3 ways to calculate distortion in flexography

This is one of the biggest concerns of those who work in flexography, that's why we have brought 3 ways to calculate elongation. Two calculations through mathematical formulas and a totally different way that will surprise you.

Why is distortion applied in flexography?

You are probably already familiar with applying an elongation percentage on files for flexo, but you don't understand why.

If you take a photopolymer sheet or cirel (common name in other countries) and place it on a flat surface, in this position the lower part (Xd) and the upper part (Yd) have the same length.

Distortion factor

However, when the iron is wrapped over a cylinder, the surface of the iron begins to stretch. Then the distance from the top of the iron becomes larger than the distance from the bottom of the iron.

When engraving a photopolymer plate, it is done in a completely flat position. Therefore, the original file must be reduced or the measurement distorted, only in the direction in which it will be wrapped around the perimeter of the cylinder.

All this, so that when the plate is wrapped around the cylinder, it has the correct measurement.

The distortion percentage is simply the Xd / Yd ratio. Where Xd is the circumference of the inner circle and Yd is the outer circumference of the outer circle.

Mathematical formula

We will begin by understanding something very simple, which is to know the difference between the radius, the diameter and the perimeter of a circumference.

The radio is the distance from the center to the edge of the circumference. Its formula is diameter ÷ 2.

The diameter is the straight-line distance from edge to edge of a circle. If you draw that line, two parts will remain exactly the same. Its formula is perimeter ÷ π (π = ~ 3.14159)

The perimeter is the edge of the circle, that is, the total distance that the edge of a circle travels. Its formula is, 2 * π * R (π = ~ 3.14159)

Below we leave a video so that you understand these concepts that are fundamental in a better way.

So we know that there are two circumference measurements that we must find. The top of the plate (Yd), and the base where the plate is mounted (Xd).

Yes, the distortion formula is:

 % Distortion = Xd / Yd

So we replace the formula as follows:

% Distortion = 2πR₁ / 2πR₂

Where R₁ is the Radius of the lower circumference and R₂ is the Radius of the upper circumference of the plate.

The values of R₁ and R₂ depend on the thickness of the plate (P), the thickness of the mounting tape (T), the radius of the cylinder (C), and the thickness of the polyester supporting the plate.

It should be noted that one of the key elements so that the iron does not stretch at the bottom, it is support polyester of the plate or mylar which is very resistant and does not allow that at the time of assembly of the plate it is stretched. Yes, you have seen flexographic plates, you will surely know that this plate base is very resistant.

Following the formula, we proceed to calculate the Radius of the two circles.

The R₁ equals the radius of the cylinder plus the thickness of the mounting tape plus the thickness of the polyester base of the sheet.

R₁ = C + T + M

The R₂ equals the radius of the cylinder plus the thickness of the mounting tape plus the thickness of the plate.

R₂ = C + T + P

We would have our elongation formula as follows:

% Distortion = (C + T + M) / (C + T + P)

Distortion with repeat length

In order to find the distortion percentage taking the repetition length (RL), we must understand the following.

The repeat length is the perimeter of the circle of the plate in the upper part when it is assembled (upper perimeter).

How is distortion in flexography

With the RL we can find the radius of that circle which is Yd.

Now to find Xd, we must subtract Yd from the height of the plate (Plate (P) – Polyester Base (M)). It seems complicated, but we will see an example.

The formula would look something like this, % Distortion = [RL ÷ (2π) + (MP)] / [RL ÷ (2π)]  

For our example we will take the following conditions. A job with a 25 "repeat length and using a 0.067" gauge plate.

Plate (P) = 0.067 ”or 1.702 mm

Polyester base (M) = 0.005 ”or 0.127 mm

Repetition (RL) = 25 ”or 635 mm

% Distortion = [635 ÷ (2 x 3.1416) + (0.127-1.702)] / [635 ÷ (2 x 3.1416)]

% Distortion = 99.4885 / 101.0633

% Distortion = 0.9844 or 98.44%

The percentage of distortion to apply to the job in the printing direction is 98.44%.

Distortion with the distortion factor

We have already seen the most complex way to calculate, now we will see a very practical way through an elongation constant according to the size of the plate.

This constant or elongation factor C was found after many studies and is summarized in the following table.

Cliché thicknessFactor C
1.14mm – 0.045″6,10
1.70mm – 0.067″ 9,89
2.54mm – 0.100″ 15,16
2.84mm – 0.112″ 17,08
3.94mm – 0.155″ 23,94

If you want to know where this Factor C comes from, it is done using this formula,

Factor C = (2π) + (MP). 

Note: Polyester for 1.14mm gauge is 0.178mm, for other gauges it is 0.127mm.

And the formula using Factor C is as follows,

% Distortion = [1- (C / RL Factor)] * 100

Using the same data from the previous exercise, we would have,

% Distortion = [1- (9.89 / 635)] * 100

% Distortion = 98.44 %

Simple calculation and easy to do

This form has been one of the ways in which our clients have been able to determine the elongation when they do not have the data that the formulas need.

The way is very simple. You take a piece of photopolymer sheet that is longer than the development of the roller and that has a surface (preferably a solid). You stick the mounting tape you commonly use and stick it to the roller.

As the plate is longer than the diameter of the roller, the two mouths will come together and one will overlap the other. When this happens, make a mark with a pen, right where they overlap. It is recommended to make a long mark.

Then the plate is detached and pasted on a flat surface, and with a tape measure, it will be measured from the mark to the beginning of the plate along the length. This measurement is what the files should have once elongated when using that cylinder for printing.

This has given us the experience of accompanying many printers and advising them, therefore if you require support in this type of calculations or something additional, our team is fully available to support you.

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