Author Topic: Checking a 45 degree square?  (Read 18568 times)

Offline loply

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Checking a 45 degree square?
« on: May 26, 2015, 08:31:19 AM »
Hi folks,

Some time ago I made myself a whole set of precision references for scraping/inspecting etc, including a very accurate master square.

I want to make a 45 degree reference from a slab of cast iron I have but I'm struggling to think of a way of checking it. I can think of a way of doing it if I make two or three, but that's 2x or 3x the work!

Anybody know an ingenious way to test for 45 degrees without a known standard to compare to, and without making 2x of them?

Cheers,
Rich

Offline loply

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Re: Checking a 45 degree square?
« Reply #1 on: May 26, 2015, 08:31:58 AM »
I have a high precision level too, but no sine bar or sine plate.

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #2 on: May 26, 2015, 09:25:28 AM »
Two 45's make a right angle, four make- a straight line whilst 8 get you back to where you started.

source Euclid.


Offline Arbalist

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Re: Checking a 45 degree square?
« Reply #3 on: May 26, 2015, 10:19:08 AM »
Yes, bit tricky. Easy to make one but not so easy to check!  :scratch: the only thing I can think of is to place it on a flat and scribe the outline, then flip and scribe it three times and see if it meets the starting point! If there's a gap it's under 45° and if it goes over the line it's over 45°...

Here's how I make mine.



« Last Edit: May 26, 2015, 12:58:53 PM by Arbalist »

Offline Lew_Merrick_PE

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Re: Checking a 45 degree square?
« Reply #4 on: May 26, 2015, 10:32:43 AM »
Rich,

One of the tricks I use with great regularity is to drill and ream a set of dowel pin holes in a piece of (say) 1/4 X 6 inch material (usually either aluminum or steel).  My Trav-a-Dials (the forerunner of DRO's) allow me to do so ±.0005 inch, so my result will be quite accurate.  I then press in dowel pins and mill off the "outside" and end up with an angle plate of whatever (angular) size I need.

Thus, for a 45° plate, I would ream my holes at: (.375,.375), (5.250,0), & (5.250,5.250) from the corner of a 6 inch square piece.  I then insert (call it ø1/4 inch) dowel pins two at a time and mill my (call it .350 inch) offset edge around the periphery.  If I have done this as accurately as my machine is capable, then my resulting angle will be ±.0104° (0°0"2').  Would that be close enough for your purposes?

I usually make them in pairs.  The angle gets steel stamped on the "face" of the plate.    And they end up "living" in boxes where they can be found and reused.

Offline vtsteam

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Re: Checking a 45 degree square?
« Reply #5 on: May 26, 2015, 12:12:46 PM »
Rich, along the lines of Fergus' suggestion, lay a straightedge on a metal plate and clamp it down. Lay a square on the plate butting on the straightedge.

Lay your new (but reasonably close) angle casting on the plate with its vertex at the square and straightedge juncture, and one edge along the straightedge. Scribe the other casting edge on the plate. Also mark the outer end point.

Flip over and shift the casting so it contacts the square's edge, and again shares a vertex with the two standards. Scribe a second line on the plate. Again mark the outer end point. (Since you flipped it, that should be the same distance out.)

If the two lines correspond, you're at 45 degrees.

If not, measure half the distance between the two endpoints, draw a line between the two, mark the point, and scribe a line from there to the vertex. That will be at true 45 degrees.

Clamp a second straightedge to the 45 degree line and scrape your casting to either straightedge as a reference surface, bearing against the other.
I love it when a Plan B comes together!
Steve
https://www.youtube.com/watch?v=4sDubB0-REg

Offline Pete.

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Re: Checking a 45 degree square?
« Reply #6 on: May 26, 2015, 01:47:24 PM »
Why exactly? Scraping references are usually less of an angle than the dovetail, and many (probably the greater proportion) are not 45 degrees.

