An algorithm to solve coupled 2D rolling contact problems

González, José Luís Galán; Abascal, Ramón

doi:10.1002/1097-0207(20001130)49:9<1143::aid-nme991>3.0.co;2-b

Cited by 22 publications

(8 citation statements)

References 37 publications

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“…The rolling contact formulation is based on Kalker's one, which is collected on his book (Kalker, 1990) or in Johnson's book (Johnson, 1985). This formulation it has been applied on 2D and 3D problems, using the BEM, by González and Abascal (1998), González and Abascal (2000), González and Abascal (2002), Abascal and Rodríguez-Tembleque (2007) and Rodríguez-Tembleque and Abascal (2010), allowing to consider real solid geometries (not only half-spaces) and unstructured meshes. Furthermore, there is a normal and tangential cross-influence relation.…”

Section: Introductionmentioning

confidence: 99%

A boundary element formulation for wear modeling on 3D contact and rolling-contact problems

Rodríguez-Tembleque¹,

Abascal²,

Aliabadi

2010

International Journal of Solids and Structures

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a b s t r a c tThe present work shows a new numerical treatment for wear simulation on 3D contact and rolling-contact problems. This formulation is based on the boundary element method (BEM) for computing the elastic influence coefficients and on projection functions over the augmented Lagrangian for contact restrictions fulfillment. The constitutive equations of the potential contact zone are Signorini's contact conditions, Coulomb's law of friction and Holm-Archard's law of wear. The proposed methodology is applied to predict wear on different contact and rolling-contact problems. Results are validated with numerical solutions and semi-analytical models presented in the literature. The BEM considers only the degrees of freedom involved on these kind of problems (those on the solids surfaces), reducing the number of unknowns and obtaining a very good approximation on contact tractions using a low number of elements. Together with the formulation, an acceleration strategy is presented allowing to reduce the times of resolution.

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Section: Introductionmentioning

confidence: 99%

A boundary element formulation for wear modeling on 3D contact and rolling-contact problems

Rodríguez-Tembleque¹,

Abascal²,

Aliabadi

2010

International Journal of Solids and Structures

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“…GNMls is an extension of the Newton's method for B-differentiable functions formulated by Pang [9], applied to FEM by Christensen [10], and being used by the authors for different contact and rolling formulations [2,4,5,11,12].…”

Section: Generalized Newton's Methodsmentioning

confidence: 99%

“…Previous relations can be expressed using augmented variables and projection functions P n and P t , [2][3][4][5], as…”

Section: The 3d Rolling Contact Problemmentioning

confidence: 99%

Steady‐state 3D rolling‐contact using boundary elements

Abascal

Rodríguez-Tembleque

2006

Commun. Numer. Meth. Engng.

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SUMMARYThis work presents a new approach to the steady-state rolling contact problem for 3D elastic bodies. The problem solution is achieved by minimizing a general function representing the equilibrium equation and the rolling-contact restrictions. The boundary element method is used to compute the elastic influence coefficients of the surface points involved in the contact (equilibrium equations); while the contact conditions are represented with the help of projection functions. Finally, the minimization problem is solved by the generalized Newton's method with line search. Classic rolling problems are also solved and commented.

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“…Gonzalez and Abascal investigated the steady state rolling contact problem between two cylinders using the boundary element method. They solved the governing equations by applying the generalized Newtons method and used some classical contact problems to verify their solutions, including the contact problem between similar and dissimilar cylinders.…”

Section: Introductionmentioning

confidence: 99%

Two‐dimensional analysis of the fully coupled rolling contact problem between a rigid cylinder and an orthotropic medium

et al. 2017

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In this paper, the fully-coupled rolling contact problem between a rigid cylinder and an orthotropic medium is investigated. The governing equations are developed analytically; then, a numerical method, the Gauss-Chebyshev method, is used to solve the coupled integral equations. The rolling contact problem is solved by assuming a central stick zone accompanied with two slip regions. The main purpose of this study is to obtain the surface stresses in the contact area and investigate the effect of material orthotropic properties such as shear parameter and stiffness ratio and also the coefficient of friction on these contact stresses. In addition, the subsurface stresses in the orthotropic medium are determined and a parametric study, was subsequently executed. The current paper shows that the orthotropic parameters and the coefficient of friction significantly influence the contact surface stresses and the distribution of the interior field stresses. By appropriately choosing the values of these parameters, the stresses will decrease; thus, the failure behavior of the orthotropic medium improves.

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An algorithm to solve coupled 2D rolling contact problems

Cited by 22 publications

References 37 publications

A boundary element formulation for wear modeling on 3D contact and rolling-contact problems

A boundary element formulation for wear modeling on 3D contact and rolling-contact problems

Steady‐state 3D rolling‐contact using boundary elements

Two‐dimensional analysis of the fully coupled rolling contact problem between a rigid cylinder and an orthotropic medium

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