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Research Papers

Analysis of Large Deformation Wound Roll Models

[+] Author and Article Information
C. Mollamahmutoglu

Research Associate

J. K. Good

Professor Fellow ASME
e-mail: james.k.good@okstate.edu
Oklahoma State University,
Engineering North 218,
Stillwater, OK 74078

Manuscript received July 20, 2012; final manuscript received November 16, 2012; accepted manuscript posted November 21, 2012; published online May 16, 2013. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 80(4), 041016 (May 16, 2013) (11 pages) Paper No: JAM-12-1336; doi: 10.1115/1.4023034 History: Received July 20, 2012; Revised November 16, 2012; Accepted November 21, 2012

Almost all winding models incorporate the assumption of small linear deformations and strain in their development. These models treat the addition of a layer of web to a winding roll with linear analysis using linear strain theory. Very few winding models have been developed that incorporate large deformation theory although many models treat material nonlinearity. Tissue and nonwoven webs are highly extensible in-plane and highly compressible in the thickness dimension when compared to paper, plastic film, and metal foil webs. Winding models that embody large deformation theory should apply to all web materials. Such models may be wasteful in computation time for web materials such as paper, film, and foils where models that employ small deformation theory may provide sufficient accuracy. This would appear deterministic based upon the extensibility and compressibility of a web material, but the issue becomes more complex due to limitations in tension that can be exerted on the webs. Herein, a large deformation winding model will be developed. Results from this model will be used to benchmark results from other small and large deformation models, and with laboratory test data, a review of all results will be used to determine when or if large deformation winding models are required.

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References

Good, J. K., and Roisum, D. R., 2008, Winding: Machines, Mechanics and Measurements, TAPPI Press, Norcross, GA, pp. 117–172.
Pfeiffer, J. D., 1966, “Internal Pressures in a Wound Roll of Paper,” Tappi J., 49(8), pp. 342–347.
Hakiel, Z., 1987, “Nonlinear Model for Wound Roll Stresses,” Tappi J., 70(5), pp. 113–117.
Good, J. K., Pfeiffer, J. D., and Giachetto, R. M., 1992, “Losses in Wound-On Tension in the Center Winding of Wound Rolls,” Web Handling 1992, Vol. 149, ASME, New York, pp. 1–11.
Benson, R. C., 1995, “A Nonlinear Wound Roll Model Allowing for Large Deformation,” ASME J. Appl. Mech., 62, pp. 853–859. [CrossRef]
Arola, K., and von Hertzen, R., 2007, “Two Dimensional Axisymmetric Winding Model for Finite Deformation,” Comput. Mech., 40, pp. 933–947. [CrossRef]
Willett, M. S., and Poesch, W. L., 1988, “Determining the Stress Distributions in Wound Reels of Magnetic Tape Using a Nonlinear Finite-Difference Approach,” ASME J. Appl. Mech., 55, pp. 365–371. [CrossRef]
Lee, Y. M., and Wickert, J. A., 2002, “Stress Field in Finite Width Axisymmetric Wound Rolls,” ASME J. Appl. Mech., 69(2), pp. 130–138. [CrossRef]
Hoffecker, P., and Good, J. K., 2005, “Tension Allocation in Three Dimensional Wound Roll Models,” Proceedings of the 8th International Conference on Web Handling, Oklahoma State University, Stillwater, OK, June 5–8, pp. 565–582.
Mollamahmutoglu, C., and Good, J. K., 2009, “Axisymmetric Wound Roll Models,” Proceedings of the 10th International Conference on Web Handling, Oklahoma State University, Stillwater, OK, June 7–10, pp. 105–130.

Figures

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Fig. 1

The axisymmetric representation

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Fig. 2

The compact finite element

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Fig. 3

Radial pressures for spun-bond nonwoven—Tw = 115 KPa

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Fig. 4

Radial pressures for bath tissue—Tw = 92.4 KPa

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Fig. 5

Radial pressures for bath tissue—Tw = 59.2 KPa

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Fig. 6

Radial pressures for newsprint—Tw = 5.17 MPa

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Fig. 7

Radial pressures for newsprint—Tw = 3.45 MPa

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Fig. 8

Radial pressures for newsprint—Tw = 1.72 MPa

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Fig. 9

Total radial strain in the roll and the increment in strain due to the accretion of the final layer from models I and II for spun-bond nonwoven—Tw = 115 KPa

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Fig. 10

Outer lap tension variation as models converge to equilibrium for spun-bond nonwoven at Tw = 115 KPa

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