Lightweight Surface Plate Cover

[mklotz]

For minimum deflection, the plate should be supported at the Airy points. These are two points spaced a distance apart that is the length of the plate divided by the square root of 3.

1 / sqrt(3) = 0.5773

1 - 0.5773 = 0.4226

0.4226 / 2 = 0.2113

so in from the edge by 21.13% of the length from the ends.

Given that we're talking about microinches of deflection, this proves that Starrett's rule of thumb is right on the money. Nevertheless, if the manufacturer indicates the support points used for finishing, those are clearly the ones to use.

[PJs]

Thank you Paul and Marv for the 3 point leveling info. I hadn't thought about it other than leveling the stand (4pt) when I got mine. Mine is a Grizzly "B" grade but the inspection map/sheet showed it to be closer to .5 tenths OA, plus a free shipping sale. I mainly got this size so I could do the metrology on my 14" bed work on my mini. I used a Craftsman 18x24 tool stand good for 300lbs and added 1/2 Ply to the top and shelf for rigidity and left every thing loose and kept it as square as possible with my meager tools upon tightening. Also added a tool drawer liner to the top for friction and dampening...probably not as good of idea now but does keep the Spar Varnished ply from contacting the granite directly. I replaced the cheesy screws with 1/4-20 BHCS (Button Head Cap Screws) and Nylock nuts. However the leveling feet are cheesy at best and have wanted to replace them with FootMaster adjustable casters but are rather pricey. I borrowed a 6" Starrett level to set it where it is now...but it's not on concrete...so who's nose now? This 3pt system might be much better and easier in the long run but would consider some angle or a hat section to the bottom of the ply for rigidity.

Marv, I'm a bit confused about your numbers although I mostly understand Airy Points from my Drill Machine build and the catanary effects with 20' lengths of tubing and a 35' frame. Are these derived from a circle from the center of the granite? Also how is the 3rd point derived...on the same circle but at a quadrant (mid width)? I am also curious if it is better to use a small cylindrical contact or a cone point (which may damage the granite).

Thanks again for the good ideas and learning in this thread! HMT at its best, imho. ~PJ

[mklotz]

Marv, I'm a bit confused about your numbers although I mostly understand Airy Points from my Drill Machine build and the catanary effects with 20' lengths of tubing and a 35' frame. Are these derived from a circle from the center of the granite? Also how is the 3rd point derived...on the same circle but at a quadrant (mid width)? I am also curious if it is better to use a small cylindrical contact or a cone point (which may damage the granite).

Let me describe it another way. Imagine a stick whose length is the length of the surface plate divided by the square root of three. Lay this on the plate such that there is an equal gap between the end of the stick and the edge of the plate at each end of the stick. Mark lines across the short dimension of the plate at each end of this imaginary stick. These lines define the Airy lines for the plate. If you supported the plate with bars laid along these lines, it would have the minimum deflection at the midpoint.

The arithmetic in my post shows that those lines would lie a distance from the edges that is 21% of the length of the plate.

A three point Airy suspension would put two points on one of these lines, spaced equal distances from the long edge of the plate and a third point in the middle of the other line.

I wouldn't use a conical point. An elephant foot to spread the load so the granite isn't damaged makes more sense.

My feeling is that, for the typical Enco/Grizzly plate, worrying about suspension points is mostly nonsense. These small plates aren't that flat and, being short, they are stiff so bending isn't really an issue for any work done in the typical hobbyist venue. Leveling the plate isn't really an issue either unless you intend to use a level to do some of your layout; I don't so for me the major concern is flatness and that's more a production concern than a support concern.

[C-Bag]

Once again it seems as the thread leaves the rails numerous details come into perspective.

I was wondering why surface plate stands are so expensive, more than just your usual equipment stand. When I went back and looked at it again the description I'd not bothered to read closely, says it supports the plate in three places. And now I have the rest of the story. I guess the 18x24 plate w/stand for $65 from a local shop was a better deal than I knew!

Thanks Paul and Marv for another detail I'd missed.

[mklotz]

In the tiny, overcrowded Garaj Mahal my surface plate gets moved around a lot so, rather than just a cover, I made a box for it out of 1/2" pine with sturdy handles bolted to it so a firm two-handed grip for moving is possible. The sides of the box only come up to about 1/3 the height of the plate. This so, once the top of the box is removed, the edges of the plate are accessible for use as references or clamping surfaces and height gage bases, etc., can overhang the edge. The latter is an important feature on these small plates.

The top is roughly a copy of the bottom, grossly overbuilt with 1/2" pine. I live in earthquake country so my greatest fear is that a temblor will dislodge one of the many tools hung from the joists and have it fall on the plate. The thick pine will protect the plate from that. Naturally stuff gets placed on the plate when it's not in use. With that thick top I don't have to worry about what gets plunked down on it.

Our club toured a shop here in LA that manufactures giant granite references (plates, angles, tombstones, beams) for the aerospace industry. We learned a lot but one of the most surprising things was the fact that they recommend orange hand cleaner for cleaning the plates. Apparently it leaves behind a lanolin-like coating that enables gages to slide easily and not scratch the surface.

