The mechanics of wrinkles

8/10/2019 The mechanics of wrinkles

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PEER REVIEWED WEB DEFECTS

RINKLING ISA MOSTCOM-

mon and costly web defect encounteredin the manufacturing and converting oflightweight grades of paper, film, foils,nonwovens, and textiles. Wrinkling isso common that it has been givensynonyms and appellations no less

diverse than the wide variety ofmaterials, machines, and applications ithas appeared on. In this paper,however, we use the word wrinkling todenote any deviation from absoluteflatness of the web. Its severity canrange from an almost imperceptibletroughing of the web in an open span toa trough that is so pronounced that itfolds over and creases when crossing aroller or upon entering a nip. We alsoinclude the baggy web or the layflat

problem as subsets of this encom- passing definition of wrinkling.

Despite the ubiquitous nature ofwrinkling, however, there are only afew references that offer a brief treat-ment (1, 2). In this paper, we try toremove the mystery by explaining insimple but relevant terms how wrinklesare formed and how they can bereduced. We begin this by showing thatall wrinkling results from a single

behavior. Later, we describe somecommon mechanisms of wrinkle

causation and how to reduce wrinklesafter the fact.

COMPRESSIVE BUCKLING OF WEBS A web wrinkles because it has buckledin compression (3). We all know fromexperience that you cannot push a rope,

because it folds under the smallest ofcompressions. A web also shares this

behavior, because it, too, buckles under just a few psi (lb/in. 2) of compression.

Another analogy is a yardstick,which bows outward if too much axialload is applied. Unlike the yardstick,which is only loaded in one direction,however, a web can be loaded in threedirections. One direction is the MD(machine direction line tension), andthe other two directions are what cancause wrinkling. Because all wrinklesare a compressive buckling of the web,it is important to determine how webscan get loaded in compression.

We use Mohr's circle to show whattypes of forces may load a web incompression. Mohr's circle, as seen inFigs. 1 3, is a plot of shear stress (yaxis) vs. tensile or compressive stress(x axis). All possible states of stress fora member in planar loading, such aswebs, can be represented as a circle on

this plot. This is a useful tool forshowing both how to combinedifferent kinds of stresses and how theweb sees stresses in differentdirections.

We first look at Mohr's circle forthe simpler case of an unwrinkled webin pure MD (machine-direction)tension, as shown in Fig. 1. The rightside of the circle is the MD face, whichis loaded by web line tension. The leftside of the circle, or CD (cross-direction) face, has no stresses andthus sits at the origin. Just to the left ofthe origin and under slightcompression is the wrinkling bound-ary. As seen here, a web that is loadedin pure MD tension has a Mohr's circlethat does not cross into the buckling

boundary and thus has no tendency towrinkle.

While the figure shows a largedistance between the circle and thewrinkling boundary for illustration

purposes, in real life, the separation isvery small for thin materials. The

Wrinkling is a common proble, thinwebs of almost any material. This papershows how all wrinkling is acompressive buckling of the webinduced by either CD compression orin-plane shear stresses. Commoncauses of wrinkling are then discussed;these include roll(er) misalignment,deflection and diametral variations, andconstrained expansion as well asresidual stresses of manufacturing.Wrinkle removal via web flattening andweb spreading are briefly reviewed.

Application: The primary application of this paper isto diagnose the mode of wrinkling,which then leads to options for wrinkle

prevention or removal.

amount of compression a web canwithstand is primarily determined bythe cube of the web caliper. Web

modulus, span width, span length, andother factors are not as strong. This iswhy wrinkles are common withmaterials that are less than 10 mils inthickness, regardless of theircomposition. This is also why wrin-kles are rare for materials thicker than100 mils.

If we add a slight amount of CDcompression to the MD web tension,we push Mohr's circle past thewrinkling boundary, as seen in Fig. 2.Constrained expansion is one way tocause this to happen. Constrainedexpansion is where a web wants to getwider going through a process, suchas due to a tension drop, moistureincrease, or temperature increase.

