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Re: [ATM] Polishing / Figuring Simulator
Hi Martin,
Great start! I've been traveling a parallel path, similar to yours, for a few
years now and have yet to crack this nut, I hope you'll have better luck than I
have.
First off, I'll start with a word of encouragement, the Pro's have been using
Computer Controlled Polishing / figuring simulation since the early 1970's (at
least according to Wilson's Reflecting Telescope Optics II, pages 3-5). Using
Preston's equation (Rate of removal = Pressure * Velocity * a Constant) sure
makes this simulation seem easy, but it is not. (YMMV).
Here's where I'm stuck, solving for the pressure differential for a cantilevered
disk on top of another disk. I'm pretty certain that is my remaining constraint
yet to be modeled, and the key to cracking this nut (I think...).
Here's what I have done so far.
#1 Relative Velocity
My version of the simulation accounts for linear velocity (tool over arm
motion) as well as relative angular velocity between the mirror and tool. My
polishing machine also measures, records, and controls the linear AND angular
velocity of both the mirror and pitch lap. (driven pitch lap)
#2 Pressure per unit area
I'm not doing well here, the best I can do is assume uniform pressure in the
contact patch between mirror and lap. As the size of the contact area changes
(lap overhang) I scale the relative pressure per unit area Up / Down as needed.
However, I am confident this is NOT TRUE to the real world situation, as Donald
Good recently wrote.
#3 Surface Profiling.
At the bottom of your program, you have a chart showing the cumulative
amount of glass removal. As a first approximation, this is an OK start, but it
needs a little more work to provide an accurate representation as to what
happens to the optical surface.
For instance, assume you started with a spherical surface with a known
Radius of Curvature and manifested the simulation onto that optical surface.
The result wouldn't be the graph you see at the bottom of your program. What
you would get (after measurement via some method) is two fold
A) A change in the Radius of Curvature
B) A change in the surface error profile relative to some conic constant
(sphere, parabola, or best fit)
In my case, I've experimented with exporting an error profile to a surface
profile, modifying the surface profile according to the simulation, then
reducing the surface profile back to an error profile using a modified version
of FigureXP. To some extent this worked. One interesting result was the
simulation and observation of the "Left Behind Edge" phenomenon, AKA "Turned
Down Edge" to some, where insufficient tool overhang produces the appearance of
turning down the edge of the mirror.
In summary.
#1 The Pro's have been doing Computer Controlled Optical Surfacing for 30+
years, and have achieved a level of sophistication that allows them the luxury
of taking the guess work out of figuring optics.
#2 I'm pretty certain the only unconstrained (and substantial) variable left to
solve for is the cantilevered disk pressure distribution problem. The closest
equation I can find is based on cantilevered beams, but cantilevered disks
appear to be substantially different than cantilevered beams.
Take Care,
James Lerch
http://lerch.no-ip.com/atm (My telescope construction,testing, and coating site)
http://lerch.no-ip.com/ChangFa_Gen (My 15KW generator project)
"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.
Talent will not; nothing is more common than unsuccessful men with talent.
Genius will not; unrewarded genius is almost a proverb.
Education will not; the world is full of educated derelicts.
Persistence and determination alone are omnipotent. "
Calvin Coolidge
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