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #7 on: May 26, 2015, 02:56:08 PM »
All of this appeared in several references by Philf only in March this year.

Why the repetition at such a short interval, please?

Thank you Phil. I did read- well most of it. :scratch:

Norman

Offline Arbalist

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Re: Checking a 45 degree square?
« Reply #8 on: May 26, 2015, 03:04:44 PM »
Who's Philf?  :scratch:

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #9 on: May 26, 2015, 03:42:37 PM »
Philf?  Isn't he a Hero Member here with 500 odd posts


Offline philf

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Re: Checking a 45 degree square?
« Reply #10 on: May 26, 2015, 04:11:38 PM »
Who's Philf?  :scratch:

I'm philf but I don't remember anything about 45 degree squares!

Phil.
Phil Fern
Location: Marple, Cheshire

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #11 on: May 26, 2015, 05:06:28 PM »
Correct me if I'm wrong but you listed the various books on machine tool restoration and measurement- one of which was Edward Connelly's treatise.
In Connelly, the details of the creation of 30, 45, 60 degree references were included using the 3 plate system which refers to both flat and angled work.

I recall fairly clearly what advice was there and used it many years ago.

I hope that this throws light on the matter

Regards

Norman

Offline philf

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Re: Checking a 45 degree square?
« Reply #12 on: May 26, 2015, 05:09:10 PM »
Correct me if I'm wrong but you listed the various books on machine tool restoration and measurement- one of which was Edward Connelly's treatise.
In Connelly, the details of the creation of 30, 45, 60 degree references were included using the 3 plate system which refers to both flat and angled work.

I recall fairly clearly what advice was there and used it many years ago.

I hope that this throws light on the matter

Regards

Norman

Hi Norman,

Ah - now I understand - sorry.

Phil.
Phil Fern
Location: Marple, Cheshire

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #13 on: May 26, 2015, 05:35:14 PM »
Phil,
       Amongst other things, I had to train my memory. Used something called Pelmanism and for my maths, I used Trachtenberg which was developed in a concentration camp- to keep the poor bloke sane.

As the years go galloping past, I'm glad- I think?

My regards- thank you for your most valuable contributions here.

Norman

Offline vtsteam

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Re: Checking a 45 degree square?
« Reply #14 on: May 26, 2015, 06:47:39 PM »
Rich, your question is perfectly reasonable. It produced several interesting results. Glad you asked it. :beer:
I love it when a Plan B comes together!
Steve
https://www.youtube.com/watch?v=4sDubB0-REg

Offline loply

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Re: Checking a 45 degree square?
« Reply #15 on: May 26, 2015, 07:52:53 PM »
Hi guys,

Thanks for the replies.

In truth I don't have that much use for an incredibly accurate 45 degree square, but precision scraping has become something of a joy to me. I made by 12" master square which appears, as far as I can measure, to be within a few microns of 90 degrees 12 inches high, and I'd love a similarly accurate 45 just to complete the set. Within 10 microns would be nice and if I can get it within 5 I'd be chuffed for the rest of my days :D That kind of rules out any methods involving scribing though.

I'm aware that two 45s should make 90 which can be verified on a surface plate with an indicator easily but you'd need to make 3 to ensure you don't have a 44 and a 46... My next best idea is that I'd have to make a sine bar and set it at 45, then lay the 45 degree square in top and it should be flat... but then the accuracy is limited by the sine bar and the accuracy of all the gauges you used to prop it up. Maybe that's the best we can do though?

I like the idea about using the mill to drill holes in a triangle though. I feel like the general concept may have some mileage.

Will let you know how I get on,

Rich

Offline vtsteam

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Re: Checking a 45 degree square?
« Reply #16 on: May 26, 2015, 08:10:03 PM »
Rich, there's a little confusion between distance and angle here.

Do you mean you want a 10 micron tolerance at the end of the new tool's leg, measured from a straightedge set at an absolute 45 degree angle to a baseline?

