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Prediction model of paper-web wrinkling and some numerical calculation examples with experimental verifications

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Abstract

A web is continuous, flexible materials such as paper, plastic film, metal foil, textiles, etc. Web wrinkle is a problem which plagues the process industries. Most webs are very thin and prone to buckle or wrinkle. The effects of wrinkling can range from compromised product quality to down time of a processing operation, leading to less profitability in the manufacturing operation. The web wrinkles which will be treated in this paper are those that can be affected by roller misalignment and friction characteristics between web and roller. In this paper, observation method is presented for paper-web wrinkling and the prediction model of wrinkling is proposed with experimental verifications.

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Abbreviations

a :

web span (m)

B :

web wrap angle (rad)

E x :

Young’s modulus of web in machine direction (GPa)

E z :

Young’s modulus of web in cross machine direction [GPa]

h :

air film thickness (m)

k :

web permeability (m2)

L :

web width (m)

N x , N z :

normal forces (N/m)

R :

roller radius (m)

T :

web tension (N/m)

T cr :

critical web tension to sustain wrinkle (N/m)

ΔT :

work done by normal forces (Nm)

t f :

web thickness (m)

U :

total velocity (U r  + U w )(m/s)

U r :

roller velocity (m/s)

U w :

web velocity (m/s)

ΔU :

strain energy (Nm)

x :

coordinate in the machine direction (m)

y :

coordinate in the vertical direction (m)

z :

coordinate in the cross machine direction (m)

γ xy :

strain

ɛ:

web speed parameter (6ηU/T)

ɛ x , ɛ z :

strains

η:

air film viscosity (Pa·s)

κ:

web permeable parameter (kTB / (ηt f RU))

λ:

web width parameter (L / (2Rɛ1/3))

μ:

friction coefficient

μ1 :

local friction coefficient

μ s :

static friction coefficient

ν x , ν z :

Poisson’s ratios

σ:

composite RMS roughness

σ r :

RMS roughness of roller surface (m)

σ w :

RMS roughness of web surface (m)

σ x , σ z :

normal stresses (Pa)

σ zcr :

critical buckling stress (Pa)

τ cr :

critical shear stress (Pa)

τ xz :

shear stress (Pa)

References

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  • Hashimoto H, Nakagawa H (2001) Improvement of web spacing and friction characteristics by two types of stationary guides. Trans ASME J Tribol 123:509–515

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  • Hashimoto H, Okajima M, Numakura T (2004) Effect of permeability on traction characteristics between web and roller for a wide range of transportation velocity. CD-ROM proceedings of 2004 ASME/STLE tribology international conference

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Authors and Affiliations

  1. Department of Mechanical Engineering, School of Engineering, Tokai University, 1117 Kitakaname, Hiratsuka, Kanagawa, 259-1292, Japan

    H. Hashimoto

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  1. H. Hashimoto
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Correspondence to H. Hashimoto.

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Hashimoto, H. Prediction model of paper-web wrinkling and some numerical calculation examples with experimental verifications. Microsyst Technol 13, 933–941 (2007). https://doi.org/10.1007/s00542-007-0388-z

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  • DOI: https://doi.org/10.1007/s00542-007-0388-z

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