Flat From Scratch, revised - The 3 plates method

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Here I share my experience on making flat the ways of my home made lathe with the 3 plates method, and a discussion about some caveats and the history of the method.
So how to make a true flat surface without a flat surface? Before any true flat surface was ever made there were only pseudo-flat surfaces, far to be really flat, a fact that had many implications in hampering the technological development. Who, for the first time, formalized a method to obtain a (quite) true flat surface (from scratch) was Joseph Whitworth who revealed his 3 plates method in a paper addressed to the British Association in Glasgow on 1840. There are no much information online about this method, and the few lines mentioning it, that one could find in a book of mechanical technology, are not enough to let understand how actually this method can be carried out. Eventually I found some information online, enough to try myself the method on the occasion to make the ways of my home made lathe.
This video is a revision of a previous one with the same title where some issues have been addressed. I provided both historical e technological context, and a detailed illustration on how I carried out this method, with some variations introduced to speed up the work.
Some caveats related to the described method are also discussed.
I made this video with the hope others will find it interesting and useful.
00:00:00 Introduction
00:01:00 About flat surfaces
00:03:05 History of the method
00:05:54 Why we need flat surfaces
00:06:13 Definitions
00:07:01 Description of the method
00:07:18 Caveat on the description
00:11:27 Discussion on the limits of the method
00:14:49 My experience and trick to overcome the limits
Acknowledgments
There is no much information online about this method, but digging the net eventually I came up to the original paper (a scan still available through Archive.org), its transcript on Wikipedia, and an useful article written by Eric Weinhoffer that directed me to an other document, a PDF titled “Reference Planes” written by Doctor Alessandro Anzalone, for the Hillsborough Community College - Brandon Campus, both helped me a lot and confirmed what I intuitively figured out when I read the paper for the first time.
Many thanks to both the cited authors, without their work I would not have been able to get the results I got.
Lately I had some more insights and many thanks goes to Johan (DIYSwede) that directed me to the good video of Robin Renzetti on the 3 plate method. Many thanks even to them.
Also I have to thanks “12L14” from Homemadetools forum who directed me to the comment of Forrest Addy at the Practical Machinist forum.
Links & References
[1] The Whitworth method presented in 1840 in “Miscellaneous Papers on Mechanical Subjects”, with the paper titled “A Paper on Plane Metallic Surfaces or True Planes”:
en.wikisource....
Blog article of Eric Weinhoffer
ericweinhoffer....
Reference Planes by Alessandro Anzalone, Hillsborough Community College, Brandon Campus
etshare.pbwork...
Wikipedia page on Sir Joseph Whitworth:
en.wikipedia.o...
[2] “Foundations of Mechanical Accuracy” Wayne R. Moore - 1970
mooretool.com/p...
[3] Robin Renzetti ROBRENZ ATD #1 Intro, 3 Plate Method
@ROBRENZ
• ROBRENZ ATD #1 INTRO, ...
[4] Forrest Addy, his comment on Practical Machinist forum (post #11):
[quoted post:]
«Square or round or rectangular plate makes no difference in the final flatness provided the work is rotated a RANDOM amount. The object of rotation of the plates in successive cuts is to prevent "radial lobing" of the surface. If the plates are rotated exactly 90 degrees, 72 degrees, 60 degrees, or any other angle corresponding to a regular polygon, there is the hazard of radial "lobing" to appear in the surface. » [...]
«I disagree with the Moore assertion of only square or round plates being capable of generating truly flat surfaces. Square or round plate shapes may be helpful but not essential. »
www.practicalm...
Other sources: www.circuitousr...

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17 авг 2024

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Комментарии : 110

@ared18t 3 года назад

I use this method to flatten my sharpening stones. Though it's not necessary to get them perfectly flat nothing gets them flatter with as much ease or as little money which makes sharpening tools a lot easier.

@3516C Год назад

I do the same thing!

@xostler Год назад

This! I’d bet this is how the Industrial Revolution started. You gotta have flat to have square and so on.

