The most interesting problem of the last two weeks

[font=&quot]There was a thread that delt with a wire or rebar mill that moved steel at a speed of up to 100 m/s. The metal is rolled through 'stands', each stand has rolls where the gaps are closer together than the proceeding stand. The stands themselves are equally spaced. This means that a bars of steel that is 100x100mm is rolled to rebar size wire or smaller. I have seen these mills. These can be very dangerous because the steel coming out of the 4th or later stands is moving very quickly and if it goes astray, it can impale or seriously burn people that may be nearby. This is not a project for rookies.
This is a deadly serious topic.

The thread states that there is 5m between stands and that the steel bows up about .1m between the stands. One can get an idea of how fast the metal moves between stand 3 and 4 by the ratio of the gaps between the rolls in stands 2 and how fast the roll is moving at stand 3.

The problems are these:
1. How much excess steel is there in the bow of steel when it bows .1 m I a distance of 5m?
2. At 100 m/s, what does a 1% error in speed regulation mean? 3. How fast could a 1% error in speed control use up the excess material in the .1m bow of steel?
4. There was an even earlier post that ask about how many PIDs can be executed in 0.1 seconds. Is 0.1 seconds fast enough for this application?

Question 1 is a good one for starters. It is the most difficult. Does anyone have a clue how to solve this? What assumptions have to be made?
Question 2 and 3 is much easier.
Question 4 is what the forum is all about. Is an PLC appropriate for this application? Which one?

This application is similar to a winder application but the are some important differences. I thought that only Tom Jenkins provided a good answer to the person that originally posted the problem. However, no one provided hard numbers.

Note, if the person that originally asked these questions posts, I will not respond to this thread. There will be no more answers.

Finally, the reason I didn't respond to my earlier thread about 'Forever Knowldge' is because it contributed to the forum 'noise' and hoped it would go away much earlier that it did. DickDV, I was not laughing. There still are Ludites.




[/font]

Peter just a clarification first. Is 100m/s equal to 100 meters per second. I have been in rebar and rod mills before but nothing that fast.

And in my opinion NO job in any steel mill is a job for a beginner

Oh wait, you said wire or rebar, I thought you said rod and rebar. I could see 100m/s on wire depending on the diameter.

I'm only familiar with hot down to 1/2". After that I only know of cold drawn

But regardless it is going to be dependant on the diameter of the steel. Also usually there is a positive pull, are you saying there isn't in this one?

I did not see that thread.

Peter I have worked in the steel industry, it was not that long ago that I modified a "bar straightener" which sounds more like what you are talking about.

At the same plant I also worked with "draw" machines that took steel wire that ran it through dies to make it smaller.

You of all people should be able to calculate the speed capabilities but I can bet you that you will never ever see a steel wire system, the size of rebar, running 100m/s.

http://www.vulcanthreaded.com/

1. What is the length of steel between the stands?

The person that wrote the thread did not make it clear what end result was except for that it was about 10mm in diameter.
I thought 100 m/s was fast too. Ok, lets use 10 m/s. Rebar or rod, that makes no difference to the question. The point is there is 5 m between the stands and there is an arc of .1 m. What is the length of the steel between the stands? This is important because the speed control must be very good to keep this bow constant.

An velocity error %1 will use up this excess quickly or it may cause the bow to be too large. In either case the metal can 'cobble'

I have spent a lot of time in steel rolling mill installation but I have only taken a tour of a relatively local rebar mill. The rebar mill had stands with rolls and it was not extruded.

Now back to the problem. First one must make an assumption on the shape of the metal. Just to get started lets assume the equation is y(x)=0.05*(1-cos(2*PI*x/5). This equation will provide a smooth curve with a .1m bow at 2.5m. y is the verticle distance and x is the horizontal distance. What is the distance along the line? Terry, you actually made me think of posting this question when you posted on the 'Forver Knowledge' thread.

I know this problem can be solved on a PLC. One method requires a 'for' loop. Another method just requires a simple, for the PLC, calculation.

For those that want to play along. Download SciLab ( it is free), cut and paste the program below and run it.

