Surface plates history and theory

Hello Everyone.
I've been thinking about Joseph Whitworth and his 3 plate method. In the 1830s, Whitworth formalised a method for creating flat (reference) surfaces, using scraping, correct to around 1/1,000,000”. (Not‘smooth’, but geometrically flat). This was called the three plate method - because it involved three plates. As I understand it, he did not actually invent the three plate procedure, it had been used with grinding (paste?) techniques). But he increased its accuracy and was able to measure it with the bench micrometer he built, accurate to 1/100,000”. This was a milestone in the history of precision engineering.

Question 1. Is it necessary to have 3 plates? Is there a simpler method to create flat surfaces?

Discussion.
Imagine we have two 1’ square plates. For arguments sake, imagine they’re the kind if concrete pavers you get at Home Depot.
Put the undersides together and label the the ends NSEW for both plates.
Line them up N over N.
Rub the plates back and forth in a NS direction. What kind of surfaces may be generated?
A.Both might get NS striations.
B, the rubbing make create a longitudinal valley or valleys - big striations effectively.
C. transverse hill or valley may develop on the lower or upper plate.
D. a combination of 3 and 4 will produce toroidal surfaces
E. by some miracle, both might be flat.

Assuming not E, rotate the top plate 90 deg, so its N is over E on the bottom plate.Continue rubbing as before, on the NS axis of the lower plate.

Question 2. will this remove all the possible errors induced in the previous process.

Question 3. if not, what procedure, if any, using two plates, will result in two flat plates?

I'd be very interested ty hear any opinions, or preferably, proofs
with thanks,
A

I believe that if you extend your "thought experiment", you will find there is no way to avoid a situation in which you create a spherical surface, convex on one, and concave on the other.

By introducing a third plate, you will end up grinding two concave (or convex) plates together (call them 2 and 3), which will reduce their convexity (concavity).

Then when you again grind one of those against the formerly mating errors of the first one, the result will be to reduce the errors of the first plate.

For every error you imagine in grinding plates 1 and 2 together, then you reproduce that error in 3 when grinding 1 and 3 together, but reduce it when grinding 2 and 3 together, and further reduce the error in 1 when 2 and 3 are ground against it.

The system tends toward flat, as that is the ONLY condition in which all three can fit against each other in any combination.

With just a pair, you cannot prevent or undo the spherical surface error.

Jerry speaks in sooth. The technique has been developed to the extent that optical people can hand grind glass mirrors and lenses correct to a few light waves.

An English teacher, who unfortunately moved away, was also a well known amateur astronomer, wrote a column in an astronomical magazine. One night his 10 year old daughter showed me Jupiter's moons with a 3" Newtonian telescope using a mirror she ground herself.

Bill

If you build a planetary lapping machine you can get very close to perfect if you can measure sag. The machine is capable of making errors other than spherical, but if you do things right you can get very close with only one plate.

Believe the intention of the exercise is to start from zero. Can one build a planetary lapping machine without a flat surface available?

Anatol said:

Question 1. Is it necessary to have 3 plates?

Click to expand...

Yes. The moore book "foundations of mechanical accuracy" has details, try to read this.

Question 2. will this remove all the possible errors induced in the previous process.

No. There are other errors which are best corrected using three plates, and you need to rotate
them 90 degrees between each spotting and scraping cycle. Otherwise you develop saddle errors.

Thanks to everyone for prompt and informative responses. Jerry (JST), the point about sphericity is well taken. I saw the possibility for toroidal sections but not sphericity. Silly me. Brain just not good enough
Jim - I have the Moore book, I guess i didn't think to look there.
One day I will do this - scrape 3 plates. Has anyone here actually done it?
Thanks again everyone, its such a pleasure to find a (small) community who understands such questions and their significance.
A

fciron said:

Believe the intention of the exercise is to start from zero. Can one build a planetary lapping machine without a flat surface available?

Click to expand...

Yes, you can start from zero. Sure, you have to machine parts to make the thing run, but nothing special. It then laps itself flat so long as you have an indicator to measure sag, nothing more than a decent dial indicator in the middle of a bar.

I have great respect for great minds. Reading this kind of thing makes me realize how little I know.

If you have "Foundations..." it's all in there - why rectangular is bad, and what more to do to get millionths (inch) flatness numbers.

A friend who worked in the grinding department at Sunnen described making plates, I think for internal use by the inspection dept. He blued one and rubbed them together, then scraped the blue points, just as described in the literature. After he retired, they called him back to teach others because no one else could get it right. Unfortunately he is gone now, so I can't ask him about it.

Bill

Conrad Hoffman said:

Yes, you can start from zero. Sure, you have to machine parts to make the thing run, but nothing special. It then laps itself flat so long as you have an indicator to measure sag, nothing more than a decent dial indicator in the middle of a bar.

Click to expand...

I think we have different ideas of zero. I thought the purpose of the thought exercise was to create a flat surface so you could invent modern machining á la Maudslay, but looking back at the first post I see the OP referenced Whitworth, so I guess the lathe, and likely some form of indicator already exist. :-)

fciron said:

I think we have different ideas of zero. I thought the purpose of the thought exercise was to create a flat surface so you could invent modern machining á la Maudslay, but looking back at the first post I see the OP referenced Whitworth, so I guess the lathe, and likely some form of indicator already exist. :-)

Click to expand...

It's a fair point. I too speculate on what you accomplish on a desert island, starting with absolutely nothing. In my case it's also about what physical constants could you create in terms of time and distance. Maybe electrical stuff too, like voltage and current. Since my memory is bad, we'll make it interesting by saying the island has a good internet connection and solar powered computer, so you can get knowledge but no "stuff". We'll also allow that the island is well supplied with fresh water and fruit and that you can fish, so you don't spend 100% of your time just surviving.

Obviously humanity has gotten this far, but how much could one man/women accomplish in a lifetime, working alone, on the same problems?

I had a purpose, we're gonna invent the modern lathe and build the Lord Chancellor.

It's not as though the original question wasn't answered in the first reply "you need a third plate to prevent spherical error".

I hope this desert island has a nice beach and maybe a bar.