Calculate Error from uneven rail and reference

[feldah]

Hello and sorry because i allready asked some question about cheaper ways to straighten my linear guideways. But I had an idea where I wanted your opinion on. So in my case I have a linear guideway of 4m but it can also be smaller for my idea. I want to have it as precise as possible. A straight line reference is too expensive for my hobby project. So I had the idea to buy a Granite tile by the size of 1mx10cmx1cm. I won't know the error of it of course. So my idea is by using a dial indicator to align it at 0 on tip (M0) and end (Mn) of the Granite. Now I would take measurements (M_i) every 5 cm. Every M_i will consist of two errors A_i from the Granite and B_i from the linear guide way. So that I could write for the first measurement M1=A1+B1. For the last one I could write Mn-1=An-1+Bn-1. Now when I flip the Granite and align it again to Mf0=0 and Mfn=0. And i would get Mf1=An-1+B1 and Mfn-1=A1+Bn-1. Now I would have 4 equations with 4 unknown. Which I can solve. Does that work? I am aware that you can buy linear reference second hand cheaper. But my question is more of theoretical interest.

[Neale]

I think that you have forgotten one variable in each equation. You have shown each measurement as the sum of two errors, but you need another variable in there which is the "correct" distance. For example, if this is Cn, then you should be writing M1=A1+B1+C1. Unfortunately, when you flip the reference surface, you then get Mf1=An+B1+D1 - as the surface will not be the same distance away. In any case, I suspect that there is at least one more unmeasured/unmeasurable variable involved.

As an alternative, how about buying a length of, say, aluminium bar the cutting length of your machine. Clamp it as parallel as possible to the axis, and take a light cut off one edge. Then flip the bar by rotating along its long axis, so that the cut surface is now on the other edge, so to speak. Then run a dial gauge in place of the tool along the cut edge. I think that theoretically this will then read twice the rail alignment error at each point. Haven't tried this myself but I have been thinking about problem recently. First thought was to cut two identical bars as above, then flip one, push them together, and check the gap between them. I really need to do something like this on my own machine, but I'm too busy using it to find time to tune it!

[feldah]

I think that you have forgotten one variable in each equation. You have shown each measurement as the sum of two errors, but you need another variable in there which is the "correct" distance. For example, if this is Cn, then you should be writing M1=A1+B1+C1. Unfortunately, when you flip the reference surface, you then get Mf1=An+B1+D1 - as the surface will not be the same distance away. In any case, I suspect that there is at least one more unmeasured/unmeasurable variable involved.

As an alternative, how about buying a length of, say, aluminium bar the cutting length of your machine. Clamp it as parallel as possible to the axis, and take a light cut off one edge. Then flip the bar by rotating along its long axis, so that the cut surface is now on the other edge, so to speak. Then run a dial gauge in place of the tool along the cut edge. I think that theoretically this will then read twice the rail alignment error at each point. Haven't tried this myself but I have been thinking about problem recently. First thought was to cut two identical bars as above, then flip one, push them together, and check the gap between them. I really need to do something like this on my own machine, but I'm too busy using it to find time to tune it!

Now I had to think about it ;-)

But In my understanding D=Df would do the trick. Because You can choose D freely. Honestly I also suspect another unknown. But I don't see it ;-) Maybe some kind of cosine error. But it shouldn't be large. Actually I have a drawing for it. Werkstück1 refers to linear guideway and Werkstück2 to our reference25382

[mekanik]

You stated in your previous post that you had a length of heavy duty aluminium 1500mm long and an acurate machined surface that was straight to within 0.004mm if memory serves, use this to adjust your rail, i did explain how to do this some time ago as this question has been asked countless times, start fixing the rail from the center work your way alternately towards each end, you will then in your case have a section of rail 1500mm straight to the given accuracy of your reference gauge, you then use your secured section of rail as a datum for setting the remaining unsecured section of rail.

[feldah]

Sorry when I asked the question again. I had to give back the Aluminium. As my rail is set now. But my question was more out of theoretical interest.

[John McNamara]

Hi all

One quite simple way to set rails straight is with a stretched wire. Together with a cheap digital microscope (Get one with electronic cross-hairs) off the net. Alternately an optical microscope can be used with a cross-hair reticle. Mount the microscope on a rail slider on the already positioned rail beside the stretched wire you have mounted in your machine frame already positioned in line with where the rail will be placed, best you offset it say 20mm to allow access to the rail screws.