@jancornelis378 10 месяцев назад

Interesting to read. Do you prefer this method instead of what everybody is doing: a flat surface with sand paper or a diamond plate? Does it remove a lot of material on your water stones before it gets flat? I'm going to try it myself as well and will report back :)

@giovannipezzin5707 3 года назад

I hit like because you explained brilliantly the method, but after seeing how much you wrote in the video description I instantly subscribed. Excellent work.

@AccidentalScience 3 года назад

Thanks bud, glad you're here.

@scififan698 2 года назад

by rotating 90 degrees for flatness checking (and scraping), you can attain good efficiency and reduce the number of scraping cycles significantly, but it still remains necessary to also rotate other angles to avoid systemic symmetry errors, which you would not be able to detect by using 90 degrees only. So the requirement is not so much to have square plates to get them flat, but to use as many angles as possible for ultimate flatness. If your plates are very long and not square at all, you can also use offsets and angles of 180 degrees, as you discovered quite naturally. It's all about averaging out the errors in all offsets and angles, to approach flatness to a certain degree. When your plates leave such a small air-gap they they feel like they are sucking together, it is very satisfying, isn't it!

@AccidentalScience 2 года назад

Thanks for commenting. Yes it is. But for me the most satisfying part was living the whole process for the historic scientific achievement it was.

@luderickwong 3 года назад

To examine which theory is right, someone already did a lot of work for us. telescope lens maker, especially those who make Newton style reflecting telescope at home. they only use 2 round plate, A and B, a lot of changing angle on grinding, a lot of long stroke, and the end result will be one concave len and the other one will be matched convex surface. we simply avoid what they did and that will hopefully will give us a reasonable flat result.

@NissimDeij 2 года назад

That’s why you use 3 plates. The only common surface of the 3 plates is a plane

@laughingachilles 3 месяца назад

16:40 - I think you came up with quite an elegant solution for the problem. It would greatly reduce the possible errors in the flat surface and the results would be more than suitable for a lathe or similar project.

@ai1.0 2 года назад

Thank you for links in the description!

@ElizabethGreene 3 года назад

I was pointed here from the comments section of @Applied Science's channel, and it's fantastic. These gentlemen were separated at birth. (by the Atlantic Ocean)

@stephaniea9722 7 месяцев назад

Hey, excellent video and I love that it picks up on some points that people miss. I've recently become interested in the science of making flat surfaces, and eventually decided to create a Python program to simulate lapping two surfaces together (lapping can be much better for making the initial surfaces, because it averages the two surfaces together). Some notes: when referencing two surfaces together, do your scraping and then rotate them, then scrape some more, then rotate again, scrape some more. This is where lapping is easier, as you just need to rotate it, no checking or bluing. What happens when you do this, is end up with the two surfaces matching, one concave and it's matching is convex. As you move on, you will end up with two concave and one convex surface, or two convex and one concave surface. Matching the two concave or two convex surfaces together will net you with them both being very flat, but again one will be concave and the other convex. Essentially you're averaging spheres together, increasing the diameter of the spheres with each iteration. Another thing is that you should overhang the surfaces as much as you can without them bending. Ideally this would be 1/3rd of the surface overhanging. This removes localized errors. Say your pieces have a 10mm by 900mm surface, you would try to overhang 3mm and 300mm, then rotate it and do it again in all directions. You can test how much the surface is bending from it's own weight by putting a test indicator with a magnetic base on the top and extending the arm to the edge and zero it when there is zero overhang, then move it and see how much it moves.

@AccidentalScience 7 месяцев назад

Thanks. Lapping is possible only if you have rounded (or at least squared) surfaces. It is quite complex to rotate a thin and long part as it was in my case. Set apart the guidelines taken from reading the Withworth's paper, I reached the conclusion that for a extreme length to width ratio it is not necessary to rotate the parts since the error on the shorter side is unavoidably smoothed out by the process for the reason of the given extreme ratio. Interesting idea making a software simulation, at the time I did a rough simulation as well. What features your program sports? Do you plan to release your software open source?

