Guhan S K

Maths and me @ Printing Industry

Blog ;- Application of Maths in Web offset Printing industry,
For Users:- Articles designed for printers and students worldwide.
Trust worthiness ;- The projects and articles presented here are based on the author's own observations and, to the best of his knowledge, data compilations from the Internet.

Introduction

Greetings to All,

This is Guhan S. K. from 6JXRX849+2HH, a printer with over 25 years of web-offset printing experience. Welcome to my blog. Gaining knowledge about my workplace makes me joyful and strong.

Tell me, and I forget;

teach me, and I remember;

include / involve me, and I become knowledgeable.

-- Benjamin Franklin

Here at work, I learned about a number of technical topics that helped me develop a blog that mostly focuses on the application of mathematics in the printing industry. I wish to impart my knowledge to printers and students around the world.

Even though machines are made to produce high-quality results, we occasionally fail to see or understand their full efficiency. Asking "How," "Why," and "what are they?" while concentrating on them is a useful practice for this.

Let's start by loading a sample formula into the Spectro-densitometer, which is used to assess quality.

Know your device :

In addition to having all the features of a densitometer, modern pressroom "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 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, Read more ..

RPM and Diameter - Real time calculator

I began tracking each roller's RPM in our printing machine's ink train and plotted the information on a sheet. I discovered that one of the ink vibrator drum rollers takes longer to finish a single spin since plate cylinders are typically larger than ink rollers. This idea inspired me to determine the rollers' diameter without taking any actual measurements. It assisted me in creating a basic calculator that uses the RPM to determine the diameter of a newsprint reel, ink roller, or cylinder in relation to machine speed.

Calculator to determine the diameter of the cylinders, rollers, and newsprint reels that are attached to the web offset machine at a steady speed. This excludes RTF and PIV rollers with variable RPM adjustments for specific machine speeds, input the value and click the Cal.RPM button to convert the seconds to minutes per rotation if we know the rotation per second. Alternatively, input the RPM directly and then click the Submit button. Diameter is the outcome.

Example 1 : - Let product height is 546 mm, M/c speed is 800 IPH (in inch mode/crawl speed), RPM of cutting cylinder is 6.6667 (were 9 sec per rotation), submit in the form - we get 347.46 mm as diameter.
Two product length = Circumference of cutting cylinder, so 546 + 546 = 1092 mm; C =πD,

then D = C / π ; Now D = 1092 / 3.1428 (π) = 347.46 mm by formula

Try various entries and get the unknown diameter of Newsprint reel / roller / cylinder.

[Note : Formula for RPM = 60 / Sec, here 60 / 9 = 6.666666666666667]

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 900.29 mm. [ Cut-off - 546mm; Speed - 800IPH; RPM - 2.5729 ;]

Maths give way to find things by following simple steps here;-

An encoder electronic device that generate pulse per rotation, help to record the unwinding newsprint reels during production. The number of pulses per second is then translated to RPM as mentioned in above Example 2 .
After collecting RPM data, this information is used with the calculator above Module #01 and 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 Module #02.
By using a formula, we can determine the length of the web based on the diameter and paper thickness Module #05.
We calculate the net weight of the newsprint reel using the web length and the GSM indicated by the paper mill Module #06.
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 - PRESS REEL ROOM CALCULATOR (PR²C) :

The newest machines program and display the real-time data (RTD) provided by each phase. After my machine showed the newsprint reel diameter in production, I started by figuring out the second phase. We can use formulas to go both forward and backward. For example, diameter can be used to determine the RPM for a particular machine speed. Additionally, a mathematical method is used to predict newspaper reel consumption before to manufacture.

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 : Module #03 - Calculator to find damaged reel flat / strip waste weight, before stripping off them 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 : Module #05 - Paper thickness based on diameter of reel and length of reel.
GSM calculator : Module #06 - based on GSM used we can calculate net weight and web length.
Ink mileage calculator : Find ink consumption and mileage based on average image value for web offset Newspaper 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). If the reel's diameter decreases, the RPM increases both are inversely related. The machine and reel are thought to be rotating at the same RMP when the newsprint reel's diameter reaches the plate 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 mileage is determining its thickness. Read more..

