figuring roll diameter with encoder

I need to monitor the diameter of a roll of paper as it winds onto
a core bar. The speed is constant, the core roll diameter changes with each product,
the paper thickness never changes. The winding roll sits on two driven rolls
and is turned that way. The only input i have use of is an encoder
running from a wheel on the paper itself. The object is to stop the
roll at a certain given diameter. The above is my only info. And choice
of additionsl sensors or gear is not an option.

Can this be done only with math and the given information. I can't
Even monitor the roll rpms since it rides on drive rolls and is
not constant due to different core roll sizes. I do know core size
for each product.

So for each product I have core size, paper thickness and encoder
feedback for paper length, and speed of paper.

Any help would be great.

Thanks ahead of time

It sounds like this is called a surface winder. There are different ways to go about this. (paper area)+(core area) = roll area What is paper area? Area, of course, is length multilpied by width. paper thickness = width and the total amount of paper rolled is the length. The way to get the length is to integrate the paper (encoder) speed with respect to time. The core area is simply Pi * Radis * Radius Once you do the all the math you are left with paper area. Simply place area into the previous equation (area of a circle = Pi * radius * radius) Solve for radius and multiply by 2 to get your roll diameter.

I hope that helps. This method is not perfect, but it may be close enough for your needs.

Thanks,

thats about what i was trying to figure out. Ill mess with it some and
see how close i can get.

I had a similar situation, and I think I was given the same formulae as accidentalengineer provided you with, but I will post the link to the thread, in case it may help you.

http://www.plctalk.net/qanda/showthread.php?t=19333

Since you know line speed, you need to be able to keep track of each rotation of the roll to calculate diameter. Divide line speed by the time it takes for one revolution of the roll. That gives you the length of paper for one rotation, which is equal to the circumference of the roll. Circumference is equal to PI times diameter.

AS you read from the circumferance the smaller diameter will be running faster - it will slow down as the Diameter increases.
do you need to know what lenght of material is on the roll?
the alternative may be to measure the diameter by using your encoder to measure the angle of a pivot with the free running wheel following the roll.

I do this type of calculation on a pretty regular basis with the major caveat of making multiple thickness reductions along the way. At the end of the day the best way to look at is as a mass flow calculation. Length x Width X Thickness is the volume of product; past that it is all simple geometric calculations.

The major problem I ran into the first couple of iterations of this calculation process was error introduced into the length calculation in respect to time. Due to scan times in a processor 1 second rarely ever one real second. This can be over come by firing the event on a time base but using the the elapsed time between scans of the code to run the calculation if you find that your result is not accurate to what is occurring in the real world.

Another thing to consider in selecting your time base is that the shorter the time between calculations the more accuracy of speed "slices" (read calculated length) but a higher accumulated error and on the other side the longer the time base the less accurate the speed "slice" but a lower accumulated error in the calculation. This is something to be aware of and to play with to tune the calculation process.

PS - With a touch more thought I realized that in this way of doing the calculation the encoder is an extra variable that just muddies the waters. I would probably only use it to error check the calculation, ie. I calculate I am this big so I expect to see X roll velocity and given moment Y.

PPS - I am slow this morning. Encoder speed is line speed which is claimed to be constant so it will never vary. Mass flow is the only way that you can do this calculation without knowing the velocity of the drive rolls. Sheet (outer roll) velocity never changes so the drive roll velocity must always change or sheer point is exceeded and rip and crinkle occurs or in my world kaboom and smash. I assume the drive rolls are torque controlled to maintain line tension.

It is time for a 'duh' moment

I would divide the the number of encoder counts by the counts per revolution to get the number of wraps of paper. Then multiply the number of revolutions by the thickness of the paper per ply and then add the core radius. Multiply that by 2 to get the diameter.

Simple.

@Peter - You do not know the counts per revolution due to the fact that that is a function of the diameter of the roll which is the value being determined. Encoder counts are purely linear distance measurement and according to the OP the line speed is a constant which in turn means the outer surface of the roll where the encoder is measuring is going to be a constant. At some point a mass flow calculation must occur to determine the diameter of the coil, this could occur up front to say I need X linear feet of sheet to create a coil of Y diameter (straight preset) or X linear feet of sheet is Y diameter (dynamic coil diameter). Basically I am saying with the given set of variables nothing is going to change with respect to diameter that will have to be calculated either up front or continuously.

Put the encoder on the core.

Peter Nachtwey said:

I would divide the the number of encoder counts by the counts per revolution to get the number of wraps of paper. Then multiply the number of revolutions by the thickness of the paper per ply and then add the core radius. Multiply that by 2 to get the diameter.

Simple.

Click to expand...

Yes, if encoder would be on roll where paper is wrapped, but its seems that it is somewhere else on the way and only calculates distance.3

Peter Nachtwey said:

Put the encoder on the core.

Click to expand...

lstacys said:

The above is my only info. And choice
of additionsl sensors or gear is not an option.

Click to expand...

That is not an option.

From the description of the system it would appear that this is an arborless rewind configuration. A pressure arm would ride down on the outside of the roll to give the drag needed to generate line tension leaving the variable diameter core with nothing but inside of it to mount the encoded to physically. He has enough info already to extrapolate the diameter of the core at any given moment. I actually use the same info (speed, width, thickness and a density value) to generate a calculated coil weight.

Simplest Solution,

( ( (Pi * (Desired Diameter / 2)^2) - (Pi * (Core Diameter / 2)^2) ) / Material Thickness ) * Pulses per Linear Measure = Encoder Pulses for Preset Diameter

jdbeal,

As a polite junior member of the forum I must extend a virtual handshake and say, "Well done!" I feel certain your compact formula will meet the requirements of the OP. Just plug in the core size being used and the desired roll diameter and away we go!

Thanks.