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Research Papers

Particle Dynamics Modeling of the Creping Process in Tissue Making

[+] Author and Article Information
Kui Pan

Dynamics and Applied Mechanics Laboratory,
Department of Mechanical Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: Kui.pan@mech.ubc.ca

A. Srikantha Phani

Dynamics and Applied Mechanics Laboratory,
Department of Mechanical Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: phani@mech.ubc.ca

Sheldon Green

Applied Fluid Mechanics Laboratory,
Department of Mechanical Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: green@mech.ubc.ca

1Corresponding author.

Manuscript received October 29, 2017; final manuscript received March 1, 2018; published online April 4, 2018. Assoc. Editor: Donggang Yao.

J. Manuf. Sci. Eng 140(7), 071003 (Apr 04, 2018) (10 pages) Paper No: MANU-17-1670; doi: 10.1115/1.4039649 History: Received October 29, 2017; Revised March 01, 2018

The manufacturing of low-density paper such as tissue and towel typically involves a key operation called creping. In this process, the wet web is continuously pressed onto the hot surface of a rotating cylinder sprayed with adhesive chemicals, dried in place, and then scraped off by a doctor blade. The scraping process produces periodic microfolds in the web, which enhance the bulk, softness, and absorbency of the final tissue products. Various parameters affect the creping process and finding the optimal combination is currently limited to costly full-scale experiments. In this paper, we apply a one-dimensional (1D) particle dynamics model to systematically study creping. The web is modeled as a series of discrete particles connected by viscoelastic elements. A mixed-mode discrete cohesive zone model (CZM) is embedded to describe the failure of the adhesive layer. Self-contact of the web is incorporated in the model using a penalty method. Our simulation results delineate three typical stages during the formation of a microfold: interfacial delamination, web buckling, and post-buckling deformation. The effects of key control parameters on creping are then studied. The creping angle and the web thickness are found to have the highest impact on creping. An analytical solution for the maximum creping force applied by the blade is derived and is found to be consistent with the simulation. The proposed model is shown to be able to capture the mechanism of crepe formation in the creping process and may provide useful insights into the manufacturing of tissue paper.

