It sometimes becomes necessary to print or slit rolls to diameters smaller than the
original, or master, rolls. Knowing beforehand what diameter master rolls should have can reduce the number of splices, down time, and scrap. One way of determining the correct master roll
diameter is to assume that the total side area of the rolls rewound from a master roll is equal to the side area of that master roll. It then follows that, if we determine the total side area of the rewound
rolls, we can calculate the master roll diameter.
For example, let's say that we expect to rewind about four 18" diameter rolls on 4" O.D. cores from a master roll whose core O.D. is
7". Using the following formula:
At= n(pi)[rr2- rc2]
Where:
At = Total side area
n = Number of rewound rolls per master roll
rr = Radius of a rewound roll
rc = Outer radius of rewound core
We get:
= n(pi)[rr2- rc2]
At= 4(3.1416)[(9in)2- (2in)2
]
At= 4(3.1416)[81in2- 4in2]
At= 967.613in2= 968in2
This is the total side area of the rewound rolls. We can then "plug" this figure into another formula to get the master roll diameter. Using the formula:
Where:
rmr = Master roll radius
rmc = Outer radius of the master roll core
At = Total side area
of the rewound rolls = Total side area of the master roll
(the area calculated previously with the first formula)
We get:
= [ (At/pi)+ rmc2]1/2
rmr = [ (968in2/3.1416)+
(3.5in)2]1/2
rmr = [320.373in2]1/2
rmr = 17.899in= 18in
This is the radius of the master roll. It's diameter is twice that, or 36inches.
If you'd like a larger or smaller diameter use a larger or smaller value for "n"
.
This method should work regardless of core diameters. However, variables such as tension, substrate compressibility, etc. may affect it's accuracy.
I hope that this
information proves useful to you. I will post the derivations of the above formulas as soon as possible. If you have any questions, please contact me at:
