Math help for Rolled Length of Roll of Material

Hi all.
I`m modernizing our current foil rollers at my plant with analog position sensors with 0,1mm resolution, for "nearly empty" and "stop" alarms for the foil rollers on the packing machines instead of laser-sensors with Digital Outs to get maximal precision and reduce waste of foil.

And when I`m now installing analog sensors I would like to show the Lenght left on the roller on WinCC.
I try Google for the mathematic formulae for this and I found this calculator http://www.handymath.com/cgi-bin/rollen.cgi?submit=Entry
But they don`t show the mathematic formulae.

Could someone help me with the mathematic formulae in Metric?

Tanks in advance
And pardon my english

Regards
Kas

Length of material x thickness = Area of end of cylinder

L D[AR2 said:

Length of material x thickness = Area of end of cylinder

Click to expand...

Hi L D[AR2,P#0.0] Thanks for your replay, too be honest i did not understand your formula, I`m not sow good in math obviously


This is the known factors ( the values is just for example )
Outside Diameter of Rolled Material = 1000mm
Thickness of Material =0,1mm
Diameter of Center Hole = 100mm
Length of Material = ????????????

L = length of material
t = thickness
D = outside diameter
d = hole diameter

pi(D*D - d*d)/4 = L t

L = pi(D*D - d*d)/4t

Thank you L D[AR2,P#0.0], you have been grate help

Keep an eye on your units when you do this. Usually roll diameter will be in millimeters, length will be in millimeters and thickness will be in microns or millimeters.

At least you are using the metric system. If you are wrong you will be wrong exactly by a power of 10.

Keith

Hi Keith, Thanks for your replay.
My only concern now is the thickness of the foil, I dont think I would be able to measure each foil layer as you mention the unit microns. But this is not a issue, because the Display of the Lenght is just for practical help for the operator to know approx how long time it is befor he have to change a foil roller.
The plc just want to know when to automatic stop the machine befor the foil runs empty, and a "nearly empty" alarm on the SCADA for the operator.

Kas

Hi all,

Hope you all doing great, I am new PLC programmer and have limited experience, therefore your feedback will be very important to me.
I have a machine which has two rolls of material and what I want to do is to measure the length of the roll that has been used at the end of each core. Notice that the machine used state machine what I mean is not running continuously instead it runs five states and repeated and the last state has unwound the roll to do pleating.

My first thought is by using analog sensor which measures the change in the outer diameter and by using the following equation:

N = (D1-D0)/2*h

L = pie *N (D0+ h (N-1)
Where:
N = Number of turns
D1= outer Diameter
D0= Inner Diameter
H= Thickness of the material
L = length that used.

I found this formula while I was searching on how to calculate the length of roll but I am not sure if will work fine in my case, therefore, I am sending this email to get your feedback and if you have another way to share it with me would be great.