[sdiy] Programmable Logic?

[Magnus Danielson]

From: Tim Ressel <madhun2001 at yahoo.com>
Subject: Re: [sdiy] Programmable Logic?
Date: Tue, 20 Jul 2004 08:03:09 -0700 (PDT)
Message-ID: <20040720150309.13505.qmail at web40311.mail.yahoo.com>

> Yo,

Hej Tim,

> 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. 

Yes, in a tone-wheel organ will the phase of a tone-wheel be some integer
multiple of the tone-wheels angle on the shaft (compared to some reference
position, which can be arbitrarilly selected). Now, any variations in the angle
of the tone-wheel will result in phase-modulation.

> 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.

Also, for non-equal teething gears, these periods will mix and have a new 
longer range. For a 2:3 gear it will take 3 turns of the small weels and
consequently 2 turns of the large wheel before their pattern cycles.
Thus, for ratios having higher relative prime components the pattern will 
become much longer. 

Add to that you also have the case of multiple gears ganged down. Another
aspect is that different gears sitting on the same shaft will modulate each
other, since they have a time-variant torque-impedance loading the motor with
its output torque-impedance. So, when one gear temporarilly "looses touch" with
a wheel (or nearly), the torque-load lowers and the engine force makes the axis
turn a little quicker until the gear gets in touch and now sees the force and
the decellerate the motor with a higher load. The average torque-load of each
gear will thus have deviations and thus will the load of the motor vary.

Naturally will this all appear down the gear-chain too. We also see various
spring actions by flexible axis (could probably be ignored here) as well as
the movement of gear and shaft movements due to the variation of teeth-to-teeth
powers. We could even expect there to be resonant parts in the system, even if
the Q of those probably is fairly low.

So, what we end up with is an electronic simulation with a linear or quasi-
linear kind of property depending on the details. Now, does'nt that sounds like
fun? ;O)

> 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.

Yes, thinking some more about it, we are looking at something _similar_ to a
DDS, but I rather think there is only one DDS, namely the engine-model and from
there is a line of phase-processing (modeling the gear-boxes) before comming to
the individual tone-wheel waveshapes. 

Generalizing this concept we end up with a modular phase-processing library
where one or more phase-sources is being processed to produce one or more
phases for waveshapers/waveforms/wavetables to convert into waveshapes to be
sent to traditional processing.

The phase-processing would include both linear processing (add, sub, mult,
linear filtering) as well as non-linear processing (phase-deviation tables for
teeth-shape for instance).

Doing stuff like that in a FPGA is fairly trivial. Hey, it would be fun to 
design the DSP engine which does this! ;O)

Anyway, I don't know why I am thinking DX7 all over this...

Cheers,
Magnus