The procedure is simple. just work your way along the rail centering the microscope cross-hairs on the wire as you go.

You will need to make up some sort of mounting for the wire to position it accurately. One end will be fixed one end will have a large weight attached to it.
The weight is normally calculated to b about .75% of the breaking strain of the wire. http://www.roeslau-draht.de/fileadmin/user_upload/Downloads/music3B_Zb_2.pdf (http://www.roeslau- draht.de/fileadmin/user_upload/Downloads/music3B_Zb_2.pdf)

Thinner is better mine is .17 Round not hex.

This is not a new technique Wire alignment goes way back in time. It is still used to this day.

https://www.google.com/search?rlz=1C1ASUT_enAU791AU791&ei=LRNWXNbFBIOkwgPhyYQo&q=stretched+wire+alignment+cerne&oq=stretched+wire+alignment+cerne&gs_l=psy-ab.3...30223.33244..34616...0.0..0.267.2021.0j7j3. .....0....1..gws-wiz.tTYd1bOv-T0

Accuracy of 0.001" is obtainable over long lengths.
Gravity will affect the vertical plane, to check the flatness of your rail mounting surface the Catenary sag of the wire will need to be calculated for various positions along the wire. Think of sagging power lines. https://www.google.com/search?q=catenary+sag+table&rlz=1C1ASUT_enAU791AU791&oq=catenary+sag+table&aqs=chrome..69i57.10632j0j7&sourceid=chrome&ie=UTF-8

Over less than a metre the sag is very small.

Cost
https://www.google.com/search?q=usb+microscope+cross+hair&rlz=1C1ASUT_enAU791AU791&source=lnms&sa=X&ved=0ahUKEwjwtpzhiJ7gAhXMTX0KHW-FB5wQ_AUI0QEoAA&biw=1008&bih=537

You do not need or want high power about 40 is fine.
A handy tool to have anyway
100 feet of wire
https://www.fortepiano.com/index.php/products-menu-item/wire-menu-item/high-carbon-menu-item/roeslau-music-menu-item

Regards
John

[AndyGuid]

Thanks John, I love the simplicity and low cost of that idea!

[mekanik]

Hi John
Do you have a link to a cheap digital microscope, we used to use the Taylor Hobson kit @ work but there are no cheap options that i know of.
Regards
Mike

[John McNamara]

Hi mike

I also have a Taylor Hobson alignment telescope, not the digital just the older optical model, It is quite a fiddle to set it up and once set if it is knocked it will go out of alignment, having to set the targets and keep checking is slow.

I restored a lathe a while back and used wire, it was a Heidenreich and Harbeck 20 Ro 2.4 metres between centres. to check the straightness of the bed I attached the wire along the side of the bed level with the top of the V's and used an optical microscope. not fancy just a student microscope. the wire was firmly attached and did not need to be constantly checked it never went out of alignment being firmly bolted in position. The microscope was attached to a stage that was guided by the V ways was fixed over the wire and positioned with a Mitutoyo micrometer stem (They are available to be built into an instrument). error readings were taken with the micrometer after positioning the microscope over the wire. it worked very well.

I later purchased a cheap USB microscope About 40AUD it came with software. regrettably I lent it out and it never returned! Hmmm.

So I also need to buy a new one too with cross hair measurement software.
The trouble is there are hundreds of models available for a few quid.

Maybe someone in here has purchased one and can report on it?

Regards
john

[mekanik]

Hi John
Thanks for your reply, since i have been thinking about the rail alignment issue i have wanted to go with optical alignment as this seems the best way to do it, but the cost of a Scope/targets ect makes it a none starter. if i had still been working i could have borrowed the kit from work. will look into USB microscope idea.
Regards
Mike

[John McNamara]

Found a photo of the setup I mentioned, it was just a lashup for a one off, it worked well. Note the bolted on wire support and adjustment unit

25421

[feldah]

Hey love the idea simple and good.

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[feldah]

Found a photo of the setup I mentioned, it was just a lashup for a one off, it worked well. Note the bolted on wire support and adjustment unit

25421

I was digging a bit deeper in the wire alignment. It sounds quite interesting as I said. previous. I am considering that in our days even a smartphone camera should do the trick. In my case I can go as close as 7cm without loosing focus. one pixel takes then the picture of a 0,015 mm square. One thing I would be interested in if you could explain the construction for the support of the wire. More in detail. As I see it as difficult to keep it in place.