@stephaniea9722 6 месяцев назад

@@AccidentalScience I plan on open sourcing it. Right now it's very rudimentary. I can change the resolution of the surfaces, set the number of lapping operations and rotation of the surfaces. I use a heightmap which is not ideal. The lapping process is essentially doing an averaging operation on the two surfaces - again not ideal. One of the induced errors in the program I've found is from the surfaces not sitting flat on each other. Say you have two surfaces that are convex, if you offset them by 30%, your top surface would be tilted and your point of contact moves. My software doesn't account for that. I'm looking for off the shelf libraries that can perform the functions needed, but it's hard to find. Ideally the surfaces would be represented as a mesh, and use collision detection. As for making surfaces that are narrow, this guy really has the technique down: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-s3fMIAPs6jU.htmlfeature=shared There's another recent video of someone making them, he tried cheating and making his CNC mill move the surfaces back and forth, one issue is that it wore lines into the surfaces. You need some rotational movement, even just a few degrees is better than none. I'm curious how you did your program?

@matthewmoilanen787 4 месяца назад

@@stephaniea9722 You're not studying the process of making things flat you're trying to make a computer program about it with no actual work being done and no measurements. It matters not what your program says but matters greatly what the measuring tools say. Creating a program has no purpose at all.

@stephaniea9722 4 месяца назад

@@matthewmoilanen787 everything has a mathematical proof. Measurements are meaningless unless you know the math behind it. You can just say "This works, trust me." Or you can prove why it works. Math is that proof, and every single operation that you do on a machine or in engineering has a mathematical proof behind it. It's not about measuring results, but understanding them. Because if you can understand something, you can improve it, modify it, or apply it to other methods. That's entirely the point. Like what if you wanted to find out how long it would take to make two surfaces complementary within a certain margin, using a specific rate of material removal? What if you wanted to find out how and where errors are introduced into a surface and how to avoid it? What if you wanted to test alternative methods like using the front and back of two plates instead of 3 surfaces? Testing all of this through experimentation and measurements would be extremely time consuming and expensive. But if you could model it, you could test everything in minutes for practically zero cost. It's why things like FEA exist. You can test a design or method before expending resources (which you would measure the results of anyways!)

@FilterYT 3 года назад

Thanks for your videos and thanks for doing them in english.

@jameswiz Год назад

Multiple degrees of rotation will always work best. Yes it's harder to do, but will always end more accurate. Think about a large 150mm end milling head. As it comes around, each bit takes a bite, and the lowest bit will always leave the deepest groove right.. Now, if you slowly moved the milling head back and forth while it spins, that lowest bit, will cut the same "groove" completely everywhere thus making it flat. It's the same process but you're the milling machine, and the bit is either a, b, or c in the manual reference, and instead of it spinning, you apply linear motion, but rotate slowly and over and over and over, you cut down all the "hills" until they MATCH they valleys. Although, like you said, it depends on how accurate you need it to be.

@AccidentalScience Год назад

Sure, more angular rotations is better. With the specific case I had, because the surface ratio is so wide at the point it resembles a kinda rule, even small angular rotations was enough to achieve a very acceptable result. Thanks for commenting. Greetings.

@muratbasarir6046 2 года назад

Really good idea brother. I will do it.especially window glass is very effective for this method.I have seen a German mechanic man while use glass

@rameezsheikh7576 3 года назад

I was really waiting for your video 🙂

@ashanavbhattacharyya3517 3 года назад

I think it is better to rotate and look for flatness in more angular orientations between 0 and 180 because there might be surface irregularity profiles which are symmetrical about the parallel axis to the plane of rotation and hence not being picked up by the dye.Should lead to higher accuracy.pls let me know your thoughts guys!

@mubafaw Год назад

Great explanation and illustration

@VitaliyTym Год назад

It is interesting how were made first machine tools when there were no machine tools

@AccidentalScience Год назад

Yep!

@VitaliyTym Год назад

@@AccidentalScience Can you make a theory video about how to make a cube and a cylinder using three plates method?

@AccidentalScience Год назад

@@VitaliyTym I'd love to but It goes beyond my current knowledge, but it is an interesting topic ... maybe one day .

@VitaliyTym Год назад

In this video is shown how to make an angle plates using 3 plates method

@VitaliyTym Год назад

This is a video about making screws without machine tools

@wiradharma7030 3 месяца назад

So, my idea to use two orbital sander where two plates attached together to the sander might be plausible.🤔

@Rover109able 3 года назад

Good informative Vid! the three plate method worked for Whitworth He made some really marvelous Machines!?

