Unwinding roll diameter calculation

Jim G. · Mar 15, 2017

I pretty sure this has been covered before, but I need to ask. I have an Unwinding roll of paper and I want to display the diameter of the roll and the length of paper remaining. I have 2 signals available to do the calculation from.
The first signal is 4-20 mA based on line speed (1500 fpm max) and the other signal is a 4-20mA based on the rotational speed of the roll. I need to program the math expression in a Do-More program. Can anyone help me with the math? Thank you.

daba · Mar 15, 2017

If the line speed is X ft/min, and the rotation speed of the drum is Y revs/min

(X/Y) gives you feet per revolution of the drum.

1 revolution is pi x diameter, so the diameter is given by...,

(X/Y)/pi

Still working out how to determine length of paper remaining, but I'm sure it will need the "core" diameter, i.e. what it is rolled onto (like toilet paper cardboard tube, for example)

Steve Bailey · Mar 15, 2017

You need to know the thickness of a single layer of the paper (caliper) to establish the relationship between the diameter of the roll and the length of paper on the roll. The area of the circle represented by the roll of paper (remembering to subtract the area of the core) is equal to the length of the paper times its thickness.

PI x (OD^2/4 - Core diameter^2/4) = Length x caliper

Mispeld · Mar 15, 2017

For remaining length I am thinking along the lines of estimating thickness by monitoring diameter change over enough revolutions to get a stable signal, but not too long to introduce error from non-linear rate of change. Then subtract current diameter from core diameter and divide by thickness for estimated remaining loops. Then multiply this by average circumference (pi * (current dia - core dia) / 2) to get total length.

daba · Mar 15, 2017

Mispeld said:
For remaining length I am thinking along the lines of estimating thickness by monitoring diameter change over enough revolutions to get a stable signal, but not too long to introduce error from non-linear rate of change. Then subtract current diameter from core diameter and divide by thickness for estimated remaining loops. Then multiply this by average circumference (pi * (current dia - core dia) / 2) to get total length.

Do you know the length of paper on the roll at the start of unwinding ?

Steve Bailey · Mar 15, 2017

Have the operator enter the caliper at the HMI. As long as the paper comes from a reliable source, the thickness will be constant for any roll of that grade. Your calculated caliper will show some variance over the course of unwinding a roll.

Mispeld · Mar 15, 2017

Mispeld said:
For remaining length I am thinking along the lines of estimating thickness by monitoring diameter change over enough revolutions to get a stable signal, but not too long to introduce error from non-linear rate of change. Then subtract current diameter from core diameter and divide by thickness for estimated remaining loops. Then multiply this by average circumference (pi * (current dia - core dia) / 2) to get total length.

There are two problems here: (1) remaining loops should be the difference in radius divided by thickness, and (2) the average circumference should be (pi * ((current dia - core dia) / 2 + core dia)).

With these corrections, this approach is equivalent to the area-based solution provided in reply #3.

If thickness is known, it would certainly be better for data entry than estimating on-the-fly since error in that parameter will likely have a big effect on the length calculation.

MaReKA · Mar 15, 2017

Steve Bailey said:
PI x (OD^2/4 - Core diameter^2/4) = Length x caliper

Just a quick thank you, you solved a problem that I had a few years ago with a wind up application. Back then I had to calculate the spool diameter to regulate the motor speed. I was sure that I could differentiate this value given the wound material length and the material & liner thickness. After 2 days of wrecking my head I cheated and installed a sensor...
Just revisited an old excel file and the calculated values are close to my measurements.

Unwinding roll diameter calculation

Jim G.

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daba

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Steve Bailey

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Mispeld

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daba

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Steve Bailey

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Mispeld

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MaReKA

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