Simulation of creping pattern in tissue paper - Innventia.com

PAPER PHYSICSSimulation of creping pattern in tissue paperJukka-Pekka Raunio and Risto RitalaKEYWORDS: Simulation, Creping, Tissue paper,Welch spectrum, ImageSUMMARY: The key operation in tissue production isthe creping at the Yankee cylinder. The tissue sheet isadhered to a Yankee cylinder and then detached from thesurface with a blade. As a result a strong microstructure –crepe folds – is generated on the web. In this work thestructure of creping pattern in CD and MD of tissue paperwas studied. The samples available in this work consistedof bath tissue and towel grades. The significant differencebetween the samples was in the number of crepe folds.The tissue sheets were analyzed with an imaging system.The variation of crepe folds in images was studied inspatial frequency space through 2D Welch spectrum. Itwas noticed that the difference in creping patternstructure between the samples can be seen clearly inspectra. The creping pattern was simulated based on thecreping pattern variation found from the Welch spectra oftissue paper images. The simulation was based on a set ofsinusoidal terms representing several orientations andamplitudes. The amplitudes of sinusoidal terms located inregular grid in spectra were approximated with 2Dnormal distribution. Thus, the structure of creping patterncan be represented with three parameters originating fromthe deviations and location of 2D normal distribution.The creping pattern reconstructed with simulationscontains the relevant features in the creping pattern oftrue tissue images.ADDRESSES OF THE AUTHORS: Jukka-PekkaRaunio (jukka-pekka.raunio@tut.fi) and Risto Ritala(risto.ritala@tut.fi): Tampere University of Technology,Department of Automation Science and Engineering, FI-33101 Tampere, Finland.Corresponding author: Jukka-Pekka RaunioTissue products have promising future markets due totheir sustainable raw material and lack of competingmaterials. Therefore it is expected that tissuemanufacturing will continue to increase, which increasesthe financial significance of understanding thephenomena in tissue making process.The wet-end of tissue machine is quite similar to that ofthe printing paper machines. The most common type oftissue machine is the dry crepe machine in which thesheet is dried on only one drying cylinder. This isbecause the strength of the low basis weight sheet is notenough to support sheet transfer. Such cylinder is calledthe Yankee cylinder. The tissue sheet is adhered to theYankee cylinder and then detached from the surface witha blade. As a result a strong microstructure – crepe folds– is generated on the web. The detaching, known ascreping, generates high softness (Hollmark, Ampulski,2004) and also stretches such that the sheet can betransformed from the Yankee cylinder to the reel withouta web break. As a result also the basis weight of the sheetincreases which is a consequence of creping and speeddifference between the reel and the Yankee cylinder.The creping mechanism is studied mainly in runningdirection of paper machine (Hollmark, 1972; McConnell,2005; Ramasubramanian, 2011; Sun, 2000). Hollmark(1972) was the first who studied the creping mechanismfrom the experimental point of view by imaging theprocess with high speed cameras and by developing adescription of the creping process. Ramasubramanian(2011), Sun (2000) and McConnel (2005) describedmathematically the creping process. Contrary to thepublications referred to above this paper studies andsimulates the structure of creping in both cross direction(CD) and machine direction (MD) of tissue paper. Thispaper focuses on the scale of crepe folds whereas thedetailed small scale structure of the crepe folds isignored. It is known that the crepe folds are not regularoscillations in tissue paper. This is mostly because of thevariation in adhesion between the paper sheet and theYankee cylinder, and the small scale variation of basisweight and thickness in tissue paper (Archer, Furman,2005). In this work the variations are studied bycomputing the power spectra of images captured fromtissue paper. The creping pattern is physically interpretedbased on these variations. Furthermore, the structure ofcreping is intended to describe with only few parameterswhich represent the variation of creping pattern in CDand MD. Thus, the tissue grades can be classified easilybased on these parameters and the connection betweenthe interesting physical properties of tissue and thestructure of creping can be studied.The pronounced spatial frequencies in MD and CDdirections present in creping pattern were studied fromreflectance images of tissue paper. The variations werestudied with the 2D Welch spectrum (Welch, 1967)estimation method.The structure of this paper is as follows. The secondsection describes the material