Rolling of an Elastic Ellipsoid Upon an Elastic-Plastic Flat

2007 ◽  
Vol 129 (4) ◽  
pp. 791-800 ◽  
Author(s):  
Daniel Nélias ◽  
Eduard Antaluca ◽  
Vincent Boucly
Keyword(s):  
Surface Deformation ◽  
Normal Load ◽  
Permanent Deformation ◽  
Computing Time ◽  
Equivalent Plastic Strain ◽  
Numerical Procedure ◽  
Theoretical Background ◽  
Rolling Contact ◽  
Von Mises Stress ◽  
Elastic Plastic

The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio k—ranging from 1 to 16—and of the normal load—from 4.2 GPa to 8 GPa—are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.

Rolling of an Elastic Ellipsoid Upon an Elastic-Plastic Flat

2007 ◽  
Author(s):  
D. Ne´lias ◽  
E. Antaluca ◽  
V. Boucly
Keyword(s):  
Surface Deformation ◽  
Normal Load ◽  
Permanent Deformation ◽  
Equivalent Plastic Strain ◽  
Numerical Procedure ◽  
Bearing Steel ◽  
Theoretical Background ◽  
Rolling Contact ◽  
Von Mises Stress ◽  
Elastic Plastic

The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The effects of the ellipticity ratio k — ranging from 1 to 16 — and of the normal load — from 4.2 to 8 GPa — are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of AISI 52100 bearing steel under a load of 5.7 GPa. The results which are presented are first the permanent deformation of the surface, and second the contact pressure distribution, the Von Mises stress field, the hydrostatic pressure and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.

A Numerical Solution for Fretting Contacts

2010 ◽  
Author(s):  
Zhan-jiang Wang ◽  
Yuan-zhong Hu ◽  
Wen-zhong Wang ◽  
Hui Wang
Keyword(s):  
Dynamic Load ◽  
Normal Load ◽  
Contact Region ◽  
Computing Time ◽  
Numerical Procedure ◽  
Surface Displacement ◽  
Dissimilar Materials ◽  
Fretting Wear ◽  
History Of ◽  
Analytical Relations

When two surfaces in static contacts are subjected to combined loads applied in the normal and tangential directions, or just a normal load for dissimilar materials, microscopic slip would take place at certain areas of the contact region even though the contacting bodies remain still without macroscopic movement. The micro-slip is considered a major cause of fretting wear for the materials in contacts under alternating dynamic load or vibration, referred as the fretting contacts in this study. The fretting contact problem was solved using a semi-analytical method (SAM), in which analytical relations between a unite stress and corresponding surface displacement were obtained on the basis of Green functions. The contact pressure and shear tractions were then calculated by minimizing the complementary energy, and by a numerical procedure based on Conjugate Gradient Method (CGM) and Fast Fourier Transform (FFT) technique. The algorithm is very effective since the meshes are applied to the positions just in the contact areas of interest, which saves the computing time. The fretting contacts of dissimilar materials were studied and the effects of surface roughness were analyzed. Results show that the coupled effects of shear traction and material dissimilarity make the traction distributions quite different with the solutions from similar materials. The solutions under dynamic load depend on the path or history of the loading process, but the stress distributions and load-displacement curves will quickly converge to a periodic stability after several load cycles.

A Full Numerical Solution to the Mixed Lubrication in Point Contacts

1999 ◽  
Vol 122 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Yuan-Zhong Hu ◽  
Dong Zhu
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Surface Deformation ◽  
Full Range ◽  
Computing Time ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Asperity Contact ◽  
Point Contacts ◽  
Severe Condition

A full numerical solution for the mixed elastohydrodynamic lubrication (EHL) in point contacts is presented in this paper, using a new numerical approach that is simple and robust, capable of handling three-dimensional measured engineering rough surfaces moving at different rolling and sliding velocities. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions including the full film, mixed and boundary lubrication. In the hydrodynamically lubricated areas the Reynolds equation is used. In the asperity contact areas, where the film thickness is zero, the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. In order to save computing time, a multi-level integration method is used to calculate surface deformation. Sample cases under severe condition show that this approach is capable of analyzing different cases in a full range of λ ratio, from infinitely large down to nearly zero (less than 0.03). [S0742-4787(00)00101-6]

Sliding Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces

2001 ◽  
Vol 124 (1) ◽  
pp. 46-61 ◽  
Author(s):  
Wei Peng ◽  
Bharat Bhushan
Keyword(s):  
Surface Deformation ◽  
Rough Surfaces ◽  
Normal Load ◽  
Three Dimensional ◽  
Sliding Contact ◽  
Fast Fourier Transformation ◽  
Maximum Pressure ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Von Mises

