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.
Time line : 2016-2019

Paper thickness (caliper);

Paper caliper is physically measured in thickness gauge meter / 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 ~ 75 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.

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.

Paper thickness / caliper calculator :

Calculator for Paper Thickness and Reel Length: Enter values such as 1016 mm for the reel's diameter and 10602 m for its length. Click the Calculate button in the paper thickness field to obtain the answer.

To obtain the reel length in meters based on the caliper, try adjusting the paper thickness and press the Calc. button in Reel length.

Used to determine the number of copies from the balance reel (using thickness and diameter)
Paper calipers, only provide the length of the reel and not its weight.
Without diameter of reel we can't compute paper thickness. So both diameter and paper thickness are important data part to find web length.

[Note: To help us determine the number of copies at a time, practice by writing Balance reel after production by the side as diameter / thickness example, 540/65.]

GSM of paper- calculator:

The GSM of a paper is used to determine the reel's net weight. These two calculators serve to highlight the differences between GSM and caliper. While a paper caliper only offers the reel's length and not its weight, GSM provides both the reel's weight and length.

The number of copies of fresh reels without length on the label is computed here.
Here, for balance reel weight the length form above caliper calculator Module #05 can be used.

Relation between Paper caliper & GSM :

GSM of paper

GSM stands for grammage per square meter of paper measured with a digital gauge. Today, we utilize newsprint paper that is between 40 and 55 GSM, while our writing paper (A4 Bond) is between 70 and 100 GSM. When buying paper, we must be aware that every product label contains this information, which also provides the product's weight.

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

Example;
(755 kg reel wt * 1000) g / (1.392 W * 12782 L size of newsprint) sq.m = 42.43 GSM (trade tolerance ± 2 is acceptable), by rearranging the above formula we can get length of web with respect to GSM.

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:

According to our research, paper mileage solely depends on paper thickness rather than GSM, which will aid in determining the product's weight (length -> weight conversion). The length of the web changes when the thickness of the paper changes.

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 the length by GSM and length by paper thickness are not same.

Thickness of paper determine accurate length of web, GSM give standard length like 1000/GSM. So paper mileage no of copies strictly depend on paper thickness.

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 formula to find 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 = 1500mm / 0.1mm = 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 - in sheet 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 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.

Additionally, the paper caliper is not consistent throughout the reel; the outer surface will be loosely wound, and the inner part will be compressed. Based on every examination, we discovered that the thickness always decreases to a specific range. The range is crucial since ± 2 µm deviation is visible in imported reels, therefore let's use the average range for further computation.

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.

Online calculator for paper caliper check Module #02 is provided in our blog.

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.

Example actual workout to find paper thickness 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 doing a thorough analysis and creating a database for the diameter of the reel and the quantity of copies, we concluded that both have a parabolic shape relationship, as seen in the chart above. The distance between the focus and the parabolic curve's vertex point increases when paper thickness rises, such as at 82, and it continues to reduce as thickness falls. Additionally, this chart shows that the variance between paper thickness at minimum (40-42, 42-44, etc.) is greater than the deviation between paper thickness at maximum (82-80, 80-78, etc.).

When comparing diameter and output (number of copies), this kind of pattern is frequently seen. The data sheet is created using a formula on different paper thicknesses. However, actual results may differ from theoretical results because to variations in paper thickness during the course of the web.

Here, we dived further to see how the number of copies varied for different paper thicknesses at a maximum diameter of 1250 mm of reel deviation. As previously indicated, this also takes the form of a modest parabolic curve, with the minimum distance between reels at higher paper thickness and the maximum at lower parts.

According to our research, variables like unequal winding or paper compression could be the cause of inaccuracies in the output number of copies. Aside from that, the maker of paper cannot guarantee that the paper will be the proper thickness from end to end of a reel, which could change the output at any point.

The graph above illustrates how paper thickness changes when reel unwind diameter decreases for a single reel with an average of 81µm. The environment and handling can alter the caliper characteristics of paper in an uneven pattern like this because the outer portion of the reel loses more than the inner area owing to compression. However, we can take into account average data, and this variance often falls between ± 2 or 3 µm for the length of the reel.

Therefore, calculating the paper caliper at a certain location will not determine the real result, and sometimes converting to length based on this criterion will also produce an incorrect result.

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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