
> relationships of the cogs in the individual gears as
> well as the number of
> wobbles on the tone-wheels themselfs. This should
> all result in some common
> frequency from which you can do divide down. Thus,
> instead of the traditional
> phase-accumulator you end up with something very
> similar to a TOG. Naturally 
> should a power of 2 multiple be used for tonewheel
> shape waveform playback
> (sine with distorsion). If you do the drawbars
> analogue or digital is a matter
> of taste, but it should be fairly easy to do.
> 
> So, anyone with the gear-box details at hand that
> could shift them my way?
> 
> Cheers,
> Magnus
> 



		
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