A novel study of head motion hysteresis issues in contact probe recording systems

Abstract

Contact-based recording on ferroelectric media and polymer media have been proposed and investigated for high-density probe storage. To achieve fast data rate, it is necessary to perform reading or writing with multiple probe heads simultaneously. However, localized variations in tribological behavior at the contact interface between the probes and recording media and variation in normal contact force would result in variation in friction and stiction over the interface and therefore amongst individual heads in the probe head array. This causes variation in the hysteretic motion of the heads over the array, which in turn results in off-track motion during track-positioning and timing errors during scanning. In this paper a novel method of modeling these effects is developed to study the effect of relative head-motion hysteresis (RHMH) on timing-error during data read–write and off-track errors during seek-settle. A mathematical model of RHMH during scanning along the bit-wise direction is developed based on the idea of stochastic averaging. A transient response model is similarly developed for estimating hysteresis effects during seek-settle. These models help to understand parametric dependencies of RHMH and can be used in designing the probe heads, the probe–media interface (PMI) and the probe system in general. Further several schemes involving modulation of the normal force at the PMI are proposed to mitigate RHMH and their benefits are analyzed using the models described in this paper.

Appendix A: Governing SDE in amplitude-phase form

The governing SDE in the amplitude-phase variables (a, ϕ) is given by Eq. 7. Carrying out the stochastic averaging calculations described in Sect. 2.1, the terms on the right-hand-side of Eq. 7 can be obtained as

$$ \begin{array}{*{20}c} {\mu_{a} \left( {a,\phi ,t} \right) = - 4\zeta \omega_{n} a\sin^{2} (\phi ) + \left( {\sigma_{f} f_{N} (t)\mu_{0} (t)\text{sgn} \left( {v_{m} } \right)} \right)^{2} \frac{1}{{\omega_{n}^{2} }}\left( {1 - \sin^{2} (\phi )} \right)} \hfill \\ {\sigma_{a} \left( {a,\phi ,t} \right) = 2\sqrt a \sigma_{f} f_{N} (t)\mu_{0} (t)\text{sgn} \left( {v_{m} } \right)\frac{1}{{\omega_{n} }}\sin (\phi )} \hfill \\ {\mu_{\phi } \left( {a,\phi ,t} \right) = - \zeta \sin \left( {2\phi } \right) - \frac{1}{2}\left( {\sigma_{f} f_{N} (t)\mu_{0} (t)\text{sgn} \left( {v_{m} } \right)} \right)^{2} \frac{1}{{\omega_{n}^{3} }}\sin \left( {2\phi } \right)} \hfill \\ {\sigma_{\phi } (a,\phi ,t) = \frac{1}{\sqrt a }\sigma_{f} f_{N} (t)\mu_{0} (t)\text{sgn} \left( {v_{m} } \right)\cos (\phi ).} \hfill \\ \end{array} $$

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