// The assumed shape of steel between the stands
H = 0.1 // Height of the bow between the stands in meters
L = 5.0 // Distance between the stands in meters.
x=0 : 0.01 : L; // This is a FOR loop that iterates x from 0 to L in increments of 0.01
y = (H/2)*(1-cos(2*%pi*x/L));
plot(x,y)
legend("y")

I would be tempted to make a first pass calculation using standard solid beam mechanics. Given the weight of a segment, the length of the bar and the type of supports most intermediate level mechanical engineering textbooks should allow you to make a calculation of deflection mid-span. The only production variable should be the axial force created by the rollers. Luckily, since both ends of the suppors are rollers each segment should be a statically determinate beam and hence can be analyzed using simple equations.

Once you've done this in Excel, you can estimate changes by varying the estimated support axial force by a few % and see the predicted change in mid-span deflection. The axial force should be predictable by measuring the speed difference between adjacent rollers. This will give you an engineering estimate of the change in deflection relative to change in speed. Then I'd run a few simulations of roller speed over a temperature range to make sure I had a nice conservative estimate of the necesssary speed regulation.

Be sure to allow for any changes in material properties at elevated temperature or from cold working...

By the way, the theoretical curve for a so-called "heavy string" (i.e. a string with weight but no stiffness) is called a caternary, and I know it is used to predict the "hanging" position" of cables on suspension bridges.

PS I don't know anything about steel mills, just some ideas.

Peter,

It appears that Phil has removed that thread. Good! I couldn't stand looking at it... except that the problem was so interesting to me.

I wrestled over and over with the idea of posting to that wire-thread. But everytime I went back to it and read it, I kept feeling like I should be wearing some sort of frilly, lacey, kinda thing! Except for the particular problem, it was way the hell too creepy, way too weird. I still shudder!

And then I saw the conditions and the constraints... they just didn't sound reasonable... certainly not in terms of a standard PLC control. It appeared that the potential for error was so great that the control system would be in a continuous state of radical corrections - simply because of inherent timing and resolution issues (without using a specialized dedicated controller).

The original question, without all of the very weird "I Love You, I Miss You" stuff, was...

A hot steel material is fed from one roller to another. The speed of the two rollers was to be controlled such that the material between the rollers maintained a "hump" of a particular height, "h".

Who, or whatever it was, wanted to know the formula for controlling the height of the hump. Then, there were questions of what to use for feedback for height information.

Assuming that the conditions and constraints were well within the ability of an operator to manually control the process, by hand (by joystick or whatever), my thoughts were...

Certainly, this can be done by Calculus. However, there are many that haven't got the slightest idea of what Calculus is all about. But, there is a good chance that many of them understand Algebra and, hopefully, Geometry. So... I decided to take an Algebraic approach (an Algebraic approximation).

I'm still working on it...

And by the way, my approximation will be based on the Isosceles Triangle and the assumption that the ductility of the material remains reasonably constant between the Infeed and Outfeed Rollers.

Now, of course, the actual shape will be some sort of rising and falling S-Curve... however, the real issue here is more about controlling the rate of change in the height rather than the actual height - that will be controlled by the height feedback mechanism.

Once you get the height you want, you bring your rate of change for "h" to zero. Of course you might have to dither it a bit to get it dialed in, and then keep it dialed in.

However, it occurred to me that, theoretically - and only theoretically, the height could be controlled without any height feedback... "open-looped" as it were.

Anyway, I'm still working on it.

Terry Woods said:

And by the way, my approximation will be based on the Isosceles Triangle.

Click to expand...

That is where I started. If the triangle is divided at 2.5m then the hypotenuse is sqrt(2.5^2+0.1^2)=2.501999. This must be multiplied by 2 because we were working with only one half of the triangle. This means there is only 4mm of excess material. The point is that this is not much material so the controller had better be very good keep the height of the bow constant. Especially when acceleration and decelerating.
A .004m error over 1 second is only a .04% error!

Terry Woods said:

Now, of course, the actual shape will be some sort of rising and falling S-Curve...

Click to expand...

I provided an example curve. Did you plot it? The steel mill OEMs probably have the true equations.

Terry Woods said:

however, the real issue here is more about controlling the rate of change in the height rather than the actual height

Click to expand...

Yes, Tom Jenkins said that at on the orignal thread.

Terry Woods said:

Once you get the height you want, you bring your rate of change for "h" to zero.

Click to expand...

Terry Woods said:

However, it occurred to me that, theoretically - and only theoretically, the height could be controlled without any height feedback... "open-looped" as it were.

Click to expand...

I don't think so. Any errors could quickly use up the 4mm of bow or add 4mm which would make the bow larger.

Terry Woods said:

Anyway, I'm still working on it.

Click to expand...

