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Solving curl problems: the basics: practical solutions for reducing paper curl.

Curl problems are a complex interaction of furnish fur·nish  
tr.v. fur·nished, fur·nish·ing, fur·nish·es
1. To equip with what is needed, especially to provide furniture for.

 properties, sheet formation, drying conditions, and printing conditions. Despite the underlying complexity, papermakers can reduce curl by focusing on a few key production parameters.

The degree of curl in end use can be reduced by minimizing the coefficient of moisture expansion (CME CME

See: Chicago Mercantile Exchange


See Chicago Mercantile Exchange (CME).
) in the papermaking pa·per·mak·ing  
The process or craft of making paper.

 furnish. Even more important is the need to adjust wire- vs. felt side structure and composition so that they are more alike. For laminates and board, this means making the structure of individual layers more alike. There is also a need to balance wire- and felt-side coating or surface sizing. Sheet shrinkage Shrinkage

The amount by which inventory on hand is shorter than the amount of inventory recorded.

The missing inventory could be due to theft, damage, or book keeping errors.
, top-to-bottom drying, and moisture content also affect the degree of curl. Finally, it is highly recommended that papermakers continually test their products in the end-use machines for which they are intended.

The key to control of curl is good test methods that can provide meaningful measurements of curl.

Note that the examples in this article are based on information from testing xerographic xe·rog·ra·phy  
A dry photographic or photocopying process in which a negative image formed by a resinous powder on an electrically charged plate is electrically transferred to and thermally fixed as positive on a paper or other copying surface.
 (laser) paper samples, but much of the discussion can be applied to understanding curl problems in other types of paper, as well.


Curl is a direct reflection of the way the sheet of paper is put together. The process variables that control curl include furnish, sheet structure, and drying. Furnish variables include the inherent CME for the fibers, refining conditions, and additives. Sheet-structure effects include the development of differences in top-vs.-bottom CME from fiber orientation and material stratification stratification (Lat.,=made in layers), layered structure formed by the deposition of sedimentary rocks. Changes between strata are interpreted as the result of fluctuations in the intensity and persistence of the depositional agent, e.g. . The following outline identifies the adjustments that papermakers can make to reduce curl.


* Measure freely dried CME or tensile tensile,
adj having a degree of elasticity; having the ability to be extended or stretched.
 stiffness index (TSI TSI Total Solar Irradiance (sum solar light in energy per unit of time)
TSI Trading Standards Institute (UK)
TSI Transportation Safety Institute (US DOT) 

* Lower the furnish CME by reducing the level of refining or changing the refining method and/or choosing fibers with lower CME. (Brushing-type refining increases fiber CME, while cutting-type refining results in less reactive fibers. Hardwoods typically have lower CME than softwoods, but this is not always the case.)

Sheet structure

Fiber orientation.

* Measure CME of split sheets.

* Reduce wire side (WS)-to-felt side (FS) difference in CME (or TSI) in both the MD and CD.

* Reduce CME differential by adjusting jet-to-wire speed. (Generally, a jet-to-wire ratio of 1.0 produces the least curl, but trials are required to confirm this for a given paper machine.)

* Measure tensile stiffness orientation (TSO (Time Sharing Option) Software that provides interactive communications for IBM's MVS operating system. It allows a user or programmer to launch an application from a terminal and interactively work with it. The TSO counterpart in VM is called CMS. ) of the sheet in the full CD.

* Minimize TSO by balancing the manifold manifold

In mathematics, a topological space (see topology) with a family of local coordinate systems related to each other by certain classes of coordinate transformations. Manifolds occur in algebraic geometry, differential equations, and classical dynamics.
, adjusting headbox edge-control valves, and adjusting jet-to-wire ratios.

* Alternatively, use heated curl tests to estimate WS and FS CME differentials and then balance the process to minimize differences.

Curl tests are an indirect measurement of WS-to-FS difference in the "effects" of differential CME. Any curl test that measures it can be used. Two tests--the "hot bend" and "warm oven" curl tests--are described at the end of this article.