If so, and you give the length of the leg, the angular tolerance you want can be calculated.

You will obviously need some standard (no matter what method constructed) that is true to that angular tolerance.

Scribing can be extremely accurate if it is checked afterwards by reversal as mentioned earlier. If it isn't true after checking, whatever distance makes up the error can be halved and re-scribed, and then checked again. You can keep doing this until you are at the tolerance of a scribed line's thickness -- which at whatever distance out the leg extends is a tight angular tolerance indeed.

To get the last bit of tolerance possible, placing a straightedge on the scribed line, checking the workpiece against horizontal baseline straightedge. Layi another straightedge against the first angled straightedge and removie the first. This eliminates the visual aspect, and the thickness of the scribed line, and substitutes contact (which is the means of all scraping tests). Then the piece is placed against the second straightedge and checked for contact with the vertical 90 degree block edge.

When they both match side to side, by contact, it is as close as contact can measure. Which is as close as can be scraped by conventional methods.
« Last Edit: May 26, 2015, 08:34:37 PM by vtsteam »
I love it when a Plan B comes together!
Steve
https://www.youtube.com/watch?v=4sDubB0-REg

Offline S. Heslop

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Re: Checking a 45 degree square?
« Reply #17 on: May 27, 2015, 12:26:21 AM »
If it's triangular shaped couldn't you measure the lengths of the sides, and just make sure they match and the angle between them is 90 degrees?

Offline mexican jon

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Re: Checking a 45 degree square?
« Reply #18 on: May 27, 2015, 01:04:32 AM »
I'm guessing that you can accurately check that you have 1 90 degree angle, therefore using pythagoras you can work out if the other angle you require is indeed 45 degrees.  :D :D

If it's triangular shaped couldn't you measure the lengths of the sides, and just make sure they match and the angle between them is 90 degrees?

Or you could just do what he said   :D
People say you only live once ! I say thank F@*K can't afford to do it twice.

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #19 on: May 27, 2015, 02:51:27 AM »

It's a bit early and the streets have to aired but surely Simon you have moved into describing and isosceles triangle which cannot have equal sides and 90 degrees somewhere.  If you split an isosceles triangle exactly down the middle you get back to the Euclidian solution of right angled triangles.

But enough 14 to 16 year old Matriculation antics, two practical thoughts emerge. The first is to cannibalise   a scrap machine tool to find the unworn sections and the second is to use things like Moglice, Devcon and Turcite in the construction of references.

These were not around when Connelly penned his epistle to the great unwashed.
My old mangle is running on Turcite! :bang:

Back to the coffee

Norman

Offline Bluechip

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Re: Checking a 45 degree square?
« Reply #20 on: May 27, 2015, 03:52:57 AM »

 isosceles triangle which cannot have equal sides and 90 degrees somewhere. 

Back to the coffee

Norman

??? Surely a 45o set square is just that  ......  two equal sides, ditto 45o angles and 90o at the apexy end ??

Enjoy your coffee, I'm back to fence painting ...  :bang:

Dave
I have a few modest talents. Knowing what I'm doing isn't one of them.

Offline mexican jon

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Re: Checking a 45 degree square?
« Reply #21 on: May 27, 2015, 04:49:34 AM »

 isosceles triangle which cannot have equal sides and 90 degrees somewhere. 

Back to the coffee

Norman

??? Surely a 45o set square is just that  ......  two equal sides, ditto 45o angles and 90o at the apexy end ??

Enjoy your coffee, I'm back to fence painting ...  :bang:

Dave
What is needed here is a Isosceles Triangle   :scratch: 2 equal sides and 2 equal angles  :clap: and in this case 2 45 degrees and a 90  :clap:
People say you only live once ! I say thank F@*K can't afford to do it twice.

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #22 on: May 27, 2015, 04:56:41 AM »
Yes Dave- the coffee is not strong enough! Thank you.
I can't deduct 2 x 45=90 from 180 degrees.

