In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a duality algorithm are developed to cope with the convection dominating and nonlinear diffusion features, respectively. Furthermore, in the duality method the convergence and optimal choice of the parameters are analyzed. At each fixed point iteration, in the elastic model a complementarity formulation is required and appropriate numerical techniques are used. For the spatial discretization different finite element spaces are chosen. Finally, numerical test examples illustrate the theoretical results, as well as the good performance in the simulation of real devices.
Mots-clés : head-tape devices, elastohydrodynamic lubrication, compressible Reynolds equation, rod model, duality methods, finite elements
@article{M2AN_2008__42_4_645_0,
author = {Arregui, I\~nigo and Cend\'an, Jos\'e Jes\'us and Par\'es, Carlos and V\'azquez, Carlos},
title = {Numerical solution of a {1-D} elastohydrodynamic problem in magnetic storage devices},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {645--665},
publisher = {EDP-Sciences},
volume = {42},
number = {4},
year = {2008},
doi = {10.1051/m2an:2008021},
mrnumber = {2437777},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2008021/}
}
TY - JOUR AU - Arregui, Iñigo AU - Cendán, José Jesús AU - Parés, Carlos AU - Vázquez, Carlos TI - Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 645 EP - 665 VL - 42 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008021/ DO - 10.1051/m2an:2008021 LA - en ID - M2AN_2008__42_4_645_0 ER -
%0 Journal Article %A Arregui, Iñigo %A Cendán, José Jesús %A Parés, Carlos %A Vázquez, Carlos %T Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 645-665 %V 42 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008021/ %R 10.1051/m2an:2008021 %G en %F M2AN_2008__42_4_645_0
Arregui, Iñigo; Cendán, José Jesús; Parés, Carlos; Vázquez, Carlos. Numerical solution of a 1-D elastohydrodynamic problem in magnetic storage devices. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 4, pp. 645-665. doi : 10.1051/m2an:2008021. http://www.numdam.org/articles/10.1051/m2an:2008021/
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