[PJs]

Let me describe it another way. Imagine a stick whose length is the length of the surface plate divided by the square root of three. Lay this on the plate such that there is an equal gap between the end of the stick and the edge of the plate at each end of the stick. Mark lines across the short dimension of the plate at each end of this imaginary stick. These lines define the Airy lines for the plate. If you supported the plate with bars laid along these lines, it would have the minimum deflection at the midpoint.

The arithmetic in my post shows that those lines would lie a distance from the edges that is 21% of the length of the plate.

A three point Airy suspension would put two points on one of these lines, spaced equal distances from the long edge of the plate and a third point in the middle of the other line.

I wouldn't use a conical point. An elephant foot to spread the load so the granite isn't damaged makes more sense.

My feeling is that, for the typical Enco/Grizzly plate, worrying about suspension points is mostly nonsense. These small plates aren't that flat and, being short, they are stiff so bending isn't really an issue for any work done in the typical hobbyist venue. Leveling the plate isn't really an issue either unless you intend to use a level to do some of your layout; I don't so for me the major concern is flatness and that's more a production concern than a support concern.

Thanks Marv and do agree that these smaller blocks for "Hobbyist" probably don't warrant 3 point system but I do like the idea of it. I made a drawing to hopefully help others should they decide to pursue this, but mainly to log it into my descriptive math dense noggin this morning. Hopefully I interpreted your description properly? I still don't get where the SQRT of 3 came from...probably because I didn't have my Wheaties today.

[mklotz]

That looks good to me. I've never seen a standard for how far in from the long edge the pair of holes are placed but your choice seems logical. The square root of three comes from the equation for the Airy distance. A fuller explanation is here...

https://en.wikipedia.org/wiki/Airy_points

Note that there is an equation for n equally spaced support points...

c = (n^2 -1) ^ (-1/2)

which, for n = 2, yields the sqrt(3) relation.

A slight misunderstanding. I think worrying about suspension deflection for hobbyist plates is unwarranted. Three point support is another matter. If you want to use levels to do layout or just don't want stuff rolling off the plate, leveling is certainly justified.

[Paul Jones]

Thanks Marv and PJs,

I occasionally use levels for some of my layout work because that is the way I learned some of the techniques back in the 1960's by reading tool-making books from the 1930's and 1940's. I also check my larger lathe for being level with a master level. Calibrating the master level is so much easier when the surface plate is very close to level. I still have to use a heavy right angle plate as the reference line to find the true level position when turning the master level 180 degrees to adjust the level to exactly zero degrees. Rotating the master level end-to-end 180 is used to self verify the level is truly reading zero degrees. The master levels with sensitivities of 0.0005"/10" seem to settle the bubble faster when the direction of the angle plate is perfectly level on the surface plate.

Interesting tip about using orange hand cleaner for cleaning the plates. I wonder if the orange oil based degreasers would be acceptable? Do avoid using acetone or alcohol as a cleaner because it spot chills the surface plate and can distort areas of the surface plate by a few 0.0001" for several minutes until the surface temperature across the plate becomes constant again.

Regards,
Paul

[PJs]

Thanks for checking my drawing Marv. The reason I did it that way was it just made sense. The Airy Points are for Uniform Beams in particular and originally for standards preservation, but the plane of a surface plate accounts for 2 axis so I just did it in both directions. Interestingly after doing a bit of rabbit holing I found the Fed specs for surface plates and all the manufacturers I found adhered to the spec.

Here is a link to the GGG-P-463c Federal spec. Here it is interesting to note that the Airy points in my drawing fit into the federal standard, closer to the 1/5 distance values. The other nice thing about the standard is on Pg. 5 they give the spec for circular plate support as .7 the OD and 3 "equally spaced points" (assuming an equilateral triangle). Additionally 3.2.3 (pg.4) of the spec covers the Thickness and Stiffness to a 50lb/sqft, centered with a half flatness tolerance deflection. Even with my 14" bed and measuring tools I doubt I have even approached that value.

Additionally I found the Physical Properties of Granite from the Precision Granite USA. From these one could see how much flexure would occur with a particular block and based on the Modulus of elasticity for both directions one could quickly asses that it would be a very small order of magnitude for the 3" slab of 18x24 dimensions. Definitely not worth digging out the Marks manual to run the numbers as you indicated, and especially on a B grade plate in my shop.

Thank You Paul for the info on calibrating a master level on a surface plate. I watched Pierre's Garage (Baudrie?) YT video tutorial a while back on it and found it to be an enlightening process. I always admire your precision approach to projects including this simple idea of a surface plate cover with craftsmanship and precision.

Hopefully I haven't hijacked your thread beyond recognition but the info here lit my Metrology candle and will hopefully provide others with some basic information toward the work they do. Marv bringing up the Airy Points is applicable to lots of things we do in our home shops and brings up those physical properties of materials in the world we live and operate in. I've been interested in metrology since I used an Old Optical comparator back in the day up until I used a very large (48" x 6"slab) CMM (Computer Measuring Machine) in 2001 to measure some of the output off of my drill machines.

Thanks as always for another great thread here on HMT's! ~PJ

[thehomeengineer]

Hi Paul
It looks great. That great I would not want to place anything on top of it in fear of marking the protective cover.
One of those jobs I must get around to do (one day). Thank you for sharing.
The Home Engineer