Think divide and conquer.

I have been in rolling mills and tube mills for most of my career.

When I saw the first post I immedietly assumed, I guess without reading the post thoroughly, that he meant 100m/min. Running a hot extruding process at 100m/S would be suicide.

Most of the mills I have worked at have ran between 80fpm and 400 fpm. I have heard of but never seen conduit mills that run at up to 800 fpm.

I will leave that as my $.02. I will however be following the post closely as I am curious to see what you guys come up with.

I'm still working on how to account for the temperature. It will make a difference

The temperature will definately be an issue, even more of an issue is the fact that the temperature is going to change between stands significantly. The delta T between stands is also going to change as line speed changes.

Terry Woods said:

Peter,


And by the way, my approximation will be based on the Isosceles Triangle and the assumption that the ductility of the material remains reasonably constant between the Infeed and Outfeed Rollers.

Click to expand...

Unfortunately the ductility of the material is not going to be anywhere near constant because of the temperature issues noted above. Also as the material passes through the rollers it is being squeezed, meaning that it will also work harden to a degree.

Another problem that must be dealt with in this industry is the fact that the raw material changes with each "heat" run out of the furnace. Steel makers try as hard as they can to make their steels to a certain specification. Unfortunately when you are tossing raw materiels into a furnace it doesn't always turn out exactly the same. Therefore each specification has a certain tolerance. Some tollerance examples of steel include UTS (Ultimate Tensile Strength), mallability, stress over strain, etc.... What I am saying is that the material is not going to be the same each time.

It is because of these reasons that I know there isn't any way this could be controlled open loop. I also think this would be a challenge to control with feedback. Which is why I am here, to learn what you guys think.

I will do my part in the research and try to model (or at least come up with some formulas), for what the temperature difference would look like with different line speeds and different guages of steel. I think I will just stick to mild steel and assume it can be constant.

And please Terry, I don't want to fight. If this takes 2500 rungs of logic in one routine, so be it.

Typically a 50,000 yield steel will actually put above 80,000 psi

It is done with PLCs but we are talking about running structural steel here, not a precious metal. If you have ever seen a bundle of rod or rebar you know that it is not straight, it looks like spaghetti. Even if it makes it through straight it's going to get bent some when it is sheared on the fly. If a customer wants straight rebar then first he is going to get laughed at then they may run it through a straightener which will help it some

Working backs through the posts...

TWControls said...
"If you have ever seen a bundle of rod or rebar you know that it is not straight, it looks like spaghetti."

In a previous life (before electrical stuff) I worked in High-Rise construction. The highest I ever went before I got tired of working on hi-rise buildings on the Chicago Lakefront, in the middle of Winter, was 60 stories. Enough was enough.

And yes, the re-bar is anything but straight. As soon as you cut the binding wires, you have a mess... curly-fries comes to mind (nah, not really that bad).

allscott said...
Oh, heck. allscott said what he said.
And TWControls is talking more about temperature.

Yes. There is a temperature condition, and it is what it is. The question is... Is the temperature difference significant enough to make a significant difference in terms of the control scheme?

First of all, the original post appears to be removed, so I can't refer to any specific constraints. At this point, I'm assuming a distance of 36" between rollers, and a "hump" of several inches. ALSO, I'm assuming that the process runs as fast as it can. In that, I'm thinking there is not much time for a significant, critical, temperature change.

I envisioned the worst-case "hump", being attributed to a significant temperature difference, looking like a wave that was only moments away from "breaking". That shape would look like a normal s-curve on the infeed-side (back-side of the wave), and then a negative-rake on the outfeed-side (front-side of the wave). Even that sounds manageable as long as the speed of the outfeed doesn't go lower. If the speed goes lower, momentarily... then aren't we looking at the "Inverted Pendulum" problem? Imagine trying to keep a breaking-wave right at the point of breaking... forever! Yeah, we can do that! But this problem sounds far more simple than that!

Even still, in that case, wouldn't the outfeed roller have to be operating in a variable plane different from that of the infeed roller?

So, now... for lack of any specified constraints, my vision of the process is...

A Master Control that controls the "NOMINAL LINEAR VELOCITY", the speed at which both rollers run (that is, linearly) when there is no hump-correction occurring.

At the start, both rollers run at the same linear velocity - no hump-correction.

Then, after the leading edge reaches the outfeed roller, the outfeed roller speed (linear velocity) slows a bit, under control, to start developing the "hump".