Table I shows the results of tests on two papers using the hot-bend test. Positive numbers indicate curl toward the WS, and data are in millimeters of hanging curl. The interpretation of the data is that paper A has more oriented o·ri·ent  
1. Orient The countries of Asia, especially of eastern Asia.

a. The luster characteristic of a pearl of high quality.

b. A pearl having exceptional luster.

 fibers on the wire side, while paper B has more oriented fibers on the felt side.

An interpretation of the "dual" curl effect is presented in Appendix D. Attempts to improve unbalanced test results should be made by changing jet-to-wire speed and perhaps ether ether, in chemistry
ether, any of a number of organic compounds whose molecules contain two hydrocarbon groups joined by single bonds to an oxygen atom.
 adjustments such as headbox jet impingement impingement (impinj´mnt),
n the striking or application of excessive pressure to a tissue by food or a prosthesis.
 angle, forming board placement, and headbox consistency. Since drainage can affect sheet structure, conditions and changes in foils and the forming board may be factors.

If a dandy roll dandy roll
A cylinder of wire gauze pressed on moist pulp before it starts through the rollers of a papermaking device and resulting in the production of a watermark. Also called dandy roller.
 is used, its speed relative to the wire may be a factor in cases where the stock consistency under the dandy is low enough for fiber realignment re·a·lign  
tr.v. re·a·ligned, re·a·lign·ing, re·a·ligns
1. To put back into proper order or alignment.

2. To make new groupings of or working arrangements between.
. Changes in percent long fiber or softwood softwood

Timber obtained from coniferous trees (mainly of the pine and fir families). With the exception of bald cypress, tamarack, and larch, softwood trees are evergreens.
 could also be a factor, since higher percentages could increase differential orientation. Ideally, both halves of the sheet should be nearly the same, but this is very difficult on a single-wire, fourdrinier paper machine. Twin-wire paper machines are much better in this respect, although the fiber orientation at the edges of a twin-wire sheet is always different than in the center.

Sheet composition.

* Determine the effect of filler fill·er 1  
One that fills, as:
a. Something added to augment weight or size or fill space.

b. A composition, especially a semisolid that hardens on drying, used to fill pores, cracks, or holes in wood, plaster,
 and fines distribution on CME.

* Establish the effect of moisture diffusion diffusion, in chemistry, the spontaneous migration of substances from regions where their concentration is high to regions where their concentration is low. Diffusion is important in many life processes.  on curl.

* Balance WS/FS coating binder binder: see combine.

An earlier Microsoft Office workbook file that let users combine related documents from different Office applications. The documents could be viewed, saved, opened, e-mailed and printed as a group.

Experiments in which two sheets of copy paper are simultaneously run through a copy-machine fuser roller indicate that the moisture-diffusion characteristics of paper affect curl. Tables II and III show results for two sheets of 75-g/[m.sup.2] twin-wire paper after passage through a set of heated rollers.

The results in Table II show that a backing sheet moves curl toward the hotter roll, i.e., the printed side. It may increase curl if curl is already toward the print side, or reduce curl if the sheet curls away from the print side.

Table III shows that the backing-sheet curl increases toward the hot roller as moisture content increases, whereas the sheet touching the hot roller shows a normal decrease in toward-print curl as moisture increases. What appears to be happening is that moisture is settling near the interface of the two sheets. With this, we may have an explanation for toward-print curl for heavy sheets, in that moisture ends up in the center of the sheet thickness, rather than in the side away from the heat.

Surface-sizing distribution between the two halves of a split sample can be measured by performing a hotwater extraction and measuring starch starch, white, odorless, tasteless, carbohydrate powder. It plays a vital role in the biochemistry of both plants and animals and has important commercial uses.  concentration. With coatings, the weight of binder added to each surface should be balanced.


* Control moisture to 4.5%-5.0%.

* Reduce internal stain (reduce felt tensions, draws).

* Adjust top-to-bottom drying.

Moisture. We can deduce de·duce  
tr.v. de·duced, de·duc·ing, de·duc·es
1. To reach (a conclusion) by reasoning.

