1/3 or Normal stroke mathematically proven

The Normal stroke or 1/3 stroke is used to reach a spherical shape and get the mirror and tool to reach the same curvature. While earlier generations of ATMs and professionals achieved perfectly functional mirrors by means of MOT-only current literature and ATMs recommend switching MOT and TOT once the desired radius of curvature is reached. The tendency to grind the edges (increase the radius of curvature/focal length) is done via <1/3 strokes, while grinding the mirror center (decrease the ROC/focal length) is done via 1/3< strokes.

I am wondering: is the 1/3 stroke only an experimentally proven value, albeit valid over centuries, or is it also mathematically proven as the turning point between increase and decrease of focal length?

Edited by stargazer193857, 02 December 2020 - 02:51 PM.

 

or is it also mathematically proven as the turning point between increase and decrease of focal length?

there is a math formula since polsim.exe is a program that graphically shows how the stroke / tool wear the mirror.

Math for stokes? Well for decades we just adjusted as needed.    1/3 to 1/2 diameter most times. But now with computers spread sheets are the norm.   Young people today have it so easy, iPads and iPhones to call out the stoke, we did it in our heads. Sorry old Master here.

Starry Nights

Edited by Oregon-raybender, 02 December 2020 - 10:55 PM.

Math for stokes? Well for decades we just adjusted as needed.    1/3 to 1/2 diameter most times. But now with computers spread sheets are the norm.   Young people today have it so easy, iPads and iPhones to call t out the stoke, we did in our heads. Sorry old Master here.

 

Starry Nights

.......you can't put experience on a spreadsheet. Young engineers use a micrometre- my late Grandfather was a tool maker during the second World War- he could feel the difference of a few thou with his fingers- he never needed a micrometre.

A couple of things::

a) the tool and mirror are separated by the thickness of the grit being used and are therefore not exactly equal before one finishes polishing.

b) one achieves a zone free sphere by randomly introducing errors in the strokes

grinding two equal size disks made of hard material such as glass is different than polishing one of those disks on an equal size lap made of flowing pitch.  

The two glass disks grind only where they touch (except thin layer of abrasive) and become spherical or flat because those are the only shapes that will stay in contact throughout the length of stroke and all rotational orientations (assuming the glass is rotated during the work).

Polishing is different because the pitch is pliable and can flow to a different shape, allowing areas of of the lap to become more or less effective during during the work session.  With a 1/3 COC stroke the central 2/3 of the mirror is always in contact with the lap throughout the entire stroke, while the outer 2/3 of the mirror is sometimes not in contact with the lap and so gets less wear, and the result is an oblate spheroid, degree depending mostly on pitch hardness.

regarding the mathematically proven conjecture...I don't know.  I do know that a 1/3D stroke will get you a good sphere.  But I think even a 1/3D stroke MOT will shorten the ROC, while a 1/3D stroke TOT will lengthen the ROC.  Longer strokes or more sidethrow cause loss of contact, which causes the shape to depart from a sphere.  With a very short stoke MOT, the edge rises, and once again contact is lost.  No math, unfortunately.  I like math.

I don’t start a mirror 1/3 coc. To generate the curve MoT overhang the edge of the tool to dig the hole to get the sag going.

after that, to smooth things out, MoT / ToT to maintain sag 

grinding two equal size disks made of hard material such as glass is different than polishing one of those disks on an equal size lap made of flowing pitch.  

 

The two glass disks grind only where they touch (except thin layer of abrasive) and become spherical or flat because those are the only shapes that will stay in contact throughout the length of stroke and all rotational orientations (assuming the glass is rotated during the work).

 

Polishing is different because the pitch is pliable and can flow to a different shape, allowing areas of of the lap to become more or less effective during during the work session.  With a 1/3 COC stroke the central 2/3 of the mirror is always in contact with the lap throughout the entire stroke, while the outer 2/3 of the mirror is sometimes not in contact with the lap and so gets less wear, and the result is an oblate spheroid, degree depending mostly on pitch hardness.

My pet theories and ideas are along these ideas.  The action of polishing has to do NOT with contact between the glass and the pitch,  but with the fluid medium, pH, the pressure and speed of the layer of slurry because it is very much a chemical process of dissolving.

When the surfaces are sliding past one another there is no contact between the glass and the pitch, rather, there's a layer of turbulent flow that is creating the action.  I think that the pushing motion of MOT or TOT creates a difference in the thickness of this layer...since we're measuring surface changes in millionths, and the particle size is generally several microns, there's wedge in the layer.  Push too hard and you'll feel not drag, but a contact and local scrub of pitch on glass.  Oops. 

How thick is the layer of slurry anyway?  

Also, the increase and changes in turbulence and wedge as I reverse the movement at the end of the stroke increases the action at the edge of the lap.  I think this is why a short rapid stroke MOT creates an area of higher action just inside the edge of the mirror and relatively turns the edge up....wherever the edge of the lap stops and reverses, there's greater wear there.

If this is true, then that suggests why a 1/3 stroke will go oblate...the 70% zone is just where the edge of the lap stops, reverses, and deepens the curve there.