I hope that I have not caused 'a fence' said he 'hedging' away. Lawn and ordure,
 that's me!

I ought to go back as a manure student :loco:

 :hammer: :bow: arriba, arriba

Wor Norm

Offline awemawson

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Re: Checking a 45 degree square?
« Reply #23 on: May 27, 2015, 05:38:09 AM »
Can one not precisely check or set angles by turning (and / or grinding) precisely sized disks and abutting them? Three such disks firmly in contact with each other can have straight edges tangentially touching two disks and forming an easily calculated precise angle between them?
Andrew Mawson
East Sussex

Offline PekkaNF

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Re: Checking a 45 degree square?
« Reply #24 on: May 27, 2015, 05:45:29 AM »
If it's triangular shaped couldn't you measure the lengths of the sides, and just make sure they match and the angle between them is 90 degrees?

There are some practical considerations on how sharp you can make the edges....therefore this is not very accurate.

Can one not precisely check or set angles by turning (and / or grinding) precisely sized disks and abutting them? Three such disks firmly in contact with each other can have straight edges tangentially touching two disks and forming an easily calculated precise angle between them?

Yesh, this is old "book" method and used to check squares etc. I would take some roller bearing parts or ball bearings or such. Surely there are three of them proper sized lurking somewhere? But you need a good square or four identical bearing rings to check the square first :wave:

Pekka

Offline DMIOM

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Re: Checking a 45 degree square?
« Reply #25 on: May 27, 2015, 06:52:12 AM »
Rich,

Given you've already got an accurate 90 degree master square, I think you could make an assessment by adding just a flat base plate, 'something' with one known good straight edge, and a short length of known parallel bar - and no need for any scribing or interpretation thereof:

(i) Lightly clamp your straight edge to the plate. (ii) lay your new one against the straight edge (iii) lightly clamp the parallel against the upper edge of your new one, (iv) ease the new one out and re-lay it against the top side of the parallel, (v) compare this against your known good 90 degree master square.

Sketch below .....

Dave

Offline loply

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Re: Checking a 45 degree square?
« Reply #26 on: May 27, 2015, 08:06:33 AM »
DMIOM, I see how that would prove that the two 45s add up to 90, but you wouldn't know if you had a 44 and a 46 though? Or am I missing something?

I thought about using Pythagoras but I can't see a way to accurately measure the length of the thing, plus the slightest bit of damage to the edge of the triangle would make it hard to measure.

I'm trying to understand the method for using rings/bearings but I'm not getting it... Could someone explain? Do you mean to put two discs of different sizes side by side (like oO), having made the sizes of them such that an object laying over them would be at exactly 45 degrees? That seems like a plausible method?

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #27 on: May 27, 2015, 08:07:26 AM »
Can one not precisely check or set angles by turning (and / or grinding) precisely sized disks and abutting them? Three such disks firmly in contact with each other can have straight edges tangentially touching two disks and forming an easily calculated precise angle between them?

As stated, you get 3 x 60degrees not 45. Mind you, I was wrong this AM :Doh:

You can ,Andrew,  work a set of tool makers buttons but of different sizes- I think

Cheers

N

Offline loply

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Re: Checking a 45 degree square?
« Reply #28 on: May 27, 2015, 08:12:03 AM »
Just to clarify one other point, to be comparable with the accuracy I managed to get on my scraped parallel and master square ideally I'd want to get the 45 degree surface to be accurate to within about +-5 microns (ie 0.005mm) of where it should be, I mean the 'top' of it won't be any more than that from where it should be, if you see what I mean. I don't know what angular accuracy that translates to, but I'd probably make the thing about 6 inches tall...

Offline loply

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Re: Checking a 45 degree square?
« Reply #29 on: May 27, 2015, 08:22:12 AM »
I guess the attached image is what I was thinking.

