Numerical simulation of head–tape magnetic reading devices by a new 2-D model

Arregui, Iñigo; Cendán, J. Jesús; Vázquez, Carlos

doi:10.1016/j.finel.2006.10.006

Cited by 5 publications

(5 citation statements)

References 20 publications

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“…The extension to two spatial dimensions has also been studied by the authors, from the modelling and numerical point of view [3]. In fact, for example, the increasing use of smaller flow factors in recording requires narrower tapes, leading to side flow effects which are neglected in one dimensional approaches.…”

Section: Discussionmentioning

confidence: 99%

“…Also, in the 2-d setting, the fixed point iteration should uncouple the hydrodynamic equations and the appropriate elastic model. In [3] a new elastohydrodynamic Reynolds-Koiter model governing a head-tape magnetic reading device is proposed and the numerical methods here applied to the nonlinear compressible Reynolds equation are extended to the 2-d case. In order to take into account curvature effects, the tape movement is governed by a Koiter model and appropriate numerical methods are used.…”

Section: Discussionmentioning

confidence: 99%

“…Next, different appropriate classical numerical techniques (Hermite finite elements combined with projection or Uzawa algorithms) are applied to the fourth order elliptic variational inequality. Although the theoretical results are partial and limited to 1-d models, the extension to 2-d models of its implementation is straightforward and has already been developed in [3], where a new Reynolds-Koiter model is proposed, mathematically analyzed and numerically solved.…”

Section: Introductionmentioning

confidence: 99%

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Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices

Arregui¹,

Cendán²,

Parés

et al. 2008

ESAIM: M2AN

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Abstract. 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.Mathematics Subject Classification. 76A20, 76D08, 35J60, 65J15, 65N60.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices

Arregui¹,

Cendán²,

Parés

et al. 2008

ESAIM: M2AN

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“…In order to compute the solution we reformulate the problem in terms of an obstacle one relative to the unknown h = u − δ, so that we can guarantee that h > 0, that is to say, the tape keeps above the head. We shall follow the ideas of [1,2], and apply a finite element method together with a duality algorithm handling Yosida approximation tools for maximal monotone operators. These techniques have already been successfully used for example in [7] and [8].…”

Section: Numerical Resolutionmentioning

confidence: 99%

“…In Figure 3 we show the results obtained with δ = 1+ 1 − (x − 4.5) 2 . From these simulations one can derive the same conclusions as the ones commented regarding Figure 2.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Mathematical Analysis and Numerical Simulation in Magnetic Recording

Muñoz

Tello

2014

Mathematical Modelling and Analysis

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The head-tape interaction in magnetic recording is described in the literature by a coupled system of partial differential equations. In this paper we study the limit case of the system which reduces the problem to a second order nonlocal equation on a one-dimensional domain. We describe the numerical method of resolution of the problem, which is reformulated as an obstacle one to prevent head-tape contact. A finite element method and a duality algorithm handling Yosida approximation tools for maximal monotone operators are used in order to solve numerically the obstacle problem. Numerical simulations are introduced to describe some qualitative properties of the solution. Finally some conclusions are drawn.

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