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References

Oliver, J. F. , 1980, “ Dry-Creping of Tissue Paper-a Review of Basic Factors,” Tappi, 63(12), pp. 91–95.
Raunio, J. P. , and Ritala, R. , 2012, “ Simulation of Creping Pattern in Tissue Paper,” Nord. Pulp Pap. Res. J., 27(2), p. 375. [CrossRef]
Patterson, T. , 2013, “ Evaluating and Enhancing Tissue Softness,” Tappi Papercon Conference, Atlanta, GA, Apr. 28–May 1.
McConnel, W. , 2004, The Science of Creping, Tissue World Americas, Miami Beach, FL.
Hollmark, H. , 1972, “ Study of the Creping Process on an Experimental Paper Machine,” STFI-meddelande, Serie B, p. 144.
Ramasubramanian, M. K. , and Shmagin, D. L. , 2000, “ An Experimental Investigation of the Creping Process in Low-Density Paper Manufacturing,” ASME J. Manuf. Sci. Eng., 122(3), pp. 576–581. [CrossRef]
Ho, J. , Hutton, B. , Proctor, J. , and Batchelor, W. , 2007, “ Development of a Tissue Creping Test Rig,” Chemeca, Melbourne, Australia, Sept. 23–26, pp. 1334–1340.
Boudreau, J. , and Barbier, C. , 2014, “ Laboratory Creping Equipment,” J. Adhes. Sci. Technol., 28(6), pp. 561–572. [CrossRef]
Hamalainen, P. , Hallback, N. , and Barbier, C. , 2016, “ Development and Evaluation of a High-Speed Creping Simulator for Tissue,” Nord. Pulp Pap. Res. J., 31(3), pp. 448–458. [CrossRef]
Pan, K. , Phani, A. S. , and Green, S. , 2017, “ Mechanics of Creping Process in Tissue Making: Modeling and Experiments,” Tappi Papercon Conference, Minneapolis, MN, Apr. 23–26.
Ramasubramanian, M. K. , Sun, Z. H. , and Chen, G. , 2011, “ A Mechanics of Materials Model for the Creping Process,” ASME J. Manuf. Sci. Eng., 133(5), p. 051011. [CrossRef]
Gupta, S. S. , 2013, “ Study of Delamination and Buckling of Paper During the Creping Process Using Finite Element Method—A Cohesive Element Approach,” Ph.D. thesis, North Carolina State University, Raleigh, NC.
Hutchinson, J. W. , and Suo, Z. , 1992, “ Mixed Mode Cracking in Layered Materials,” Adv. Appl. Mech., 29, pp. 63–191. [CrossRef]
Jabbar, K. A. , and Pagilla, P. R. , 2017, “ Modeling and Analysis of Web Tension Dynamics Considering Thermal and Viscoelastic Effects in Roll-to-Roll Manufacturing,” ASME J. Manuf. Sci. Eng., 140(5), p. 051005.
Bergou, M. , Wardetzky, M. , Robinson, S. , Audoly, B. , and Grinspun, E. , 2008, “ Discrete Elastic Rods,” ACM Trans. Graph., 27(3), p. 63. [CrossRef]
Bergou, M. , Audoly, B. , Vouga, E. , Wardetzky, M. , and Grinspun, E. , 2010, “ Discrete Viscous Threads,” ACM Trans. Graph., 29(4), p. 116. [CrossRef]
Krenk, S. , 2009, Non-Linear Modeling and Analysis of Solids and Structures, Cambridge University Press, Cambridge, UK. [CrossRef]
Persson, J. , and Isaksson, P. , 2013, “ A Particle‐Based Method for Mechanical Analyses of Planar Fiber‐Based Materials,” Int. J. Numer. Meth. Eng., 93(11), pp. 1216–1234. [CrossRef]
Persson, J. , and Isaksson, P. , 2014, “ A Mechanical Particle Model for Analyzing Rapid Deformations and Fracture in 3D Fiber Materials With Ability to Handle Length Effects,” Int. J. Solids Struct., 51(11–12), pp. 2244–2251. [CrossRef]
Pan, K. , Phani, A. S. , and Green, S. , 2016, “ Particle Dynamics Modeling of Buckle-Delamination of Thin Film Materials,” 24th International Congress of Theoretical and Applied Mechanics, Montreal, QC, Canada, Aug. 21–26, pp. 2092–2093.
Edvardsson, S. , and Uesaka, T. , 2009, “ System Dynamics of the Open-Draw With Web Adhesion: Particle Approach,” ASME J. Appl. Mech., 77(2), p. 021009. [CrossRef]
Etzmuss, O. , Gross, J. , and Strasser, W. , 2003, “ Deriving a Particle System From Continuum Mechanics for the Animation of Deformable Objects,” IEEE Trans. Visual Comput. Graph., 9(4), pp. 538–550. [CrossRef]
Marynowski, K. , and Kapitaniak, T. , 2002, “ Kelvin–Voigt Versus Bürgers Internal Damping in Modeling of Axially Moving Viscoelastic Web,” Int. J. Non Linear Mech., 37(7), pp. 1147–1161. [CrossRef]
Sano, T. G. , Yamaguchi, T. , and Wada, H. , 2017, “ Slip Morphology of Elastic Strips on Frictional Rigid Substrates,” Phys. Rev. Lett., 118(17), p. 178001. [CrossRef] [PubMed]
Xie, D. , and Waas, A. M. , 2006, “ Discrete Cohesive Zone Model for Mixed-Mode Fracture Using Finite Element Analysis,” Eng. Fract. Mech., 73(13), pp. 1783–1796. [CrossRef]
Spackman, C. C. , Nowak, J. F. , Mills, K. L. , and Samuel, J. , 2017, “ A Cohesive Zone Model for the Stamping Process Encountered During Three-Dimensional Printing of Fiber-Reinforced Soft Composites,” ASME J. Manuf. Sci. Eng., 140(1), p. 011010. [CrossRef]
Domokos, G. , and Holmes, P. , 1993, “ Euler's Problem, Euler's Method, and the Standard Map; or, the Discrete Charm of Buckling,” J. Nonlinear Sci., 3(1), pp. 109–151. [CrossRef]
Cromer, A. , 1981, “ Stable Solutions Using the Euler Approximation,” Am. J. Phys., 49(5), pp. 455–459. [CrossRef]
Press, W. H. , 2007, Numerical Recipes 3rd Edition: The Art of Scientific Computing, Cambridge University Press, Cambridge, UK.
Lavrykov, S. , Lindström, S. B. , Singh, K. M. , and Ramarao, B. V. , 2012, “ 3D Network Simulations of Paper Structure,” Nord. Pulp Pap. Res. J., 27(2), p. 256. [CrossRef]
Ramasubramanian, M. K. , and Wang, Y. , 2007, “ A Computational Micromechanics Constitutive Model for the Unloading Behavior of Paper,” Int. J. Solids Struct, 44(22–23), pp. 7615–7632. [CrossRef]

Figures

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Fig. 1

(a) A schematic of the dry-creping process. (b) The web-blade contact point with the definition of creping angle and creping ratio. (c) A schematic of periodic fold pattern in tissue paper with the definition of creping wavelength and amplitude.

