Guhan S K - Paper caliper

Maths and me @ Paper thickness

Project on Paper thickness or Caliper of paper.
Aim : To develop best method/formula to calculate paper caliper of Newsprint reel on real time (online).
Time line : 2016-2019

Paper caliper

Paper caliper is physically measured in micrometer or screw gauge and result denoted as thickness in microns ɥm (1/1000 mm) or points mils (1/1000 inch). Newsprint paper caliper for example 42 GSM may be between 45 ~ 70 ɥm (microns) approximately. Our writing paper (A4 Bond) has 80 ~ 115 ɥm range according to paper manufacturer, high quality Bond has maximum thickness like 110 ɥm with 80 GSM.

The caliper or sheet thickness is one of the important basic physical properties of paper and paperboard.

Caliper or thickness of paper is depends on : -

• Refined stock • Category of fiber used • dryer temperature • load on press section • calendars • moister content • filler etc for a given basis weight. Thickness is related to bulk or dense of paper.

Uniform caliper or sheet thickness is very important for mother roll building up quality of paper, whether it is printing papers, condenser paper, saturating papers etc. If the caliper changes, then it could be affect some fundamental properties like :-

• quality of the paper as like bad formation • uneven drying • strength • stiffness • bad mother roll development • optical quality etc.

Furthermore cutter machine have to face problem for bad mother roll building up. Caliper is most important for printing press; print quality and press runnability is affected by caliper variation. Hence controlling the caliper is very significant for a papermaker; it is good always trying to keep optimum and uniform caliper.

Paper thickness / caliper calculator :

Here I have provided calculator for computing - Paper thickness. Enter data for example - Diameter of reel 1016 mm and Reel length 1062 m.

Now hit Calc. button to find the result - 76 ɥm. Like this try some input of your own data and get the result.

How to increase the caliper of the paper in manufacturing?

Caliper is affected by refining of the fiber; well refined or beaten of stock reduce the thickness. In addition consistency in the headbox also effect on it. So a papermaker always should check out the degree and consistency of the stock and should be keep it at optimum level.
Press and calendars nip pressure, number of press section, number of calendars and stacks are significant for caliper. If press and calendars load is reduce then caliper increase. On the other hand, if calendars and press section increase than the caliper decrease. Hence it should be used optimum press and calendars load.
Caliper is also affected by ash content or filler. If ash content is reduced then increase the thickness. Using of PCC as filler can increase the caliper of paper.
Short fiber pulp such as hard wood or straw pulp can reduce the caliper. Mechanical pulp such as BCTMP increases the caliper.
If first group dryer temperature differs then the caliper also differ. It should be low to increase the caliper.
Moisture content is another parameter for caliper. It should be kept standard level.

Relation between Paper caliper & GSM :

GSM of paper

GSM - grammage per square meter of paper weighed in digital gauge. Newsprint paper that we use today is around 40 ~ 50 GSM, our writing paper (A4 Bond) comes in 70 ~ 80 GSM. While purchasing paper we have to notice this GSM that every product label bear this data, it gives weight of our product as well.

Weight in grams by dimension in meter of the product gives GSM data,

example (755 kg reel wt * 1000) g / (1.392 W * 12782 L size of newsprint) m = 42.43 GSM (trade tolerance +/- 2 is acceptable). Here using formula we can compute paper thickness from length of web and diameter of reel, so changes in GSM affect paper thickness/caliper.

Density of Paper:

GSM by Paper caliper gives density of paper, for example [ (42 GSM / 65 ɥm) * 1000 ] = 646.154 kg/m³ . Here density of paper is described to show the relation between GSM and paper caliper.

Paper mileage:

From our study paper mileage is only depend on paper thickness and not GSM it will help to find weight of product (length -> weight conversion) . When paper thickness varies length of web get different, even GSM are same.

We in Newspaper industry use reels of 40 GSM with caliper 65 ɥm thickness, 42 GSM with 47 ɥm thickness and so on. Like said above 42 GSM reels comes with different thickness range from 45 to 75 ɥm, so there is no direct relation between paper caliper and GSM both are different.

Physical measurement using screw gauge to measure sheet thickness:

Easy way to find paper thickness - Example:

A4 Bond 70 GSM - I folded paper 2 times so 4 sheets and measured the thickness using screw gauge, it shows 0.42 mm. Now 0.42 / 4 = 0.105 * 1000 caliper = 105 ɥm as result.
[ Note : 1 meter = 10^-3 millimeter or 10^-6 micrometer ]
Newsprint paper Kondapoga 42 GSM - 0.25 /4 * 1000 = 62.5 ɥm (in picture)
Newsprint paper Albury 40 GSM - 0.27 / 4 *1000 = 67.5 ɥm
Uncoated paper 65 GSM - 0.37 / 4 * 1000 = 92.5 ɥm

This method can be done more precious by average calculation like below;

1st fold - 2 sheet > 0.145mm = 72.5 ɥm; 2nd fold - 4 sheet > 0.29mm = 72.5 ɥm; 3rd fold - 8 sheet > 0.57 mm = 71.25 ɥm >> Average caliper = 72.08 ɥm

Even we can use formulas for finding paper caliper without physical measurement, let us see in detail about this calculation in this blog,

How to calculate A4 paper thickness in bulk using scale?

