math problem

[daved]

The reason for the minutes to splice is only for operator info.
I used the HSCE counter on the running roll to calculate the diameter of the roll. I then calculate the area of the diameter.
I use the HSCE on the outgoing cylinder to calculate the amount of area I am consuming per min. A little more math and out pops minutes to splice.
Last splice I was off by 4 seconds.
Thanks again to all replies

 

[Peter Nachtwey]

Re: Dumb question, NOT!

This is outside my normal area of expertise, so I'm going to ask a few stupid questions. Instead of working off the feed roll, which is a changing diameter and varying ft./revolution, isn't there a pinch roll or similar feed mechanism that is going to accurately indicate the fpm of the paper? And then, would it be easy to do one calcuation for ft per roll vs. caliper and diameter? Then his timing job get's easy, doesn't it?

Not a dumb question. It is possible to compute the break time using the winder encoder provided one knows the initial or current radius and the ending radius. Every once in a while this number can be updated using the current counts/sec and the current radius. It is not necessary to measure the radius at each update, this can be calculated using the initial radius, paper thickness and counts. I was waiting to see if some one has figured it out. Hint, PI is not required! The answer is simple.

Let's see equations! I am working so I don't have time to give a full explanation till this evening.

 

[Peter Nachtwey]

OK, here it is

Assuming the material comes of the roll at a constant speed and the current radius is know at start. In the veneer industry there are scanners that can measure the radius of a block of wood.

length * thickness = PI * ( MaxRadius^2 - MinRadius^2 )

This is just equating two areas. The width of the paper has no part in this. This eliminates the need for calculus.

length = speed x time

time = PI * ( CurrentRadius^2 - MinRadius^2 ) / speed * thickness

time is the time it takes to get to the MinRadius from the Current radius.

Now we need to measure velocity by using a counter that provides us revolutions per second.

speed = revolutions per second * 2 * PI * CurrentRadius.

Combining.

time = ( CurrentRadius^2 - MinRadius^2 ) / ( CurrentRadius * revolutons per second * 2 * thickness )

Notice that PI cancels out!

This equation can be updated every second or so like the progress bar on a download. One always knows the CurrentRadius because after it is initially measured you can use the counter to tell how many revolutions or plies have come of the roll.

For those that are bored.

Winder scheduling Equations

 

[nif]

Hello !
exellent formulas here !
I just wan't to add one thing. You said you know the speed of the paper ? Then it's easy to calculate the actual diameter of the reel.
You just simply calculate the paperspeed <- >circumferencespeed then you get the diameter.

I hope this formula is right because my math is at the least said bad..

actual diameter = paperspeed/ rotations_per_sec *2pii

the you use peters formulas to calculate the time

 

[Peter Nachtwey]

Not quite right

Nif,

actual radius = paperspeed/ rotations_per_sec *2pii

Someone in a previous thread said you can get the speed of the paper by using another roller with an encoder. I automated veneer lathes ( lots of fun ) and I the radius because the block ( a log ) had just been scanned using lasers or photocells. Once peeling began, I always knew the radius because we knew the position of the knife that was peeling of the veneer. However once the radius is known one can alway count shaft encoder pulses to calculated how many revolutions ( by thinknesses ) have gone by since starting.

Tangent, the world leaders in veneer lathes are in NIF's home turf of Lahti, Finland. These guys are sharp. Veneer lathes are very demanding mathematically, mechanically and computationally. Most veneer lathes have laser scanners that can measure the wood and compute how to orient the ends of the block ( log ) so that one can peel off the longest full width sheets of plywood. I used to associate Finland with veneer lathes long before Nokia made phones.

See Raute Wood They are in Lahti.