The distortion of the lap after a period of stroking is another factor that I ponder while working with small laps and accented pressure on the lap edge.  Frequent pressing will eliminate that, but if I press a small lap....or any lap in the center of a deep paraboloid, then use it on the outer edge...what happens to that very thin layer of slurry?  The lap no longer fits the flatter curve of the outer zones......

Edited by ccaissie, 05 December 2020 - 06:32 AM.

@stargazer193857

What I would try without ever having come to polishing stage yet: do 1/3< center over center strokes MOT to deepen the center again. Under the assumption that 1/2 stroke works the most in the very mirror center, I'd go through all stroke lengths from 1/2 to 1/3 in decreasing lengths (or from 1/3 up to 1/2 stroke lengths) in order to work through all inner radii of the mirror until the 1/3 normal stroke length is reached which is widely claimed to end up in an overal spherical mirror-tool contact. With very frequent testing to make sure that the center is not deepened again. That's what I would try.

But I am curious what experienced ATMs would do and if my approach is correct. So please chime in with your knowledge.

Edited by Lucullus, 05 December 2020 - 05:44 PM.

The action of polishing has to do NOT with contact between the glass and the pitch,  but with the fluid medium, pH, the pressure and speed of the layer of slurry because it is very much a chemical process of dissolving.

This is not really true.  Polishing is a combination of physical contact between the glass and the polisher and the chemical reactions that proceed during the process - both uptake from the glass and redeposition from the silicate compounds suspended in the slurrry.  Glass being polished gets warm due to friction, not chemical process.

Increasing wear by plowing at the zone where the lap stops and reverses seems to be the commonly accepted theory of why the oblate figure happens.

 
I have an alternative theory that was only partially hinted at in my previous post. I mentioned that with the 1/3 COC strokes it was harness of the tool that makes the sphere in grinding and softness of a pitch lap makes the oblate figure. A little more on that…

There is that stroke stop/reverse zone but it’s not increased wear from plowing.  It is simply because of different durations of time in contact with the lap inside and outside that stop/reverse zone that causes the oblate shape. Inside that stop/reverse zone is always in contact with the lap and is wearing throughout the entire stroke.  Outside the stop/reverse zone sometimes is not in contact with the lap and is not worn during parts of strokes.

Remember we are dealing with millionths of an inch. The reduced time the edge is on the lap reduces wear of the mirror’s outer zone. Pitch being softer than glass, its ability to momentarily flex under pressure allows the mirror’s high outer zone to push the outer zone of the lap down. This action continues to increase the positive conic until the edge is so high that the pitch can no longer flex fast or far enough and the high edge puts enough pressure on the lap so that increased wear resulting from increased pressure equals the reduced wear from less time in contact with the lap. The figure has reached the terminal shape for this stroke and lap conditions, in this case oblate, and won’t change without a change of stroke or lap condition.

This is just fine for polishing. The mirror reaches that terminal shape and stays there throughout polishing.  When polishing is complete it takes only a short while to remove the oblate and make a sphere.

Strokes of small overhang, short, near center have negligible increase of pressure on the edge of the bottom disk under the overhang. Overhang pressure becomes more significant with increased overhang. Longer strokes and/or offset from center (Ws or chordal strokes) MOT can increase wear and reduce ROC in the central zone to compensate for the reduced wear and short ROC at the mirror’s edge.  Or longer and or more offset TOT can increase wear on the outer zone by overhang pressure and compensate for less time in contact with the lap.

If this time on lap thing is the way it works I would expected with that 1/3 COC stroke softer pitch would make a more oblate figure than hard pitch. If it is plowing at the stop and reverse I would expect the hard lap to plow deeper making more oblate than soft pitch.

Some say it is easier to make a sphere with a hard lap.

Polishing is physics, so there will be some physical law that could be written down mathematically. But it is also a complex process, so you have to resort to certain abstractions to describe it macroscopically.

Early last century, Frank W. Preston proposed the following simplification:

wear-rate = C * P * v

also called Preston's law for obvious reasons. Here P stands for (local) pressure and v for relative velocity. The wear-rate is the wear per unit of time at a given location. The constant C is in fact the abstraction of all kinds of chemical and other processes, which you can indeed consider constant when you use the same recipe for every polishing session.

So, like also indicated by Dogbiscuit, the parameters that are under control are pressure and velocity. When you manage to keep these constant as well, the amount of wear is simply proportional to the percentage of the time that tool and glass are actually in contact.

I think that the model Martin Cibulski used in polsim.exe (mentioned by Pinbout) is actually based on this approach. I have put this in an Excel for the circular stroke technique I use. In principle you can do this for any stroke, so also for the 1/3 normal stroke, but then you do need to take the varying velocity into account as well.

A complicating factor that you should also take into account is the fact that pressure is higher at the edge of the contact area, where the overhang happens. I have found an OSA article by Haitao Liu e.a. modelling this behavior. When you apply (high) pressure through the center of the top piece (i.e. inside the contact area) the relative influence of the overhang is decreased.

Edited by stargazer193857, 06 December 2020 - 05:54 AM.