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Fig. 2

(a) Schematic of creping model which includes the web, the adhesive layer, and the Yankee. (b) The corresponding discrete model for the web and CZM for the adhesive.

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Fig. 3

(a) A schematic of bending forces in the local bending system formed by particles (i−1)−(i)−(i + 1). (b) A schematic of viscous bending forces applied on particle i: fv1,i is due to the angular velocity ω1,i, fv2,i is due to the angular velocity ω2,i.

Grahic Jump Location
Fig. 4

A schematic of interfacial nonlinear springs connecting particles and the corresponding substrate nodes: fcn,i and fct,i represent the normal and tangential cohesive forces, respectively; δ and γ represent, respectively, the normal and tangential displacement jump between the particle and the substrate node

Grahic Jump Location
Fig. 5

Bilinear cohesive zone model: (a) the relation between normal traction σ and the normal separation δn and (b) the relation between shear traction τ and shear separation δt. The shaded area represents mode I and mode II energy release rate GI and GII. The total area of the triangles represents mode I and mode II fracture energy GIc and GIIc.

Grahic Jump Location
Fig. 6

(a) Schematic of the first scenario of self-contact, where fs0 is the self-contact force on particle C, and fs1 and fs2 are the reactive self-contact forces. dc is the critical distance for self-contact and ds is the current distance between particle C and the line AB. (b) Schematic of the second scenario of self-contact, where fs0 is the self-contact force on particle D and −fs0 is the reactive self-contact force on particle B.

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Fig. 7

The evolution of the web morphology during creping: (a) t=3μs, (b) t=8μs, (c) t=10μs, and (d) t=25μs. (The scale bar only applies for the length of the web and the deflection of the web. To aid in visualization, the thickness of the web and adhesive layer is not scaled).

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Fig. 8

The evolution of the creping force (a) and the length of delaminated web (b) during the formation of single fold

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Fig. 9

A schematic of the web being pushed against the blade. (a) When the web first touches the blade. (b) When the section AB becomes delaminated from the substrate. The web is subjected to the maximum creping force Fm during this process.

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Fig. 10

(a) The maximum creping force versus the creping velocity. The parameters for the simulation are chosen as h=50μm, E=100MPa, ρ=300kg/m3, μ=20kg/ms, and GIC=GIIC=200N/m. (b) The maximum creping force versus Young's modulus of the web. The parameters are chosen as h=50μm, ρ=300kg/m3, μ=20kg/ms, Vin=5m/s, and GIC=GIIC=200N/m.

Grahic Jump Location
Fig. 11

Evolution of the web shape during the creping process. For simplicity, the adhesive layer and the Yankee are not shown. (a) t=10μs, (b) t=26μs, (c) t=36μs, (d) t=66μs, (e) t=120μs, and (f) t=200μs.

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Fig. 12

The evolution of the creping force (a) and the delamination length (b) under three different creping angles. The parameters for the simulation are chosen as h=50μm, E=100MPa, ρ=390kg/m3, μ=20kg/ms, GIC=GIIC=100N/m, Vin=20m/s, and Vout=12m/s.

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Fig. 13

The averaged creping force (a) and the creping wavelength (b) versus the creping angle. The parameters are chosen as the same in Fig. 12.

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Fig. 14

The effects of fracture energy on (a) the creping wavelength and (b) the average creping force. The parameters for the simulation are h=50μm, E=100MPa, ρ=390kg/m3, μ=20kg/ms, Vin=20m/s, and Vout=12m/s.

Grahic Jump Location
Fig. 15

Schematic of the buckle-delamination process of thin film/substrate system under residual compression with an initial delamination zone: (a) Initial compressed state, (b) buckling within pre-existing delamination zone, and (c) buckling driven delamination

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Fig. 16

Convergence check of the model. The normalized maximum deflection of the film converges to a constant value as the number of particles increases. The parameters are chosen as ε0=0.02, b0=10h, L0=100h, GIC=0.8Γ0, GIIC=10GIC, and Γ0=Ehε02/2.

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Fig. 17

The normalized maximum deflection of the film in the quasi-static buckle-delamination process as a function of the mixed-mode interfacial fracture energy. The solid line represents the analytical solution ζ=h(4/3)(ε0/εE−1).

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