Unwind/Rewind formulas...

[OkiePC]

Hi all... I have a machine that processes rolls of rubber coated fabric product through a slitter and rewinds the slit stock. The current PLC code doesn't do a very good job of controlling letoff tension and has several other problems, so I am working up a new program for it. I have a very accurate speed feedback signal that tells me the surface speed of the "main pull rolls" (0-400fpm). I know the diameters of the letoff and rewinder rolls both empty and full. I am accurately calculating the length of stock that has been processed (and resetting it as each roll is changed) based on the main pull roll speed feedback. I would like to be able to calculate the diameter of the rewind rolls at any point in the cycle based on the number of linear feet in the roll and the known empty and full roll diameters. I know since the circumference is constantly changing that it's not a linear relationship between feet of stock and diameter. What should the formula look like to do this?

Example values:
Roll length = 1650 feet
Rewind core diameter = 3.5"
Rewind full diameter = 28"
Stock thickness = 0.031" *

The thickness of the stock can be inconsistent, so I'd prefer not to use that value unless absolutely necessary. The final calculation doesn't have to be perfect, but obviously the more accurate it is, the better the final result will be.

Once I have this formula figured out, I will do the same to calculate the diameter of the letoff roll and web rewind rolls. All of this information will be applied to controlling speed and tension to make the machine more user friendly. Currently, the operator has to frequently adjust tension values to keep the machine running well, and if they are running an oddball sized letoff core, the speed control is all out of whack.

Thanks in advance...Paul C.

P.S. adding a device to measure the diameter is not an option on this machine.

 

[Steve Bailey]

The formula is based on area. For the purpose of calculation, the area can be considered the same whether the material is rolled up or laying flat on the floor. Flat on the floor, the length of the material times its thickness is its cross-sectional area. Rolled up, the area of the material is (PI/4) * (OD^2 - ID^2). Now you have a formula:

L * t = (PI/4) * (OD^2 - ID^2)

Solve for OD and you've got it.

Since you say there are variations in the material thickness, there is an alternative method, but it does require you to add additional sensors. You need a sensor that will give you a signal once per revolution of the unwind (or rewind). In your PLC, keep track of the time between signals from the sensor. Multiply your line speed by this time to get a length. This length is equal to the circumference of the outer layer of material. Divide the circumference by PI to get the diameter.

 

[SimonGoldsworthy]

Here are the formulae. They are derived by equating the total volume of material in the roll from the total length and material thickness to the volume in the roll as a cylinder. (Just assume the roll is 1 unit wide)

Length = (diameter ^ 2 - core Diameter ^ 2) * PI/(4 * Thickness)

Thickness = (Diameter ^ 2 - core diameter ^ 2 ) * PI/(4 * length)

Diameter = SQRT(( Length * 4 * Thickness / PI ) + core diameter^2)


NB: Simultaneous post, sorry for any confusion.

 

[panic mode]

since diameter of the roll is inconsistent, i'll have to ask where do you get speed feedback from? from the unwinding roll of stock or from other piece of equipment that is pulling stock from your machine?

 

[OkiePC]

Thanks for the formula.

The formula is based on area.

DOH! I should have thought of that...

Panic: The main pull rolls drive, which supplies my line speed feedback, controls rollers of a fixed diameter. It is independent of the variable diameter letoff and rewinders.

I'll take a bunch of measurements of finished rolls and calculate the average thicknesses of each type of stock we run. Then I'll have values that should give me accurate results using the formula. If I'm accurate to within a couple of percent, the machine is going to run much, much better than it ever has before.

I love this site. I can spend five minutes typing up a question, then go to lunch. When I get back here I always find accurate answers from experienced people. You guys have taught me so much ... and saved me so much time doing research ... I can't thank you enough!

Paul C.

 

[Thomas Sullens]

i`ve read your post and see

P.S. adding a device to measure the diameter is not an option on this machine.

i still have to ask have you considered something like an ultrasonic sensor to find your diameter. These sensors will work on rubber. This still may not be an option, but i had to ask. The model we use is a UC2000-30GM-IU-V1 it`s teachable and gives you 4 to 20. If one of these would work you know the rest of the story.
http://www.am.pepperl-fuchs.com/pdf/fa/documents/SC02_AnalogCurrentandVoltageOutput-p290-293.pdf

 

[russrmartin]

Almost all of the production in the plant I work in requires tension loops where we unwind something, perhaps coat it, and either wind the original roll back up, or roll it up to certain diameters around a core. The real issue is that you want to control tension, thus, it would be much easier for you to install a transducer which measures tension, not speed. Of course, money is always an issue, and I don't know if this would be a viable option. All of our systems run a winder at a set speed, and the unwind or pull-off roll speeds are controlled with the tension feedback. All of them are extremely accurate once calibrated. This would be my suggestion.

Russ

 

[bill4261]

We use a prox switch on a gear located on the shaft of the coreholder to read the speed of the rewind and calculate the diameter. This has to be averaged because the rolls are not true.
How acturate do you need?

 

[OkiePC]

I have incorporated the logic required to do the math based on the line speed and it's accurate to within 3% already. It turns out, based on measuring finished rolls, that our average stock thickness is within .002" of the specification even though it does vary some throughout each roll.

The layout of the machine makes it nearly impossible to use ultrasonic sensors, and I don't need them anyway.

This machine does not have a dancer or accumulator to help with speed/tesnion control. It uses Reliance Webpak DC drives. The main drive sends a frequency signal directly to the letoff web drive. The letoff drive internally calculates the required speed to maintain the correct amount of tension. The PLC sends a tension reference to this drive also. The existing code that manipulates this trim reference is where the main problem lies. Now that I have the PLC5/15 making accurate measurements of the running diameters, I'm confident I can improve the tension trim logic.

I agree that a tension feedback device would help a great deal, and, if I can't get rock solid results from my software changes alone, that will be the next step.

The rewinder rolls are driven by a WebPak drive also, but get a speed reference from the PLC. The rewinder arms center drive the slit stock. The rewind arms run faster than required, and the individual slit rolls' cores actually slip on the shafts. There are pressure arms that apply variable pneumatic pressure to the sides of the cores to control how much friction is present to drive them. It makes controlling the rewind speed much less critical so that part is already pretty reliable.

I appreciate all the feedback ... Paul C.

 

[ELGC]

How do you solve it? Currently I need to do something similar but I have 3 vfd. And I do not have a sensor to measure the diameter. Best regards...

 

[AlfredoQuintero]

ELGC, I recommend you start a new thread writing down the background information of your issue.. The last post for this thread was in 2005.

 

[aruljothi1987]

Here are the formulae. They are derived by equating the total volume of material in the roll from the total length and material thickness to the volume in the roll as a cylinder. (Just assume the roll is 1 unit wide)

Length = (diameter ^ 2 - core Diameter ^ 2) * PI/(4 * Thickness)

Thickness = (Diameter ^ 2 - core diameter ^ 2 ) * PI/(4 * length)

Diameter = SQRT(( Length * 4 * Thickness / PI ) + core diameter^2)


NB: Simultaneous post, sorry for any confusion.

Great Conclusion