Guhan S K - Ink Mileage

Maths and me @ Ink Mileage

Project : Ink mileage calculation (For Newspaper production).
Aim : To create best ink mileage calculation specially for Newspaper industry.
Time line : 2016-2017
Project detail posted in WAN-IFRA forums Printing>>Ink ; Print-planet forums printplanet.com/threads/

What is Ink mileage?

Similar to how reel mileage is calculated in newspaper printing, we can express ink mileage in pages per kilogram, for instance, 94,500 pg/kg of ink. This indicates that 1 kilogram of ink is needed to print 94,500 pages. Here 94500 pages * 0.190008 (product size) = 17955 m²/kg of ink is the result of converting pages to square meter per kg. We know that 1 kilogram is equal to 1000 g, for our convenience we can reduce this to 17.955 m²/grams of ink. This small figure, which rounds off to 18 m²/g, is easy for us to remember and convey. Changes may now be easily identified as 18.00, 17.75, and 17.50 (in m²/g), max. and min. tolerance settings can be easily fixed with the target.

For example, the average ink mileage data is => C - 18.02, M - 15.61, Y - 13.12, and K - 7.151 (m²/g).

Why mileage unit is m²/g and not g/m² :

Newspaper printing has images and text in a page that change frequently, thus ink coverage is not even always some time black (text) or colour content. So consumption of ink varies accordingly and there is no constant amount of ink per square meter of paper- for example gsm >> 1000 / (94500 * 0.190008 * 2) => 0.02784 g/m², so having constant material in numerator (paper/ink) is easy to calculate.

Square meter of Newsprint in which gram of ink is spread - based on total consumption (pg/kg method), an integer number as square meter per gram (Example; Black ink mileage = 5.85 m²/g as average) then,(1,20,500 total page printed * 0.190008 product size) Total m² coverage / 5.85 m²/g mileage => gives consumption 3914 g or 4 kg.

SMG - Square meter per gram method is a perfect solution to consider as unit of Ink mileage calculation for Newspaper production. This help us to easily communicate, remember and compare ink mileage.

Factor that influences ink-mileage :

Pigment strength and content of the ink-formulation.
Stock quality that used for printing (Newsprint).
Ink feeding style of the production plant.
Water / ink balance behaviour in production.
Pre-press adjustment or settings like UCR/GCR etc. TIC % standards may reduce or increase the consumption of ink.
Press (machine) condition settings like ink duct roller gap, pressure setting of ink roller train etc.. may affect consumption pattern.

How to get ink consumption?

Now a days machines are with auto inking system and tracking ink consumption for a particular production is difficult. Before calculating mileage we have to practice some alternative method to get consumed ink, let us discuss in detail ;

My mom says 50 ml of milk is short today, by observing the bottle of milk purchased from the vendor. How this is possible? - By percentage method level of milk daily purchased is compare with the day of shortage; from 1000 ml (1 L) of milk it is possible to find 50 ml shortage that is 5%. Yes we can do so, then apply same concept of percentage method to find ink consumption is also possible.

Ink duct picture shows percentage method to calculate consumed ink. 20 * 70/100 = 14 so reduction of ink is 20-14 is 6 kg like that we are able to find following duct 20 * 50/100 = 10 = 10 kg and other one 20 * 15/100 = 3 = 17 kg like that.

By using measuring scale or percentage method as discussed above we can calculate ink consumption in tank on daily basis. For example if we have ink tank @ full capacity (on open) is 1500mm (100%) and empty cane is @ 20mm (0%), mark top and bottom end. Now centre mark is >>1500-20 = 740mm (50%), then rest of readings can be marked in scale and used to calculate remaining ink (balance) in tank.

Can a worksheet will hep to calculate consumption?

Yes, in our style we prepared worksheet to do this calculation for ink mileage;

This image is an excel sheet snap short that hold data of physical picture of opening balance and closing balance of ink with percentage method. The out put we get from here is variant- m² of paper per gram ink covered and we combine average image value per page on that day with this data.

Getting average of this two data from 3 to 5 days reading and fix them as standard, based on this standard values we can bring daily consumption. It is enough to check bimonthly of ink consumption with percentage method, and rest we can do with help of average image per page data by calculation.

So with help of worksheet we are able to calculate ink mileage in daily basis based on actual consumption. To get consumed ink for example C 17.95 m²/g - then expanding 17.95 * 1000 / 0.19 = 94474 pages/kg ; divide this by total production pages 43,10,526 / 94474 - we get total consumption as 45.6 kg of Cyan ink finally.

In this case fixing tolerance and monitor the deviations is not so difficult -Example 18 ± 1 give deviation to ± 10,000 pages approx. If we feel that more deviations, then we reset the tolerance as ± 0.5 (~ ± 5000 pages) as our customs settings. If my ink mileage for cyan comes between 92105 to 97368 pages - it is safe and we say with in tolerance (18.5 to 17.5 m²/ g).

Can we compare ink mileage?

