[ATM] Machine polishing simulator, looking for help

[jlerch1 at tampabay.rr.com (James Lerch)]

Greetings All,

Several month's ago I took a very crude stab at creating a machine polishing
simulator.  While the results of this crude version matched experimental
observation, any relationship with reality was sheer luck.

Current efforts are being applied to writing a simulator based on proven
kinematics laws.  Fortunately, a lot of the work has already been done by the
folks simulating chemical mechanical polishing of semi-conductor wafers.  For
example, here are a few articles with some very applicable theories, data and
formulas:

http://www-mtl.mit.edu/Metrology/PAPERS/PAPERS/AdvMetal97.pdf

https://dspace.mit.edu/retrieve/4079/IMST011.pdf

http://www.lle.rochester.edu/pub/review/v83/83Understanding5.pdf

The problem I have applying all this great data is, in all cases they assume
that both the polishing lap and wafer are driven at constant speeds.  I know of
very few ATM polishing machines where both the mirror and lap are directly
driven at constant speeds..(perhaps this should change?)

Consequently, I need help with a method to calculate the effective rotational
speed of a pitch lap driven by the friction of the mirror underneath.

My supposition is once we know the following:

#1 Size of Mirror vs. Lap
#2 Position of Mirror vs. Lap
#3 Rotational speed of the mirror

we can calculate the rotation speed of the Lap.  Knowing the rotational speed of
the lap, the mirror, their relative sizes and positions, we can calculate the
relative velocities for a finite number of points on the mirror.  Knowing the
relative velocities, we can apply the Preston equation and calculate the
relative amount of material removal over time.  "Ta-Da" instant polishing
simulator :)    (yea right.....)

Assuming we can get this far, we can then start addressing all those annoying
difficulties to the process such as:

A) Non-linear coefficient of friction vs. relative velocity (it appears friction
may go down as velocity goes up)
B) Non uniform pressure (for instance when the lap hangs off the mirror)
C) Slurry thickness, hydroplaning, and wedge
D) The ability of the pitch to conform to the changing surface
E) Over-Arm travel distance and speed

In any event, until we can devise a method to calculate the imparted speed of
the pitch lap, I'm stumped :)  I believe the rotational speed of the lap will be
the sum of the velocities tangential to the center of the lap, but for some
reason I can't wrap my brain around this..  Any Thoughts??

Thanks,
James Lerch
http://lerch.no-ip.com/atm (My telescope construction,testing, and coating site)

"Anything that can happen, will happen" -Stephen Pollock from:
"Particle Physics for Non-Physicists: A Tour of the Microcosmos"

" Press on: nothing in the world can take the place of perseverance.
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