Since the web cannot effectively push its edges outward, it may instead buckle out of plane. Also, a web maygather because a slender rollerdeflects too much, or at a spreaderthat is not operating properly. Thedistinctive feature of CD

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The mechanics of w rinkling

DAVID R. ROISUM w


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WEB DEFECTS

Element stress Web Causes

No wrinkles

//// I (oMD=IO,T = 0) \

/o"X(Co np.) a (Tensile) | ^X

/ / / s \

1 T

//A //// Element stress Web Causes

Constrained expansion Rollercrown Roller deflection Bad'spreading'

11

1

/. Pure MD tension 2. AID tension + CD compression

compression is that the wrinkles runexactly in the machine direction (4).

If we add a slight amount of shearstress to the MD web tension, weagain push Mohr's circle into thewrinkling boundary, as seen in Fig. 3-The causes for shear stress share acommon theme: either a web and/or aroller is crooked. The distinctivefeature of shear wrinkles is theirangled orientation (5).

As we have seen, Mohr's circle is a

powerful tool for diagnosing wrinkles.First, you can cut troubleshooting timein half by merely noting whether thewrinkle is oriented exactly in themachine direction or at a slight angle.Second, you can gauge shear stressseverity by the angle of the wrinkle.Third, you can theoretically pull outshear wrinkles with enough tension(left as an exercise for the reader).However, wrinkles return when the

product is cut or sheeted if its sourcewas the material itself. Finally, Mohr'scircle shows

just how close to trouble we run, evenunder the best of conditions.

CONSTRAINED EXPANSION Many web machines contain anexpansive process that tends toincrease the width of the web. Forexample, plastic films may be heatedin air-float ovens or over heatedrollers. Here, the web tries to growwider due to hygrothermal expansion.Similarly, many paper webs see a

moisture increase in coating and printing operations, which tries toincrease the width due to hygroscopicexpansion (6). Finally, two other

processes that often expand the webare calendering and embossing.However, expansion can also occur inweb handling merely due to a drop intension somewhere in the line. Here,the web tries to expand because ofPoisson's ratio. While Poisson's ratio istypically approximately 0.3 for mostmaterials, nonwovens can exceed aratio of

3. This means that the changes inwidth are three times the changes inlength.

The fractional expansion of widthfor linear elastic processes can becalculated as:

V Ten

4r--H ----- +a Ar + p AX E.c 2 2

(1)where

w = width

u = Poisson's ratioTen = lineal web line tensionE, = MD modulusc = calipera, = CD coefficient of thermal

expansionT = temperature62 = CD coefficient of solvent

expansion

218 TAPPI JOURNAL OCTOBER 1996

1


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3. MD tension + shear

4. MD trough wrinkle

These expansive forces do not always result in the edges ofthe web moving outward (to a greater width), especially onlighter grades. Rather, the web may take that extra width as

the arc length of a buckled sinusoidal shape. There aremany reasons that this buckling behavior is more commonthan edges moving outward, but the "you cannot push arope" analogy suffices as a visual tool. As seen in Fig. 4, theconstrained expansion of a free web results in a curtain-likeappearance, where the troughs are oriented precisely in themachine direction. Furthermore, the spacing or wavelength

between the troughs iscalculated as (7):

1+ 1.95 JL -Ten ( - %-

(2) where

X = wavelength L = web span lengthTen = lineal web line tension

E = web modulusoCj = longitudinal stress = Ten /caliper.

5. Excessive deflection wrinkling

The amplitude can be estimated from:

Aw _ / TL4_\w " 2b " V % )

where

_, = buckled lateral strainID

A = amplitude A.= wavelength.

A web begins to show a noticeable troughing at CD buckling

strains of as little as 0.1%. By the time the strains reach 1%, theweb looks like curtains and is at great risk for foldovers andcreases. A 0.1% thermal expansion of polymers may require atemperature rise on the order of 100-200 CE In one case, aconverter built an expensive vacuum treater with a heated rollerthat increased the film temperature to nearly 400F in a singlestep. Unfortunately, the web buckled off the hot roller surface dueto expansion so that a uniform treatment was not possible. A morecommon situation is passing a film through an air flotation oven.To address the MD troughing, the

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bt.iL Web travel MisalignmentTension profileDraw profileMaterial skew Deflection

Net TensionWeight

0.25 m


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WEB DEFECTS

7. Rol l er mi sa l i gnmen t wr ink l e

first roller after the oven should be a spreader to avoidcreasing the web over a conventional roller. Unfortunately,this first position after the dryer is also coveted by guide rolland/or vacuum pull roll functions.