2. To infer from a general principle; reason deductively:
 the effect of moisture on copy-paper curl by looking at Tables II and III. At low moisture, curl is toward the printed side, while at higher moisture curl is away from the printed side (3). This is seen in lighter basis-weight sheets such as 75 g/[m.sup.2]. In heavier basis weights, curl is always toward the printed side. It appears that moisture-vapor diffusion plays a role (Table III).

Internal strain. When a sheet with different moisture expansion properties on each side is dried, there is a natural formation of internal strain (4). (See Appendix C for a discussion of internal strain.) Figure 1 depicts a two-layered sheet with differing shrinkage properties in each layer, illustrated in Fig. 1a by partial lengths in layers x and y. If the sheet is freely dried without constraint, it will form a curvature curvature

Measure of the rate of change of direction of a curved line or surface at any point. In general, it is the reciprocal of the radius of the circle or sphere of best fit to the curve or surface at that point.
 toward layer x, as seen in Fig. 1b. However, in normal drying, there are flattening
Ellipticity redirects here. For the mathematical topic of ellipticity, see elliptic operator.

The flattening, ellipticity, or oblateness of an oblate spheroid is the "squashing" of the spheroid's pole, down towards its equator.
 constraints that cause the sheet to dry flat or nearly so, as seen in Fig. 1c, which depicts the differences in internal strains that have formed in the structure. Each length ([DELTA][x.sub.i] and [DELTA][y.sub.i]) represents a potential shrinkage that can take place if the internal strains are released. If the strains are released equally, curvatures formed will tend toward the freely dried shape (Fig. 1b).

Internal strain has the undesirable effect of being released by heat and moisture. When there is differential internal strain produced by drying an inherently different CME on the wire and felt sides, additional curl can be produced. We can reduce the average internal strain by using looser felts and draws, which in turn can reduce curl. The results in Table IV show that a reduction in internal strain reduces curl in copy paper at both levels of moisture content. Another useful approach is to reduce the inherent CME of the furnish.

Top-to-bottom drying. Drying also affects curl of the final sheet in its packaged form. We know that the relative temperature of the top and bottom dryers affect this type of curl (5). Experimental results have been previously reported (4). Curl is often controlled on the paper machine by adjusting top and bottom dryers in the last section. While under tension in the dryer, paper curls towards the wetter side. Normally, paper curls away from the last hot dryer can. Since paper made on a fourdrinier machine Fourdrinier machine

Machine for producing paper, paperboard, and other fibreboards, consisting of a moving endless belt of wire or plastic screen that receives a mixture of pulp and water and allows excess water to drain off, forming a continuous sheet for further drying by
 commonly has wire-side curl, top dryer cans are run hotter than the bottom cans to correct this problem. However, curl is still caused primarily by sheet structure, and correction of curl with differential drying is only a hand-aid.

MULTILAYERED mul·ti·lay·ered  
Consisting of or involving several individual layers or levels.

To reduce curl of carton board or labels, we need to determine the basic reasons why it occurs. This may require extensive testing. No doubt the fibrous fibrous /fi·brous/ (fi´brus) composed of or containing fibers.

Composed of or characterized by fibroblasts, fibrils, or connective tissue fibers.
 arrangements within the layers and the inherent moisture expansion and contraction properties of the fiber both can play a role in making the board and labels prone to curl. The printing process may also play a role in making the board curl, especially if it puts water or moisture into the board. A copy machine easily produces curl with a label product with different properties in the two layers.

With a multilayered board or label, the individual layers can be analyzed using sonic modulus See modulo.  or moisture expansion techniques. Freely dried samples of the individual layers or freely dried handsheets of each layer are needed to make good comparisons. For good curl characteristics, board or label layers should exhibit properties that are very similar, especially the outer layers. The analysis also should include the effects of internal strain.