studied in this work. Thethird section introduces the creping mechanism andspecifies the forces affecting in the creping process. Thefourth section studies the variation in creping pattern anddiscusses the source of variation. In the fourth section thesimulation method of creping pattern is presented. Thesection assesses the method by simulating the structuresin bath tissue and towel samples. Section 5 concludes theresults and discusses the validity of the evaluation and theusability of the results in controlling and developing thetissue making process.MaterialMaterial consists of two single ply tissue sheetsmanufactured in dry crepe machines in US. The gradesrepresent two easily distinguishable tissue products: theat-home bath tissue product which has low wet strengthand high softness, and the away-from-home towelproduct which has high wet strength and low softness.The basis weight of both samples was 20 g/m 2 and theNordic Pulp and Paper Research Journal Vol 27 no.2/2012 375

PAPER PHYSICSFig 3. The propagation of creping.The Propagation of CrepingThe forming mechanism of crepe folds is the following(Ramasubramanian, 2011; Hollmark, 1972). The tissuesheet starts to buckle when the sheet hits the blade. Thebuckling is the consequence of that the force whichpresses the sheet against the blade overcomes theadhesion which crosslink the sheet and the Yankeecylinder. The buckling continues until the sheet collapsescompletely and forms the crepe fold. At this point theformed crepe fold moves over because of the pullingforce of the machine reel and as a result the adhered sheetbehind the crepe fold moves towards blade. The adheredsheet starts to buckle and the entire cycle is repeated andas a result a creping pattern to the sheet is generated (seeFig.3).The adhesion, the angle between the surface of the bladeand the Yankee cylinder, and the structure of the sheet(e.g. thickness, basis weight) determines the crack point(see Fig. 3, bottom right) in creping process. The crackpoint is rather same in CD and MD but it can varyslightly as a function of time and in CD when theadhesion and the structure of the sheet vary in MD andCD.The basis weight, the creping ratio, and the anglebetween the Yankee cylinder and the top surface of theblade were identical for bath tissue and towel samples.However, the properties such as softness and wet strengthdiffer between the samples. The differences are due to theadhesion difference and the other differences such as theproperties of fibers and the moisture of the sheet increping process. The differences of creping patternsbetween the samples are studied in next chapter to detecthow the varying variables in tissue making process affectto structure of creping pattern.Variation of creping pattern in tissue samplesThe variation of the length and the width of the crepefolds and the distance of the crepe folds can be studiedthrough wave numbers. Wave describes in this work theamount of crepe folds in mm, in units 1/mm. The wavenumber variation in CD and MD of tissue images wereanalyzed with 2D power spectrum (Lim, 1990). The 2Dpower spectrum describes the squared amplitude of eachsinusoidal with a wave number and orientation found inthe image and hence the spectrum provides thedistribution of variance over wave numbers andorientations. Power spectrum is the absolute value ofFourier transform squared. The spectrum was computedwith the Welch method, which attenuates the effect ofmeasurement noise by calculating the spectrum as anaverage over several, possibly overlapping spectrumsamples (Welch, 1967). Each Fourier transform waswindowed with the Hamming window (Lim, 1990)before the computation of Welch spectrum. Windowingdecreases the spectral side lobes in the finite-sampleFourier transform. The Welch spectrum is symmetricalwith respect to both CD and MD direction axes.Therefore, the high variations originating from crepingstructure in spectra repeat themselves twice.The spectra of tissue sheets were computed from 10images sampled over entire machine width of the web.The general behavior of creping pattern was found byaveraging the spectra. Fig.4 shows averaged Welchspectra computed from the bath tissue and towel sheets.The intensities of Welch spectra are normalized to thevariance of tissue image which means that the sum ofspectral values equals the variance of image pixelsvalues. The variables k CD and k MD describes the wavenumbers (=number of crepe folds in mm) respectively inCD and MD.It can be seen that the intensity of Welch spectraconcentrate on certain locations. The centers of highintensity areas are due to the average creping pattern inthe tissue samples whereas the spread of the areas is dueto the variation in the creping pattern. The width of thehigh intensity area in k MD direction describes thevariation of crepe fold width in MD. The width