A4 packet of 500 sheets with size - 0.210*0.297 (m) - 0.06237 m²,

Let weight of 500 sheets pack is 2.5 kg then = (2.5*1000) / (0.06237*500) = 80.16 GSM (to find GSM of paper)
If 500 sheets height is measured using scale as 50 mm then = 50 / 500 = 0.1 mm or 100 ɥm caliper (find caliper of paper)
Paper loaded in sheet-fed in-feed board measure height with scale eg. 1.5 m and if known paper caliper is 100 ɥm then = 1500 / 0.1 = 15,000 sheets (find no.of sheets)

Need ISO paper size calculation formula - then click here

Automation for finding GSM and Paper caliper

With simple technique we can automate our printing machine to do this calculation for paper caliper and GSM - both in sheet fed and web fed offset machines.

We get GSM by weight of paper and their dimension -

in-feed board with help of load cell that calculate weight can be attached (like in digital weighing m/c)
by using sensors we get dimension and height of paper loaded.

Now after 10 or 20 sheets pass for printing - then difference can be monitor online, the weight and height are readings of 10/20 sheets after pass. With this it is possible to derive GSM and as well as paper caliper, by simple technique using hardware and software integration we can automate the process. Result can be monitored online for full production in closed loop on display and it help to know our substrate quality even better.

Calculating Paper thickness or caliper in web offset machine:

Reel mileage is mainly depend on paper caliper. Paper caliper differ from reel to reel based on type of composition of raw materials used like - virgin and recycled fibers, fillers, binders by paper mills. For example at an average diameter of reel, when paper caliper down ▼ we get more copies by physical count and if paper caliper is up ▲ we get less copies. This phenomenon clearly gives that paper caliper is most important criteria to decide paper mileage. Paper manufacture maintain their standard GSM, but reels with 62 ɥm caliper and other with 55 ɥm caliper gives different (yield) number of copies, even though they have same diameter and GSM.

• NP - Langer:
• GSM - 42.0 • Calculated paper thickness - 49.75 ɥm
• Diameter ᵠ - 1250 mm
• Length - 23915 m (Mileage - L / 0.546 - 43800 copies)
• Weight - 1403 kg ( Actual wt - pages/250.6=1398.2 kg )
Mileage as per GSM 250.6*1403/8 = 43949 copies
• Physical measure: 2 fold- 0.20 mm / 4 *1000 = 50ɥm

• NP - Soucy:
• GSM - 42.0 • Calculated paper thickness - 76.18 ɥm
• Diameter ᵠ - 1016 mm
• Length - 10602 m (Mileage - L / 0.546 - 19417 copies)
• Weight - 628 kg ( Actual wt - pages/250.6 =620 kg )
Mileage as per GSM 250.6*628/8 = 19672 copies
• Physical measure: 2 fold- 0.32 mm / 4 *1000 = 80ɥm

How to find Paper caliper using formula in web offset machine?

By recording unwind pattern of RPM or diameter of a reel, that your machine display on production can be used to calculate paper caliper. When diameter of reel reduce RPM get increased, here I used diameter of reel - as my machine display real time data in production. Recording time taken for every interval (eg. 5mm) reduction of diameter is calculated to find paper caliper.

This worksheet calculation is tested with our machine MHI DIAMOND SPIRIT, it too calculate paper caliper and display on production. Our result is compared with machine calculation and displayed here.

Machine calculated paper caliper as - 66.79 ɥm
Excel work sheet result as 66.77 ɥm forAlbury 40 GSM reel.

Entry ; 60100 IPH; Ø 750 mm; Lap time 18.95,18.86,18.62,18.95

Excel worksheet for calculating Paper caliper :

This worksheet has 3 data part,

Pre-production - basic reel label data like GSM, weight, length etc..
Production - Lap time for recording the reel pattern on production time.
Post-production - Total no. of copies consumed and core/wrapper weight is used to record.

Pre Production data :

As picture shows input data - product size, reel size, GSM, diameter of reel, weight and reel length are basic data. After entering we get result (text in red color) by formula as follow ;

In this pre production data module, here we calculate caliper for Kondapoga Reel 42 GSM based on weight and length as in picture.