By turning the two cylinders to size (and presumably finishing really carefully with some fine sandpaper) I could do the maths and end up with a parallel or suchlike lying across them at 45 degrees, I could then indicate off that to assess the one I was making/testing.

Kind of just like a sine bar really, but since I don't have a sine bar or a set of gauge blocks it saves having to buy them  :clap:

Offline DMIOM

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Re: Checking a 45 degree square?
« Reply #30 on: May 27, 2015, 08:30:35 AM »
DMIOM, I see how that would prove that the two 45s add up to 90, but you wouldn't know if you had a 44 and a 46 though? Or am I missing something?......

The key is to keep the same face up and just rotate it about one corner ('A' in the sketch below), so you're doubling the angle of one corner - and if its the desired 45 degrees, then you'll match your 90 degree master square, if not the discrepancy will be magnified by a factor of two.

Annotated version of sketch attached.

Dave
« Last Edit: May 27, 2015, 09:10:25 AM by DMIOM »

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #31 on: May 27, 2015, 08:38:20 AM »
I would stick with something which equates to 5 or 10" which are normal Imperial sines.

They make things easier in the trig!

My 5" sine bar- I've just discovered is heavily corroded from when the roof came off my workshop( in Newcastle) Again, I have to find( if they are there) what my Jo blocks are doing. I got the Myford sorted out- without too much damage.

Anyhow, settle for multiples of 5 which are easy-er.

Regards

Norman

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Re: Checking a 45 degree square?
« Reply #32 on: May 27, 2015, 09:18:45 AM »
Norman

With ref to sine bars first what language are your Jo blocks if they are inferior then by all means use a 5 inch sine bar the the Jo block stack would be in imp, but if like me you have metric Jo blocks then a 127 mm sine bar is needed
As then the answers would be in mm


To the OP

The level of truth that you are wanting is get is less that 1 arc second  if my brain cell is ok today but other will no doubt correct this and this is going to be tricky you will have to put a insulating handle on it to stop thermal changes .

How long have you had the material ageing they use to make Jo blocks down the road ,they used to bury the steel for a year befor use

Stuart
Good luck in your quest

Offline loply

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Re: Checking a 45 degree square?
« Reply #33 on: May 27, 2015, 09:31:37 AM »
Dave - that's boggling my mind a bit! I'm still a bit unsure how I would know which way the error was, I'm sure it's possible I'm just getting confused  :hammer:

Having said that - I think I've just come up with a way of doing it which only requires one 45 degree part and the master square-

If I set up an indicator on the master square such that it's tip is about 10mm off the surface of the square, pointing downwards, and bring the 45 degree and butt it up against the master square such that the indicator reads off it's height (say about 10mm 'in' to the 45), note the indicator reading, then turn the 45 around and do the same on the other side. If it's not 45 the reading will be different, if it is 45 the reading should be the same.

It would then just be a case of scraping off whatever the error was from the 'high' side, and re-flatening the thing.


Offline loply

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Re: Checking a 45 degree square?
« Reply #34 on: May 27, 2015, 09:34:45 AM »
This is what I mean:

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #35 on: May 27, 2015, 09:43:47 AM »
Both sine bar and Jo blocks are Imperial. Again, all my measuring tackle is Imperial.

Of course, I can work in Metric but my tools are also Imperial- apart from the Unimat clone. Just old fashioned, I guess.




Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #36 on: May 27, 2015, 09:46:06 AM »
This is what I mean:
If you make Two, you become parallel!

Offline vtsteam

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Re: Checking a 45 degree square?
« Reply #37 on: May 27, 2015, 10:03:38 AM »
Loply you don't need an indicator. An adjustable hard point will do. You just need contact both ways.

Besides, do you have an indicator that measures the 10 microns which is your goal?


The real question that has been missed all along, is not how to measure or get an angle, which you can do with many methods discussed and others as well, but how to rub and scrape it to that angle using contact methods, rather than measurement methods, which are the inevitable step in any mathematical determination of angle.

