Safety Analysis and Optimization of Travelling Webs Subjected to Fracture and Instability

Баничук, Н. В.; Ivanova, S. Yu.; Kurki, Matti; Saksa, Tytti; Tirronen, Maria; Tuovinen, Tero

doi:10.1007/978-94-007-5288-7_21

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…Web tension too high may cause material fracture, which deteriorates production ef ciency and the strength properties of the processed material (see e.g. studies by Banichuk et al [7], Robertson [8], Sanborn [9] and Skowronski and Robertson [10]). In this paper, we seek the maximal tension under the constraint that the probability of fracture is limited.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Analysis of the Critical Stable Velocity of a Moving Paper Web in the Presence of a Crack

Tirronen,

Tuovinen,

Jeronen

et al. 2013

Trans. Of the XVth Fund. Res. Symp. Cambridge, 2013

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In this study, we present a probabilistic approach for analysing runnability of a moving paper web with random defects. The paper web is modelled in the case of an open draw as an axially moving elastic plate that has an initial crack of random length. We derive a formula for the optimal velocity, at which the probability of fracture is limited. We study edge and central cracks perpendicular to machine direction (mode I cracks) and oblique central cracks (mixed mode). The crack length is modelled with the Weibull distribution. The effect of changing the value of distribution parameters and the probability of fracture on the optimal velocity is illustrated. It is found that the optimal velocity decreases when the expected value and variance of the crack length increase. The results also show the relation between the effect of edge and central cracks on the optimal velocity. The study is fundamental for rigorous analysis of the paper making process.

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Section: Introductionmentioning

confidence: 99%

Stochastic Analysis of the Critical Stable Velocity of a Moving Paper Web in the Presence of a Crack

Tirronen,

Tuovinen,

Jeronen

et al. 2013

Trans. Of the XVth Fund. Res. Symp. Cambridge, 2013

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“…Mass conservation requires that the flow rates at the incoming and outgoing flow control areas match; this requirement is readily obtained from (2). Let us consider a Figure 2: Solid web continuum flowing between the incoming and outgoing flow control areas (twodimensional surfaces) A 1 and A 2 , at longitudinal speeds U 1 and U 2 at the beginning and ending traction lines (respectively).…”

Section: Strain Generated By Velocity Difference Of Subsequent Rollersmentioning

confidence: 99%

“…On the other hand, high tension may cause web breaks, which deteriorates production efficiency (see e.g. [2,56,58,62]). …”

Section: Introductionmentioning

confidence: 99%

The origin of in-plane stresses in axially moving orthotropic continua

Kurki

Jeronen

Saksa

et al. 2016

International Journal of Solids and Structures

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Highlights• In-plane motion of an axially travelling orthotropic sheet was modelled• Velocity difference between supports generates strain due to mass conservation• In a travelling viscoelastic material the axial strain varies along the length• Small deformations of free edges due to the Poisson effect affect the velocity• Inertial effects lead to additional cross-directional contraction AbstractIn this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modeling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange-Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges in the two-dimensional case, are both seen to influence the velocity field. We concentrate on solutions of a steady-state type, and study briefly the coupled nature of material viscoelasticity and transport velocity in one dimension. Analytical solutions of the one-dimensional equation are presented with both elastic and viscoelastic material models. The two-dimensional elastic problem is solved numerically using a nonlinear finite element procedure. An important new fundamental feature of the model is the coupling of the driving velocity field to the deformation of the material, while accounting for small deformations of the free edges. The results indicate that inertial effects produce an additional contribution to elastic contraction in unsupported, free webs.

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Safety Analysis and Optimization of Travelling Webs Subjected to Fracture and Instability

Cited by 2 publications

References 18 publications

Stochastic Analysis of the Critical Stable Velocity of a Moving Paper Web in the Presence of a Crack

Stochastic Analysis of the Critical Stable Velocity of a Moving Paper Web in the Presence of a Crack

The origin of in-plane stresses in axially moving orthotropic continua

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