The basic statement of sheet deviation from the flat is given in Eq. 1 (1):

(1) w(x,y) = 0.5([K.sub.x][chi square chi square (kī),
n a nonparametric statistic used with discrete data in the form of frequency count (nominal data) or percentages or proportions that can be reduced to frequencies.
] + [K.sub.y][y.sup.2] + [K.sub.xy]xy)


x = machine direction (MD) coordinate on the sheet

y = cross-machine direction (CD) coordinate on the sheet

[K.sub.x] = MD curl component

[K.sub.y] = CD curl component

[K.sub.xy] = diagonal curl component

The curl components (curvatures as inverse (mathematics) inverse - Given a function, f : D -> C, a function g : C -> D is called a left inverse for f if for all d in D, g (f d) = d and a right inverse if, for all c in C, f (g c) = c and an inverse if both conditions hold.  radius) are defined in Eqs. 2-4:

(2) [K.sub.x] = 2 [[([DELTA][[epsilon].sub.MD]).sub.bottom--top]]/z (MD)

(3) [K.sub.y] = 2 [[([DELTA][[epsilon].sub.CD]).sub.bottom--top]]/z (CD)

(4) [K.sub.xy] = 2 [([DELTA][[PHI phi
Symbol The 21st letter of the Greek alphabet.

n See health information, protected.
]])([DELTA][[epsilon].sub.CD] + [DELTA][[epsilon].sub.MD])]/z (diagonal)


z = thickness

[epsilon] = strain

[PHI] = fiber orientation angle

Curl is the effect of differential change in two halves of the sheet for MD and CD curl, while diagonal curl is an effect of differential fiber orientation angle between the wire side (WS) and felt side (FS). If we take [DELTA][epsilon] in percent (2) and sheet thickness in mils as z, we can use Eq. 5 to obtain a hanging curl (cord height of 8.5-in.), h, in mm:

(5) h = 1935([DELTA][epsilon])/z [congruent con·gru·ent  
1. Corresponding; congruous.

2. Mathematics
a. Coinciding exactly when superimposed: congruent triangles.

 to] 2000([DELTA][epsilon])/z

APPENDICES ap·pen·di·ces  
A plural of appendix.

A: Hot-bend curl test

Figure 2 illustrates the hot-bend curl test. The aluminum block is heated to 300[degrees]F [+ or -] 10[degrees]F, and the paper strip is then held by fingertips "Fingertips" is a 1963 number-one hit single recorded live by "Little" Stevie Wonder for Motown's Tamla label. Wonder's first hit single, "Fingertips" was the first live, non-studio recording to reach number-one on the Billboard Pop Singles chart in the United States.  and pulled against the heated block for 2 seconds. Curl of the paper sample is measured using a previously described method (6).


B: Warm-oven curl test

Figure 3 illustrates the warm-oven curl test. Oven air temperature is 180[degrees]-200[degrees]F and heating time is 1-2 min. Curl of the paper sample is measured using a previously described method (7).


C: Internal strain

Internal strain, or net shrinkage from wetting and drying without shrinkage constraint, is important because it is an indication of what paper will do when it is exposed to high humidity or is wet. It is especially important if only one surface is wet (or exposed to high humidity), since that surface will shrink more when the sheet dries.

Sheet dimensions are measured at some chosen moisture content, such as that obtained at 50% relative humidity relative humidity
The ratio of the amount of water vapor in the air at a specific temperature to the maximum amount that the air could hold at that temperature, expressed as a percentage.
 (RH). An alternative is to accurately weigh a number of sheets to be tested. The sheets are soaked soak  
v. soaked, soak·ing, soaks
a. To make thoroughly wet or saturated by or as if by placing in liquid.

b. To immerse in liquid for a period of time.

 in water for a few minutes until thoroughly wet. (Adding of 5%-10% isopropyl alcohol isopropyl alcohol: see isopropanol.  to the water accelerates the wetting.)

The sheets are dried lying flat, making sure that there is no significant constraint to their shrinkage. To obtain the same starting moisture content, the sheets should be thoroughly dried in a very low RH (0%-10%) or in an oven at about 175[degrees]-200[degrees]F. After drying, the sheets are allowed to rehumidify. The weight of the sheet should closely match the starting weight. Any difference in weight will be moisture, which can be used to compensate sheet dimension measurements.

