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[ATM] Polishing / Figuring Simulator
> From: "James Lerch" <jlerch1@tampabay.rr.com>
>
> 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).
Yes, I remember a picture of a robot arm holding a polishing device on
a large mirror (8 meters ?).
> 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...).
In a german forum (www.astrotreff.de) I got valuable comments about this.
A similar problem occurs in building fundaments.
There it must be avoided to get zones of negative pressure, so the pressure
distribution is important.
Generally the pressure is assumed as a linear function of the X/Y
coordinates.
f = ax+by+c
For the tool on the mirror we have to find a,b,c that three equations are
fulfilled:
1. Sum of forces of all contact points = Tool weight + additional downward
force
2. Sum of turning moments of all points = turning moment of tool weight and
additional downward force (X direction)
3. Sum of turning moments of all points = turning moment of tool weight and
additional downward force (Y direction)
If these equations are solved for an array of contact points the cointact
forces can be calculated.
Fortunately these formulas give a simple 3x3 matrix filled with expressions
containing Sum(X), Sum(X*Y), sum(Xsquared), . .
If ax+by+c gives negative forces on some points these points don't have
contact and must be removed from the calculation.
Then a next iteration on the remaining points must be done.
If the downward pressure point is inside the overlapping area the iteration
will converge.
If not ...
> #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)
I simulate a freely rotating tool from its moment of inertia and the added
forces
of all contact points. But the friction factor can only be estimated by
comparing
a real pitch tool with the simulation.
> #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.
As a next programming step I plan to implement the iteration I mentioned
above.
> #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.
I programmed a data reduction for foucault measurements where took a
reference
parabola which can be reached only be glass removal. The usual tools give
a best fit parabola which implies to ADD glass on some zones.
My spreadsheet gives a parabola having the same slope as the mirror
at the edge. Then a starting sphere looks like a big hill in the middle
relative
to the parabola. Then I can use W strokes with more action in the middle
to reduce this hill.
This is the way I figured my last 14" mirror (without computer simulation).
Regards,
Martin Cibulski
http://www.martin-cibulski.de/atm/
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