Until the proper "hump" is developed, the leading material is waste. This, of course, is based on the idea that material processed without the "hump" is not adequate. That section is eventually cut off and recycled back to the furnace.

All process owners like to run those processes as fast as they can be run. How fast can this process run? Is there a long-time, ramp-up issue?

I'm assuming that raw material can be made available as quickly as the downline devices are ready to accept it and process it. Also, that the downline devices will run as fast as possible.

So... we're talking distance between rollers, and the linear velocity of that material.

What kind of dT are we talking about here?

I ASSUME that the material is NOT being quenched by anything other than the ambient temperature in the area between the rollers. GRANTED... the ambient temperature around the rollers is considerable less than furnace temperature. However, how close are the rollers to the last heat source?

I believe that "h" can be reasonably averaged, in terms of an isosceles triangle despite the temperature difference between the back-side and the front-side of the "hump", despite the fact that the "crown of the wave" might pass (only slightly - too much would be catastrophic!) the perpendicular at the center of the roller to roller distance.

This is definitely NOT an easy problem, one which could be solved "off-the-cuff". And, of course, without having a real system to test our theories on, it's all academic. And yet, all valid solutions are developed ONLY through academic discourse! Anything else is nothing but "hacking"! And "hacking", we all know, will bite you in the A$$ EVERY DAMNED TIME!

And then... allscott also said...
"And please Terry, I don't want to fight."

Oh, c'mon... I don't fight with anyone here at PLCnet! I defy anyone to stand-up and show a bloody nose that I might have given them!

Anything less than a bloody nose is DEFINITELY not a fight! C'mon man! Ain't you street-wise? Or maybe you think that using rhetoric is the same as using a fist? C'mon, rhetoric is nothing but words!

Don't you remember... "Sticks and stones might break my bones, but names will never hurt me!"

allscott also said...
"If this takes 2500 rungs of logic in one routine, so be it."

We're talking about the basic control "concept" at this point. Once we figure out the basic concept, go ahead and employ that concept (program that concept), if you need it, any way you want. I couldn't care less how you do what you do... that is, until what you do really and truely affects me and mine. At that point, stand-by. Until then, knock yourself out!

Terry Woods said:

Working backs through the posts...


allscott said...
Oh, heck. allscott said what he said.


Yes. There is a temperature condition, and it is what it is. The question is... Is the temperature difference significant enough to make a significant difference in terms of the control scheme?

First of all, the original post appears to be removed, so I can't refer to any specific constraints. At this point, I'm assuming a distance of 36" between rollers, and a "hump" of several inches. ALSO, I'm assuming that the process runs as fast as it can. In that, I'm thinking there is not much time for a significant, critical, temperature change.

And then... allscott also said...
"And please Terry, I don't want to fight."

Oh, c'mon... I don't fight with anyone here at PLCnet! I defy anyone to stand-up and show a bloody nose that I might have given them!

Anything less than a bloody nose is DEFINITELY not a fight! C'mon man! Ain't you street-wise? Or maybe you think that using rhetoric is the same as using a fist? C'mon, rhetoric is nothing but words!

Don't you remember... "Sticks and stones might break my bones, but names will never hurt me!"

allscott also said...
"If this takes 2500 rungs of logic in one routine, so be it."

We're talking about the basic control "concept" at this point. Once we figure out the basic concept, go ahead and employ that concept (program that concept), if you need it, any way you want. I couldn't care less how you do what you do... that is, until what you do really and truely affects me and mine. At that point, stand-by. Until then, knock yourself out!

Click to expand...

You should have "worked back through the posts" a little more carefully. We are assuming the stands are 5m apart not 36". The stands in a mill such as this are going to be driven by motors somewhere in the neighbourhood of 600HP to 1000HP, 36" is going to be a tight squeeze. We're making steel not licorice.

16.5' is more than enough room for the steel to cool down significantly. I am still working on exactly how much but it is in the 100's of degreec C, significant.

As far as your last set of comments go, I can see that this thread is going to turn into another p__sing match for no good reason, so I am officially taking my ball and going home. I'm sure you'll be a steel mill expert too by the end of it.

I have asked Phil to unregister me. I think we should change the name of the forum to "Ask Terry", the slogan can be something like "I don't know everything but I will sure try to make you think I do".

Knock YOURSELF out.

AllScott - Do you work for a steel mill? Just curious the basis of this topic. I'm a little confused because I don't remember the first thread.