Forrest Addy
Diamond
- Joined
- Dec 20, 2000
- Location
- Bremerton WA USA
This is the strategic method for generating flat surfaces via the three plate method I wrote in the comments of Robin Renzetti's YouTube video :"Attention to Detail 1" (1/23/18). It's my rendering of "Production of Surfaces by Averaging of Errors" drawn from Charles Porter's autobiography: “Engineering Reminiscences” Chapter 22. The virtue of this method is it requires no external references. It's recognized by NIST and other world standards organizations as an intrinsic method for generating flat surfaces to any desired tolerance.
There's a misconception that the so-called "three plate method" involves working three plates together in strict rotation and somehow a flat surface is produced. The method works in practice but is wastefully laborious if pursued to the bitter end.
The following presumes competence in basic precision scraping, some experience in scraping surfaces to conform to references, and cast iron surface plates of roughly equal size and aspect ratio no greater than 3:2 of a design ensuring rigidity and stability.
This is a more direct and economical way to produce reference flats by scraping three plates together. It employs a strategic method developed by Whitworth and disciples as a series of separate steps performed collectively called "equaling and averaging:"
Many of you have browsed https://circuitousroot.com/artifice/machine-shop/surface-finishing/hand-scraping/index.html wheret he original papers written by Whitworth et al describe their technique for generating flat surfaces. I think the best account of this process is in Chapter 22 of Charles Porter's "Engineering Reminiscences" where the equaling and averaging stages are defined and their roles explained.
Production of [Flat] Surfaces by Averaging of Errors:.
Number the plates 1, 2,and 3. Scrape 1 to 2 and 2 to 1 alternately rotating by random amounts to avoid lobing. The object is to generate a very large but unknown spherical radius - concave on one plate and convex on the other while pursuing a 4 spots per square inch print. Plate 3 is idle during this process which is preliminary to the equaling and averaging mentioned earlier.
Note: When generating flat surfaces, you need to rotate the work on the reference by random angles. If you rotate equal amounts on a center point it's possible to generate a "ruffle," a surface of radial symmetry that when accurately meshed will print perfectly. If the rotation is randomized the ruffle can never develop and the desired large radius spherical surface may be cleanly developed.
Once plates 1 and 2 print consistently the surfaces are checked with a straight edge (a perfect straight edge is not required. Merely one from which the concave surface may be distinguished from the convex.) and identified as such. Let's assume 1 in our example is convex and 2 concave.
Next is the first equaling step.Using 1 as a reference, scrape 3 to be the concave equal of 2. Plates 2 and 3 are now concave and of equal concave radius.
The first averaging step is where plates 2 and 3 are "averaged." Using 2 as a reference scrape 3 to it for five scraping cuts. Clean 2 of pigment. Using 3 as a reference, scrape 3 to 2 for five scraping cuts. The object is to reduce the chordal height of the spherical radius by fairly precise increments. Five cuts per increment is the number I use here but any small number will do for successive equaling alternations. Continue, alternating one plate then the other as reference until both 2 and 3 plates print over the full surface. Refine the print, alternately rotating and sliding so both surfaces print. The two plates are now averaged and may be quite close to flat but not proven.
Second equaling, first phase: set aside 3 or 2 and using the other as a reference,scrape 1 to fully print. Note: since 1 starts convex, it's best to scrape out the center for a few blind cuts to ensure against rolling contact errors. The equaled plates are not scraped in this first phase.
Second equaling, second phase: using 1 as a reference, scrape 2 and 3 to equal each other. By now the surfaces should be very close to flat. Scrape 2 and 3 carefully to ensure good prints. 2 and 3 are now equaled.
Second averaging: using 2 or 3 as a reference, print the other. Note if the print indicates concavity or convexity and take suitable precautions when averaging as before. This time take three scraping cuts per alternation. When both plates are perfectly averaged, perform a second two phase equaling cycle.
Continue equaling and averaging until the desired flatness is attained and all three plates print interchangeably to the desired spot count and density. I've personally found when using Prussian blue as a transfer medium and red lead as a contrast medium, the practical limit of flatness error detection is about 40 millionths.
If you desire finer resolution, your best bet is to resort to pinpoint technique where the work is hazed by some means and then rubbed to the reference. The indications show as pinpoints of high gloss seen from a shallow angle to the surface in grazing light. These may be picked off by individual strokes of the scraper. If the previous scraping is up to snuff, ten or twenty cuts of pinpointing can develop accuracies of small millionths. However this is painstaking, exhausting work very hard on the eyes and back suited only for trophy projects and the most demanding precision gaging applications - reference squares for example. Fully pinpointing a 18" x 24" cast iron surface plate can add $1K or more to the cost of scraping and calibration if charged at shop rates prevailing in 2017. It should be pointed out that and the additional accuracy has the same service life in general use to re-calibration as a lesser degree of refinement.
The equaling and averaging method method while laborious and painstaking is quite efficient compared to three plates scraped or lapped in strict rotation, requiring perhaps 1/3 the effort and time.. Acceptable flatness of three surface plates may be generated in few as two equaling and averaging cycles provided they were pretty close to begin with and you were meticulous in incrementing your alternating cuts in the equaling steps.
