scholarly journals Convergence Analysis of a Fourier-Based Solution Method of the Laplace Equation for a Model of Magnetic Recording

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
John L. Fleming
Keyword(s):  
Magnetic Recording ◽  
Solution Method ◽  
Infinite System ◽  
Formal Analysis ◽  
Mathematical Problem ◽  
Linear Equations ◽  
Head Model ◽  
Hard Drives ◽  
Recording Heads ◽  
Read Head

When engineers model the magnetostatic fields applied to recording heads of computer hard drives due to a magnetic recording medium, the solution of Laplace's equation must be found. A popular solution method is based on Fourier analysis. However, due to the geometry of the read head model, an interesting mathematical problem arises. The coefficients for the Fourier series solution of the desired magnetic potential satisfy an infinite system of linear equations. In practice, the infinite system is truncated to a finite system with little consideration for the effect this truncation has on the solution. The paper will provide a proper understanding of the underlying problem and a formal analysis of the effect of truncation.

Head Instability Detection for Testing Process in Perpendicular Magnetic Recording System

2013 ◽  
Vol 770 ◽  
pp. 319-322 ◽  
Author(s):  
Piya Kovintavewat ◽  
Santi Koonkarnkhai ◽  
Aimamorn Suvichakorn
Keyword(s):  
Magnetic Recording ◽  
Signal To Noise Ratio ◽  
Disk Drive ◽  
Detection Algorithm ◽  
Recording System ◽  
High Signal ◽  
Signal To Noise ◽  
Perpendicular Magnetic Recording ◽  
Read Head ◽  
Pass Through

During hard disk drive (HDD) testing process, the magneto-resistive read (MR) head is analyzed and checked if the head is defective or not. Baseline popping (BLP) is one of the crucial problems caused by head instability, whose effect can distort the readback signal to the extent of causing possible sector read failure. Without BLP detection algorithm, the defective read head might pass through HDD assembling process, thus producing an unreliable HDD. This situation must be prevented so as to retain customer satisfaction. This paper proposes a simple (but efficient) BLP detection algorithm for perpendicular magnetic recording systems. Results show that the proposed algorithm outperforms the conventional one in terms of both the percentage of detection and the percentage of false alarm, when operating at high signal-to-noise ratio.

On the Stresses in a Notched Strip

1952 ◽  
Vol 19 (2) ◽  
pp. 141-146
Author(s):  
Chih-Bing Ling
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Numerical Results ◽  
Theoretical Solution ◽  
Experimental Results ◽  
System Of Linear Equations ◽  
Transverse Bending ◽  
Longitudinal Tension

Abstract In a previous paper by the author (1), a theoretical solution for a notched strip under longitudinal tension is given. The result demands the solution of an infinite system of linear equations. A considerable amount of labor is involved in solving such a system. It seems, however, that the labor can be diminished by adapting to the solution a process known as the promotion of rank. In this paper such a process is described and then applied to solve the problem of a notched strip under transverse bending. The solution of this problem seems also to be new. The numerical results obtained are compared graphically with the experimental results available.

Imaging magnetic noise sources in magnetic recording heads (Invited Paper)

2005 ◽  
Author(s):  
Lu Yuan ◽  
Jian-Xiang Shen ◽  
Bharat B. Pant ◽  
Sy-Hwang Liou
Keyword(s):  
Magnetic Recording ◽  
Magnetic Noise ◽  
Noise Sources ◽  
Recording Heads ◽  
Magnetic Recording Heads

New magnetic alloys for magnetic recording heads

1972 ◽  
Vol 8 (3) ◽  
pp. 501-502 ◽  
Author(s):  
T. Miyazaki ◽  
R. Sawada ◽  
Y. Ishijima
Keyword(s):  
Magnetic Recording ◽  
Magnetic Alloys ◽  
Recording Heads ◽  
Magnetic Recording Heads

A Diagonally Dominant Solution for the Cylinder End Problem

1981 ◽  
Vol 48 (4) ◽  
pp. 876-880 ◽  
Author(s):  
T. D. Gerhardt ◽  
Shun Cheng
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Infinite Cylinder ◽  
Algebraic Equations ◽  
Precise Calculation ◽  
Linear Algebraic Equations ◽  
Present Solution ◽  
Diagonally Dominant ◽  
Expansion Coefficients

An improved elasticity solution for the cylinder problem with axisymmetric torsionless end loading is presented. Consideration is given to the specification of arbitrary stresses on the end of a semi-infinite cylinder with a stress-free lateral surface. As is known from the literature, the solution to this problem is obtained in the form of a nonorthogonal eigenfunction expansion. Previous solutions have utilized functions biorthogonal to the eigenfunctions to generate an infinite system of linear algebraic equations for determination of the unknown expansion coefficients. However, this system of linear equations has matrices which are not diagonally dominant. Consequently, numerical instability of the calculated eigenfunction coefficients is observed when the number of equations kept before truncation is varied. This instability has an adverse effect on the convergence of the calculated end stresses. In the current paper, a new Galerkin formulation is presented which makes this system of equations diagonally dominant. This results in the precise calculation of the eigenfunction coefficients, regardless of how many equations are kept before truncation. By consideration of a numerical example, the present solution is shown to yield an accurate calculation of cylinder stresses and displacements.

Micromagnetics and Eddy Current Effects in Magnetic Recording Heads

2007 ◽  
Vol 43 (6) ◽  
pp. 2184-2186 ◽  
Author(s):  
Kenichi Takano ◽  
Xiaofeng Zhang ◽  
El-Amine Salhi ◽  
Lijie Guan ◽  
Masanori Sakai ◽  
...  
Keyword(s):  
Eddy Current ◽  
Magnetic Recording ◽  
Recording Heads ◽  
Magnetic Recording Heads
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