Maths and me @ Printing Industry
Blog ;- Application of Maths in Web offset Printing industry,
For Users ;- Articles framed for printers and students all around the world.
Trust worthiness ;- Projects and articles discussed here are author's personal observation and based on collections of data from Internet to his knowledge.
Introduction
Dear All,
Welcome to my Blog, this is Guhan S K from 6JXRX849+2** a printer more than 20 years of experience in web-offset printing. Learning things around my work place gives me strength and joy.
“ TELL ME AND I FORGET
TEACH ME AND I REMEMBER,
INVOLVE ME AND I LEARN. ”
– Benjamin Franklin
Here, I learned some technical aspects in my working environment and it helped me to develop blog that mainly focus on mathematical application in printing industry. I would like to share my experience to printers and students all around the world.
Machines are meant for quality production, and sometimes we forget to notice / understand their actual efficiency. This can be workout effectively by giving attention / focus towards them, like How / Why / & for what they are?
Let's start with an example formula loaded in Spectro densitometer (that we use for quality checking);
Know your device :
Today’s pressroom spectrophotometers (sometimes called “spectro-densitometers”), offer all of the capabilities of a densitometer and also have the ability to actually measure color and numeric color differences according to how the human visual system see and interprets color.
We @ printing press room use spectro-densitometer like Xrite 528, 530, they are superior (L*a*b*) than Xrite series below < 520. Lower series only measure ink layer density and not colour visuals.
This picture shows the working principle of Spectro densitometer, and calculation to measure density is ;-
D = LOG ( 1 / R % ) here, R is the reflectance of light observed by photo code (no.6 in picture) and display result in numerical value (no.7).
We can inverse this density formula to find reflectance as well like R = ( 10 ^D ) ^-1 * 100 .
Example :- We measure SID (solid ink density) of Cyan colour printed in the copy, if photo code (no.6) receive - 10.5 as reflectance observed in an angle (2°/10°) from the light source (illuminants like D50, D65) then,
R % = 10.5 / 100 = 0.105.
D = LOG ( 1 / 0.105 ) = 0.98 D
So as the result when reflectance of cyan is 10.5 we get density 0.98 D.
R = ( 10^( 0.98 ) )^-1 * 100 = 10.5 thus we can also reverse the formula to get reflectance.
We know this formula already in theory, practice in a worksheet using this formula by trying some other values of reflectance to find the density. Now you will feel the difference when using densitometer, and for quality check.. Read more ..
RPM and Diameter - Real time calculator
I started recording RPM of every roller in the ink train of our printing machine and plotted in a sheet, and I found one of the ink vibrator drum roller in the train takes more time than plate cylinder to complete one rotation (usually plate cylinder will be bigger than ink rollers). This concept trigger me to calculate the diameter of rollers without physical measurement. It helped me to develop simple calculator to find diameter for Newsprint reel / ink rollers / cylinders by its RPM with reference to machine speed.
Calculator to find the diameter of Newsprint reels / rollers / cylinders that are connected to the web offset machine at constant speed. This exclude RTF and PIV rollers having variable adjustment of RPM for particular machine speed.
Example 1 : - Let product height (cutting cylinder Knife to Knife) is 546 mm then M/c speed is 800 IPH (in inch mode/crawl speed), RPM is 6.666 (were 9 sec per rotation), submit in the form - we get 347.59 mm as diameter of our cutting cylinder. Two product length = Circumference of cutting cylinder,
so 546 + 546 = 1092 mm; C =πD, then D = C / π
Now D = 1092 / 3.141 (π) = 347.59 mm by formula
Try various entries and get the unknown diameter of Newsprint reel / roller / cylinder.
Example 2 : - I got 23.32 sec / rotation of a reel in inch mode (@ 800 IPH), then how to find the diameter of the Newsprint reel ? RPM = 60 / 23.32 = 2.572 then using calculator above we derived diameter as 900 mm.
Maths give way to find things by following simple steps here;-
Newsprint reel unwind while production, that can be recorded using encoder (electronic device that produce pulse per rotation) and number of pulses per second is converted to RPM,
Using calculator above RPM is used to derive - Reel diameter,
By observing unwinding pattern of Newsprint reel diameter that descend at particular interval (frequency) with constant speed, we can calculate - paper thickness (caliper) of the reel.
With diameter and paper thickness we are able to get - length of web by formula
From length of web and GSM denoted by paper mill we derive net weight of Newsprint reel.
Finally using length of web, it is easy to get number of copies - called Newsprint mileage. And this can be compared with Net weight of reel by saying Example; 247pages/kg at the end.