I've never found it particularly difficult to scrape rectangular plates together provided I could cook up some way to relieve the overhanging weight. I've used springs, counterweight, tool balancers, a little muscle, etc and gotten consistent results. There's practical limits, of course, but with suitable precautions considerable disparity may be overcome.
I'd appreciate critique and informed discussion
There's a misconception that the so-called "three plate method" involves working three plates together in strict rotation and somehow a flat surface is produced. The method works in practice but is wastefully laborious if pursued to the bitter end.
The following presumes competence in basic precision scraping, some experience in scraping surfaces to conform to references, and cast iron surface plates of roughly equal size and aspect ratio no greater than 3:2 of a design ensuring rigidity and stability.
This is a more direct and economical way to produce reference flats by scraping three plates together. It employs a strategic method developed by Whitworth and disciples as a series of separate steps performed collectively called "equaling and averaging:"
Many of you have browsed https://circuitousroot.com/artifice/machine-shop/surface-finishing/hand-scraping/index.html wheret he original papers written by Whitworth et al describe their technique for generating flat surfaces. I think the best account of this process is in Chapter 22 of Charles Porter's "Engineering Reminiscences" where the equaling and averaging stages are defined and their roles explained.
Production of [Flat] Surfaces by Averaging of Errors:.
Number the plates 1, 2,and 3. Scrape 1 to 2 and 2 to 1 alternately rotating by random amounts to avoid lobing. The object is to generate a very large but unknown spherical radius - concave on one plate and convex on the other while pursuing a 4 spots per square inch print. Plate 3 is idle during this process which is preliminary to the equaling and averaging mentioned earlier.
Note: When generating flat surfaces, you need to rotate the work on the reference by random angles. If you rotate equal amounts on a center point it's possible to generate a "ruffle," a surface of radial symmetry that when accurately meshed will print perfectly. If the rotation is randomized the ruffle can never develop and the desired large radius spherical surface may be cleanly developed.
Once plates 1 and 2 print consistently the surfaces are checked with a straight edge (a perfect straight edge is not required. Merely one from which the concave surface may be distinguished from the convex.) and identified as such. Let's assume 1 in our example is convex and 2 concave.
Next is the first equaling step.Using 1 as a reference, scrape 3 to be the concave equal of 2. Plates 2 and 3 are now concave and of equal concave radius.
The first averaging step is where plates 2 and 3 are "averaged." Using 2 as a reference scrape 3 to it for five scraping cuts. Clean 2 of pigment. Using 3 as a reference, scrape 3 to 2 for five scraping cuts. The object is to reduce the chordal height of the spherical radius by fairly precise increments. Five cuts per increment is the number I use here but any small number will do for successive equaling alternations. Continue, alternating one plate then the other as reference until both 2 and 3 plates print over the full surface. Refine the print, alternately rotating and sliding so both surfaces print. The two plates are now averaged and may be quite close to flat but not proven.
Second equaling, first phase: set aside 3 or 2 and using the other as a reference,scrape 1 to fully print. Note: since 1 starts convex, it's best to scrape out the center for a few blind cuts to ensure against rolling contact errors. The equaled plates are not scraped in this first phase.
Second equaling, second phase: using 1 as a reference, scrape 2 and 3 to equal each other. By now the surfaces should be very close to flat. Scrape 2 and 3 carefully to ensure good prints. 2 and 3 are now equaled.
Second averaging: using 2 or 3 as a reference, print the other. Note if the print indicates concavity or convexity and take suitable precautions when averaging as before. This time take three scraping cuts per alternation. When both plates are perfectly averaged, perform a second two phase equaling cycle.
Continue equaling and averaging until the desired flatness is attained and all three plates print interchangeably to the desired spot count and density. I've personally found when using Prussian blue as a transfer medium and red lead as a contrast medium, the practical limit of flatness error detection is about 40 millionths.
If you desire finer resolution, your best bet is to resort to pinpoint technique where the work is hazed by some means and then rubbed to the reference. The indications show as pinpoints of high gloss seen from a shallow angle to the surface in grazing light. These may be picked off by individual strokes of the scraper. If the previous scraping is up to snuff, ten or twenty cuts of pinpointing can develop accuracies of small millionths. However this is painstaking, exhausting work very hard on the eyes and back suited only for trophy projects and the most demanding precision gaging applications - reference squares for example. Fully pinpointing a 18" x 24" cast iron surface plate can add $1K or more to the cost of scraping and calibration if charged at shop rates prevailing in 2017. It should be pointed out that and the additional accuracy has the same service life in general use to re-calibration as a lesser degree of refinement.
The equaling and averaging method method while laborious and painstaking is quite efficient compared to three plates scraped or lapped in strict rotation, requiring perhaps 1/3 the effort and time.. Acceptable flatness of three surface plates may be generated in few as two equaling and averaging cycles provided they were pretty close to begin with and you were meticulous in incrementing your alternating cuts in the equaling steps.
I've never found it particularly difficult to scrape rectangular plates together provided I could cook up some way to relieve the overhanging weight. I've used springs, counterweight, tool balancers, a little muscle, etc and gotten consistent results. There's practical limits, of course, but with suitable precautions considerable disparity may be overcome.
I'd appreciate critique and informed discussion
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