Yes we can compare easily ink brands or batch by average data collected like below ;

INK A (D** *NK)-> C - 18.2 ; M - 15.6 ; Y- 13.12 and K - 10.5 (m²/g)

INK B (SA**T* *NK)-> C - 19.11 ; M - 11.50 ; Y- 9.44 and K - 7.47 (m²/g)

INK C (HU*** *NK)-> C - 15.5 ; M - 14.50 ; Y- 13.54 and K - 5.11 (m²/g)

Now can we say the difference between these two company's / batch INK - A has more mileage in Magenta, Yellow ,K-Black compared to INK B. Is this correct? - Yes, when calculated as average for more than a month ( mostly 1 quarterly period). Total square meter of paper for 3 months / consumption of ink in grams for 3 months will be near to target.

When INK A & B covers equal % of image in single day production when consolidation, then we say in this case mileage is true. For ink mileage we have to consider the image ratio into account for correct comparison. Some time average (image ratio/month may be approx. equal) data per month in 3 to 6 cycle can be graphed and monitor to get conclusion as said in above example.

Image value and Ink pre-set value:

What is Average image value or Average ink coverage (AIC)?

It is a integer value of every column of Image usually calculated by imaging software for individual color, Full image is divided into columns for example I have 700 mm image width, it is divided by 50 mm of each column 700/50 = 14. So I have 14 column as Zone 1-14.

There are number of software companies that provide this image coverage calculation, you can check out free version also available (like APFill, printcal etc..). Image coverage value differ from company to company full solid coverage in a column may be 60 and another may be 80 it depends upon software in-account of TIC (total image coverage).

Four color image CMYK - separated with 14 column and weight of ink / image is summed and average is taken. Let us consider average value for a page as 15 for K (so n = 105 then, n / 7 = 15), sum of all column in every pages and compute average (average image/page), then total image/page >> and divide by number of pages we get average image value per production. With this single integer number start to calculate ink consumption, when average image value / average ink coverage increase ▲there will be drop ▼in ink mileage number of pages per kg or sq.m/g. - More image value - more ink consumption << result >> less mileage = less coverage area.

Mean coverage calculations

To calculate the mean coverage for the ink zones of one separation, the corresponding preview image is divided up into columns, each one with a width that is matching the width of the ink zones in the press. When the image has been divided, the mean coverage of each column is calculated.

In reality it is not as simple as this, mainly because of three things. First, the screened tint blocks at each long side of the plate have to be removed (Nc). Second, it is not likely that the width of the preview image matches the width of the total numbers of ink zones. The third difficulty is that the number of pixels per ink zone is probably not an integer.

To solve these problems, the approach is to divide the mean calculation in four steps;

find and remove the ink traps
add paper white in both ends of the image to make the image width match the width of the total numbers of ink zones.
make the number of pixels per ink zone as integer and,
divide the image into columns corresponding to the ink keys and calculate the mean over each key.
Sum of all mean average of total plates has been derived as Avg. Image-Value, a whole number that represent individual K,C,M,Y plates image ratio's average used as in below calculator to find mileage and ink consumption.
Example; Cyan Avg. Image ratio = Sum of total image ratio value of cyan ink zone / No. of cyan plates
This mean coverage and ink key opening curve is set based on trial and error method. Note they are just numbers to open ink key initially that support for start-up printing only.

Ink key setting;

To calculate volume of ink in each zone is based on key opening, from the image ink layer area is calculated by following formula;

Area = π(h²+2rh),

when we are able to calculate area of each zone with time and speed of machine then, it is possible to derive consumption of ink based on this formula. The thickness of ink layer is said to be ink profile, this is based on image coverage in that particular zone. We can say ink profile is area (A) that cover the image area of plate and reproduce on substrate, if output is heavy or low inking has to be adjusted using key opening that is decided by manual (production staff) or Auto correction (PID).

Here graph show that when ink key opening is more then area (profile) also get increased, but not in linearity manner.

Ink consumption based on AIC - average ink coverage;

Simply press Submit button you will get the result mileage in Sq.m/g and total consumption in kilo gram.

Try your hand for some other values - get ink consumption based on average image value. Higher the image part lower the mileage Sq.m/g and increase the ink consumption.

Example; K90 Img.value =5.4Sqm/g=54kg con.; Y90 Img.value = 3.9sq.m/g= 75.73kg.

Here Image value is sum of zones output image set value of ink-preset provided by software like below chart

This calculation is an example module to get ink mileage and consumption based on image value, it works on preset value that differ from press to press. Following are criteria that affect results of this Ink mileage Calculator ;

If my TAC % suggested by ISO standard get change,
If there is change in ink curve setting in press,
If ink brand or batch change (depth ratio of pigment change)
When we adjust image size production (No change in product size)
Change in image ink conversion software or settings.

Above said is a sample program to show the power of mathematical calculation. Provided values are current settings in our press - trial basics we have to find the actual consumption and ink factor value, that has to be feed in background of this program to calculate such mileage.

Image value - number based on image zone coverage generated by ink value software. This can be convert to pre-set ink value (key opening) - ink screw value calculation with single formula in excel - FORECAST, below image is an example for calculation using (x,y) coordination and linear interpolation formula [ (y2-y1)/(x2-x1)*(x-x1) ]. We can generate pre-set (key opening) ink screw value for our press standard as below.

Ink pre-set value is based on curve settings (custom), that we do with trial and error method. If we feel image more dark with pre-set value then, we can control by adjusting the curve value. We tried this concept with Excel worksheet and displayed images here. Based on external ink coverage software and curve settings >> image-ratio vs key opening we can convert values by above said manner.

Google Sites

Report abuse