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 reference

[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

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=1C...iz.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=cate...hrome&ie=UTF-8

Over less than a metre the sag is very small.

Cost
https://www.google.com/search?q=usb+...w=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...usic-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