Wire line computer analysis 2

[Ralph2]

Hello
Any one familiar with the process of using a taut wire to check if a series of bores are in line? Typically piano wire stretched with a 60 pound pull, centered to the outermost bores and then a measurement is made to the wire from the inner bores. By analysing the results one can determine if the bores are "in line"
There is some serious math involved with determining the sag of the wire which must be incorporated in the results. Some one at work has made an excel spread sheet but it is cumbersome and (in my opinion) not accurate.
So,, does anyone have or have a link to software that would do the analysis. Ideally something that would make a pictorial reptesentation of the relationship of the bores to a true line.
Thanks
Ralph

 

[GregLocock]

The deformed shape of a tensioned wire under its own weight is called a catenary. That may help you find an equation or a spreadsheet.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IRstuff]

Sounds like you're asking about lateral alignment of the bores? e.g., that a row of bores are within some tolerance of being centered on a hypothetical line?


One issue with your posited procedure is that ostensibly, you're trying to perform a least squares regression of the bore centers to a line. However, by centering the cable on the outermost two bores, the line is is arbitrarily fixed and the remaining bores are compared to THAT line as opposed to the nominal best-fit line through ALL the bores.

TTFN

 

[IRstuff]

Why is the sag an issue?

What level of uncertainty are you trying to achieve?

TTFN

 

[VEBill]

Is there a way to use a "laser beam" ;-) instead of a taut wire ?

 

[mshimko]

I'm familier with using surveying techniques for many alignment situations. (Strike "familier", in that I'm not a surveyer, merely one who has worked many projects involving surveyors).

I'm oft amazed at the precision these techniques provide.

Is there a reason surveying isn't used?

 

[MintJulep]

Is the part sufficiently small that it can be oriented with the bores aligned veritcally rather than horizontally?

If yes, then sag of the line is not a concern.

 

[Ralph2]

Thanks for all the comments / questions. We use this process to check the alignment of bores (most often) in large crank cases where the bearing bores are (normally)in excess of 5 inches. The process is also used to check the alignment of bearing bores in other large pieces of equipment. ie a steam turbine where there may be several bearings covering in excess of 150 feet. The wire is insulated electricaly and a 12 volt battery is attached to the wire. Then using an inside micrometer one measures from the bore to the wire and essentially makes a short (ground)to the wire. A micrometer is attached to a head set (or light bulb) and one can "hear" the static created at the point of contact.
The accuracy depends a lot on the enviroment but in good conditions one can easilly diffentiate up to .0002". The measurement is relative, to one side one may have 6.0205 and the other side 6.021. This would only mean that from the edge of the wire to the bore differs by .0005 or that the bore is .00025 off a true line.
Based on an analyis of the result one can determine the location of the bores are true to the ends. This then can determine if the housing can be moved to create a "better" alignment or if some of the bores need machining the correct the location.
So... the sag is important, even though not much ~.0015 over 20 feet it does affect the results one is trying to obtain.
Ralph

 

[Denial]

Under the assumptions
[•] the sag is small;,
[•] the wire is inextensible axially,
[•] the wire has zero bending stiffness,
[•] the two endpoints are at the same level,
the catenary equation can be approximated by a parabolic equation.

It is then relatively easy to show that the vertical sag at midspan is given by
w*L^2/(8T)
where
[•] w is the weight per unit length of the wire,
[•] L is its horizontal length, and
[•] T is its tension.

HTH

 

[Ralph2]

Thanks.. what units are you using (Metric of Imperial)? What do you mean by "unit lenght of wire", the whole length in ounces, pounds, grams.

 

[Denial]

The formula I gave is dimensionally consistent, and so applies for any CONSISTENT set of units. By "weight per unit length" I mean the weight per metre, or per foot, or per cubit, depending in which units take your fancy.

As an example, if you use kilonewtons per metre for w, metres for L, and kilonewtons for T, the formula will give you your sag in metres.