Paper is generally thicker than many films and thus isslightly more buckling resistant. However, problems should

be anticipated on paper when the hygroscopic expansion

reaches 1%; this is approximately equivalent to a 5%moisture increase. This amount of water addition iscommon in most latex coaters and some treaters and

printing operations. Again, we would consider a spreader inthe first position after the coater station.

OTHER MD TROUGH WRINKLE CAUSES Other causes of MD trough wrinkles include excessive rollor roller deflection. We illustrate this tendency with theschematic given in Fig. 5. As seen here, the roller deflectsdownward due to roll weight and moves to the right due to anormally smaller web tension. The net shape of thedeflected roller is similar to a bowed roller, except that it is

pointed backward or in the contracting direction. The webdoes not know whether we call an

R

egion

II

Slack edge

MISALIGNMENT

ANGLE

Corrugation

Misalignment

3- ~C

WebWeb Region IPlanar

Increase L/W

Increase gauge Region IIIWrinkled O

Shell Shell Groove Thread

LU Wide grooving:Web may slideinward intogrooves

Raised thread: Webmay slide inward tolands and gatherdue to high diameter

6. Wrinkl in g at wide grooves/ threads

8. Misal ignm ent wrinkle relat ionsh ips

Partial drive

Rivers & lakes

b/l

-c >

-Ci Zh A T- -c

Material skew Trim removal

Zh -c fcZh

D- -C


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Zh -c

9. Other shear wrinkle causes

element a mere idler roller, a spreader, or a contractor. It reacts to agiven geometry in the same manner. Thus, if the "roller" looks likea bowed spreader pointed backward, the web reacts with the

tendency to trough wrinkle. Other orientations, such as reversing the path of the web in

the figure, result in neutral or even spreading effects. For a varietyof reasons, however, the web may tend to wrinkle more easilythan it tends to spread. Thus, the net effect of excessive deflectionof a system of rollers is the tendency for MD trough wrinkling ofthe web. To avoid this type of wrinkling, rollers should not deflectmore than about 0.015% of roller width. This

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Symptoms: Wrinkle oriented precisely inthe machine direction.Troughs are evenlyspaced with the exception of somediametral variations.

Fundamental behavior: CD compressivebuckling strain

Modes: Constrained expansion

Moisture increase Solventincrease Temperatureincrease Tension drop

Roll(er) geometry Roller deflection excessive Groovingwidth excessive Raised threads orfeatures High-diameter position(tracking) Low-diameter position(sliding)

/. MD trough wrinkle summary

value is about one-tenth of the 0.15% bow value often specified for the bowed-roller spreading of unslit stiffwebs. Thus, for example, it would takea typical bowed-roller spreader to cleanup the troughing caused by ten rollerswhose deflection just met standard butwhose deflection was pointed in aninopportune direction. As a rule ofthumb, rollers that are adequately sizedfor deflection have a slenderness ratio(length/diameter) of 10-15 if nippedand 15-20 if unnipped (8).

Another cause of wrinkling isexcessive grooving width. It is ironicthat many people believe that groov-ing, especially if spiraled outward, hasa spreading effect. Unfortunately, thetendency of all grooving is just theopposite. As seen in Fig. 6, the webtends to pull into the overly widegroove. It may do this elasti-cally, in

which case there is no damage.However, the web could slip slightlysideways, especially at the edges,which can induce trough wrinkling. Toavoid MD troughing caused bygrooving, the groove width should beno wider than 10-20 times theminimum web

Roll diameter increase Roll wrap angle decrease Roll/web speed difference (sliding or

floating vs. tracking) Roll orweb roughness change

(depends on application)Speed increase Tensiondecrease Web permeabilitydecrease Width increase

//. Factors to increase web flattening

caliper (9). Another reason to avoidwide grooves on film is to avoidmarking of the web. Many film prod-ucts bear the tractor-tire tread marks ofidler rollers they have touched.