A three-dimensional numerical model is presented to investigate the quasi-static sliding contact behavior of layered elastic/plastic solids with rough surfaces. The model is applicable for both single-asperity contact and multiple-asperity contacts. The surface deformation is obtained based on a variational principle. The surface and subsurface stresses in the layer and the substrate are determined with a Fast Fourier transformation (FFT) based scheme and von Mises and principal tensile stresses are computed accordingly. Contact statistics, such as fractional contact area, maximum pressure/E2 and relative meniscus force are predicted. The results are used to investigate the effect of the contact statistics on friction, stiction, and wear problems such as debris generation, brittle failure, and delamination of layered media. Optimum layer parameters are identified. It allows the specification of layer properties, according to the contact statistics, to reduce friction, stiction, and wear of materials. A normalization procedure is presented to apply the results on various combinations of surface roughness, material properties, and normal load.

Modeling of the Rolling and Sliding Contact Between Two Asperities

2006 ◽  
Vol 129 (2) ◽  
pp. 235-245 ◽  
Author(s):  
Vincent Boucly ◽  
Daniel Nélias ◽  
Itzhak Green
Keyword(s):  
Permanent Deformation ◽  
Equivalent Plastic Strain ◽  
Indentation Test ◽  
Load Ratio ◽  
Plastic Body ◽  
Time Step ◽  
Normal Contact ◽  
Elastic Plastic ◽  
New Feature ◽  
The Way

A semi-analytical method for the tridimensional elastic-plastic contact between two hemispherical asperities is proposed. The first part of the paper describes the algorithm used to deal with the normal contact, which can be either load-driven or displacement-driven (dd). Both formulations use the conjugate gradient method and the discrete convolution and fast Fourier transform (DC-FFT) technique. A validation of the code is made in the case of the displacement-driven formulation for an elastic-plastic body in contact with a rigid punch, simulating a nano-indentation test. Another new feature is the treatment of the contact between two elastic-plastic bodies. The model is first validated through comparison with the finite element method. The contact pressure distribution, the hydrostatic pressure and the equivalent plastic strain state below the contacting surfaces are also found to be strongly modified in comparison to the case of an elastic-plastic body in contact with a purely elastic body. The way to consider rolling and sliding motion of the contacting bodies consists of solving the elastic-plastic contact at each time step while upgrading the geometries as well as the hardening state along the moving directions. The derivations concerning the interference calculation at each step of the sliding process are then shown, and an application to the tugging between two spherical asperities in simple sliding (dd formulation) is made. The way to project the forces in the global reference is outlined, considering the macro-projection due to the angle between the plane of contact and the sliding direction, and the micro-projection due to the pile-up induced by the permanent deformation of the bodies due to their relative motion. Finally, a load ratio is introduced and results are presented in terms of forces, displacements, and energy loss in the contact.

Contact Analyses for Bodies With Frictional Heating and Plastic Behavior

2005 ◽  
Vol 127 (2) ◽  
pp. 355-364 ◽  
Author(s):  
Vincent Boucly ◽  
Daniel Ne´lias ◽  
Shuangbiao Liu ◽  
Q. Jane Wang ◽  
Leon M. Keer
Keyword(s):  
Stress Field ◽  
Thermal Stresses ◽  
Frictional Heating ◽  
Equivalent Plastic Strain ◽  
Engineering Application ◽  
Von Mises Stress ◽  
Normal Displacement ◽  
Plastic Behavior ◽  
Important Indicator ◽  
Elastic Plastic

The stress field within machine components is an important indicator for contact failures. Since both thermal stresses due to frictional heating and plasticity are significant in engineering application, it is critical to predict the total stress field. In this work, the steady-state thermal effect is considered and a thermo-elastic–plastic contact model is developed. The model is applicable for rolling and/or sliding contact problem, as far as small equivalent plastic strain hypothesis is respected. Influence coefficients for surface normal displacement, temperature, and strain and stress tensors are used with the discrete convolution and fast Fourier transform algorithm. The single-loop conjugate gradient iteration scheme is also applied to achieve fast convergence speed. Simulations are presented for several academic examples ranging from elastic to thermo-elastic–plastic. The thermo-elastic–plastic analyses show that the heat factor in a contact situation has significant effect not only on the critical Hertzian pressure and on the pressure distribution, but also on the magnitude and depth of the maximum von Mises stress during loading and the residual ones found after unloading.

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

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