(Putting it crudely, the kilonewtons sort of cancel each other out as you evaluate the formula.)

 

[dwedel]

Yes, I have heard of it, and have used a laser verion of the process. I will try to respond with more info this weekend.

dwedel
Hotrod Big Engines!
For site policies and guidelines
see faq731-376

 

[Ralph2]

In trying to research this a bit more..... "The curve described by a uniform, flexible chain hanging under the influence of gravity is called the catenary".

Assume this chain is slowly shortened, the "sag" will be reduced. Is it a catenary throughout? Or, at some point as the catenary approaches a straight line it is no longer a catenary.

Is "my" tensioned wire even properly considered a "catenary"? Are the formula to determine the shape of a catenary valid for my tensioned wire?

Denial (Structural) makes this comment....
the catenary equation can be approximated by a parabolic equation.

Does this mean my (tensioned wire)is closer to a parabolic than a catenary? or just an easier formula?

 

[GregLocock]

It is always a catenary, no matter how tight the wire.

I don't know when it is safe to assume that it is a parabola

The horizontal force, in terms of total cable length and sag is

Fh = w / (8*h) * (S^2 - 4*h^2)

The y coordinate (height) of any point in terms of the horizontal force

y= Fh / w * (cosh(w * x / Fh - 1 ) )

We assume that the origin is at the center of the span.

Total span = L
Sag in the cable = h
So, the coordinates of the endpoints are (+/- L/2,h).

The weight per unit length = w

Total length of wire/cable = S

Length along the cable from the origin = s

Fh is the horizontal force component everywhere, and is equal to half the tension at the center.




grabbed from

http://home.earthlink.net/~jimlux/radio/math/catenary.htm

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[teb1]

We use a 30 pound weight on the end of an isolated wire. Looking back over some previous engines that we have align bored. A wire length of 233" will have a sag of approx. 0.014" at midspan. This significant when you are trying to get the bores within .002" of each other and .003" from end to end.

 

[Denial]

As Greg says, the shape (provided the bending stiffness is zero) is always a catenary, and therefore described by a cosh() equation. As the tension in the chain is increased, the sag decreases, and any errors associated with the parabolic approximation decrease. In the limit, the two equations become the same, as can be seen from a Taylor's Series expansion of the catenary equation. In the even greater limit, both equations degenerate into straight lines. For general engineering purposes it usually assumed that the parabolic equation is adequate provided that the sag is less that one tenth of the span. However methinks that Ralph2's application requires greater precision than would "general engineering purposes".

Ralph2 asks whether his wire can validly be considered a chain for this exercise. The key assumption a wire might violate is the one about negligible bending stiffness. I do not know of any simple rule of thumb that provides an answer here. Not only does wire have a bending stiffness, but it also usually has a non-straight unstressed shape as a result of being wound into a coil for transportation.

You could always do a quick calculation as follows. Calculate the plastic moment capacity of the wire's cross-section, and divide that by the proposed tension. That will give you a length, and that length will be the maximum possible deviation that the actual wire could have from its theoretical path.

Please note that Greg's last statement seems to have fallen victim to a cut&paste&edit error. It should read:

"Fh is the horizontal force component everywhere, and is equal to the tension at the centre." (The word half needed to be removed.)

PS. For the etymologically inclined, the word catenary comes directly from the Latin word for chain.

 

[dwedel]

Now that I have read the thread I don't think that I can add anything to it. Pruftechnik BoreAlign which is laser system I use, wouldn't have an accuracy of .0002" in a operating recip compressor station. (too much vibration) I'm not sure how well it would work in a quiet station. They do make a more accurate system that the steam turbine operators would like.

I did get to compare the laser to a machinist's boring bar, so I am confident of the .001" results I was getting.