GSM is converted to pages/kg, here 42 GSM - gives 250.6 pg/kg by formula
Weight of reel 746 Kg with GSM data - gives paper thickness as 62.98 ɥm by formula.
Length of reel 12564 m is converted to copies, pages/kg and approximate weight of reel that exclude core and wrapper weight. Using length and diameter gives paper caliper as 63.11 ɥm, that can be compared with weight - caliper (cross verification)
After entering total copies consumed - it gives the difference from actual consumption here 81 copies i.e 648 pages and equal to 2.5 kg.

Production Data:

In production we take LAP time using stop clock for recording the reel unwind pattern - using this we can get paper caliper.

Frequency interval set here is 5mm, we can change this setting. At every 5 mm reduction of reel diameter while production with constant speed 50 IPH Lap time is recorded and based on this data we derive paper caliper 63.41 ɥm here.

With this Caliper data and net reel weight worksheet convert total pages as projection and efficiency 248.8 pg/kg
Page yield with 65.13 sec is 7190 pages - with this calculation we derive run time of reel @ 50000 IPH as 27.7 min.
Using GSM and calculated caliper we derive Density of paper 662.4 kg/m²

Post Production Data:

After production completed enter copies printed, empty core weight and wrapper weight. This calculate white waste from reel length, as said above total copies is compared with length data again. To find more accuracy and cross verification we do conversion at all possible places for comparison.

Newsprint Efficiency graphical representation:

Apart from numbers and formula we extend this worksheet with graphs. As we know a diagram speak thousand words -

Pages / kg based on:- GSM, Caliper that get from LAP time and with actual consumption
Total copies:- Mileage based on Reel diameter and weight is given for comparison,
Caliper of Paper :- When time increase between intervals caliper get down and if it reverse paper caliper move up - it shows the caliper position in graph for better understanding.

Example actual workout to find efficiency of Newsprint reel :

It is possible within a few seconds to know the efficiency of our reel used. Let start workout to do as follows;

Collect Reel data from the label as above
Prepare for auto pasting and let the reel start its production
While production record the LAP time (using Stop watch in your mobile) with particular diameter interval as shown in 4 & 5
Input all data in following worksheet as below
After completion of the particular reel, collect total no.of copies printed and fill in the post production data. Now you will get chart sheet as follows.

Report documentation :

As we recorded LAP time for fixed diameter (eg. 5 mm here) from 950 dia to 930 dia, chart plotted accordingly and formula extend here to find the caliper of paper as 61.93 ɥm.
Time taken for a reel at constant speed of machine, that descend at unique pattern is observed and calculated to find caliper. When time taken reduce, caliper of paper increase and vice-versa.

Worksheet provide comparison between actual diameter and weight of reel. If there is difference in calculated paper caliper it shows abnormality as in case of A (in picture) otherwise, it look good as B.
This total copies mileage graph is best and easy to understand the performance as well as accuracy of caliper, GSM and weight of the reel used.

After collecting number of copies printed (post production data) by the reel, we can compare the efficiency by pages / kg with GSM and caliper data.
As we see here when number of copies / caliper changes we get different visual graph to identify them.

NP Diameter Vs Output-> No. of copies - w.r.t PAPER THICKNESS :

After deep analysis by preparing database for diameter of reel and number of copies we came to conclusion that both are not in linear, but it takes parabolic shape relationship as shown in above chart. When paper thickness increase high like @ 82 we see more distance between focus and vertex point of parabolic curve and it keep on decreasing as thickness decreases below. And also deviation between paper thickness at maximum like 82 - 80, 80-78,... is less and deviation between paper thickness at min. 40-42, 42-44,... is more from this chart. This type of pattern is common while comparing Diameter and output - No. of copies, data sheet is prepared by formula on varies paper thickness. But actual may be different from what we get theoretically, this happened because fluctuation / inconsistency in paper thickness throughout the web length.

With help of this single chart we can get result number of copies at any diameter/paper thickness of reel in press reel room.

Here we drilled more deep to visualize variation in number of copies @ maximum diameter 1250 mm of reel deviation for varies paper thickness. This too take slight parabolic curve in shape as mentioned above, minimum distance between reels at higher paper thickness and maximum at lower part.

As we studied factors like uneven winding or paper compression may be reason for errors in accuracy of getting output no. of copies here. Apart from that paper manufacturer can't sure to maintain correct paper thickness from end to end of a reel, this may varies the output at any time.

When reel unwind diameter decrease, we observe paper thickness as shown in above graph for a single reel that has 81µm average. As outer area is loser than inner area of reel due to compression, environment and handling may change the caliper characteristics of paper in un-uniform pattern like this. But we can consider average data and also this deviation usually lies between ± 3µm throughout the reel length.

So calculating paper caliper at particular point will not decide the actual result, and converting to length based on this criteria will also ends wrong result sometime.

By increasing the scale of the graph we can see average uniform pattern of paper caliper shown in above GIF image.

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