About Diameter Calculation

Hi~ I have some question about diameter calculation.
Hope someone explain for me. Thank you~

I read two version now.
#Version 1 :
"Line Speed Integration" divided by "Motor Speed Feedback Intergration", then result divided by PI (3.14159).

(a)What's meaning "Line Speed Integration" and "Motor Speed Feedback Intergration"? I don't understand What we get after integrating.
(b)Why can we get diameter from this equation ?

#Version 2 :
Version 2 is also using "Line Speed" divided by "Motor Speed Feedback", but something is different from version1.

(a)What's meaning "core diameter" divided by "max diameter" (it is called "Scaled Core Diameter" on diagram)?
and we have a parameter called "Diameter Buildup" on diagram, it is "Diameter calculated" divided by "Scaled Core Diameter".
(b)What's meaning "Diameter Buildup" ? and Why "Our Drive's "Speed Reference" is divided by "Diameter Buildup" ?

Maybe questions are too easy, but I don't understand. Thanks your time for reading and replying, Thank you very much.

BTW, Version 1 is from Allen Bradley Logix5555 PLC program and Flexpak3000 Drive. This is our paper winder.
Version 2 is from Simoreg digital DC Drive Armature Winder Function diagrams.
Thank you very much!!

I am going back to school here in the late 1950s - is not diameter py squared r? wher r is the radius.
I use a computer based calculator these days.

Circumference = Pi X Diameter

Diameter = Circumference/Pi

therefore "Line Speed Integration" divided by "Motor Speed Feedback Intergration", must = Circumference

Line Speed = distance/time,
Motor Speed = revolutions/time

(dist/time)/(rev/time) = (Dist/time)X(time/rev)
time is cancelled = Dist/rev = circumference


As for the core diameter scaling stuff, it looks to be trying to give a linear relationship between rpm and dist/time of the roll. I don't have any winding applications but if the linear speed of the material is to be kept constant then the rotational speed of the motor/spool must be higher RPM at low spool diameters and lower RPM at higher spool diameters. Thats where the math comes in.

Brian.
(how's that for a wirepulling, light bulb changing sparky?)

Sliver said:

Circumference = Pi X Diameter

Diameter = Circumference/Pi

therefore "Line Speed Integration" divided by "Motor Speed Feedback Intergration", must = Circumference

Line Speed = distance/time,
Motor Speed = revolutions/time

(dist/time)/(rev/time) = (Dist/time)X(time/rev)
time is cancelled = Dist/rev = circumference


As for the core diameter scaling stuff, it looks to be trying to give a linear relationship between rpm and dist/time of the roll. I don't have any winding applications but if the linear speed of the material is to be kept constant then the rotational speed of the motor/spool must be higher RPM at low spool diameters and lower RPM at higher spool diameters. Thats where the math comes in.

Brian.
(how's that for a wirepulling, light bulb changing sparky?)

Click to expand...

That is truly impressive for a conduit bender

(how's that for a wirepulling, light bulb changing sparky?)


Impressive. You didn't have to resort to the old "If you can't dazzle them with brilliance, baffle them with bullsh!t" tactic!

One word of caution about using these equations: I would not "trust" the output of these equations during the early stages of the roll buildup as the least little errors in speed feedback can cause significant variations in the output. You might not want to use the output until the motor speed goes below a certain rpm and/or a certain rate of change.

I have cut and pasted the comments for a winder program that I am writing (line speed is given in fpm - the equation gives the coil diameter in inches):

"These three rungs perform the following equation to calculate coil diameter:

diameter = (line speed)(gear ratio) / (motor rpm) (PI / 12)

(PI / 12 = 3.14 / 12 = .261799 The / 12 part is done so that diameter will come out in inches rather than feet)"

I have used diameter calc on Eurotherm drives in the past.Basically it reduces the speed of the spool as the diameter of the spool grows with increased material.

Normally I have used it for wire. In that case it gets complicated because not only the wire diameter ,but the traverse across the spool width must be factored in. With film or web it is more simple.

I have had the best results using an ultrasonic or laser sensor to constantly measure spool diamater as it grows and adjust spool RPM accordingly.

Thank you guys!! Thank you all very much!!

It looks similar to rpm to mpm conversion.
-->> mpm = rpm * pi * D , but D is constant diameter.
Here we talk about variable diameter calculation, is it integrer function here ??
And I'm thinking a question, take a paper winder as example, the line speed is the distance that has run out, right ??!! If the paper motor runs slowly (lower rpm) causing the paper loose not tight, is it correct diameter in this situation ??
Another question is about paper winder control below.
Our paper winder uses main line speed plus offset(offset of unwinder is negative value, rewinder is positive value) as its speed reference, and follows the main line running. But I think paper winder is used tension control to maintain the paper tension, right ?? How do I do the tension control ?? Please advise, thanks.
Sorry my poor English, Thank you very much !!

As you already realised the speed ratio diameter calculator won't work all by itself. It needs to work in conjunction with a control method that tries to maintain tension or roll surface velocity. If you don't have this additional control the winder spindle speed won't have any real reference to product roll tangential speed and the diameter calculator will either freeze (unlikely) or move in a random direction based on random speed errors.

The reason you use a diameter calculator at all is you don't want the tension control algorithm to have to generate all the speed command. If thye winder is a high speed winder it will be very difficult to find tension control gain settings that react quickly enough to keep up with accel and decel but are low enough to give you a stable system. The diameter calculator allow you to use the machine speed reference (line speed) to generate the majority of the spindle drive speed reference. You then use a tension control algorith to adjust the spindle speed a small amount to maintain tension.

Here's the fun part. Ultimately, the small changes from the tension control algorithm become part of the total spindle speed, which is used for diameter calculation. So the tension adjustments tend to drive the diameter value, ultimately decreasing the amount of tension adjustment required.

Hope this helps.
Keith