Calculating Distortion Factors Without a Chart

by Frank Burgos

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​Most flexo plates are exposed on a flat surface.  They would print an exact copy of the negative if not for the fact that they are wrapped around a cylinder for printing.  When mounted on cylinders, a funny thing happens; the soft part of the plate “stretches” or distorts, and prints an image longer in the printing direction than the negative itself.  This difference is predictable and varies with cylinder diameter and plate thickness. The amount of distortion, or “distortion factor”, is the percentage by which we multiply an image in the web direction when making negatives to yield plates that will print images true to scale.

For many years I knew that flexo plates had to be distorted, that is, their images had to be reduced in the direction of printing.  However, until recently, I simply relied on charts for the distortion factor for each of our cylinder sizes.  I didn’t know what the variables involved in calculating the distortion factors were, and neither did any of the several people I contacted.  We were all using charts without knowing how the factors were derived.

Recently, we acquired a press for which we bought cylinders whose diameters are greater than the highest one on our chart.  Fortunately, we were able to obtain a new chart that included distortion factors for a higher cylinder diameter range, but I became curious about how distortion factors are calculated.  Pencil, paper, and calculator in hand, I set out to derive the formula.  I am now pleased to share this formula with you.

As it happens, the distortion factor is, simply, the ratio of the diameter less twice the plate’s “soft” thickness, that is, not including the hard plate backing (photopolymer plates), to the printing diameter,  or: 

[print diameter – ( 2 x soft thickness )] / print diameter  = distortion factor

For example, let’s say you’re printing with:
 
     8.000” repeat cylinders and 0.067” thick plates
 
The printing diameter is: 8.000”divided by Pi (3.14159) = 2.5465”
 
The soft part of the plate is: 0.062” thick (0.067" minus the usual 0.005” thick backing). Multiplying 0.062" x 2 gives us 0.124"
 
Using these values, since:

[print diameter – ( 2 x soft thickness )] / print diameter = distortion factor
 
    [ 2.5465 – ( 0.124 ) ] / 2.5465  = distortion factor
  
      2.4225 / 2.5465 =0.9513 = 95.13%

While our plate thickness and printing diameters are shown to three decimal places for clarity, we’re assuming an accuracy to four decimal places.

Try a few calculations and compare them to your charts.  If you have any questions, don’t hesitate to contact me: frankb@flexoexchange.com.

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