A final source for MD trough

wrinkling is diametral variations. If thevariation is large and intentional, suchas with raised threads, the web may be

pulled inward, just as in the case ofwide grooves. However, any large-diameter area of a roller also tends togather material there into a trough foranother reason. The principle for this isthe mechanism for the centering of

belts on a crowned pulley (which alsocreates CD compression) and isopposite to that of a concave spreader.Because the diametral variation need

be as little as 0.1% to start gatheringthin-gauge materials, rollers must becut accurately and caliper controlledclosely for wound rolls. If the web isslipping instead of tracking, it gathersat small-diameter areas.

As we have seen, there are manymechanisms that can cause the MDtrough wrinkle. They can be broadlycategorized as due to constrainedexpansion or roller geometry. Table Isummarizes the various modes of the

MD trough wrinkle. However, they allshare the common features of a troughthat is oriented exactly in the machinedirection and result from acompressive CD buckling strain.

Simplex Concave roller Bowed spreader roller D-bar or bent pipe

Duplex Dual bowed roller Pos-Z

Expander rollers Slatted Banded Covered

Edge stretchers Edge pull stretcher rollers Tenter chains

///. Spreading devices

DIAGONAL SHEAR WRINKLES

From the Mohr's circle of Fig. 3, thesuperposition of a shear stress on aweb line tension produced a circle thatcould cross beyond the buckling

boundary. However, the direction ofmaximum compression for a web inshear is at a slight angle from thecross direction. Thus, the troughs areoriented at a right angle to themaximum compression, which is, inother words, at a slight diagonal to themachine direction. The angledwrinkle uniquely identifies the

presence of a shear component; thesteeper the angle, the larger the shearstress.

Aside from the commonality of anangled wrinkle, the numerous dif-ferent sources share another feature.Shear wrinkles always result fromsomething being crooked, such as a

profile variation problem. In manycases, the crooked element is amachine component, such as a roller,instead of the web. If the web is

crooked, it often displays a discerniblerope or corrugation, or it is baggy inspots. Since there are so many sourcesof shear, we cover only the morecommon cases here (5).

ROLLER MISALIGNMENT Undoubtedly, the classic shear wrinklecase is caused by a misaligned

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WEB DEFECTS

10. CD wrinkles and air entrainm ent

/^TpX Winding: / |

\ Outside ( 6 ) ti z htens

Winding: insideloosens

MD

c MD

'\f\f\f\f\f\f\.

/ /. Interlayer slippage and the crepe wrinkle

roller pair. It has the fingerprint of diagonal wrinkle thatwalks sideways on the downstream roller of the misalignedroller pair. As seen in Fig. 7, the specific misalignment thatcauses this wrinkle is the component of misalignment that isin the plane of the roller pair. One can use several rules todetermine the direction of misalignment. First, the trough

points to the short side of the downstream roller. Second,the wrinkle walks uphill or toward the long side of thedownstream roller. Misalignment in this sense is the lack of

parallelism of one roller with respect to the other, ratherthan with respect to an alignment datum. Thus, both rollerscan be misaligned in the machine sense of level and square

but not cause wrinkles in that span because they are

mutually parallel. Alignment tolerances needed to avoid thismode of wrinkling can either be calculated or determined byexperience. A model has been pioneered for misalign-

T E N S I O N

, l b / i n

.

x- -------- Yield

\ A' B' l

(yc / )CJ / * / s / / s

s / s s / ' ' / ' ' / / / / / /

\/s /" / /

k / A" B" STRAIN, in./in. or%

12. Baggy w eb stress-strain diagram

ment wrinkling in a joint research project by 3M and the WebHandling Research Center (10). The results are summarized inFig. 8. There are three web states on this plot of web tension vs.misalignment angle. Region I is for a flat and unwrinkled web,which occurs when misalignment is sufficiently small. Region II

is for a web with a slack edge but no wrinkling, which occurswhen tension is sufficiently small. Region III is where thediagonal wrinkle crosses the downstream roller. There are severalcourses of possible treatment given a web in the wrinkled statedenoted by the heavy dot. The most obvious and preferable would

be to reduce the misalignment angle; this would move the point tothe left and into the flat web region.