@AccidentalScience 3 года назад

Thanks. Whitworth was great in making fine equipments and parts but more importantly, standards recognizing the importance of replaceable (spare) parts. For a real genius of mechanics one should look at Vaucansone (not sure I've written his mame correctly) who made the first precision metal lathe (among many other things). You can see its beautiful machines at the Musee des Arts et Metiers in Paris, FR.

@MrLuigge 2 года назад

I have to say, I just searched on the RU-vid, how people created flatness on first place, and your video shows one method and I can kinda have an idea how must people have done on the past. I would say since is 3d, instead of rubbing back and forth, it would be better to spin, so it tries to flatten all the sides but in any case it depends of the thickness and shape of the object

@fitito500 Год назад

I never thought wicus van der merwe from district 9 have a channel in yt...😁 Naahh 👍 so great material and the way what you explained everything 👍 just great A new subcriptor from Argentina bs as. My like👍

@AccidentalScience Год назад

LOL

@trackie1957 2 года назад

Fascinating!

@TheWizardGamez 3 года назад

cant wait until I can use this

@MrInnovativeEnergy 6 месяцев назад

It appears logical that the more plates you add to the equation, the less errors, or rather the average surface becomes smoother because we are averaging across more variation. Is this logical to assume?

@AccidentalScience 6 месяцев назад

Interesting point. Intuitively I think that adding more plates would certainly add costs/labor with no significant improvements and on the contrary would increase uncertainty, in particular with an even number of plates. Intuitively, no proof here. Cheers.

@albertofabbri4010 6 месяцев назад

great video!!! compliments!

@ace0918 Год назад

I use the same method, ared18t uses, for all my sharpening stones.

@jaygremillion3501 7 месяцев назад

Great explanation of this thank you

@AccidentalScience 7 месяцев назад

Thank you. Happy new year!

@kokeskokeskokes 12 дней назад

Renzetti was scraping diagonally.

@jimf2525 3 месяца назад

Very nice video, but I have to disagree with you on your shift/offset method. The same curvature could exist with each shift.

@richharr 3 года назад

Fantastic video.

@NovemberBegin Год назад

I have never felt more European watching this

@broughttoideas 2 года назад

Really good video surprised theres not more view my father told me about the beginnings of a flat surface but he was drunk

@cravenmoorehead5636 2 года назад

Sometimes when us dads are drinking is when our children should listen. Because a tool maker is easier to open up with a little alcohol. Not sure why but we just do.

@piotrlenarczyk5803 3 года назад

Thank you for video.

@freightshayker Год назад

Good stuff

@jamcdonald120 3 года назад

So how do you make a plate with 2 parallel flat surfaces?

@JohnDoe-rx3vn 2 года назад

If you use the three plate method, you can span two plates across one, so the edges grind each other. Then you'd have a perfect right angle out of nothing, and you could somehow use that to make a parallel surface lol

@jamcdonald120 3 года назад

13:30 you need to be able to rotate, but the angle doesnt have to be exactly 90

@luxmandesilva9919 2 года назад

Hi, I need a very flat surface to be established while I make a gel in a tray. The gel is poured into a tray. How can I keep the tray precision flat while gelling occurs which takes about an hour. After the gelling process is complete the product is dried by evaporating water. If the surface is not absolutely flat the resulting dry film is not flat enough and all the time was wasted as the film cant be used for it's intended purpopse. Any ideas on how to keepa surfacce about 0.5m by 1m size very precision falt?

@AccidentalScience 2 года назад

Try to give a look at the process used to spread resist on semiconductor wafers.

@IslandHermit 3 года назад

The plates don't have to be square but they should be symmetric under some angle of rotation less than 180 degrees. So the plates could be triangular, hexagonal, etc. Or they could be circular.

@wibblywobblyidiotvision 3 года назад

There's nothing magical about 180°, or 90°. For any fixed angle symmetry, there's a corresponding saddle shape that can fit 3 plates, along with "flat".

@billyjoelization Год назад

Am I wrong in assuming that you just rotate each bar 180 degrees every time and you will be able to reach flatness? Like A-B, A-C, B-C rot, A-C rot, B-A rot, and so forth. It makes total sense in my head, but maybe the guru's will think it's stupid.