of thehigh intensity area in k CD describes the orientationvariation of crepe folds in tissue sheet.In bath tissue (Fig. 4, top) most of the variation isbetween the wave numbers 1 and 5 1/mm in k MDdirection corresponding wavelengths 1 mm and 0.2 mm.The wave number of highest squared amplitude in MDwas 2.6 1/mm corresponding to wavelength of 0.38 mm.On the contrary, the towel spectrum (Fig. 4, bottom)spreads widely to wave numbers between the 2 and 91/mm in k MD direction corresponding wavelengths 0.5mm and 0.11 mm. The maximum number of crepe foldsin MD was 4.7 crepe folds per mm corresponding towavelength of 0.21 mm. In the towel spectrum (Fig.4,bottom) the high intensity area is wider in k CD direction.However, the wide variation exist at large wave numbersin k MD direction. Therefore, the variation in theorientation of crepe folds is rather similar in both thetissue grades as can be seen more clearly when thespectra are transformed into polar coordinates (see Fig.5). In this representation wavenumbers are pairs of angleϕ and distance k from the origin.The main difference between the samples was thevariation in the number of crepe folds which is probablydue to changes in adhesion between the sheet and theYankee cylinder. The higher number of crepe folds inthe towel can be seen clearly in the polar spectra as amore stretched high intensity area in the k compared tobath tissue grade. The squared amplitude of variation inNordic Pulp and Paper Research Journal Vol 27 no.2/2012 377

k CD(1/mm)(rad)k CD(1/mm)PAPER PHYSICShigh intensity area in the towel spectrum is lower by amagnitude compared to that in bath tissue. Indeed, thetotal variation in towel image was roughly one third ofthat in bath tissue which is partly due to the heightdifference of crepe folds between the samples.Representation of creping patternIn this work the structure of creping was illustrated with aset of sinusoidal wave fronts. In ideal creping process the-10-8-6-4-20246810-10 -5 0 5 10k MD(1/mm)-10-8-6-4-20246810-10 -5 0 5 10k MD(1/mm)Fig 4. Welch spectra computed from the bath tissue (top) andtowel (bottom) images. The grey level of spectrum shows thesquared amplitude of variation. The gray-scale to squaredamplitude conversion is given on the right. High intensity areasin spectra are due to variation caused by the creping pattern.012x 10 -5Fig 5. Welch spectra of bath tissue (right) and towel (left)transformed to polar coordinate system.654321x 10 -64.53.52.51.50.5330 5 10 0 5 10k ( 1/mm)k ( 1/mm)01254321creping pattern would be regular wave front having novariation. Such creping pattern, assuming that the crepingis a sinusoidal wave front, would produce infinitelynarrow wave number peak pair to the power spectrum,and in the case of non-sinusoidal wave front containharmonics of the peaks. However, the creping pattern isnot regular but both the orientation and planar size ofcrepe folds vary. Such variations broaden the narrowspectral peaks of regular structure causing the wide highintensity area to power spectrum (see Fig. 4-5).Simulation of creping patternLet x denote the point (x MD ,y CD ) in 2D spatial space and kthe point (k MD ,k CD ) in 2D dimensional wave numberspace. The Fourier transform of f(x) written as F(k),describes the amplitude, orientation and phase ofsinusoidal terms so that when summing the sinusoidsreproduces f(x). In this work the creping pattern wassimulated by set of sinusoidal wave fronts whoseorientation and amplitude follow the simplifiedrepresentation of the 2D Welch spectra of tissue images.The simulation in general is obtained as followsCrepingPattern x,W,H,k Ni1I(ki, k0, W,H)sin(2k0ix (i))where N is the number of sinusoidal terms chosen forsimulating the creping pattern and ϕ(i) is the phasefunction of the sinusoidal term. The phase function ϕ(i) ischosen uniformly distributed in [0, 360] as this is theonly distribution leading to translational invariance i.e.the pattern will not depend on the choice of worldcoordinate origin. The k i x can be denoted with polarcoordinates as followsk x k cos x k siny[2]iMDwhere k is the radial wavenumber of the sinusoidal term,θ its orientation (Sonka et al. 1998)..The distribution of the intensities of sinusoidal terms insimulated creping pattern is a 2D normal distributionapproximating the high intensity area in Welch spectra inCartesian coordinates. However, the intensity distributioncan be approximated with other distributions as well. Theintensity function is obtained as followsI(k , k , W , H ) i1Texp( ( ki k0)22W0 , k2 0 H k k 2WMD0MD01CD( ki k0CD 2H,and)), whereThe standard deviations W and H determine the width ofthe intensity function in k MD and k CD directions in powerspectrum. The W describes the width variation of crepefolds in MD and H describes the waviness and CD lengthof crepe folds. The orientation and the wave number ofsinusoidal terms are adjusted such that they form a regulargrid in wave number space. The regular gridsimplifies generating of 2D intensity function. The center[1][3]378 Nordic Pulp and Paper Research Journal Vol 27 no.2/2012