Another possibility would be to increase tension, which maymove the point above the wrinkling boundary. By Mohr's circle,this reduces the intrusion into the buckling zone. Ironically,however, one could also reduce tension to move the point belowthe wrinkled region. By reducing tension, web-to-roll traction is

also decreased; this can allow the web to partly break instead ofconforming to the violent bend required to make normal entry tothe downstream roller (11). In other words, low tension provides asafety valve for misalignment. However, using tension to reducewrinkling may not be desirable, because there are other web-handling limits that may be exceeded. If tension is too low, theweb becomes floppy and ill behaved. Conversely, if tension is toohigh, the web may be damaged or even break. An appropriate webtension for most applications is between 10 and 25% of the web'stensile strength (12).

222 TAPPI JOURNAL OCTOBER

Unwinding:

Outsideloosens

Unwinding: Inside

tightens

Top view of a crepe wrinkle tl

ZD Side view of a crepe wrinkle

(enlarged)
http://%20/f/f/f/f/f/fhttp://%20/f/f/f/f/f/f


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wound roll layers may slip upon themselves in the presenceof an internal or external nip and during winding orunwinding. If the slippage is nonuniform and in theuncinching (loosening) direction, the roll may crepewrinkle. Nip-induced defects are common with light slip-

pery grades of paper (lightweight coated or newsprint) andwith bulky grades such as tissue.

THE BAGGY WEB Most of the wrinkling cases discussed earlier are due more to ashortcoming in web handling or machine design rather than any

prior web defect. That is, while web properties andnonuniformities can affect the propensity to those wrinkles, the

basic mechanism operates even on perfect webs. However, thereare at least as many web defects that are the result of a priormanufacturing defect, such as web bagginess. Here, the web may

be ill behaved even going through a perfect machine.

The baggy web has two distinct visual differences from theMD troughs discussed earlier (21). First, the tight and loose bandsare irregularly spaced across the width. Second, the product doesnot lie flat and straight. However, it is important to determine ifthe web is naturally crooked or is elastically (temporarily) forcedthat way through the machine. If the web lies flat on a table butnot through the machine, then the web is not being handled

properly through the machine, perhaps due to causes discussedearlier. If the web does not lie straight and flat on a table, then youhave a case of residual stresses. A web that does not lie flat on atable has uneven stresses built into it during manufacturing and, insome cases, rough handling after manufacturing.

It is helpful to understand what residual stresses are and howthey cause the web to be crooked. Figure 12 shows a stress-straincurve for a material lying on a table under no external stress. Onthis sample are two points labeled A and B. Note how one iscompressive and the other is tensile. Residual stresses indicatethat the web has nonzero stresses inside it, even though noexternal stresses are imposed on it.



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The effect of the residual stressesis made clear by two examples. If Aand B were at the same point (x, y) butone was on the top and the other on the

bottom, the web has a curl in themachine direction or the crossdirection. If the points had the sameMD position but were on differentedges of the web, the web would be

baggy or cambered. Of course, thereare many other combinations of MD,CD, and shear stresses that can causecrookedness or lie-flat problems in aweb.

Thus, one way to define a baggyweb is as a variation of the web ten-sion across the width of a parallelroller pair, as seen in Fig. 13. How-

ever, the difficulty in using this defi-nition is that measuring the tensionvariation is extremely difficult. Theinstrumentation that is capable oftension profiling may have poormeasurement quality, be extremelyexpensive, or be very complex.

Alternatively, a baggy web can bedefined as one where the "naturallength" of the material is differentacross its width. Surprisingly, a webwhere lengths vary by only 0.1%results in severe bagginess on almostany material or product. Lighter websmay tolerate only about 0.01% beforethe web appears visibly baggy or has anoticeable lie-flat problem. The baggylane is a position that is just slightlylonger than the rest. It buckles out ofthe plane of the web to accommodatethe extra length, because it cannot

push and stretch the adjacent tight bands.

