An elastic strip in plane rolling contact

Bentall, R. H.; Johnson, Kenneth L.

doi:10.1016/0020-7403(68)90070-2

Cited by 118 publications

(54 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under these conditions the contact width exceeds A * ,since the compliant layer swells at the contact edge due to the incompressibility, as shown in figure 4(b). Finally, for α =O(1) a finite-strip model (FSM) is required, such as that formulated for elastic layers by Bentall & Johnson (1968). Compressibility of the compliant layer is represented by Poission's ratio, ν,a n d in the industrially relevant case of incompressible layers ν =0.5.…”

Section: Formulation Of a Mathematical Modelmentioning

confidence: 99%

“…These equations can be solved by the method of Fourier transforms (Bentall & Johnson 1968) and in the general case, the deformation at any position on the surface of the compliant layer is influenced by the entire normal surface stress distribution, P (X), and this is expressed via an integral equation: 26) whereP is the Fourier transform of P ,…”

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%

See 2 more Smart Citations

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

et al. 2003

View full text Add to dashboard Cite

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.

show abstract

Section: Formulation Of a Mathematical Modelmentioning

confidence: 99%

Section: Boundary Conditionsmentioning

confidence: 99%

Section: Boundary Conditionsmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2003

View full text Add to dashboard Cite

show abstract

“…2 and Ref. [26]). The stress components can be expressed in terms of the complex potential () z and its derivatives.…”

Section: Problem Imentioning

confidence: 91%

A coupled approach for rolling contact fatigue cracks in the hydrodynamic lubrication regime: The importance of fluid/solid interactions

Balcombe

Fowell

Olver

et al. 2011

Wear

View full text Add to dashboard Cite

This article presents a novel approach for modelling rolling contact fatigue cracks in the presence of lubricants. The proposed formulation captures the interaction between fluid pressure and solid deflections both at the contact interface and along the crack faces using a fully coupled finite volume/boundary element solver. This enables shedding light on the mechanisms which govern crack propagation in various loading conditions and geometrical configurations. It is shown that by linking the fluid behaviour and the elastic deflections within the crack to the film formed at the contact interface it is possible to overcome one of the main limitations of classical models available in the literature, which consists in having to prescribe pressure and/or pressure gradient at the crack mouth during the each loading cycle. The application of linear elastic fracture mechanics principles for the determination of crack stress intensity factors suggests that the results obtained using the approach developed by the authors produce a more realistic characterisation of the crack tip behaviour and it is capable of producing an improved estimate of crack propagation rates. Implications of these findings for the development of rolling contact fatigue lifing tools and potential extensions of the technique are also discussed.

show abstract

“…Several analytical and numerical analysis techniques [19][20][21][22][23][24] have been presented in the literature considering the three dimensional nature of the contact problem. The problem has been simplified by considering an elastic analysis of a ball pressed against a flat surface characterized by half-space as shown in Fig.…”

Section: Local Fatigue Damagementioning

confidence: 99%

Review of Fatigue of Coatings/Substrates

Sadananda

Holtz

2000

Nanostructured Films and Coatings

View full text Add to dashboard Cite

A review of fatigue of coatings/substrates is presented. Fatigue damage is either local or general, depending on the range of cyclic loads. Local fatigue damage includes rolling contact fatigue (RCF), fretting fatigue, fatigue-wear and general wear. Applied loads are localized consisting of rolling contacts or sliding contacts, and the resulting damage is mostly surface related. Crack initiation, surface pitting, delamination, spalling, buckling and enhanced wear can result from local fatigue damage of coatings. General fatigue damage results when the loads are of longer range such as cyclic bending, torsion or uniaxial or biaxial tension/compression etc. The mechanics of fatigue, role of microstructure, micromechanics in terms of crack nucleation, growth and fracture are reviewed. Defects produced during processing form precursors for crack nucleation. It is shown that optimization of the processing conditions to minimize defect density is essential to enhance fatigue resistance of coatings/substrates.

show abstract

An elastic strip in plane rolling contact

Cited by 118 publications

References 12 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

A coupled approach for rolling contact fatigue cracks in the hydrodynamic lubrication regime: The importance of fluid/solid interactions

Review of Fatigue of Coatings/Substrates

Contact Info

Product

Resources

About