At each step we get real time data (RTD), this is programmed and displayed by latest machines. Here my machine displays diameter of Newsprint reel in production and then I started from the second step to calculate others. Using formula we can move forward and backward step, for example using diameter we can find the RPM of reel at particular machine speed. Math formula is also used to predict consumption of Newsprint reel before production Read more ...
Smart Links ;
As provided above RPM calculator, here I have given some important real time calculators links within my blog for quick access;
Strip waste (flat) calculation : Calculator to find damaged reel flat / strip waste weight, before stripping off the damage from the reel.
Balance reel - weight calculation : Calculator used to find Balance reel weight and Production calculations in Newsprint press reel room.
Analysis for grammage of Newsprint : Program to compute actual GSM / Knowing accuracy rate of GSM
Paper thickness / caliper calculator : Paper thickness based on diameter of reel and length of reel.
GSM to pages/kg : based on GSM used we can calculate pages / kg of Newsprint.
Ink mileage calculator : Find ink consumption and its mileage based on average image value.
SPANK ink mileage calculator : International method to calculate ink consumption
Without measuring tool can we calculate paper thickness?
Yes, we can find paper thickness of Newsprint reel without physical measurement - In web offset machine recording the unwind pattern of reel @ particular time interval (frequency), it is possible to calculate thickness of paper with in few seconds. If diameter of reel descends RPM get increased, both are inversely proportional. When Newsprint Reel diameter reach cutting cylinder diameter, then consider both machine and reel are rotating at same RMP. The paper with 42 GSM and 60 μm thickness unwind faster than that of reel with same diameter and GSM with 55 μm thickness, this pattern will be unique from reel to reel and paper mileage depends on paper thickness and not with GSM of paper. So calculating Paper thickness is most important to find paper mileage. Read more ...
Chart above show relation between diameter of paper and number of copies with respect to paper thickness. From this chart graph we understood both diameter and no. of copies are not linear, we get less copies/mileage with max. caliper and more copies/mileage with min. caliper or paper thickness thus deciding on paper mileage.
Newsprint Production Worksheet :
Production worksheet based on Diameter of reel data by converting to weight and documented here, following are features of this project work ;
Documentation of production report by calculating cost of materials consumed,
Report for single or multiple production can be document in a single sheet,
Day to day closing of production is possiable and no carry forward.
Suitable for both main productions and outsourcing works in combined.
Easy data entry worksheet based on diameter of reel, that is designed to suit for all productions with customized setup. - view pdf format
Ink Yield Vs Mileage ;
Ink mileage Sq.m/g
Ink mileage is said to be ; • Cyan 18 • Magenta 13 • Yellow 15 • K 7 .32 (m²/g)
This small value can be stretched to long data here - • Cyan = 18 (mileage) / pg.size (0.19) * 1000 = 94737 pages / kg of ink. we know our total pages printed, then total pages / mileage as above (94737 pg/kg) = we get ink consumption. Read more ...
Average NP paper thickness in μm
NP monitor paper caliper :- Like example average data for • 42 GSM reels ->Jeonju 55.2 μm ; Kondapoga 62.50 μm; Aspex 57 μm
• 40 GSM reels -> Albury 62 μm , tells us - Caliper data determines the performance (mileage) of the reels unlike GSM does, so it is important to monitor paper thickness carefully.
In such cases of reel mileage, it is easy to move with paper caliper apart from GSM that is labelled on reels. Small variation in caliper of above reels can be noticed, fix a tolerance value ± 2 like reel jeonju as 55 [ 53 ~ 57 ] is possible by analysing . Read more ...
Hickeys ;
Hickeys problem in printing has been discussed from my point of view. Theoretical collections of data from internet sources to justify the solution is discussed here. Read more ...
Colour Space ;
I expressed my observation on printer's point of view to my knowledge, about colour space and How to measure, test and plot our printed colour gamut? Read more ...
This picture is a comparative study of SWOP/FOGRA/IFRA colour gamut (created with actual values of target colours). The size of gamut shown here are real and measured one, prepared by myself and used in this post.
CIE31 & CIE76
CIE colour space both CIEXYZ 1931 and CIELAB 1976 discussed here conversion between xy to u'v' Read more ...
following pictures are actual measured comparative IFRA target and our own gamut printed for testing is displayed here as example for both CIE1931 and CIE1976 chromaticity diagram.
Calculations mathematical formula drive many things in printing industry - our GOAL is to learn things better to reach success by giving attention / dedication / hard work to secure knowledge ;
>> comment and suggestion is the most powerful RESPONSIBILITY - SO DO REPLY.
Keep in touch.. have a good day.
Thank you.
Regards,
