[sdiy] Programmable Logic?

[James Patchell]

Very interesting....I can see that it is maybe even more complicated than I 
imagined...


At 08:03 AM 7/20/2004 -0700, Tim Ressel wrote:
>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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         -Jim
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