The relationship between reel 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.

Web offset M/c Newsprint Paper caliper program;

Machines lacking a function for calculating paper thickness can use this Module #02 program. The diameter of the reel is often shown in real time on the console of most machines, but the caliper function might not be there. We can precisely reach the paper caliper range by using this module #02 software. Click the submit button after entering the information as below, you'll get an average paper thickness (caliper range).

A stopwatch (sec.ms) is attached. When the diameter reaches the first goal (initial dia), press the start button. Then, to automatically fill in the lap entries and stop the timer, press the lap button three times for three segments in 5mm dia interval difference.

Example;

To calculate the final paper thickness, the initial diameter (in this case, 570 mm) of the reel that drops every 5 mm frequency is recorded in Laptime (sec). We used three segments for computation and recorded the laptime activity in seconds (1st segment 570-565 -> 7.76 seconds, 2nd segment 565-560 -> 15.66 seconds, and 3rd segment 560-555 -> 23.48 seconds) because the reduction of 570 to 565 dia (5 mm) is considered a single segment in this situation. There may occasionally be a slight variation in the outcome because each segment's laptime is manually locked in the stopwatch here.

I tried data like

50000iph/570dia/5/LAP>7.76, 15.66, 23.48 from my stop watch and got 74.47μm result
45800iph /1100dia/5/LAP>17.48, 35.4, 53.23 >> 69.66 μm
50000iph/810dia/5/LAP>13.34, 26.78, 39.46 >>63.25 μm
45000iph/950dia/5/LAP>17.51, 35.13, 52.38 >>62.15 μm

As mentioned in Module #01, we can use RPM instead of diameter, and it should be converted to dia. This concept (paper thickness calculation) may be applied to existing outdated machinery.

We are aware that, similar to Module #05, the length of the web can be accurately determined using reel diameter and paper thickness.

If we have a balance reel with a diameter of 550 mm and an average caliper of 74.47 μm, we may use module #05 to submit the data and obtain a length of 3063 meters, which yields 5610 copies. Knowing the paper thickness of the reel makes it simple to compute the number of copies at any diameter and size of reel. In order to determine the quantity of copies, it is crucial to document the paper thickness of each type of reel in the reel room on a chart.

Program paper thickness calculation;

Following are data which is compared with MHI machine paper thickness calculation readings;

KPPL Reel 44 GSM >> 45200iph/820dia/5/Lap>13.63,27.59,41.16 >> Avg. caliper 67.88 μm matched with MHI m/c .
Aspex Reel 42 GSM>> 45500iph/1185dia/5/Lap>23.93,47.68,71.42 >>56.32 μm - 0.22 μm deviation with MHI m/c.

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 ;

Production report documentation by figuring out the cost/page in daily basis,
Reports for one or more productions can be contained on a single sheet. There is no carryover and daily production closure is possible (NP Reel net weight and BR weight).
Ideal for both primary productions and joint outsourced projects.
This simple data entry worksheet, which is based on reel diameter, is made to operate with any company that has a unique setup. View the PDF format

The documentation procedure is important when manufacturing a product since it helps with the more important duty of unit pricing computation. The profit/loss element, which is crucial to the workflow, was determined by the product's unit pricing, which takes into account all raw material and production expenses. After the project is completed, this unit pricing derivation will help prove our productivity. This criterion, Cost/page (Total pages / Total cost), may make the daily production document more efficient.

Ink Yield Vs Mileage ;

Yield is used in ink testing, were

Ink Yield = grams of ink (quantity) per sq. meter of paper - g / m²

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 ;

From the perspective of the printer, I explained what I knew about color space and how to measure, test, and map our printed color gamut. Go on reading...

The SWOP, FOGRA, and IFRA color gamut are compared in this graphic, which was created using the target colors' actual values. The gamut images that are shown here are real, measured ones that I made specifically for this piece.

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.

Our objective is to increase our knowledge in order to achieve by investing the required time, effort, and dedication because many aspects of the printing business are driven by mathematical formulas and calculations;

>> comment and suggestion is the most powerful RESPONSIBILITY - SO DO REPLY.

Keep in touch.. have a good day.

Thank you.

Regards,

Guhan S K - Printer,

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