Sure, everyone knows Pythgoras theorem and owns a calculator, but once you've done the math how do you translate that without measuring? Sine bars and machined holes and pins are all measured somewhere along the production process -- whethere it is of the mill table calibration, mill tool size, mill movement, etc, and NONE of those are to my knowledge done to a 10 micron tolerance.

The whole essential of traditional hand scraping is a method which does not depend on measurement, but upon indicators of contact. We use math to do approximate work, and discard math in favor of contact and a contact indicator (blueing) to do extremely precise work.

I've already given a contact method which will, with a contact indictor, allow a person interested in a practical method, to scrape, and see non-contact areas. It will work as is.

I'm sure it could be improved upon (as most things can) with slight modifications to get work done more efficiently, though not necessarily more accurately. But most of what I'm reading here ignores the tolerance stated and the methods necessary to reach it. No system of measurement with a lower tolerance anywhere along the line of production will guarantee the tolerance required by the OP.
I love it when a Plan B comes together!
Steve
https://www.youtube.com/watch?v=4sDubB0-REg

Offline DMIOM

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Re: Checking a 45 degree square?
« Reply #38 on: May 27, 2015, 10:19:39 AM »
Dave - that's boggling my mind a bit! I'm still a bit unsure how I would know which way the error was, I'm sure it's possible I'm just getting confused  :hammer:

Having said that - I think I've just come up with a way of doing it which only requires one 45 degree part and the master square-

If I set up an indicator on the master square such that it's tip is about 10mm off the surface of the square, pointing downwards, and bring the 45 degree and butt it up against the master square such that the indicator reads off it's height (say about 10mm 'in' to the 45), note the indicator reading, then turn the 45 around and do the same on the other side. If it's not 45 the reading will be different, if it is 45 the reading should be the same.

It would then just be a case of scraping off whatever the error was from the 'high' side, and re-flatening the thing.

Rich - your indicator method doesn't (IMHO) make use of the full length - you're trying to make an ultra accurate measurement over a short span.

Have made another sketch to show how you would tell if one corner was too fat or too acute (the examples have 43&47 degree angles to make the differences visible)

Dave

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #39 on: May 27, 2015, 12:03:26 PM »
Steve's interesting observation etc raises the question of just how thick this thing is going to be.

Can you clear this up and tell us what tooling you have already for establishing your claims of accuracy.

Cheers

Norman

Offline loply

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Re: Checking a 45 degree square?
« Reply #40 on: May 27, 2015, 12:22:09 PM »
Dave, thanks for that, I think I get it now.

I have some nice old cast iron which is about 22 or 23mm thick which I think I can cut up for it.

I made a thread some years ago about making my other scraping tools - it's here - http://madmodder.net/index.php?topic=9039.0 they were made in 2012/2013 mainly from a large old milling cube which I cut up.

I bought a nice Mitutoyo indicator which has 2 micron increments at the time that I made those, the markings are quite nicely spaced so you can split an increment quite easily. Was expensive but I have lots of machines I intend to rescrape (ONE DAY!) so I figured I will use it over the next 20 years as I gradually do them all :D

Obviously it's no good measuring a scraped surface directly as the scrape marks are up and down, but I tend to lay a small ground parallel on top and measure off that. Even touching the parallel makes it bend though so I tend to lay things down then leave them to sit for a bit before taking the reading.

Probably the biggest limiter is my surface plate, the inspection report said that it varied by 0.3 microns from one corner to the other, but, it's an import and who knows how truthful that is.

Offline Fergus OMore

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Re: Checking a 45 degree square?
« Reply #41 on: May 27, 2015, 12:46:59 PM »
Thank you- most impressive. I am sure that you will enjoy using your tools.

I'm afraid that my tooling is far more crude looking and I haven't 20 years left to improve things.

Enjoy

Norman