Winding application formula explanation

This formula is for a Rewind application that is running correctly I am just having trouble under standing what it is doing. It tapers off the OA_Layon_Pressure_SP as the roll grows. I am just not seeing how it does it. The light bulb is has not turned on yet.


//10.6 = (10.6 inch) Min Diameter
//29.4 = Max Diameter (40 inch) - Min Diameter (10.6 inch)
//0.4 = (0.4 Bars) Pressure for Min Analog Output (0 PLC Scale = 4mA = 2V)
//2 = (2 Bars) Pressure for Max Analog Output (10000 PLC Scale = 20mA = 10V)
//1.6 = Pressure for Max Analog Output - Pressure for Min Analog Output
//10000 = Max PLC Scale
OA_Layon_Pressure_SP := ((((((Spool_Diameter - 10.6) / 29.4) * (PV_Final_Layon_Pressure - PV_Begin_Layon_Pressure)) + PV_Begin_Layon_Pressure) - 0.4) / 1.6) * 10000;

I am having trouble under standing this formula. I know it is Y=MX+B
M= ((Spool_Diameter - 10.6) / 29.4)
X=(PV_Final_Layon_Pressure - PV_Begin_Layon_Pressure)
B= PV_Begin_Layon_Pressure

But what is the - 0.4) / 1.6) * 10000

The scaling to convert the calculated EU pressure value to the 0-10000 value to send to the analog output?

Yes the card is 0~10000. I am just missing the Engineering Unit conversion

I would expect there are some limits wrapped around stuff that aren't being shown. For example, I suspect the user can't enter a value for PV_Begin_Layon_Pressure less that 0.4 or a value for PV_Final_Layon_Pressure greater than 2.0. Also, Spool_Diameter is likely limited between 10.6 and 40.

Don't try and shoehorn the numbers you have into Y=Mx + b unless you redevelop the equation from start to finish. You have two different conversions occurring here so you have two Y = Mx + b equation sets. Additionally the two equations have been 'normalized' to produce a ratio that is later multipied by a span.

The first part of the equation dealing with the spool diameter simply produces a value between 0 and 1 through the range of the roll run. The lay-on taper is linear through the diameter change and the start and end points are fixed. The second part, which determines the difference of the high and low pressure setpoints, defines the pressure change through the roll run. This combination yields a pressure value that changes from 0 to the pressure difference as the roll diameter changes from the minumum to the maximum. Add in the minimum pressure so you get the minimum loading at the minimum diameter, since the spool diameter ratio value will be zero there.

The next part is converting the resulting tapered pressure to a command output. You need to subtract the 0.4 since 0 command bits will produce 0.4 bar. Said another way, if the result of your taper equation says you need 0.4 bar of loading you need the command result to be zero. Dividing by 1.6 produces another ratio; a ratio that goes between 0 and 1 and the pressure command changes from 0.4 - 2.0. Remember we subtracted off the 0.4 just proir to the divide so the dividend is actually a maximum 1.6. this 0 - 1 ratio is now multiplied by 10000 so you get a command change ofm 0 - 10000 as the pressure command moves from 0.4 - 2.0

Keith

Keith
You just made the light start to flicker

kamenges said:

I would expect there are some limits wrapped around stuff that aren't being shown. For example, I suspect the user can't enter a value for

Click to expand...

kamenges said:

PV_Begin_Layon_Pressure less that 0.4 or a value for PV_Final_Layon_Pressure greater than 2.0. Also, Spool_Diameter is likely limited between 10.6 and 40.

Click to expand...

You are correct we are limiting the input data in the PanelView

kamenges said:

Don't try and shoehorn the numbers you have into Y=Mx + b unless you redevelop the equation from start to finish. You have two different conversions occurring here so you have two Y = Mx + b equation sets. Additionally the two equations have been 'normalized' to produce a ratio that is later multipied by a span.

Click to expand...

kamenges said:

The first part of the equation dealing with the spool diameter simply produces a value between 0 and 1 through the range of the roll run. The lay-on taper is linear through the diameter change and the start and end points are fixed. The second part, which determines the difference of the high and low pressure setpoints, defines the pressure change through the roll run. This combination yields a pressure value that changes from 0 to the pressure difference as the roll diameter changes from the minumum to the maximum. Add in the minimum pressure so you get the minimum loading at the minimum diameter, since the spool diameter ratio value will be zero there.

Click to expand...

I am good so far with the above.

kamenges said:

The next part is converting the resulting tapered pressure to a command output. You need to subtract the 0.4 since 0 command bits will produce 0.4 bar. Said another way, if the result of your taper equation says you need 0.4 bar of loading you need the command result to be zero. Dividing by 1.6 produces another ratio; a ratio that goes between 0 and 1 and the pressure command changes from 0.4 - 2.0. Remember we subtracted off the 0.4 just proir to the divide so the dividend is actually a maximum 1.6. this 0 - 1 ratio is now multiplied by 10000 so you get a command change ofm 0 - 10000 as the pressure command moves from 0.4 - 2.0

Click to expand...

kamenges said:

Keith

Click to expand...

Lost me

I added an Excel sheet just so I can try to follow what you are saying and what the system is doing.

I work for a papermill and we have rewinders that are AB Powerflex 700 driven. We have a pneumatic brake on the unwind stand with no diameter control. We set the brake pressure at a fixed setpoint until the winder reaches full speed then control the brake pressure to a torque setpoint, therefore the entire roll has a uniform torque throughout. We used to use load cells, but this works out alot better and 2 load cell simpler.

In our application the brake decreases as the roll diameter increases. Looking at your equation, the spool diameter must be the unwind spool as the pressure is directly proportional to the spool diameter.

I'm probably missing something, therefore talking garbage, so I appologise in advance.

The Spool Diameter is on the Rewind roll

Looks like the analog output goes to an I/P transducer, (probably calibrated for 4 to 20 milliamps) and the output of the processing unit is 0-10 volts. The part of the formula you are asking about would scale an analog output to produce 2 volts at minimum pressure (0), and 10 volts at max pressure. These voltages when passed through a 500 ohm resistor (load) would produce 4 to 20 milliamps. 1.6 equals 16 milliamps which equals 1.6 bar at the i/p transducer

creativepaper, you say the pressure decreases as the roll diameter increases. I believe you mean that the unwind brake pressure decreases as the rewind roll diameter increases. If both those points apply to the unwind brake then the tension would increase as the roll diameter decreases.

JeffKiper, the spreadsheet you attached appears correct to me. In effect, scaling to get from pressure to command bits is pretty much the same as the scaling to get from roll diameter to pressure. It's just that when you go from pressure to command bits all the limits are fixed (0.4 - 2.0 bar = 0 - 10000 bits). So you don't need to do any subtractions to get the ranges.

Think of it this way. The second part of the scaling takes the form of:
(Command Pressure - Min Pressure) / (Max Pressure - Min Pressure) * (Max Command Bits - Min Command Bits)
Command Pressure is the result of the taper function (the first part of the equation). Min Pressure is a fixed 0.4. Max Pressure is a fixed 2.0. Min Command Bits is a fixed 0. Max Command Bits is a fixed 10000. So if you fill in constants where you can you have:
(Command Pressure - 0.4) / 1.6 * 10000

This is similar to the taper equation:
((Current Diameter - Min Diameter) / (Max Diameter - Min Diameter) * (End Pressure - Start Pressure)) + Start Pressure

You need the offset of Start Pressure in this equation because, unlike the command bits scaling, when the result of the slope is zero you still need to output some value.

Keith