There are several ways to measurethe bagginess of a web. Figure 14

shows a bow and a fold method, whichare most suitable for narrow webswhose residual tension or naturallength varies linearly from front to

back. Camber is the term used for thisidealism of real web bagginess. Thesemethods would not, for example, beable to detect bagginess that issymmetrical about the centerline. Theadvantage of these methods is

simplicity of measurement, so they areoccasionally used for quality controltesting.

A more general method of quan-tifying bagginess is shown in Fig. 15-Here, we use a strain- or length-basedmeasure of bagginess in any CD

position(s) of interest. Indeed, onecould cut the entire width intonumerous strips to completely profile

bagginess with respect to the averagelength. Unfortunately, this method istedious and time consuming, so it isnot suitable for routine use.

The specific causes for baggylanes are as diverse as the namesgiven to the defect. However, thereare some universal troubleshooting

techniques. First, the source of thedefect must be where the material hassufficient mobility, such as the pointof manufacture, or later in processing,where there are high stresses,moistures, and temperatures. Second,the deckle position and widthcorrespond to its source. The source isin general a profile precision problem.The problem should be identified andcorrected at its source, because thereis very little that can be effectivelydone after the fact.

The one rare cure of the baggyweb is to yield it (22). This is illus-trated in Fig. 12 by pulling the web toA'B' and releasing it to A"B".However, it may be more difficult toyield the web uniformly than it would

be to make it uniform in the first place. Another advertised treatment isto use spreaders. However, the effectis almost always temporary and localto the spreader area. Also, the effectsare usually disappointingly small,

because spreaders act in the crossdirection while the baggy web

problem is in the machine direction.Thus, it is only the weak Poissoncoupling between a CD pull of thespreader that increases the effectiveMD tension

and thus may temporarily pull a baggy portion of a web into tension.

FLATTENING AND SPREADING There would be little need forspreaders in a perfect world where theweb and machine are true. Therealities are, however, that wrinklesmay remain despite our best efforts tocorrect them at their source. Then wecan, as a last resort, attempt to removethe wrinkles via flattening andspreading. Web flattening is a passive

process that allows the web to be aswide as it would prefer to be. Webspreading is an aggressive process thatforces the web to be wider than itwould prefer to be.

Flattening works on the principlethat the web would avoid compoundcurvature because it is at a high-energy state. The web, which mustfirst follow the arc of the roller or bar,would prefer not to hold a second arcas a trough or wrinkle crossing theroller or bar. As seen in Fig. 16, thewrinkle crossing the roller inducescompressive CD forces that wouldtend to push the edges outward. Theseforces are very weak and thus canseldom overcome the friction ortraction between the web and theroller. If the friction can be reducedsufficiently, however, the trough

pushes itself outward until the web isflat (23) The factors for reducingweb/roller traction are given in TableH (24).

All that is usually needed to flattena web is to lightly wrap a large-diameter bar (or roller if sliding can-not be tolerated). Caution must beexercised, however, because loss of

traction also means a certain loss ofweb-handling control.

Spreading is a more aggressive process than flattening and thus candeal with webs that are in need ofmore serious treatment. The varioustypes of spreading devices, listed inapproximate order of strength, areshown in Table in (25-27). The

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WEB DEFECTS

KEYWORDS

corrugation, crease recovery, creasing,design, flattening, rolls, tolerance, webspreaders, webs, wrinkles.

most common pitfall to avoid with thecommon concave and bowed-rollerspreaders is loss of traction. Slippingcauses a loss of the spreading functionand may even cause wrinkling.Slipping is avoided by reducing bows,wrapping the rollers adequately, andmaking sure the surface has anaggressive traction with the web.

However, spreading is only able toeffectively treat MD trough wrinklesor diagonal shear wrinkles. Bag-ginessand most other web defects are notappreciably affected by spreading. Forexample, if a web has

bubble-shaped patches of bagginess,

the spreader could not pull them out, because the flat areas around the bubble would carry all of thespreading forces. Also, spreading isgreatly limited on unbonded multiplymaterials. Here, spreading may belimited to the ply in contact if web/rollfriction is greater than web/webfriction. Also, spreading is limited tothe point where the first ply becomestaut in the cross direction. Finally, theeffect of spreading is almost alwaystemporary and local to the spreaderarea, lasting perhaps only a span or sodownstream.