Further I was reading an article where they recommended to use "stainless steel “down rigger” (fishing line) wire, rated at 150 lb" as this would be better then piano wire.
http://fwrc.msstate.edu/southernsaw/alignment1.pdf

But to pull it that hard with 75% force I would need a very rigid support.

[mekanik]

Johns post gives the weight for the required tensioning of the wire, ie 75% of breaking strain. wire is fixed solid @ one end and run via a pulley @ the other with the weight attached. Had a look on ebay and the USB microscopes are as cheap as chips.
Regards
Mike

[feldah]

Johns post gives the weight for the required tensioning of the wire, ie 75% of breaking strain. wire is fixed solid @ one end and run via a pulley @ the other with the weight attached. Had a look on ebay and the USB microscopes are as cheap as chips.
Regards
Mike
But in the article I am referring to they recommend to use sloted adjustment nuts. And a winch instead of weights. I mean from this 150lb wire 75% is a lot of force pulling on the pulley. Also I would expect that a pulley has a lot of play.

Sure for the usb microscope I am not arguing because of the price but the quality. As I am expecting it to have a really bad image sensor for that price.

But I am still trying to fully understand the method they are using in the article.
http://fwrc.msstate.edu/southernsaw/alignment1.pdf

[magicniner]

This is starting to sound all "Model Engineer" where they can achieve "almost acceptable" (but not near industry standard) results from the input of unacceptable amounts of time and effort!
:D

[John McNamara]

Hi All

Below is two images of the wire supports I made, As you can see made from scraps of mild steel rough machined to size. The dovetails (SIC) are just groves cut with a standard end mill with the parts held at 45 deg in the mill. I also machined the clamp to fit the bed of the lathe the clamps were set about 3800mm apart.

The long dovetail rail has two carriages one fixed one movable by a simple screw, that provides a simple Y axis, the slide clamps were set very tight for lateral adjustment the stack of washers on a grade 8 bolt worked fine, the wire does not run on the threads just the smooth section on the bolt For scale the large fastenings are M8. While he setup was crude it got the job done, once tightened the setup rigid and .0001" setting accuracy was easily obtained.

My objective was to get the job done fast a few hours making the jig. They are not pretty. certainly not up to the standard of a model makers work.

Stainless steel has a lower tensile strength than carbon steel.

You need the lightest weight, and that will be the the thinnest material with the highest tensile strength to resist the pull of gravity. I double checked the number on my roll of Roslau wire and it is marked #2 it measures about .008"
I remember at the time there was a finer one but it was not in stock.

The only real alternative to high carbon steel is a synthetic material like carbon fiber, Aramid etc. I have read university papers where these materials have been tried. They were more difficult to read because of uneven the surface finish on the material. They are also non conductive, one very popular method to sense the wire is by a simple electrical contact. (Actually the point where contact is lost, that guarantees you are not deflecting the wire.)

Regards
John

http://www.mediafire.com/file/cguxizswwcoxhnf/10-02-2019_9-44-05_AM.jpg/file

http://www.mediafire.com/file/ek6ivv7bp2hgbnk/10-02-2019_9-45-18_AM.jpg/file

[magicniner]

Very impressive, how does the machine run?

[feldah]

Haha great that sounds perfect. Especially the stack of washers. Thank you for the inside information. I know a bit of computer vision so I think I will go with the optical approach instead of the electrical contact. With an automatic edge recognition I could easily read out the error. Only downside now for me with the Röslau wire seems to be that it is transparent but it should be fine. Do you remember the pulling force/weight? If not I will find out.


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[John McNamara]

The weight was a 4140? 200mm dia gear blank 35mm thick I never did weigh it by calc about 11kg

Roslau blue label carbon steel wire is not transparent?

The lathe if you are referring to that works fine I use it every day. Not perfect but near.

There is a picture of Heidi in this old paper I wrote when she got her referb.

http://www.mediafire.com/file/b0rxnxd7x24wamk/Epoxy_Bearing_-_Compact.ppt/file

Regards
John

[feldah]

The weight was a 4140? 200mm dia gear blank 35mm thick I never did weigh it by calc about 11kg

Roslau blue label carbon steel wire is not transparent?

The lathe if you are referring to that works fine I use it every day. Not perfect but near.

There is a picture of Heidi in this old paper I wrote when she got her referb.

http://www.mediafire.com/file/b0rxnxd7x24wamk/Epoxy_Bearing_-_Compact.ppt/file

Regards
John
thx. I will follow your approach then. The wire on the photo just appeared to be transparent.