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
Greetings to All,
This is Guhan S. K. from 6JXRX849+2J, a printer with over 20 years of web-offset printing experience. Welcome to my blog. Gaining knowledge about my workplace makes me happy and strong.
Tell me, and I forget;
teach me, and I remember;
include / involve me, and I become knowledgeable.
-- Benjamin Franklin
I gained knowledge of several technical aspects of my workplace here, which aided me in creating a blog that mostly focuses on the use of mathematics in the printing business. I want to share my expertise with students and printers worldwide.
Sometimes we fail to recognize or comprehend the true efficiency of machines, which are designed to provide high-quality output. Effective exercise for this involves focusing on them and asking questions like "How," "Why," and "what are they?"
To begin, let's load an example formula into the Spectro Densitometer, which we use to check for quality.
Know your device :
In addition to having all the features of a densitometer, modern pressroom spectrophotometers—also known as "spectro-densitometers"—can measure color and numerical color differences based on how the human visual system perceives and interprets color.
The spectro-densitometers that we use in the printing press room, such as the Xrite 528 and 530, are better (L*a*b*) than the Xrite series below 520. Lower series do not measure color vision; they simply measure ink layer density.
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 began tracking the RPM of each roller in our printing machine's ink train and plotted the results on a sheet. I discovered that one of the ink vibrator drum rollers in the train requires more time to complete a single rotation than the plate cylinder (plate cylinders are typically larger than ink rollers). This idea inspired me to determine the rollers' diameter without taking any measurements. It assisted me in creating a basic calculator that uses the RPM of a newsprint reel, ink roller, or cylinder to determine its diameter in relation 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;-
An encoder, which is an electronic device that generates pulses per rotation, can record the unwinding of newsprint reels during production. The number of pulses per second is then translated to RPM.
Using the calculator above, the reel diameter is calculated.
We may determine the reel's paper thickness (caliper) by looking at the unwinding pattern of the newsprint reel diameter, which descends at a specific interval (frequency) at a steady speed.
By using a formula, we can determine the length of the web based on the diameter and paper thickness.
We calculate the net weight of the newsprint reel using the web length and the GSM indicated by the paper mill.
Lastly, it is simple to determine the number of copies using the web's length, which is known as newsprint mileage. And by using the following example, this can be contrasted with the reel's net weight:
Every step provides real-time data (RTD), which the newest machines program and show. I began by calculating the second step after my machine displayed the newsprint reel's diameter in production. We may move ahead and backward using formulas. For instance, we can use diameter to get the reel's RPM at a specific machine speed. A mathematical technique is also utilized to forecast newsprint reel consumption before to manufacture. Continue reading...
Smart Links ;
As provided above RPM calculator, here I have given some important real time calculators link 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 mileage based on average image value for web offset printing.
SPANK ink mileage calculator : International method to calculate ink consumption
Can we determine the thickness of paper without a measuring device?
Indeed, we can determine the newsprint reel's paper thickness without taking a physical measurement. Paper thickness can be determined in a matter of seconds using a web offset machine that records the reel's unwind pattern at a specific time period (frequency). Both are inversely related; if the reel's diameter decreases, the RPM increases. The machine and reel are thought to be rotating at the same RMP when the newsprint reel's diameter reaches the cutting cylinder diameter. This pattern will vary from reel to reel, and the mileage of the paper is dependent on its thickness rather than its GSM. The paper with 42 GSM and 60 μm thickness unwinds more quickly than the paper with the same diameter and GSM with 55 μm thickness. Thus, the most crucial step in finding paper is determining its thickness.
The relationship between paper diameter and copy count in relation to paper thickness is depicted in the above chart. We learned from this chart graph that the diameter and number of copies are not linear; we obtain less copies per mile with the maximum caliper and more copies per mile with the minimum caliper or paper thickness, which helps us determine the 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 shared what I knew about color space and how to measure, test, and plot our printed color gamut from the printer's point of view. Continue reading...
This image, which was produced using the target colors' actual values, compares the SWOP, FOGRA, and IFRA color gamuts. The gamut sizes displayed here are actual, measured ones that I created and used for this topic.
CIE31 & CIE76
The translation from xy to u'v' in CIE color space was covered in both CIELAB 1976 and CIEXYZ 1931. Continue reading...
Our own gamut printed for testing is shown here as an example for both the CIE1931 and CIE1976 chromaticity diagrams, and the accompanying images are actual measured comparative IFRA targets.
Many things in the printing industry are driven by mathematical formulas and calculations; our goal is to improve our knowledge in order to succeed by putting in the necessary time, effort, and dedication ;
>> comment and suggestion is the most powerful RESPONSIBILITY - SO DO REPLY.
Keep in touch.. have a good day.
Thank you.
Regards,