CD / mmy (mm)CD / mmk CD(1/mm)PAPER PHYSICSof the grid is k 0 denoted as (k CD0 ,k MD0 ) where k CD0 iszero and k MD0 is the average number of crepe folds inMD. The grid dimensions are four times W and H.Finally, the sinusoidal terms described in the regular gridin the wave number space are weighted with the 2D normaldistribution. The sinusoidal term in the middle of thegrid has the highest amplitude. The regular grid visualizedon the Welch spectrum of bath tissue and the normaldistribution of intensity function are shown in Fig 6.The simulation results are shown in Fig 7. The centerpoint of sinusoidal terms which describes the averagenumber of crepe folds in MD was k MD =4 1/mm. Thestandard deviation W and H were varied respectivelybetween the 0.5-4 (1/mm) and between the 0.5-1.5(1/mm).It can be seen that simulated creping patterns varysignificantly when the standard deviations in simulationare varied. The length of the crepe folds in CD is longwhen the H parameter is small (Fig. 6, top, left andright). On contrary, the length of the high amplitudecrepe folds is smaller when the H parameter is large (Fig.6, bottom, left and right). The large W (Fig. 6, top andbottom, right) disturbs the regularity in creping pattern.The simulation enables the creation of creping patternswith arbitrary parameters. Furthermore, the crepingpattern in true tissue grades can be described with onlythree parameters; the standard deviations W and H andthe average number of crepe fold k MD0 .The assessment of simulation resultsThe simulation parameters H, W and k MD0 which describethe bath tissue and towel tissue grade mostadvantageously are searched. Pointwise linear correlationbetween the simulated image and the original tissueimage is not a useful similarity measure because of thephase difference between the creping patterns. Thereforethe assessment is based on the distribution of wavenumber. The approximate shape of creping pattern inwave number space described with 2D normaldistribution is fitted to Welch spectrum of true tissueimage. The fitting is done in Cartesian coordinate system.The fitting ignores the phase and thus the similarity ofcreping patterns is meaningful to study. The 2D normaldistribution was compared to averaged Welch spectra(see Fig 4). Thus the general behavior of creping patternwas found.The similarity of Welch spectra of simulated crepingpattern and true tissue image was evaluated withKullback-Leibler divergence which is nonlinear measureof the difference between the two probabilitydistributions (Bishop, 2006). The range for divergence isfrom zero to infinity where zero is the divergence forsame distributions. The equation of Kullback-Leiblerdivergence is shown in Eq 4:KLP(i)( P || Q) P(i) ln[4]i Q(i)where P and Q are the probability distributions whosedivergence is computed. The Welch spectrum is not aprobability distribution but the spectrum values can benormalized in a way that the sum of the spectrum values-101-1-0.500.50.5 1 1.5 2 2.5 3 3.5 4 4.5k MD(1/mm)1-2 -1.5 -1 -0.5 0 0.5 1 1.5 2x (mm)Fig 6. The red crosses show the orientation and wave numberof sinusoidal terms applied in simulation. The red crosses aredrawn on the Welch spectrum of the bath tissue and they forma regular grid (top). The figure shows a small portion of theWelch spectrum in Cartesian coordinates. The shape of theintensity function (bottom) determines the intensity of eachsinusoidal term.-2-1012-2 0 2-2MD / mm-1012-2 0 2MD / mm2-2 0 2-2MD / mmFig 7. The simulated creping patterns with various simulationparameters. Top, left: W = 0.5, H = 0.5. Top, right: W = 4, H =0.5. Bottom, left: W = 0.5, H = 1.5. Bottom, right: W = 4, H =1.5. The grey level shows the amplitude: black and white colormeans respectively low and high amplitude and grey mean zeroamplitude.is 1. Now the normalized spectrum describes theprobability of each wave number.The standard deviations W and H of the intensityfunction and the center point k MD0 of regular grid wereoptimized by minimizing the Kullback-Leiblerdivergence between the 2D normal distribution andWelch spectrum of original tissue images. Theoptimization problem is not linear and the optimizationspace contains several local optima because of finitenumber of sinusoidal terms. Therefore, the simulatedannealing method is applied which should converge toglobal optimum (Kirkpatrick et al. 1983).Fig. 7 shows the optimal 2D normal distribution and thereference Welch spectrum computed from the image ofbath tissue sample.-2-101-1012-2 0 2MD / mmNordic Pulp and Paper Research Journal Vol 27 no.2/2012 379