Sheet dimension can be measured using a Quick Skan (see, with this instrument, the length can be measured within 0.002 in. The use of a ruler is not recommended, especially in the machine direction.

D: Dual curl effect

A sheet containing two layers with different fiber orientation will also have a difference in moisture expansion and contraction properties. This situation is harder to analyze than a simple difference in expansion properties due to sheet composition (4). The surface with more fibers oriented in the MD will tend to exhibit an MD axis curl when curl is toward that surface, as seen in Fig. 4a (5). Curl that forms to the side opposite of the more-oriented fibers will tend to have a CD axis. This means that the curl tendency of a sheet with differential fiber orientation can be to either surface, depending on circumstances, but with a curl axis that differs by 90[degrees].


Figure 4b shows what happens when the wire-side fiber has more alignment in the MD than the felt-side fiber (4). In the CD, the wire side has higher changes in dimension with moisture content, with higher contraction of the wire side in the CD, we obtain an MD-axis curl! Conversely con·verse 1  
intr.v. con·versed, con·vers·ing, con·vers·es
1. To engage in a spoken exchange of thoughts, ideas, or feelings; talk. See Synonyms at speak.

, there is higher dimensional change in the MD on the felt side, and we get a CD-axis curl with higher contraction of the felt side or higher expansion of the wire side. These changes can be explained by the fact that most fiber expansion occurs across its width.

I. Hot-bend test results for two papers reveal differences
in fiber orientation

                         HANGING CURL, mm *

                       MD strip       CD strip
Surface to mandrel:   Wire   Felt   Wire   Felt

Paper A                 0     -25     96     25
Paper B                15     -10    -10    -35

* Positive numbers indicate curl toward the wire side

II. Effect of moisture content on curl for twin-wire
paper (75-g/[m.sup.2]) after passing through a copy-machine
fuser roller with and without a backing sheet

                            Moisture content, % *
                                 3    4     6

Two sheets
Hot-roll side (top sheet)       35   20   -20
Single sheet                    30    0   -45

* Positive numbers indicate curl toward the heated (printed) side

III. Effect of moisture content on curl for twin-wire
paper (75-g/[m.sup.2]) after passing through a copy-machine
fuser roller with a backing sheet

                                Moisture content, % *
                                       3     6

Two sheets
Hot-roll side (top sheet)             35   -20
Unheated side (backing sheet)          5    60

* Positive numbers indicate curl toward the heated (printed) side

IV. Effect of internal strain and moisture content on curl
for twin-wire paper (75-g/m2) after passing through a
copy-machine fuser roller

                     Moisture content, % *

Internal strain, %          4     6

1.1                        25   -20
0.6                        10    -5

* Positive numbers indicate curl toward the heated (printed) side


(1.) Niskanen, K. J., Paperi Puu 75(5): 321(1993).

(2.) Green, C., "Fundamentals of paper curl," [c] 1998 (electronic correspondence available from the author).

(3.) Votava, R., Tappi J. 66(12): 64(1983).

(4.) Green, C., I&EC Prod. Res. 20: 147(1981).

(5.) Green, C., Appita 53(4): 272(2000).

(6.) Green, C., "Hot bend curl test," [c] 1999 (electronic correspondence available from the author).

(7.) Green, C., "Warm oven curl test," [c] 1999 (electronic correspondence available from the author).

About the author: Green is a retired consultant, 23 Maryvale Drive, Webster, NY 14580. Atkins is president of Atkins, Inc., 1121 Croton croton, in botany
croton (krō`tən), any of several species of Codiaeum that are widely cultivated as ornamentals and houseplants. The most popular species is C.
 Rd., Flemington, NJ 08822. Address correspondence to Green by email at, or Atkins at
COPYRIGHT 2001 Paper Industry Management Association
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2001, Gale Group. All rights reserved. Gale Group is a Thomson Corporation Company.

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Title Annotation:Paper Curl
Author:Green, Charles
Publication:Solutions - for People, Processes and Paper
Date:Nov 1, 2001
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