@AccidentalScience Год назад

Indeed I did that. But rotating by 90 deg would be even better. However because this is a bar, simply shifting the bar by let's say 10%, the same randomization effect is achieved. Also, if memory serves me well, rotation by 180 deg was what Whitworth said in his original paper.

@BBWinner48 Год назад

hey there, great videos, I've been searching for weeks looking for " How was the 1st lathe bed was created/ invented" im talking about the parallel surfaces on which the saddle slides back and forth , How as it created ?

@AccidentalScience Год назад

I have some rough ideas but I don't know for certain. It's a kind of question that I made myself, and it is the reason why I endeavored to make a lathe from scratch. If I will be able to gather more detailed information I will make a video on it. Thanks for sharing your thought. Cheers from the Alps.

@peteabc1 3 года назад

I'm too not an expert, but I noticed that besides surface plate you can buy 10mm thick steel ruler (search for smt like DIN ruler). But it's not cheap either, starts ak 90eur.

@TheOneAndOnlySame Месяц назад

2:45 3 spacial dimensions. That's it.

@billshiff2060 5 месяцев назад

Whitworth settled on a hexagon shaped surface plate so it can be rotated 60 degrees and eliminate the waves satisfactorily.

@AccidentalScience 4 месяца назад

I read his whole paper and I don't remember he mentioned any kind of hexagon shaped surface. But I agree, the hexagon is the bestagon, after all :)

@billshiff2060 4 месяца назад

@@AccidentalScience From the book "The Whitworth measuring machine" 1877 page 7 "Sir Joseph Whitworth has lately patented an hexagonal surface plate with the view of preventing irregular straining the points of attachment" - With illustrations. from page 8: "Surface plates on the principle now referred to are found to possess so many advantages over the old rectangular plates that Sir Joseph Whitworth has adopted them throughout his workshops, and has ceased to use any others" Also in an oil portrait of him by Kennington he is depicted with a pair of them. Of course He did make other shapes too. You can get that book free online, its worth reading.

@AccidentalScience 4 месяца назад

@@billshiff2060 great thanks for the information. I was thinking about his original paper, I missed that you said he "settled", sorry for the mistake.

@billshiff2060 4 месяца назад

@@AccidentalScience No problem. It gave me a chance to talk about his work which I admire. Even though he couldn't get along with anyone he achieved great things. His mentor Henry Maudslay on the other hand was much loved by all and became the father of machine tools but more memorable as a builder of men, including Whitworth and a legion of others. Every time I research any subject I find Maudslay somewhere in the back story.

@sarbojitmukherjee4430 3 года назад

Dear sir your videos are inspiring. I was wondering if we students can make linear stage that can move with sub micron level precision. We have a 3d printer that can print in PLA . Is it possible to make linear stage that can move with nanometer precision. ? I would be highly obliged if you can take up this project for future video. Thankyou

@AccidentalScience 3 года назад

Well I have not such experience. I don't know how easy would be for students. Remember I am not a mechanical engineer, my field of expertise is in electronics, firmware and automation (automatic machines, robots, etc.), but based upon my limited experience working at micron level is hard by its own. For start you need a controlled temperature environment, and about linear motion I would go with compliant mechanisms that, for proof of concept purporses, I think can be even 3D printed. To detect the actual motion you could use a capacitive sensor. Capacitive sensing can be quite easily designed to be highly sensitive to very small displacements, having care for a very good PCB design and component selection. Good luck. Cld.

@perspectivex 3 года назад

some food for thought: npoint.com/what-is-a-piezo-flexure-stage, ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uUluc_grPLI.html, ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-PaypcVFPs48.html

@peteabc1 3 года назад

Such precision is useless. You must realize the filament's width is varying, the machine is vibrating because of motion and thermal variations can easily do more than 10u. With submicron you're picking sound vibrations, not to say people walking around.