k CD(1/mm)CD / mmCD / mmPAPER PHYSICS-6-4-20246-5 0 5-5 0 5k MD(1/mm)Fig 8. Optimal 2D normal distribution (left) and Welch spectrumcomputed from the bath tissue image (right).-2-1012-2 0 2-2 MD / mm-1012-2 0 2MD / mmFig 9. Optimal simulation of creping patterns based on thevariation found from the bath tissue and towel samples.It can be seen that high intensity areas in Welchspectrum of simulated image is not smooth. It is due tothe finite amount of sinusoidal terms in simulation. Fig 8shows optimal simulated creping patterns and the originaltissue images of bath tissue and towel grades. Thesimulations reproduce sufficiently the structure oforiginal creping patterns. The optimal parameters of bathtissue grade were W = 1.2, H = 0.8, and k MD0 =2.4 and W= 2.2, H = 1.2, and k MD0 =4.2 in towel grade.DiscussionAt present the structure of creping pattern is usuallydescribed with single parameter which tells the averagenumber of crepe folds per unit length in MD (Archer atal. 2010, McConnell, 2004). However, in such methodseveral characteristics of creping pattern are ignored.We suggest that the creping pattern is bettercharacterized by k MD0 , W and H, the first being theaverage number of crepes and the latter two describingthe variability of the creping structure. The simulationssuggest that these three parameters adequately reproducethe features visible in original creping patterns.Therefore, for example in mill studies on the effectprocess conditions, the creping pattern structure data canefficiently be summarized with the three parameters. Thisalso serves as basis of understanding the differences infunctional properties of the tissue, resulting fromdifferences in the crepe structure. For instance, it is-6-4-20246-2-1012-2 0 2-2MD / mm-1012-2 0 2MD / mmknown that the physical property of tissue such assoftness is related to small scale creping structure and tocreping pattern structure (Stitt, 2002). Thus, thecorrelation between the estimated parameters of crepingpattern and physical properties of tissue paper can bestudied.The optimal parameters of the simulation were studiedwith Kullback-Leibler divergence. The method isdeveloped for the estimation of divergence between theprobability distributions which can evaluate only positivevalues (larger than zero). The Welch spectrum wasconverted to probability distribution by normalizing thevariance to one. Kullback-Leibler distance between thespectra are studied and applied also in (Veldhuis,Klabbers 2003; Georgiou Lindqvist, 2003). It is possiblethat the Welch spectrum evaluates zero values and insuch location the divergence is not determined. However,the optimization was evaluated several times and theoptimum was rather same in iterations which indicatedthat such disturbance is not relevant in this work.The divergence was computed between the 2D normaldistribution and the averaged Welch spectrum computedfrom the true tissue images. However, the phaseinformation of creping pattern was ignored. Therefore,the divergence is not the absolute measure of thesimilarity between the creping patterns.ConclusionThe creping is not a perfectly controlled process whichwould produce identical crepe folds to a regular pattern.The variations in creping structure are due to structurevariation in tissue sheet and due to adhesion variationsbetween the Yankee cylinder and the sheet. The maindifference between the samples was the variation in thenumber of crepe folds which is probably due todifference in adhesion. The difference in number of crepefolds can be seen more clearly when the spectra aretransformed into polar coordinates. Such representationalso reveals that the waviness of crepe folds and the crepelength in CD is rather same in both grades however beingbit higher in towel grade.The structure of creping pattern was illustrated with aset of sinusoidal wave fronts. The distribution ofintensities of sinusoidal terms was described with a 2Dnormal distribution which follows the shape of the highintensity area in Welch spectrum caused by the creping.Such approximation enables the characterization of thecreping pattern with three parameters the first being theaverage number of crepes and the latter two describingthe variability of the creping structure. Now, the structureof creping pattern can be representing compactly by threenumbers and correlations between the physical propertiesof tissue and the structure of creping can be studied.The assessment of simulation results is based on thesimilarity between the 2D normal distribution and theaverage Welch spectrum computed from tissue image.The similarity was computed with Kullback-Leiblerdivergence. The optimal parameters of simulation weresearched and simulated creping pattern suggest that thesethree parameters adequately reproduce the featuresvisible in original creping patterns.380 Nordic Pulp and Paper Research Journal Vol 27 no.2/2012