The contact problem of a rigid cylinder on an elastic layer

Meijers, P.

doi:10.1007/bf00382359

Cited by 161 publications

(71 citation statements)

References 2 publications

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“…The equivalent integral equation for purely elastic layers was given by Aleksandrov (1962), and used by Meijers (1968) for the dry contact of a rigid cylinder on an elastic strip bonded to a rigid undeformable backing. Contributions to the deformation from the tangential traction forces have been discarded as they are O((H 0 /R) 3/2 ) and O((H 0 /R) −3/2 E 3/2 S )i nc omparison to the normal forces in positive and negative gaps, respectively.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…The constrained column model (CCM) is derived from Hooke's law, with D(X)g i ven by 29) where the constant of proportionality is often referred to as a spring stiffness, K. Clearly, the CCM is restricted to compressible layers for which ν<0.5. For incompressible thin strips Meijers (1968), and Bentall & Johnson (1968) formulated the incompressible strip model (ICM) which yields the relationship…”

Section: Boundary Conditionsmentioning

confidence: 99%

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A model for deformable roll coating with negative gaps and incompressible compliant layers

et al. 2003

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A soft elastohydrodynamic lubrication model is formulated for deformable roll coating involving two contra-rotating rolls, one rigid and the other covered with a compliant layer. Included is a finite-strip model (FSM) for the deformation of the layer and a lubrication model with suitable boundary conditions for the motion of the fluid. The scope of the analysis is restricted to Newtonian fluids, linear elasticity/viscoelasticity and equal roll speeds, with application to the industrially relevant highly loaded or ‘negative gap’ regime. Predictions are presented for coated film thickness, inter-roll thickness, meniscus location, pressure and layer deformation as the control parameters – load (gap), elasticity, layer thickness and capillary number, $\hbox{\it Ca}$ – are varied. There are four main results: Hookean spring models are shown to be unable to model effectively the deformation of a compliant layer when Poisson's ratio $\nu\rightarrow 0.5$. In particular, they fail to predict the swelling of the layer at the edge of the contact region which increases as $\nu\rightarrow 0.5$; they also fail to locate accurately the position of the meniscus, $X_M$, and to identify the presence, close to the meniscus, of a ‘nib’ (constriction in gap thickness) and associated magnification of the sub-ambient pressure loop.Scaling arguments suggest that layer thickness and elasticity may have similar effects on the field variables. It is shown that for positive gaps this is true, whereas for negative gaps they have similar effects on the pressure profile and flow rate yet quite different effects on layer swelling (deformation at the edge of the contact region) and different effects on $X_M$.For negative gaps and $\hbox{\it Ca}\,{\sim}\,O(1)$, the effect of varying either viscosity or speed and hence $\hbox{\it Ca}$ is to significantly alter both the coating thickness and $X_M$. This is contrary to the case of fixed-gap rigid roll coating.Comparison between theoretical predictions and experimental data shows quantitive agreement in the case of $X_M$ and qualitive agreement for flow rate. It is shown that this difference in the latter case may be due to viscoelastic effects in the compliant layer.

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Section: Boundary Conditionsmentioning

confidence: 99%

Section: Boundary Conditionsmentioning

confidence: 99%

A model for deformable roll coating with negative gaps and incompressible compliant layers

et al. 2003

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“…In the past, both, solution to the contact problem and stress distribution in the coating as a function of the prescribed boundary loading have been attempted. The solution to the contact pressure profile in the case of cylindrical contact between coated elastic solids has been obtained to varying degrees of sophistication by a number of investigators [1][2][3][4][5][6]. Most of the early work [1][2][3][4][5] considered an asymptotic problem of a very thin or thick coating.…”

Section: Stress Modeling In Plane-strainmentioning

confidence: 99%

“…The solution to the contact pressure profile in the case of cylindrical contact between coated elastic solids has been obtained to varying degrees of sophistication by a number of investigators [1][2][3][4][5][6]. Most of the early work [1][2][3][4][5] considered an asymptotic problem of a very thin or thick coating. Meijers [3], while considering an elastic layer over a rigid substrate demonstrated that the solutions for a thin and thick layer overlap so well that these solutions may apply to arbitrary layer thicknesses with excellent approximation.…”

Section: Stress Modeling In Plane-strainmentioning

confidence: 99%

“…Most of the early work [1][2][3][4][5] considered an asymptotic problem of a very thin or thick coating. Meijers [3], while considering an elastic layer over a rigid substrate demonstrated that the solutions for a thin and thick layer overlap so well that these solutions may apply to arbitrary layer thicknesses with excellent approximation. Wu, Chiu and Pao [4,5] considered the classical stress function approach to the contact problem of coated solids and they clearly demonstrated the mathematical complexity of the problem, particularly the numerical convergence problem as the material of the coating tends to become incompressible.…”

Section: Stress Modeling In Plane-strainmentioning

confidence: 99%

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Tribological Modeling

Gupta¹

1998

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Elastohydrodynamic Lubrication Analysis of Layered Line Contact by the Boundary Element Method

Xue

Gethin

Lim

1996

Int. J. Numer. Meth. Engng.

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SUMMARYThis paper presents a numerical routine to compute the contact characteristics of elastomer layered cylinders lubricated by isoviscous liquids. The indentation of the elastic layer is calculated from boundary integral equations which are solved by linear and quadratic boundary element methods for a finite plane model and a circular representation of the junction. The hydrodynamic equation is also transformed into a boundary integral equation and solved by Simpson's rule. Some factors which possibly affect numerical accuracy are examined. Examples for finite plane and circular layer are analysed with reference to parameters for printing press roller contact, in which results are obtained for the indentation, film thickness and liquid pressure, as well as internal stresses through the simultaneous solution of the elasticity and hydrodynamic equations. The results show that high precision is easily achieved and the method is efficient for such layered problems.

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The contact problem of a rigid cylinder on an elastic layer

Cited by 161 publications

References 2 publications

A model for deformable roll coating with negative gaps and incompressible compliant layers

A model for deformable roll coating with negative gaps and incompressible compliant layers

Tribological Modeling

Elastohydrodynamic Lubrication Analysis of Layered Line Contact by the Boundary Element Method

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