@sarbojitmukherjee4430 3 года назад

@@peteabc1 In optics We use something called translational stage of holmarc or thorlabs which are expensive and provide 5micron step size resolution. (More step resolution more expensive) My proposal was if we can make something with 3d printer and then do post processing like to remove imperfection using acetone bath heat treatment etc. Even achieving step resolution of the plastic device less than 5micron is an achievement. Sound and expansion due to temperature is a problem with plastic . But if by clever engineering we can achieve this then lots and lots of hobbyist will be attracted to optics . Making projects like interferometer hologram etc

@sarbojitmukherjee4430 3 года назад

@@perspectivex thankyou sir

@rocifier 2 года назад

What dye do you use? What sort of store do you buy it from?

@AccidentalScience 2 года назад

It's a simple oil based color for artists, I use the hue named phtalocyanine blue, it's a very bright and deep blue color that is highly visible even in minute quantity. It is produced by all major brands of oil based colors for artists.

@FrankieJames7 3 года назад

i am a natural english speaker and intentionally pronounce words the way they are spelled to be different. i love the accent here, you just added some words to my vocabulary. in all fairness english is a garage language

@AccidentalScience 3 года назад

English is my second language, but that "my" is really significative to me. Besides German and Italian at the elementary school, I started learning English at 12, and it was a sudden love. Thereafter while I almost completely forgot German, I attended classes (electronics, computer science, philosophy) in English. So I particularly appreciate your comment. I'm always afraided that my accent could spoils my videos making them hard to understand. Yeah, English fit well in the garage, even though German is the engineering language that could drive you mad because it has a word for EVERYTHING ! :) Cheers from the Alps.

@gamemeister27 3 года назад

@@AccidentalScience I'm not surprised. French is a gigantic part of English. The basic structure is Germanic, but so much of the vocabulary is french

@IGBasov 3 года назад

Thanx!

@peteabc1 3 года назад

Sir, one thing if I may ask - which type of steel have you used for the lathe spindle and were you hardening it in any way?

@AccidentalScience 3 года назад

C40/45 (do not remember exactly what of the two), no hardening. While hardening would have been good, it would have required a further (very expensive) process of precision grinding. Because this is kind of a prototype I preferred to keep it simpler.

@peteabc1 3 года назад

@@AccidentalScience Yes, that hardening seems to be a larger problem. I'm actually thinking about trying to grind a bar between centers in some kind of fixture, using a normal bench top grinder. Just so I can slide bearings on it and then later turn it. First probably just with construction steel pipe..

@AccidentalScience 3 года назад

@@peteabc1 well, what's the purpose of hardening? If I read NSK or SKF manuals they say hardening shafts is required only where seal rings come into contact. Ground shafts are required if heavy loads or vibrations will happen in operation, but this does not refer to hardening and aims to keep a good adhesion of the ballbearing ring with the shaft/case. So after rethinking about this I conclude that hardening is not necessary. Beware, this is my personal opinion and I might be wrong.

@peteabc1 3 года назад

@@AccidentalScience Yes, probably it's not needed. Especially for home use.

@robertsteinwandel6658 3 года назад

Thanks for the follow up video!! This is going to be perfect for my lathe ways and an extra straightedge (sounds like you did the same thing hahaha) did you have any issues with the flattened surfaces being out of square with the other sides of the steel bars you used?

@AccidentalScience 3 года назад

Something but nothing too problematic. As long as there is linear consistency along the full length of the way I deemed it wouldn't cause any problem.

@robertsteinwandel6658 3 года назад

Accidental Science fair point, and Id assume it would wear slightly out of square during use anyways so I suppose it wouldn’t really matter either way

@EitriBrokkr 2 года назад

How long did the process take?

@AccidentalScience 2 года назад

Days

@silvionovais2504 3 года назад

🟢 Friend! I don't have a very thick stone (100mm). I have a lot of 20mm stones. I intend to "work" 3 large diameter stones (1000mm X 1000mm). I think 20mm is too unstable for a big rock like that. Can I glue several stones to get a more stable thickness? I chose a harder black stone in my region of Brazil. I also thought of making ribs in the shape of honeycombs between a sandwich of two 20mm stones. I'm building a universal milling machine, the stones would be to "right" the flatness of the dovetail guides and the coordinate table. I don't understand spoken English, and youtube has a bad translation.

@AccidentalScience 3 года назад

Well, I think you can glue the stones with some epoxy to give more stability, and then make them flat. It is a very hard work though. Good luck.