SUMMARY Wrinkles may appear to be as variedas the webs and applications on whichthey are found. As we have seen,however, wrinkles and lie-flat

problems share a common feature inthat they all result from a compres-

sive buckling of the web. The first

troubleshooting technique is toobserve the angle of the wrinkle. If itis directly in the machine direction,the cause is one of a few easily dis-tinguishable cases of constrainedexpansion or related behavior. If theweb is at a slight angle, determine ifthe crookedness is web or machinerelated. Finally, baggy webs are irreg-ular in character and most difficult totreat. In most cases, bagginess is theresult of manufacturing profile

problems and must be corrected at thesource. TJ

Roisum is president of FinishingTechnologies,

Inc., 1305 Orchard Ct, Neenah.WI 54956.

Received for review Dec. 11, 1995. Accepted Feb. 9, 1996. Presented at theTAPPI 1996 Polymers, Laminationsand Coatings Conference and the TAPPI 1996 Fin-ishing and Converting Conference.

LITERATURE CITED

1. Roisum, D. R., The Mechanics ofRollers, TAPPI PRESS, Atlanta, 1996, p.305.

2. Smith, R. D, Roll and Web Defect Ter-minology, No. 0I0IR234, TAPPIPRESS, Atlanta, 1995, pp. 78-83.

3. Roisum, D. R., Converting MagazineFeb. 1994, p. 16.

4. Roisum, D. R Converting MagazineMarch 1994, p. 22.

5. Roisum, D. R., Converting MagazineJune 1994, p. 22.

6. Roisum, D. R., Tappi J. 76(6):129(1993).

7. Shelton, J. J., Proceedings of SecondInternational Conference on Web Han-dling, Oklahoma State University,Stillwater, OK, 1993, p. 303.

8. Roisum, D. R., Converting MagazineJan. 1996.

9. Roisum, D. R., Converting Magazine Aug. 1995, p. 26.

10. Gehlbach, L S., Good, J. K., and Kedl, D. M Tappi). 72(8): 129(1989).

11. Daly, D. A, Tappi 48(9): 88A( 1965).

12. Roisum, D. R., Converting Magazine Nov.1994, p. 20.

13. Roisum, D. R Proceedings of Third Interna-tional Conference on Web Handling, OklahomaState University, Stillwater, OK, 1995, inpress.

14. Roisum, D. R, TAPPI 1995 Finishing and Con-

verting Conference Proceedings, TAPPI PRESS, Atlanta, p. 113.

15. Roisum, D. R., Converting Magazine March1995, p. 48.


17. Benson, R. C, Chiu, H. C, LaFleche.J., et al.,Proceedings of Second International Conferenceon Web Handling, Oklahoma State University,Stillwater, OK, 1993, p. 333.

18. Benson, R. C, LaFleche.J., and Stack, K. D.,Proceedings of Third International ConferenceonWeb Handling, Oklahoma State University,

Stillwater, OK, 1995, in press. 19. Tajuddin, B., "Mathematical Modeling of

Air Entrainment in Web Handling Appli-cations," M.S. thesis, Oklahoma StateUniversity, Stillwater, OK, 1987.

20. Roisum, D. R., TAPPI 1994 Finishing andConverting Conference Proceedings, TAPPIPRESS,Atlanta,p.89.

21. Roisum, D. R., Converting Magazine April1994, p. 22.

22. Roisum, D. R., Converting Magazine April 1995, p. 20. 23. Friedrich.C.R., Tappi). 72(2): 161(1989).

24. Ducotey, K. S., "Tractions Between Websand Rollers in Web Handling Applica-tions," Ph.D. thesis, Oklahoma State Uni-versity, Stillwater, OK, 1993.


26. Roisum, D. R TappiJ. 76(10): 63(1993).

27. Roisum, D. R., Tappi). 76(12): 75(1993).


The mechanics of wrinkles

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