I researched the possibilities of wire-lining and went with the laser because of the "art" that seemed to be part of the wire-line process. The fact that the laser alignment tool also helps us align couplings made the tool an easier sell.


dwedel
Hotrod Big Engines!
For site policies and guidelines
see faq731-376

 

[Ralph2]

Dwedel.
How complicated / easy is using the Pruftechnik BoreAlign system. Unless I am confused with something else, one rotates a target inside the bearing bore. Kind of a little 4 wheeled truck with a mast that intersects the center of the bore. It seems that this could lead to errors if the bore was out of round..
Have you had your Pruftechnik BoreAlign long.. are you happy with it? (we have the turbalign and use it only for alignments)

 

[dwedel]

We have had our RotoAlign Pro for a year now. Last year I rented the BoreAlign tool twice and measured bearing bores of an Ingersoll-Rand 82KVG frame that we had just regrouted, and then measured the bearing bores of an Ajax DPC-600, that we crashed some con-rod bearings in. We also received one demonstration free, where the salesman came and showed us how the BoreAlign worked and showed me how to operate it. That was on an Ingersoll-Rand 26KVG. Of course the crankshafts were out of the units all three times. In the first two cases, the other recip compressors in the building were still operating, and in the demonstration we had to deal with drafty cold winds in a heated building. The KVG’s were done with the just the bottom half of the bore, while the Ajax had the caps in for a complete bearing bore.

I believe the more accurate tool is called CentrAlign. Ludeca is the US importer of the tool.

I have three digital pictures of the 82KVG and a PDF of the basic report that I printed out that I could send you via email.

You are correct about most of the operation. The target is rotated in the bores and the laser is stationary outside the unit. I used the oil pump flange which spaced the laser about 12” from the nearest bearing bore. The wheeled cart you spoke of, is actually the magnetic base for the rotating point on the mast you talked about. The target is mounted on a spring loaded holder, which pushes a rod out against the bearing bore. The rod will touch down on several points. You basically have an inside mic, that is constrained to rotate about a point somewhere near the center of the bearing bore. The computer then computes a bore center line. You can see all the data points as you take them as well as the averaging the computer does. Thus the tool operator can see an out of round bore.

For accuracy, I tested taking the target out of the bore in between sets of measurements to see how well the sets of measurements compared. I also reconstructed the mast when working on the 82KVG, and the measurements before and after seemed to agree well. The vibration was a problem. The 82KVG was 14’ long with 8 bores. At the #7 and #8 bores, I had to use the maximum averaging of the computer to get results with lower standard deviations. I felt that a standard deviation that was .0005” when I wanted my resolution to be .001” was acceptable. The older sensor that I rented, may have contributed to the vibration problem. You must be careful with thermal growth of the tool as I fought with high radiant heat sources and cold drafts. On the 82KVG I compared the results to a machinist boring bar, and it seemed to be accurate. In the vertical plane, one bore was .0014” high, and another bore was .0019” low. The horizontal plane had one bore +.0016” and another -.0014”. These measurements were from a line of best fits and of course the ten-thousandths accuracy must be taken with a grain of salt considering the standard deviation of my measurements. The crankshaft web deflections also agreed with the measurements we made.

Overall the tool works well for us. I will try to train one of our mechanics this summer on its operation, which I think will go well. The higher order math is done by the computer and data doesn’t need to be transferred from a pad to computer. Bucking the laser in, seemed really simple to me. Unfortunately I cannot compare directly to the wire-line method as I have never done it. However, as the wire line method was described to me, the laser makes some of the measurement and interpretation simpler.

If you are thinking about this option, renting the tool worked well for me. Perhaps the salesman would be willing to give you a demonstration also. Hopefully this doesn’t sound too much like a sales pitch, because it is just my experience.


dwedel
Hotrod Big Engines!
For site policies and guidelines
see faq731-376

 

[Ralph2]

Thanks for the detailed report... I would be interested in having a look at your report. Send it to r2varney at telusplanet.net (not sure if this will thwart any email harvesters but its worth a try)
Ralph